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{"url":"https:\/\/www.groundai.com\/project\/n-resonances-from-k-amplitudes-in-sliced-bins-in-energy\/","text":"N^{*} resonances from K\\Lambda amplitudes in sliced bins in energy\n\n# N\u2217 resonances from K\u039b amplitudes in sliced bins in energy\n\nA.V. Anisovich 1 Helmholtz-Institute f\u00fcr Strahlen- und Kernphysik der Universit\u00e4t Bonn, Nussallee 14 - 16, 53115 Bonn, Germany\nParticle and Nuclear Physics Institute, Orlova Rosha 1, 188300 Gatchina, Russia\nThomas Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA\nRudjer Boskovic Institute, Bijenicka cesta 54, P.O. Box 180, 10002 Zagreb, Croatia\nSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom\nUniversity of Tuzla, Faculty of Natural Sciences and Mathematics, Univerzitetska 4, 75000 Tuzla, Bosnia and Herzegovina 122\nV. Burkert 33 \u2003\u2003 M.\u00a0Had\u017eimehmedovi\u0107 66 \u2003\u2003 D.G.\u00a0Ireland 55 \u2003\u2003 E.\u00a0Klempt 1 Helmholtz-Institute f\u00fcr Strahlen- und Kernphysik der Universit\u00e4t Bonn, Nussallee 14 - 16, 53115 Bonn, Germany\nParticle and Nuclear Physics Institute, Orlova Rosha 1, 188300 Gatchina, Russia\nThomas Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA\nRudjer Boskovic Institute, Bijenicka cesta 54, P.O. Box 180, 10002 Zagreb, Croatia\nSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom\nUniversity of Tuzla, Faculty of Natural Sciences and Mathematics, Univerzitetska 4, 75000 Tuzla, Bosnia and Herzegovina 133\nV.A. Nikonov 1 Helmholtz-Institute f\u00fcr Strahlen- und Kernphysik der Universit\u00e4t Bonn, Nussallee 14 - 16, 53115 Bonn, Germany\nParticle and Nuclear Physics Institute, Orlova Rosha 1, 188300 Gatchina, Russia\nThomas Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA\nRudjer Boskovic Institute, Bijenicka cesta 54, P.O. Box 180, 10002 Zagreb, Croatia\nSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom\nUniversity of Tuzla, Faculty of Natural Sciences and Mathematics, Univerzitetska 4, 75000 Tuzla, Bosnia and Herzegovina 122\nR.\u00a0Omerovi\u0107 66 \u2003\u2003 A.V. Sarantsev 1 Helmholtz-Institute f\u00fcr Strahlen- und Kernphysik der Universit\u00e4t Bonn, Nussallee 14 - 16, 53115 Bonn, Germany\nParticle and Nuclear Physics Institute, Orlova Rosha 1, 188300 Gatchina, Russia\nThomas Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA\nRudjer Boskovic Institute, Bijenicka cesta 54, P.O. Box 180, 10002 Zagreb, Croatia\nSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom\nUniversity of Tuzla, Faculty of Natural Sciences and Mathematics, Univerzitetska 4, 75000 Tuzla, Bosnia and Herzegovina 122\nJ.\u00a0Stahov 66 \u2003\u2003 A.\u00a0\u0160varc 44 \u2003\u2003 and U. Thoma 1 Helmholtz-Institute f\u00fcr Strahlen- und Kernphysik der Universit\u00e4t Bonn, Nussallee 14 - 16, 53115 Bonn, Germany\nParticle and Nuclear Physics Institute, Orlova Rosha 1, 188300 Gatchina, Russia\nThomas Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA\nRudjer Boskovic Institute, Bijenicka cesta 54, P.O. Box 180, 10002 Zagreb, Croatia\nSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom\nUniversity of Tuzla, Faculty of Natural Sciences and Mathematics, Univerzitetska 4, 75000 Tuzla, Bosnia and Herzegovina 11 Helmholtz-Institute f\u00fcr Strahlen- und Kernphysik der Universit\u00e4t Bonn, Nussallee 14 - 16, 53115 Bonn, Germany\nParticle and Nuclear Physics Institute, Orlova Rosha 1, 188300 Gatchina, Russia\nThomas Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA\nRudjer Boskovic Institute, Bijenicka cesta 54, P.O. Box 180, 10002 Zagreb, Croatia\nSUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom\nUniversity of Tuzla, Faculty of Natural Sciences and Mathematics, Univerzitetska 4, 75000 Tuzla, Bosnia and Herzegovina 12233445566\nReceived: September 24, 2019\/ Revised version:\n###### Abstract\n\nThe two reactions and are analyzed to determine the leading photoproduction multipoles and the pion-induced partial wave amplitudes in slices of the invariant mass. The multipoles and the partial-wave amplitudes are simultaneously fitted in a multichannel Laurent+Pietarinen model (L+P model), which determines the poles in the complex energy plane on the second Riemann sheet close to the physical axes. The results from the L+P fit are compared with the results of an energy-dependent fit based on the Bonn-Gatchina (BnGa) approach. The study confirms the existence of several poles due to nucleon resonances in the region at about 1.9\u2009GeV with quantum numbers , .\n\n## 1 Introduction\n\nThe nucleon and its excited states are the simplest systems in which the non-abelian character of strong interactions is manifest. Three quarks is the minimum quark content of any baryon, and these three quarks carry the three fundamental colour charges of Quantum Chromodynamics (QCD), and combine to a colourless baryon. At present it is, however, impossible to calculate the spectrum of excited states from first principles, even though considerable progress in lattice gauge calculations has been achieved\u00a0Edwards:2011jj . Models are therefore necessary when data are to be compared to predictions.\n\nQuark models predict a rich excitation spectrum of the nucleon Capstick:1986bm ; Ferraris:1995ui ; Glozman:1997ag ; Loring:2001kx ; Giannini:2015zia . In quark models, the resonances are classified in shells according to the energy levels of the harmonic oscillator. The shell structure of the excitations is still seen in the data and reproduced in lattice calculations Edwards:2011jj . The first excitation shell is predicted to house five and two resonances with negative-parity; all of them are firmly established. The second excitation shell contains missing resonances: 22 resonances (14 \u2019s and 8 \u2019s) are predicted but 15 only are found in the mass range below 2100\u2009MeV, and just 10 of them (5 \u2019s and 5 \u2019s) are considered as established, with three or four stars in the notation of the Particle Data Group Olive:2016xmw . Thus 9 \u2019s in the mass region between 1700\u2009MeV and 2100\u2009MeV are predicted to exist which are unobserved or the evidence for their existence is only fair or even poor. This deficit is known as the problem of the missing resonances Koniuk:1979vw ; Koniuk:1979vy . The search for missing resonances is one of the major aims of a number of experiments in which the interaction of a photon beam in the GeV energy range with a hydrogen and deuterium target is studied.\n\nIn elastic and charge exchange scattering, the excited states may have isospin () and (). A large amount of data was analyzed by the groups at Karlsruhe-Helsinki (KH84)\u00a0Hohler:1984ux , Carnegie-Mellon (CM) Cutkosky:1980rh and at GWU Arndt:2006bf . The 1850 - 2100\u2009MeV mass region \u2013 where the missing resonances of the second excitation shell are predicted in most constituent quark models (see, e.g.,\u00a0Capstick:1986bm ; Ferraris:1995ui ; Glozman:1997ag ; Loring:2001kx ; Giannini:2015zia ; Capstick:1998uh ; Capstick:2000qj ) \u2013 is dominated by the production of resonances with spin-parity , ; nucleon resonances are difficult to establish in this mass range due to the overwhelming background from resonances.\n\nThe production of hyperons in pion and photo-induced reactions, in contrast to elastic scattering, is ideally suited to search for new nucleon resonances and to confirm resonances that are not yet well established\u00a0(see, e.g.,\u00a0Capstick:1998uh ; Capstick:2000qj and references therein). Due to isospin conservation in strong interactions, only resonances decay into final states, there are no isospin contributions. Second, the weak-interaction decay reveals the polarization of the . Thus, the recoil polarization is measurable. In elastic scattering, the equivalent target polarization, also called , requires the use of a polarized target. In photoproduction, a third advantage emerges: the process is not suppressed even when the coupling constants of resonances in the second excitation shell are small Capstick:1998uh ; Capstick:2000qj . Photoproduction may hence reveal the existence of resonances coupling to only weakly. Indeed, a number of new resonances has been reported (or have been upgraded in the star rating) from a combined analysis of a large number of pion and photo-produced reactions Anisovich:2011fc . Some of the \u201cnew\u201d resonances had been observed before Hohler:1984ux ; Cutkosky:1980rh ; Manley:1992yb ; Penner:2002ma ; Penner:2002md or were confirmed in later analyses Shrestha:2012va ; Shrestha:2012ep ; L+P2014 . The evidence for the existence of the new states stemmed from energy-dependent fits to the data using the BnGa approach Anisovich:2004zz ; Anisovich:2006bc ; Anisovich:2007zz ; Denisenko:2016ugz . The reaction proved to be particularly useful Nikonov:2007br .\n\nThe ultimate aim of experiments is to provide sufficient information that the data can be decomposed into partial waves or multipoles of defined and unique spin-parity. It can either be done through constructing an explicit theoretical model, or as we present here, through the reconstruction of partial-wave amplitudes and of multipoles in a truncated partial wave analysis. Limiting the partial wave series to low orbital angular momenta allows us to overcome issues with the still relatively large errors in the measurements of observable quantities.\n\nThe main goal of this paper is to test if resonances in the fourth resonance region can be confirmed definitely from a fit to multipoles driving the excitation of partial waves with defined spin-parity, and to extract their properties. This is done in two ways: i.) In a standard way where a theoretical model is constructed. Its free parameters are estimated by fitting to the experimental data set base, and the partial waves of the final solution are analytically continued into the complex energy plane to obtain poles. ii.) In a way which does not depend on detailed model assumptions by using the Laurent+Pietarinen (L+P) method where a solution of the theoretical model is replaced by a most general analytic function consisting of a number poles and branch-cuts, which is embodied by a fast converging power series in a conformal variable. This variable is generated by a conformal mapping of the complex energy plane onto a unit circle. The first Riemann sheet is mapped to the outside of the unit circle, and the second Riemann sheet \u2013 where the poles are located \u2013 into the inside of the unit circle. In method ii.), poles are extracted by fitting to the single-energy partial wave decomposition, as opposed to a direct global fit to the data.\n\nMethod i.), coupled-channel energy-dependent fits, exploits the full statistical potential of the data. The effect of couplings to various other final states like , , , , etc. is taken into account exactly as well as all correlations between the different amplitudes. However, all partial waves need to be determined in one single fit, and it is difficult to verify the uniqueness of the results. In method ii.) we use single channel L+P fits (SC L+P) where each channel is fitted individually, and multi-channel L+P fits (MC L+P) where two or more channels are fitted simultaneously. The main advantage of the model-independent approach is that we can fit one partial wave at a time, and that we avoid any dependence on the quality of the model. The drawback is that you first have to extract partial waves, and this procedure depends on the choice of higher partial waves, introducing some model dependence.\n\n## 2 Construction of K\u039b amplitudes in slices of their invariant mass\n\n### 2.1 The partial wave amplitudes for \u03c0\u2212p\u2192K0\u039b\n\n#### 2.1.1 Formalism\n\nThe differential cross sections for the reaction\nreceives contributions from a spin-non-flip and a spin-flip amplitude, and , according to the relation\n\n d\u03c3d\u03a9=kq(|f|2+|g|2), (1)\n\nwhere and are the initial and final meson momenta respectively in the centre of mass frame\u00a0Hohler:1984ux . Both amplitudes depend on the invariant mass and , with being the scattering angle. The two amplitudes can be expanded into partial wave amplitudes\n\n f(W,z) = 1\u221aqkL\u2211l=0[(l+1)A+l(W)+lA\u2212l(W)]Pl(z), g(W,z) = 1\u221aqksin\u0398L\u2211l=1[A+l(W)\u2212A\u2212l(W)]P\u2032l(z), (2)\n\nwhere are the Legendre polynomials. is the total spin of the state. The sign in the relation for defines the sign in .\n\nThe decay can be used to determine the decay asymmetry with respect to the scattering plane, called recoil asymmetry . Assuming that the target nucleon is fully polarized, can be defined as\n\n (1\u00b1P)d\u03c3d\u03a9=|f\u00b1ig|2. (3)\n\nWhen the target proton is polarized longitudinally (along the pion beam line), the spin transfer from proton to yields the spin rotation angle .\n\n \u03b2=arg(f\u2212igf+ig)=tan\u22121(\u22122Re(f\u2217g)|f|2\u2212|g|2). (4)\n\nIt is defined as , where and are the polarization components in direction of the and its orthogonal component in the scattering plane. and are given by\n\n R=2Re(f\u2217g)|f|2+|g|2,A=|f|2\u2212|g|2|f|2+|g|2. (5)\n\nThe polarization variables are constrained by the relation\n\n P2+A2+R2=1. (6)\n\n#### 2.1.2 Fits to the data\n\nData on the reaction were taken in Chicago Knasel:1975rr and at the NIMROD accelerator at the Rutherford Laboratory Baker:1978qm ; Saxon:1979xu ; Bell:1983dm . From these data, the partial wave amplitudes defined in eqn. (2) should be derived.\n\nA detailed study showed that the data require angular momenta up to or even but do not have the precision to determine all partial wave amplitudes\u00a0Anisovich:2014yza . Therefore we try to determine at least the low- amplitudes, in particular , , , leading to , , and . The higher partial waves, those above , , , are taken from our current BnGa fit.\n\nFigure\u00a01 shows the data. The solid curves represent the final BnGa fit. It reproduces the data with a . The number of free parameters is 75.\n\nThe fit returns the real and imaginary parts of amplitudes for the , , and partial waves. The and amplitudes are shown in Fig.\u00a02, the amplitude in Ref.\u00a0Anisovich:2014yza only (since it could not be fit with the L+P method). The solid line represents the L+P fit described below, and the energy-dependent solution BnGa2011-02 is shown as error band. Note that the higher partial waves are constrained fixed to the BnGa solution, while the other lower amplitudes are free to adopt any values.\n\n### 2.2 The multipoles for \u03b3p\u2192K+\u039b\n\n#### 2.2.1 Formalism\n\nThe amplitude for the reaction can be written in the form\n\n A = \u03c9\u2217J\u03bc\u03b5\u03bc\u03c9\u2032, (7)\n\nwhere and are spinors representing the baryon in the initial and final state, is the electromagnetic current of the nucleon, and characterizes the polarization of the photon. The amplitude can be expanded into four invariant (CGLN) amplitudes \u00a0\u00a0Chew:1957tf\n\n J\u03bc= (8) iF1\u03c3\u03bc+F2(\u2192\u03c3\u2192q)|\u2192k||\u2192q|\u03b5\u03bcij\u03c3ikj+iF3(\u2192\u03c3\u2192k)|\u2192k||\u2192q|q\u03bc+iF4(\u2192\u03c3\u2192q)\u2192q2q\u03bc.\n\nwhere is the momentum of the hyperon in the final state, is the momentum of the nucleon in the initial state, calculated in the center-of-mass system of the reaction, and are the Pauli matrices. These four functions are functions of the invariant mass and of with and as the scattering angle. A determination of these four amplitudes requires the measurement with sufficient accuracy of at least eight well chosen observables Barker:1975bp ; Fasano:1992es ; Keaton:1996pe ; Chiang:1996em ; Sandorfi:2010uv . For each slice in energy and angle one phase remains undetermined. It needs to be fixed from other sources. In elastic scattering, the phase can be determined from the (calculable) Coulomb interference. In hyperon production, one could try to fix the phase to the phase of -channel Kaon exchange. Once the functions are known for each energy and angle, the results of all experiments can be predicted.\n\nThe relations between the functions and the observables can be found, e.g., in Sandorfi:2010uv . For convenience, we give the expressions for the observables used in the fits. The differential cross section and the single polarization observables, the beam asymmetry , the recoil asymmetry , and the target asymmetry , are given by\n\n d\u03c3d\u03a9 = kqI=kqRe[F1F\u22171+F2F\u22172\u22122zF2F\u22171+ (9a) sin2(\u03b8)2(F3F\u22173+F4F\u22174+2F4F\u22171+2F3F\u22172+2zF4F\u22173)]. \u03a3I = \u2212sin2(\u03b8)2\u00d7 (9b) Re[F3F\u22173+F4F\u22174+2F4F\u22171+2F3F\u22172+2zF4F\u22173], PI = sin(\u03b8)Im[(2F\u22172+F\u22173+zF\u22174)F1+ (9c) F\u22172(zF3+F4)+sin2(\u03b8)F\u22173F4], TI = sin(\u03b8)Im[F\u22171F3\u2212F\u22172F4+ (9d) z(F\u22171F4\u2212F\u22172F3)\u2212sin2(\u03b8)F\u22173F4],\n\nThe double polarization observables , (, ) define the spin transfer from linearly (circularly) polarized photons to the hyperon where the axis is given by the meson direction. This is referred to as the primed frame. Experimentally, the data on the spin transfer from polarized photons to the hyperon are sometimes presented in an unprimed frame, in which the photon momentum is chosen as reference axis. Observables in the two frames are related by a simple rotation:\n\n Cx = sin(\u03b8)Cz\u2032+cos(\u03b8)Cx\u2032, Cz = cos(\u03b8)Cz\u2032\u2212sin(\u03b8)Cx\u2032,,\n\nwith similar relations holding for the quantities and .\n\nThe double polarization observables , (, ) can be written as\n\n Ox\u2032I = (9f) sin(\u03b8)Im[F2F\u22173\u2212F1F\u22174+z(F2F\u22174\u2212F1F\u22173)], Oz\u2032I = \u2212sin2(\u03b8)Im[F1F\u22173+F2F\u22174], (9g) Cx\u2032I = sin(\u03b8)Re[F2F\u22172\u2212F1F\u22171+F2F\u22173\u2212F1F\u22174+ z(F2F\u22174\u2212F1F\u22173)], (9h) Cz\u2032I = Re[\u22122F1F\u22172+z(F1F\u22171+F2F\u22172)\u2212 (9i)\n\nWhen the are known with sufficient statistical accuracy they can be expanded \u2013 for each slice in energy \u2013 into power series using Legendre polynomials and their derivatives:\n\n F1(W,z) =\u221e\u2211L=0[LML++EL+]P\u2032L+1(z)+ [(L+1)ML\u2212+EL\u2212]P\u2032L\u22121(z), (10a) F2(W,z) =\u221e\u2211L=1[(L+1)ML++LML\u2212]P\u2032L(z), (10b) F3(W,z) =\u221e\u2211L=1[EL+\u2212ML+]P\u2032\u2032L+1(z)+ [EL\u2212+ML\u2212]P\u2032\u2032L\u22121(z), (10c) F4(W,z) =\u221e\u2211L=2[ML+\u2212EL+\u2212ML\u2212\u2212EL\u2212]P\u2032\u2032L(z).\n\nHere, corresponds to the orbital angular momentum in the system, is the total energy, are Legendre polynomials with , and and are electric and magnetic multipoles describing transitions to states with . or multipoles do not exist. Processes due to meson exchanges in the channel may provide significant contributions to the reaction. They may demand high-order multipoles. The minmal required to describe the data can be determined by polynomial expansions of the data\u00a0Wunderlich:2016imj . A more direct approach is to insert the functions (eqns. 10) into the expressions for the observables (eqns. 9a and 9f) and to truncate the expansion at an appropriate value of Wunderlich:2014xya . The observables are now functions of the invariant mass and the scattering angle, and the fit parameters are the electric and magnetic multipoles. In this method, the number of observables required to get the full information might be reduced if the number of contributing higher partial waves is not too big. But still, high precision is mandatory for the expansion.\n\n#### 2.2.2 Fits to the data\n\nFrom the results of the BnGa analysis we expect that in the energy range considered here the , , and yield the largest contributions, followed by , , and . The , , , , , , , all contribute with increasingly smaller importance, higher multipoles become negligible. First fits showed that it is not possible, given the statistical and systematic accuracy of the data, to determine all significant partial waves. Due to strong correlations between the parameters, the errors became large and the resulting multipoles showed large point-to-point fluctuations. Hence we decreased the number of freely fitted multipoles; the higher multipoles were fixed to the BnGa results. These multipoles are shown in Fig.\u00a03. Reasonably small errors were obtained when the four multipoles , , , and were fitted. The errors increased only slightly when the multipoles , , and were fitted in addition but constrained to the BnGa solution by a penalty function.\n\n \u03c72pen=\u2211\u03b1(M\u03b1\u2212^M\u03b1)2(\u03b4^M\u03b1)2+\u2211\u03b1(E\u03b1\u2212^E\u03b1)2(\u03b4^E\u03b1)2 (11)\n\nwhere and are the electric and magnetic multipoles from solution with , , and fitted freely; , are the multipole errors.\n\nThe reaction has been studied extensively by the CLAS collaboration. The early measurement of the differential cross sections Bradford:2005pt was later superseded by a new measurement reporting the differential cross sections and the recoil polarization McCracken:2009ra . The spin transfer from circularly polarized photons to the final-state hyperon, the quantities and , were reported in Bradford:2006ba . The polarization observables have been determined recently Paterson:2016vmc . The data are shown in Figs.\u00a04-6. The data are used to determine the photoproduction multipoles in a truncated partial wave analysis.\n\nThe final result for the multipoles are shown in Fig.\u00a09. Strong variations are observed. The imaginary parts of all multipoles, except and , show threshold enhancements due to (), (), ( and ), (). Further structures are clearly seen at about 1900\u2009MeV in the , , , , , multipoles.\n\nThese structures emerge reliably when the multipole series is truncated, and only few multipoles are fitted freely. In Fig.\u00a09 we show the results from one of our tests. In this case, the seven largest multipoles, , , , , , , and were all left free. In several mass bins, the resulting multipoles show an erratic behavior; the results become unstable. Likewise, it was important to include the multipoles with large orbital angular momenta. Even though they are individually all small, neglecting them (by assuming that they are identically zero) leads to biased results. Furthermore, these multipoles fix the overall phase.\n\nSandorfi, Hoblit, Kamano, and Lee Sandorfi:2010uv have reconstructed the photoproduction amplitudes for the reaction . For the high partial waves, they used the Born amplitude. Partly, they fitted all waves with freely and determined the phases as differences to the phase. In other fits, they had the phase free and fitted all waves with . The resulting multipoles showed a wide spread. They concluded that a very significant increase in solid-angle coverage and statistics is required when all partial waves up to are to be determined.\n\n## 3 BnGa fits to the data\n\nThe BnGa partial wave analysis uses a matrix formalism to fit data on pion and photo-induced reactions to extract the leading singularities of the scattering or production processes. The formalism is described in detail in a series of publications Anisovich:2004zz ; Anisovich:2006bc ; Anisovich:2007zz ; Denisenko:2016ugz . Here we briefly outline the dynamical part of the method.\n\nThe pion induced reaction from the initial state to the final state is described by a partial wave amplitude . It is given by a -matrix which incorporates a summation of resonant and non-resonant terms in the form\n\n A(\u03b2)ij=\u221a\u03c1i\u2211aK(\u03b2)ia(I\u2212i\u03c1K(\u03b2))\u22121aj\u221a\u03c1j. (12)\n\nThe multi-index denotes the quantum numbers of the partial wave, it is suppressed in the following. The factor represents the phase space matrix to all allowed intermediate states, , are the phase space factors for the initial and the final state. The matrix parametrizes resonances and background contributions:\n\n Kab=\u2211\u03b1g\u03b1ag\u03b1bM2\u03b1\u2212s+fab. (13)\n\nHere are coupling constants of the pole to the initial and the final state. The background terms describe non-resonant transitions from the initial to the final state.\n\nFor photoproduction reactions, we use the helicity ()-dependent amplitude for photoproduction of the final state Chung:1995dx\n\n ahb = Pha(I\u2212i\u03c1K)\u22121abwhere (14) Pha = \u2211\u03b1Ah\u03b1g\u03b1aM2\u03b1\u2212s+Fa. (15)\n\nis the photo-coupling of a pole and a non-resonant transition. The helicity amplitudes , are defined as residues of the helicity-dependent amplitude at the pole position and are complex numbers Workman:2013rca .\n\nIn most partial waves, a constant background term is sufficient to achieve a good fit. Only the background in the meson-baryon -wave required a more complicated form:\n\n fab=(a+b\u221as)(s\u2212s0). (16)\n\nFurther background contributions are obtained from the reggeized exchange of vector mesons Anisovich:2004zz in the form\n\n A = g(t)R(\u03be,\u03bd,t)where (17) R(\u03be,\u03bd,t) = 1+\u03beexp(\u2212i\u03c0\u03b1(t))sin(\u03c0\u03b1(t))(\u03bd\u03bd0)\u03b1(t).\n\nhere, represents a vertex function and a form factor. describes the trajectory, , is a normalization factor, and the signature of the trajectory. Pion and and Pomeron exchange both have a positive signature and therefore Anisovich:2004zz :\n\n R(+,\u03bd,t)=e\u2212i\u03c02\u03b1(t)sin(\u03c02\u03b1(t))(\u03bd\u03bd0)\u03b1(t). (18)\n\nAdditional -functions eliminate the poles at :\n\n sin(\u03c02\u03b1(t))\u2192sin(\u03c02\u03b1(t))\u0393(\u03b1(t)2). (19)\n\nwhere the Kaon trajectory is parametrized as , with given in GeV.\n\nThe data on partial wave amplitudes (Fig.\u00a02) and on the photoproduction multipoles (Fig.\u00a09) were included in the data base of the BnGa partial wave analysis. The data are fitted jointly with data on , , , , and from both photo- and pion-induced reactions. Thus inelasticities in the meson-baryon system are constrained by real data. A list of the data used for the fit can be found in Anisovich:2011fc ; Anisovich:2013vpa ; Sokhoyan:2015fra ; Gutz:2014wit and on our website (pwa.hiskp.uni-bonn.de). In Fig.\u00a02, the systematic errors define the error band; in Fig.\u00a09, the systematic error of the real (imaginary) part of the amplitudes is shown a grey (red\/blue) histogram at the bottom (top) line. The systematic errors are derived by a variation of the model space by adding further resonances with different spin-parities when the data are fitted.\n\n## 4 The Laurent-Pietarinen expansion\n\n### 4.1 Formalism\n\nThe main task of the single channel Laurent-Pietarinen expansion () is extracting pole positions from given partial waves for one reaction. The driving concept behind the method is to replace an elaborate theoretical model by a local power-series representation of partial wave amplitudes\u00a0L+P2013 . The complexity of a partial-wave analysis model is thus replaced by much simpler model-independent expansion which just exploits analyticity and unitarity. The L+P approach separates pole and regular part in the form of a Mittag-Leffler expansion111Mittag-Leffler expansion Mittag-Leffler is the generalization of a Laurent expansion to a more-than-one pole situation. From now on, for simplicity, we will simply refer to this as a Laurent expansion., and instead of modeling the regular part using some physical model it uses the conformal-mapping-generated, rapidly converging power series with well defined analytic properties called a Pietarinen expansion222A conformal mapping expansion of this particular type was introduced by Ciulli and Fisher Ciulli ; CiulliFisher , was described in detail and used in pion-nucleon scattering by Esco Pietarinen Pietarinen ; Pietarinen1 , and named as a Pietarinen expansion by G. H\u00f6hler in Hohler:1984ux . to represent it effectively. So, the method replaces the regular part calculated in a model with the simplest analytic function which has correct analytic properties of the analyzed partial wave (multipole), and fits the given input. In such an approach the model dependence is minimized, and is reduced to the choice of the number and location of L+P branch-points used in the model. The method is applicable to both, theoretical and experimental input, and represents the first reliable procedure to extract pole positions directly from experimental data, with minimal model bias. The L+P expansion based on the Pietarinen expansion is used in some former papers in the analysis of pion-nucleon scattering data Ciulli ; CiulliFisher ; Pietarinen ; Pietarinen1 and in several few-body reactions L+P2014 ; L+P2014a ; L+P2015 . The procedure has recently been generalized also to the multi-channel case Svarc2016 .\n\nThe generalization of the L+P method to a multichannel L+P method, used in this paper, is performed in the following way: i)\u00a0separate Laurent expansions are made for each channel; ii)\u00a0pole positions are fixed for all channels, iii)\u00a0residua and Pietarinen coefficients are varied freely; iv)\u00a0branch-points are chosen as for the single-channel model; v)\u00a0the single-channel discrepancy function (see Eq. (5) in ref. L+P2015 ) which quantifies the deviation of the fitted function from the input is generalized to a multi-channel quantity by summing up all single-channel contributions, and vi)\u00a0the minimization is performed for all channels in order to obtain the final solution.\n\nThe formulae used in the L+P approach are collected in Table\u00a01.\n\nL+P is a formalism which can be used for extracting poles from any given set of data, either theoretically generated, or produced directly from experiment. If the data set is theoretically generated, we can never reconstruct the analytical properties of the background put into the model, we can only give the simplest analytic function which on the real axes gives very similar, in practice indistinguishable result from the given model values. Therefore, analyzing partial waves coming directly from experiment is for L+P much more favourable because we do not have such demands. The analytic properties are unknown, so there is no reason why the simplest perfect fit we offer should not be the true result. As in principle we do not care whether the input is generated by theory or otherwise, in the set of formulas given in Table\u00a01. we denote any input fitted with L+P function generically as .\n\nIn this paper we fit partial wave data; the discrete data points coming from a semi-constrained single energy fit of K photo-production data, which is obtained in a way that the partial waves with are fixed to Bonn-Gatchina energy dependent partial waves, and lower ones are allowed to be free. We perform a multichannel fit () when possible by including single energy data from process, and we fit both multipoles for the same angular momentum at the same time in the coupled-multipole fit (). The regular background part is represented by three Pietarinen expansion series, all free parameters are fitted. The first Pietarinen expansion with branch-point is restricted to an unphysical energy range and represents all left-hand cut contributions. The next two Pietarinen expansions describe the background in the physical range with branch-points and respecting the analytic properties of the analyzed partial wave. The second branch-point is mostly fixed to the elastic channel branch-point, the third one is either fixed to the dominant channel threshold, or left free. Thus, only rather general physical assumptions about the analytic properties are made like the number of poles and the number and the position of branch-points, and the simplest analytic function with a set of poles and branch-points is constructed.\n\nIn the compilation of our results we show the results of four fits: a)\u00a0the BnGa coupled channel fit to the complete data base including the energy independent solutions for and presented here; b)\u00a0a single-channel L+P fit to the energy independent solution for () ; c)\u00a0a single-channel L+P fit to the energy independent solution for (); and d)\u00a0 a multi-channel L+P fit to the energy independent solution for and ().\n\n### 4.2 L+P Fits\n\n#### 4.2.1 Jp=1\/2\u2212-wave\n\nWe have fitted the partial wave from the energy independent amplitude for the reaction\n\nin a fit. A was obtained for the 28 data points with 23 parameters. We needed two poles, one at 1667\u2009MeV and second one at 1910\u2009MeV. Due to the low-statistics of the data, the results from the single-channel fit show large errors.\n\nThe 48 data points on the multipole from required only one pole close to 1900\u2009MeV. The strong peak at low mass of the imaginary part of the multipole is reproduced by the function with a branching point at the threshold. Note that the lowest mass bin for the multipole starts at 1700\u2009MeV, significantly above the mass. The data were described with a and 19 parameters in a fit. Compared to the pion-induced reaction, the errors on the higher-mass resonance (at 1900\u2009MeV) are considerably reduced.\n\nThe common fit to both data sets (with 76 data points) used two poles, the fit resulted in a for 37 parameters. The results are shown in Table\u00a03 and Figs.\u00a09 and 10.\n\nThe real part of the pole positions of the resonance are nicely consistent when the three values are compared, the imaginary part is likely too narrow in the L+P fit. The magnitudes of the inelastic pole residue are consistent at the level when the BnGa and CC L+P fits are compared. The phases, however, seem to be inconsistent.\n\nThe pole positions are well defined with acceptable errors and consistent when the four analyses are compared, only the single-channel L+P fit to photoproduction data returns a slightly too narrow width. All four analyses yield compatible magnitudes of the inelastic pole residues, the phases disagree at the level. The magnitudes and the phases of the multipole determined by the BnGa fit agree well with the values of the L+P fits within the rather large uncertainties. Note that the errors in the CC L+P and BnGa fits have different origins: The L+P errors are of a statistical nature, the BnGa errors are derived from the spread of results of a variety of different fits. Both approaches establish the need for and unquestionably require .\n\n#### 4.2.2 Jp=1\/2+-wave\n\nWe have fitted the -wave using the P energy independent amplitude for the reaction and the multipole from . The first data set required two poles. The first pole was located near 1700\u2009MeV, the second one was found near 2100\u2009MeV even though with large error bars: the admitted range covers masses from to \u2009MeV. The photoproduction data required only one pole close to 1900\u2009MeV. The CC L+P fit to both data sets was performed with two poles.","date":"2020-07-04 11:39:56","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8011122345924377, \"perplexity\": 1794.5479152250782}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-29\/segments\/1593655886121.45\/warc\/CC-MAIN-20200704104352-20200704134352-00200.warc.gz\"}"}
| null | null |
JAMES OLIVE FAMILY HISTORY
OLD JAMES OLIVE OF WAKE COUNTY NORTH CAROLINA
James Olive, the second son of William Olive, was born in 1713 in Virginia. Until recently there was little known about the background of "Old James", as he is refered to by the family. James was the father of seven sons and maybe two daughters. He seems to have arrived in Wake County North Carolina around 1740. Many descendants remain in Wake County near the area when James settled.
The sons of James Olive are:
JAMES OLIVE, JR. m. ELIZABETH BURT, daughter of John Burt, Sr.
WILLIAM OLIVE b. 1746 m. ELIZABETH HENDON daughter of JAMES HENDON and HANNAH NORRIS (NOTE CORRECTION Earlier records had stated he married ANN HENDON, daughter of Isham Hendon and Keziah Johnson)
SOUTHWOOD OLIVE b. about 1750-52 m. NANCY ANN HENDON daughter of ISHAM HENDON and KEZIAH JOHNSON and cousin of Elizabeth HENDON
JOHN OLIVE b. about 1754 m. 1st ___ PARTRIDGE 2nd NANCY WOMBLE
ANTHONY OLIVE m. Kerenhappuch "HAPPY" Hendon d. 1798 daughter of ISHAM HENDON and KEZIAH JOHNSON sister of Nancy Ann HENDON Moved to Georgia
JESSE OLIVE b. about 1755 m. MONICAH MASSEY, daughter of Richard Massey, Sr.
ABEL OLIVE b July 20, 1765 m. 1st BETTY ANN WILLIS, daughter of William Willis 2nd MARTHA PATSEY MINTER, daughter of Richard Minter Moved to Kentucky
The two possible daughters of James Olive are:
RACHEL OLIVE m. JOSEPH EMBRY or EMBROUGH of Johnston County North Caroina Joseph moved to Georgia and owned 400 acres adjoining Anthony Olive. Joseph was also guardian to some of the minor children of Anthony Olive. Documents from the Memorial Records of Alabama state; James Embry b. Clarke County Georgia 1820, son of Elijah and Frances (Noell) Embry; grandson of Joseph and Rachel (OLIVE) Embry, both natives of North Carolina.
Amy ____ m. ISSAC HILL. Amy and Issac had children named Jesse, James, and Olive. They lived in the same area as Old James Olive had lived. Issac's will was witnessed by Abel Olive and William Olive. James Olive, Jr. was an executor of Issac's will.
BOOKS ABOUT THE OLIVE FAMILY
In 1965 a book was published by the Olive Family Association which united the research of various descendants of "Old James" Olive. Although there was not an official organization, the joint efforts of Olives around the United States created the foundation for the recently formed organization. It was through the efforts of Mrs. Olive Cartwright that this book was published. The Third Printing is currently available by photocopy.
Through the efforts of Mrs. Irene Kittenger, there will soon be a revised "Old James Olive Family" book available. There have been many corrections and additions to the family history since the 1965 publication. Mrs. Kittinger has spent many years searching for descendants of the sons of James Olive and has enlisted the efforts of many relatives in the completion of this new publication.
The revised "Old James Olive Family" book will be published soon. Many families are submitting information to assure their family is correctly represented in the publication.
SUMMARY OF JAMES OLIVE
BORN ABOUT OCTOBER 3, 1713 IN GLOUCESTER COUNTY VIRGIANIA
ARRIVED IN WAKE COUNTY NORTH CAROLINA AROUND 1740
SEVEN KNOWN SONS
MARRIED AROUND 1743 TO ELIZABETH
|
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| 7,250
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ST. LOUIS, MO, February 11, 2019 – Small RNAs (sRNAs) are key regulators involved in plant growth and development. Two groups of sRNAs are abundant during development of pollen in the anthers – a critical process for reproductive success. One of these pathways for sRNA production, previously believed present in grasses and related monocots, has now been demonstrated to be present widely in the flowering plants, evolved over 200 million years ago, and is arguably one of the evolutionary innovations that made them so successful.
The research, led by Blake Meyers, Ph.D., member, Donald Danforth Plant Science Center and professor, Division of Plant Sciences, University of Missouri and his collaborators at South China Agriculture University, the University of Delaware, and the University of Maryland, published their findings, "24-nt reproductive phasiRNAs are broadly present in angiosperms," in the journal Nature Communications.
"We've been studying this pathway extensively in maize as part of a project supported by the National Science Foundation. Quite unexpectedly, we found the pathway in the tropical tree that produces lychee fruit, which, as a eudicot, is distant from the grasses. When we analyzed other eudicot plant genomes, we found that this pathway was present in many of them – a complete surprise to us, since we thought it was only in the monocots," said Meyers. "There are some key differences between the pathway in eudicots and in grasses, and characterizing these in our study has given us insights into how sRNA and reproductive biology has diverged in these groups of plants."
Meyers explained that the long-standing view was that this pathway was specific to the grasses. In a companion piece of work, Meyers and his colleagues have demonstrated that maize, a monocot and member of the grass family, requires this pathway for full male fertility. But their paper in Nature Communications upends this view, demonstrating that the pathway emerged prior to the split between eudicots and monocots. One of the big mysteries they are trying to address is the precise molecular function of these sRNAs in pollen development. To address this question in eudicots, Meyers and his team are using Fragaria vesca, a diploid, also known as woodland strawberries as a model for their experiments. The genome of Fragaria vesca was sequenced in 2010 and is often used as a model due to its small genome size, short reproductive cycle and ease of propagation.
"The explosion of flowering plants was a remarkable thing in evolution, and they represent most species used for food and fuel," said Meyers. "Understanding the genetic mechanisms by which flowers develop will be important for improving crop yields and breeding better varieties, particularly for making the high-yielding hybrid crops that support modern agriculture."
Collaborators include: Rui Xia, Chengjie Chen, Wuqiang Ma and Jing Xu, South China Agricultural University, Guangzhou, Guangdong, China; Kun Huang and Parth Patel, University of Delaware, Newark, Delaware; Fuxi Wang and Zhongchi Liu, University of Maryland, College Park, Maryland; and Suresh Pokhrel, Donald Danforth Plant Science Center.
About The Donald Danforth Plant Science Center
Founded in 1998, the Donald Danforth Plant Science Center is a not-for-profit research institute with a mission to improve the human condition through plant science. Research, education and outreach aim to have impact at the nexus of food security and the environment, and position the St. Louis region as a world center for plant science. The Center's work is funded through competitive grants from many sources, including the National Institutes of Health, U.S. Department of Energy, National Science Foundation, and the Bill & Melinda Gates Foundation. Follow us on Twitter at @DanforthCenter.
Donald Danforth Plant Science Center
Karla Roeber
Kroeber@danforthcenter.org
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And just like us, sometimes illnesses reign. We go to a doctor, get some antibiotics and all is well. Our fish don't get that. Not just because we're farming organically, but because our systems would die if we eradicate our bacterial colonies.
Humans mostly talk about stress in relation to work or social relations. That's our environment, it's what we think is important. For fish, their environment is the water they live in. In fact, they are the water they live in, with some membranes to keep them together. Just like we get the flu when we're overwrought, fishes get sick when something's wrong in their environment. Stress is the main cause of death, whatever illness takes the blame.
One prominent quality of water is that its properties change very slowly. Because fish have evolved in water, they've adapted to slow changes. If something suddenly happens, they get a shot of adrenaline and try to get away, something they can't do in our tanks.
It's not for nothing we're measuring our water all the time. All the values we measure make a difference to the ecosystem. Other things are important as well, like light, sound and temperature. Too much or not enough of something might cause stress, cause immune systems to fail and cause illnesses and death.
So, it's the farmer's job to keep values within acceptable parameters. Unfortunately, we did something wrong, because our catfish show the strangest symptoms and die.
We could spend a lot of time trying to determine what kind of illness is killing them, but instead, we'd better focus on getting the parameters right so they can take care of it themselves.
There is one thing we can do, so we did it: we took the sickest fish out of the tank and put them in a separate quarantine tank with salt water. Because of the salt, the fish need less energy to regulate osmosis, which they can use to beat the pathogens. It's like a sanatorium for them.
Less fish are dying since the quarantine, but now and then we still find a dead one floating around. It's a sad sight. It's also frustrating that every change of a water value has to be done very slowly, not to stress the fish. We sincerely hope things get better soon.
So get out of your stressful environment, breath clean forest air and you will be able to beat the flu yourself!
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Home News Administrators for insolvent LQD Markets finalize their presentation to the FSCS
Administrators for insolvent LQD Markets finalize their presentation to the FSCS
News May 26, 2015 —by Andrew Saks-McLeod 0
Following the insolvency of FX brokerage LQD Markets in January as a result of exposure to negative client balances which were brought about by the Swiss National Bank's removal of the 1.20 peg on the EURCHF pair, the Financial Services Compensation Scheme (FSCS) has been provided by Baker Tilly, the Special Administrators of the firm, with all of the information they hold in relation to the monies due to clients and the products offered to clients of the company.
The FSCS is the UK's statutory compensation scheme for customers of authorized financial services firms that facilitiates the payment of compensation if a firm is unable, or likely to be unable, to pay claims against it.
Baker Tilly has confirmed today that it understands that this information has been reviewed by the case team at the FSCS and that the case has now been passed to the FSCS' legal team to decide which products (if any) that were offered by the company, are covered under the compensation scheme.
Baker Tilly has requested that the FSCS provides a timescale for when it expects that the legal team will advise whether the products offered fall under the scheme or not. To date, Baker Tilly has not been provided with any specific timeframes.
As soon as confirmation is received from the FSCS, Baker Tilly will notify clients and provide details on how they can make a claim with the FSCS if that is the appropriate route.
The firm advises clients that if they have not already provided a claim, then this can be done by forwarding a copy of the most recent statement from LQD Markets to [email protected]
Baker Tilly requests that it be noted that the Special Administrators are continuing to carry out investigations into the reason for the deficit and will provide an update to clients and creditors as and when appropriate, and that an update will only be placed on the website if the Special Administrators have new information to provide to clients.
For the official announcement from Baker Tilly, click here.
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ABN AMRO Clearing to clear EURO STOXX 50 Variance Futures on Eurex Exchange…NewsEUREX Exchange announced today that ABN AMRO Clearing will offer clearing services for the EURO STOXX 50® Variance Futures and will be available on�…
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|
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Q: How to combine an update and delete in a single sql statement without vialoating index constraints? Is it somehow possible to execute following sql statement without violating a unique index constraint that ensures that the Position is unique?
UPDATE wl SET Position = Position - 1
FROM [dbo].[WatchList] wl
WHERE Position > ( SELECT Position FROM [dbo].[WatchList] wl2
WHERE WatchListId = @WatchListID );
DELETE FROM [dbo].[WatchList] WHERE WatchListID = @WatchListID
I want to ensure that no Positon-gaps occur when i delete one record. All records with a higher position should be updated with Position=Position-1.
But that will cause a unique index violation because the row is yet not deleted. Are the only ways to prevent this issue to ...
*
*use a stored-procedure (should be avoided if possible, logic should be in code)
*to determine the old position before i delete the record which requires two queries
Update:
Thanks for your efforts. However, since there is no easy solution for this i have used the second approach, so first determine the old postion, delete the record and then update the followers.
A: If you want to run two different (types of) statements, and have constraints maintained both before and after, use MERGE:
create table T (
ID int not null,
Position int not null,
constraint PK_T_ID PRIMARY KEY (ID),
constraint UQ_T_ID UNIQUE (Position))
insert into T(ID,Position) values
(12,1),
(22,2),
(36,3),
(47,4)
declare @ToDelete int
set @ToDelete = 22
;With Positions as (
select
Position
from
T
where
Position >= (select Position from T where ID = @ToDelete)
)
merge into T t
using (select Position from Positions) s
on
t.Position = s.Position
when matched and ID = @ToDelete
then delete
when matched then update set Position = t.Position -1
;
select * from T
Results:
ID Position
----------- -----------
12 1
36 2
47 3
A: If Position is the primary key, to cause an index violation, you might be able to make use of ALTER INDEX and do a REBUILD after the Delete.
DELETE FROM [dbo].[WatchList] WHERE WatchListID = @WatchListID
ALTER INDEX PK_Watchlist ON dbo.Watchlist REBUILD
A: But you already have two queries
declare @pos int;
set @pos = SELECT Position FROM [dbo].[WatchList] wl2
WHERE WatchListId = @WatchListID;
DELETE FROM [dbo].[WatchList] WHERE pos = @pos;
UPDATE wl SET Position = Position - 1
FROM [dbo].[WatchList] wl
WHERE Position > @pos;
|
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{"url":"https:\/\/www.mathworks.com\/help\/hydro\/ref\/pipeil.html","text":"# Pipe (IL)\n\nPipe segment in an isothermal liquid network\n\nSince R2020a\n\nLibraries:\nSimscape \/ Fluids \/ Isothermal Liquid \/ Pipes & Fittings\n\n## Description\n\nThe Pipe (IL) block models flow in a rigid or flexible-walled pipe with losses due to wall friction. The effects of dynamic compressibility, fluid inertia, and pipe elevation can be optionally modeled. You can define multiple pipe segments and set the liquid pressure for each segment. By segmenting the pipe and selecting Fluid inertia, you can model events such as water hammer in your system.\n\n### Pipe Characteristics\n\nThe pipe block can be divided into segments with the Number of segments parameter. When the pipe is composed of a number of segments, the pressure in each segment is calculated based on the inlet pressure and the effect on the segment mass flow rate of the fluid compressibility and wall flexibility, if applicable. The fluid volume in each segment remains fixed. For a two-segment pipe, the pressure evolves linearly with respect to the pressure defined at ports A and B. For a pipe with three or more segments, you can specify the fluid pressure in each segment in vector or scalar form in the Initial liquid pressure parameter. The scalar form will apply a constant value over all segments.\n\nFlexible Walls\n\nYou can model flexible walls for all cross-sectional geometries. When you set Pipe wall specification to `Flexible`, the block assumes uniform expansion along all directions and preserves the defined cross-sectional shape. This setting may not result in physical results for noncircular cross-sectional areas undergoing high pressure relative to atmospheric pressure. When you model flexible walls, you can use the Volumetric expansion specification parameter to control the method for specifying the volumetric expansion of the pipe cross-sectional area.\n\nWhen the Volumetric expansion specification parameter is `Cross-sectional area vs. pressure`, the change in volume is modeled by\n\n`$\\stackrel{\u02d9}{V}=L\\left(\\frac{A}{\\tau }\\right),$`\n\nwhere:\n\n\u2022 $A={S}_{N}+{K}_{ps}\\left(p-{p}_{atm}\\right)-S.$\n\n\u2022 L is the Pipe length parameter.\n\n\u2022 SN is the nominal pipe cross-sectional area defined for each shape.\n\n\u2022 S is the current pipe cross-sectional area.\n\n\u2022 p is the internal pipe pressure.\n\n\u2022 patm is the atmospheric pressure.\n\n\u2022 Kps is the Static gauge pressure to cross-sectional area gain parameter.\n\nTo calculate Kps assuming uniform elastic deformation of a thin-walled, open-ended cylindrical pipe, use:\n\n`${K}_{ps}=\\frac{\\Delta D}{\\Delta p}=\\frac{\\pi {D}_{N}^{3}}{4tE},$`\n\nwhere t is the pipe wall thickness and E is Young's modulus.\n\n\u2022 \u03c4 is the Volumetric expansion time constant.\n\nWhen the Volumetric expansion specification parameter is `Cross-sectional area vs. pressure - Tabulated`, the block uses the same equation for $\\stackrel{\u02d9}{V}$ as the ```Cross-sectional area vs. pressure``` setting. The block calculates A with the table lookup function\n\n`$A={S}_{N}+tablelookup\\left({p}_{ps},{A}_{ps},\\left(p-{p}_{atm}\\right),interpolation=linear,extrapolation=linear\\right),$`\n\nwhere pps is the Static gauge pressure vector parameter and Aps is the Cross sectional area gain vector parameter.\n\nWhen the Volumetric expansion specification parameter is `Hydraulic diameter vs. pressure`, the change in volume is modeled by\n\n`$\\stackrel{\u02d9}{V}=\\frac{\\pi }{2}DL\\left(\\frac{{D}_{static}-D}{\\tau }\\right),$`\n\nwhere:\n\n\u2022 ${D}_{static}={D}_{N}+{K}_{pd}\\left(p-{p}_{atm}\\right).$\n\n\u2022 DN is the nominal hydraulic diameter defined for each shape.\n\n\u2022 D is the current pipe hydraulic diameter.\n\n\u2022 Kpd is the Static gauge pressure to hydraulic diameter gain parameter. To calculate Kps assuming uniform elastic deformation of a thin-walled, open-ended cylindrical pipe, use:\n\n`${K}_{pd}=\\frac{\\Delta D}{\\Delta p}=\\frac{{D}_{N}^{2}}{2tE}.$`\n\nWhen the Volumetric expansion specification parameter is `Based on material properties`, the block uses the same equation for $\\stackrel{\u02d9}{V}$ as the ```Hydraulic diameter vs. pressure``` setting but calculates Dstatic depending on the value of the Material behavior parameter\n\n`${\\text{D}}_{static}={D}_{N}\\left(1+{\u03f5}_{hoop}\\right).$`\n\nThis parameterization assumes a cylindrical thin-walled pressure vessel where ${\\sigma }_{radial}=0.$\n\nWhen the Material behavior parameter is ```Linear elastic```,\n\n`${\u03f5}_{hoop}=\\frac{1}{E}\\left[{\\sigma }_{hoop}-v{\\sigma }_{longitudinal}\\right],$`\n\nwhere:\n\n\u2022 E is the value of the Young's modulus parameter.\n\n\u2022 v is the value of the Poisson's ratio parameter.\n\n\u2022 ${\\sigma }_{hoop}=\\frac{pD}{2t}$ where t is the value of the Pipe wall thickness parameter.\n\n\u2022 ${\\sigma }_{longitudinal}=\\frac{pD}{4t}.$\n\nWhen the Material behavior parameter is ```Multilinear elastic```, the block calculates the von Mises stress, \u03c3v, which simplifies to ${\\sigma }_{v}=\\sqrt{\\frac{3}{4}}\\frac{pD}{2t}$, to determine the equivalent strain. The hoop strain is\n\n`${\u03f5}_{hoop}={\u03f5}_{hoop}^{elastic}+{\u03f5}_{hoop}^{plastic}$`\n`$\\begin{array}{l}{\u03f5}_{hoop}^{elastic}=\\frac{1}{E}\\left[{\\sigma }_{hoop}-v{\\sigma }_{longitudinal}\\right]\\\\ {\u03f5}_{hoo{p}_{i,j}}^{plastic}=\\frac{3}{2}\\left(\\frac{1}{{E}_{s}}-\\frac{1}{E}\\right){S}_{i,j}\\end{array}$`\n\nwhere:\n\n\u2022 The block calculates the Young's Modulus, E, from the first elements of the Stress vector and Strain vector parameters.\n\n\u2022 ${E}_{S}=\\frac{{\\sigma }_{total}}{{\u03f5}_{total}}$, where \u03c3total and \u03b5total are the equivalent total stress and the equivalent total strain, respectively. The block calculates the equivalent total strain from the von Mises stress and the stress-strain curve.\n\n\u2022 ${\\text{S}}_{i,j}={\\sigma }_{i,j}-\\left[\\frac{{\\sigma }_{hoop}+{\\sigma }_{longitudinal}+{\\sigma }_{radial}}{3}\\right]{\\delta }_{i,j},$ where \u03c3i,j are the elements of the Cauchy stress tensor.\n\nIf you do not model flexible walls, SN = S and DN = D.\n\nCircular\n\nThe nominal hydraulic diameter and the Pipe diameter, dcircle, are the same. The pipe cross sectional area is: ${S}_{N}=\\frac{\\pi }{4}{d}_{circle}^{2}.$\n\nAnnular\n\nThe nominal hydraulic diameter, Dh,nom, is the difference between the Pipe outer diameter and Pipe inner diameter, dodi. The pipe cross sectional area is ${S}_{N}=\\frac{\\pi }{4}\\left({d}_{{}_{o}}^{2}-{d}_{{}_{i}}^{2}\\right).$\n\nRectangular\n\nThe nominal hydraulic diameter is:\n\n`${D}_{N}=\\frac{2hw}{h+w},$`\n\nwhere:\n\n\u2022 h is the Pipe height.\n\n\u2022 w is the Pipe width.\n\nThe pipe cross sectional area is ${S}_{N}=wh.$\n\nElliptical\n\nThe nominal hydraulic diameter is:\n\n`${D}_{N}=2{a}_{maj}{b}_{min}\\frac{\\left(64-16{\\left(\\frac{{a}_{maj}-{b}_{min}}{{a}_{maj}+{b}_{min}}\\right)}^{2}\\right)}{\\left({a}_{maj}+{b}_{min}\\right)\\left(64-3{\\left(\\frac{{a}_{maj}-{b}_{min}}{{a}_{maj}+{b}_{min}}\\right)}^{4}\\right)},$`\n\nwhere:\n\n\u2022 amaj is the Pipe major axis.\n\n\u2022 bmin is the Pipe minor axis.\n\nThe pipe cross sectional area is ${S}_{N}=\\frac{\\pi }{4}{a}_{maj}{b}_{min}.$\n\nIsosceles Triangular\n\nThe nominal hydraulic diameter is:\n\n`${D}_{N}={l}_{side}\\frac{\\mathrm{sin}\\left(\\theta \\right)}{1+\\mathrm{sin}\\left(\\frac{\\theta }{2}\\right)}$`\n\nwhere:\n\n\u2022 lside is the Pipe side length.\n\n\u2022 \u03b8 is the Pipe vertex angle.\n\nThe pipe cross sectional area is ${S}_{N}=\\frac{{l}_{side}^{2}}{2}\\mathrm{sin}\\left(\\theta \\right).$\n\n### Pressure Loss Due to Friction\n\nHaaland Correlation\n\nThe analytical Haaland correlation models losses due to wall friction either by aggregate equivalent length, which accounts for resistances due to nonuniformities as an added straight-pipe length that results in equivalent losses, or by local loss coefficient, which directly applies a loss coefficient for pipe nonuniformities.\n\nWhen the Local resistances specification parameter is set to `Aggregate equivalent length` and the flow in the pipe is lower than the Laminar flow upper Reynolds number limit, the pressure loss over all pipe segments is:\n\n`$\\Delta {p}_{f,A}=\\frac{\\upsilon \\lambda }{2{D}^{2}S}\\frac{L+{L}_{add}}{2}{\\stackrel{\u02d9}{m}}_{A},$`\n\n`$\\Delta {p}_{f,B}=\\frac{\\upsilon \\lambda }{2{D}^{2}S}\\frac{L+{L}_{add}}{2}{\\stackrel{\u02d9}{m}}_{B},$`\n\nwhere:\n\n\u2022 \u03bd is the fluid kinematic viscosity.\n\n\u2022 \u03bb is the , which you can define when Cross-sectional geometry is set to `Custom` and is otherwise equal to 64.\n\n\u2022 D is the pipe hydraulic diameter.\n\n\u2022 Ladd is the Aggregate equivalent length of local resistances.\n\n\u2022 $\\stackrel{\u02d9}{m}$A is the mass flow rate at port A.\n\n\u2022 $\\stackrel{\u02d9}{m}$B is the mass flow rate at port B.\n\nWhen the Reynolds number is greater than the Turbulent flow lower Reynolds number limit, the pressure loss in the pipe is:\n\n`$\\Delta {p}_{f,A}=\\frac{f}{2{\\rho }_{I}{S}^{2}}\\frac{L+{L}_{add}}{2}{\\stackrel{\u02d9}{m}}_{A}|{\\stackrel{\u02d9}{m}}_{A}|,$`\n\n`$\\Delta {p}_{f,B}=\\frac{f}{2{\\rho }_{I}{S}^{2}}\\frac{L+{L}_{add}}{2}{\\stackrel{\u02d9}{m}}_{B}|{\\stackrel{\u02d9}{m}}_{B}|,$`\n\nwhere:\n\n\u2022 f is the Darcy friction factor. This is approximated by the empirical Haaland equation and is based on the Surface roughness specification, \u03b5, and pipe hydraulic diameter:\n\n`$f={\\left\\{-1.8{\\mathrm{log}}_{10}\\left[\\frac{6.9}{\\mathrm{Re}}+{\\left(\\frac{\\epsilon }{3.7{D}_{h}}\\right)}^{1.11}\\right]\\right\\}}^{-2},$`\n\nPipe roughness for brass, lead, copper, plastic, steel, wrought iron, and galvanized steel or iron are provided as ASHRAE standard values. You can also supply your own Internal surface absolute roughness with the `Custom` setting.\n\n\u2022 \u03c1I is the internal fluid density.\n\nWhen the Local resistances specification parameter is set to `Local loss coefficient` and the flow in the pipe is lower than the Laminar flow upper Reynolds number limit, the pressure loss over all pipe segments is:\n\n`$\\Delta {p}_{f,A}=\\frac{\\upsilon \\lambda }{2{D}^{2}S}\\frac{L}{2}{\\stackrel{\u02d9}{m}}_{A}.$`\n\n`$\\Delta {p}_{f,B}=\\frac{\\upsilon \\lambda }{2{D}^{2}S}\\frac{L}{2}{\\stackrel{\u02d9}{m}}_{B}.$`\n\nWhen the Reynolds number is greater than the Turbulent flow lower Reynolds number limit, the pressure loss in the pipe is:\n\n`$\\Delta {p}_{f,A}=\\left(\\frac{f\\frac{L}{2}}{D}+{C}_{loss,total}\\right)\\frac{1}{2{\\rho }_{I}{S}^{2}}{\\stackrel{\u02d9}{m}}_{A}|{\\stackrel{\u02d9}{m}}_{A}|,$`\n\n`$\\Delta {p}_{f,B}=\\left(\\frac{f\\frac{L}{2}}{D}+{C}_{loss,total}\\right)\\frac{1}{2{\\rho }_{I}{S}^{2}}{\\stackrel{\u02d9}{m}}_{B}|{\\stackrel{\u02d9}{m}}_{B}|,$`\n\nwhere Closs,total is the loss coefficient, which can be defined in the Total local loss coefficient parameter as either a single coefficient or the sum of all loss coefficients along the pipe.\n\nNominal Pressure Drop vs. Nominal Mass Flow Rate\n\nThe Nominal Pressure Drop vs. Nominal Mass Flow Rate parameterization characterizes losses with a loss coefficient for rigid or flexible walls. When the fluid is incompressible, the pressure loss over the entire pipe due to wall friction is:\n\n`$\\Delta {p}_{f,A}={K}_{p}{\\stackrel{\u02d9}{m}}_{A}\\sqrt{{\\stackrel{\u02d9}{m}}_{A}^{2}+{\\stackrel{\u02d9}{m}}_{th}^{2}},$`\n\nwhere Kp is:\n\n`${K}_{p}=\\frac{\\Delta {p}_{N}}{{\\stackrel{\u02d9}{m}}_{N}^{2}},$`\n\nwhere:\n\n\u2022 \u0394pN is the Nominal pressure drop, which can be defined either as a scalar or a vector.\n\n\u2022 ${\\stackrel{\u02d9}{m}}_{N}$ is the Nominal mass flow rate, which can be defined either as a scalar or a vector.\n\nWhen the Nominal pressure drop and Nominal mass flow rate parameters are supplied as vectors, the scalar value Kp is determined from a least-squares fit of the vector elements.\n\nTabulated Data \u2013 Darcy Friction Factor vs. Reynolds Number\n\nPressure losses due to viscous friction can also be determined from user-provided tabulated data of the Darcy friction factor vector and the Reynolds number vector for turbulent Darcy friction factor parameters. Linear interpolation is employed between data points.\n\n### Pipe Discretization\n\nYou can divide the pipe into multiple segments. If a pipe has more than one segment, the mass flow and momentum balance equations are calculated for each segment.\n\nIf you would like to capture specific phenomena in your application, such as water hammer, choose a number of segments that provides sufficient resolution of the transient. The following formula, from the Nyquist sampling theorem, provides a rule of thumb for pipe discretization into a minimum of N segments:\n\n`$N=2L\\frac{f}{c},$`\n\nwhere:\n\n\u2022 L is the Pipe length.\n\n\u2022 f is the transient frequency.\n\n\u2022 c is the speed of sound.\n\n### Momentum Balance\n\nFor an incompressible fluid, the mass flow into the pipe equals the mass flow out of the pipe:\n\n`${\\stackrel{\u02d9}{m}}_{A}+{\\stackrel{\u02d9}{m}}_{B}=0.$`\n\nWhen the fluid is compressible and pipe walls are rigid, the difference between the mass flow into and out of the pipe depends on the fluid density change due to compressibility:\n\n`${\\stackrel{\u02d9}{m}}_{A}+{\\stackrel{\u02d9}{m}}_{B}={\\stackrel{\u02d9}{p}}_{I}\\frac{d{\\rho }_{I}}{d{p}_{I}}V,$`\n\nWhen the fluid is compressible and the pipe walls are flexible, the difference between the mass flow into and out of the pipe is based on the change in fluid density due to compressibility, and the amount of fluid accumulated in the newly deformed regions of the pipe:\n\n`${\\stackrel{\u02d9}{m}}_{A}+{\\stackrel{\u02d9}{m}}_{B}={\\stackrel{\u02d9}{p}}_{I}\\frac{d{\\rho }_{I}}{d{p}_{I}}V+{\\rho }_{I}\\stackrel{\u02d9}{V}.$`\n\nThe changes in momentum between the pipe inlet and outlet comprises the changes in pressure due to pipe wall friction, which is modeled according to the Viscous friction parameterization and pipe elevation. For a pipe that does not model fluid inertia, the momentum balance is:\n\n`${p}_{A}-{p}_{I}=\\Delta {p}_{f,A}+{\\rho }_{I}\\frac{\\Delta z}{2}g,$`\n\n`${p}_{B}-{p}_{I}=\\Delta {p}_{f,B}-{\\rho }_{I}\\frac{\\Delta z}{2}g,$`\n\nwhere:\n\n\u2022 pA is the pressure at port A.\n\n\u2022 pI is the fluid volume internal pressure.\n\n\u2022 pB is the pressure at port B.\n\n\u2022 \u0394pf is the pressure loss due to wall friction, parameterized by the Viscous friction losses specification according to the respective port.\n\n\u2022 \u0394z is the pipe elevation. In the case of constant-elevation pipes, this is the Elevation gain from port A to port B parameter; otherwise, it is received as a physical signal at port EL.\n\n\u2022 g is the gravitational acceleration. In the case of a fixed gravitational constant, this is the Gravitational acceleration parameter; otherwise, it is received as a physical signal at port G.\n\nFor a pipe with modeled fluid inertia, the momentum balance is:\n\n`${p}_{A}-{p}_{I}=\\Delta {p}_{f,A}+{\\rho }_{I}\\frac{\\Delta z}{2}g+{\\stackrel{\u00a8}{m}}_{A}\\frac{L}{2S},$`\n\n`${p}_{B}-{p}_{I}=\\Delta {p}_{f,B}-{\\rho }_{I}\\frac{\\Delta z}{2}g+{\\stackrel{\u00a8}{m}}_{B}\\frac{L}{2S},$`\n\nwhere:\n\n\u2022 $\\stackrel{\u00a8}{m}$ is the fluid acceleration at its respective port.\n\n\u2022 S is the pipe cross-sectional area.\n\n## Ports\n\n### Conserving\n\nexpand all\n\nLiquid entry or exit port.\n\nLiquid entry or exit port.\n\n### Inputs\n\nexpand all\n\nVariable elevation from port A to port B, specified as a physical signal. The elevation magnitude must be less than or equal to the pipe length. If the signal falls below the value of \u2013Pipe length, the value at EL is maintained at ```\u2013pipe length```. If the signal exceeds the value of Pipe length, the value at EL is maintained at `pipe length`.\n\n#### Dependencies\n\nTo enable this port, set Elevation gain specification to `Variable`.\n\nVariable gravitational acceleration, specified as a physical signal.\n\n#### Dependencies\n\nTo enable this port, set Gravitational acceleration specification to `Variable`.\n\n## Parameters\n\nexpand all\n\n### Configuration\n\nTotal pipe length across all pipe segments.\n\nNumber of pipe divisions. Each division represents an individual segment for which pressure is calculated, depending on the pipe inlet pressure, fluid compressibility, and wall flexibility, if applicable. The fluid volume in each segment remains fixed.\n\nCross-sectional pipe geometry. A nominal hydraulic diameter and nominal cross-sectional area is calculated based on the cross-sectional geometry.\n\nDiameter for circular cross-sectional pipes.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to `Circular`.\n\nInner diameter for annular pipe flow, or flow between two concentric pipes.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to `Annular`.\n\nOuter diameter for annular pipe flow, or flow between two concentric pipes.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to `Annular`.\n\nWidth of rectangular pipe.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to `Rectangular`.\n\nHeight of rectangular pipe.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to `Rectangular`.\n\nMajor axis for ellipsoidal pipes.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to `Elliptical`.\n\nMinor axis for ellipsoidal pipes.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to `Elliptical`.\n\nLength of the two equal sides of isosceles-triangular pipes.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to ```Isosceles triangular```.\n\nVertex angle for triangular pipes. The value must be less than 180 degrees.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to ```Isosceles triangular```.\n\nHydraulic diameter used in calculations of the pipe Reynolds number. For noncircular pipes, the hydraulic diameter is the effective diameter of the fluid in the pipe. For circular pipes, the hydraulic diameter and pipe diameter are the same.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to `Custom`.\n\nPipe cross-sectional area for a custom pipe geometry.\n\n#### Dependencies\n\nTo enable this parameter, set Cross-sectional geometry to `Custom`.\n\nWhether to model any change in fluid density due to fluid compressibility. When you select Fluid dynamic compressibility, changes due to the mass flow rate into the block are calculated in addition to density changes due to changes in pressure. In the Isothermal Liquid Library, all blocks calculate density as a function of pressure.\n\nWhether to account for resistance to changes in the flow rate due to the fluid mass.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility.\n\nWhether the pipe elevation remains constant or variable from port A to B.\n\nElevation differential for constant-elevation pipes. The elevation gain must be less than or equal to the Pipe length.\n\n#### Dependencies\n\nTo enable this parameter, set Elevation gain specification to `Constant`.\n\nWhether the gravitational constant is constant or variable.\n\nGravitational acceleration for environments with constant gravitational acceleration.\n\n#### Dependencies\n\nTo enable this parameter, set Gravitational acceleration specification to `Constant`.\n\n### Viscous Friction\n\nParameterization of pressure losses due to wall friction. Both analytical and tabular formulations are available.\n\nMethod for quantifying pressure losses due to pipe nonuniformities.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Haaland correlation```.\n\nLoss coefficient associated with each pipe nonuniformity. You can input a single loss coefficient or the sum of all loss coefficients along the pipe.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Haaland correlation``` and Local resistance specifications to ```Local loss coefficient```.\n\nLength of pipe that would produce the equivalent hydraulic losses as would a pipe with bends, area changes, or other nonuniform attributes. The effective length of the pipe is the sum of the Pipe length and the Aggregate equivalent length of local resistances.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Haaland correlation``` and Local resistance specifications to ```Aggregate equivalent length```.\n\nAbsolute surface roughness based on pipe material. The provided values are ASHRAE standard roughness values. You can also input your own value by setting Surface roughness specification to `Custom`.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Haaland correlation```.\n\nPipe wall absolute roughness. This parameter is used to determine the Darcy friction factor, which contributes to pressure loss in the pipe.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Haaland correlation``` and Surface roughness specification to `Custom`.\n\nUpper Reynolds number limit to laminar flow. Beyond this number, the fluid regime is transitional, approaches the turbulent regime, and becomes fully turbulent at the Turbulent flow lower Reynolds number limit.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to either:\n\n\u2022 `Haaland correlation`\n\n\u2022 ```Tabulated data - Darcy friction factor vs. Reynolds number```\n\nLower Reynolds number limit for turbulent flow. Below this number, the flow regime is transitional, approaches laminar flow, and becomes fully laminar at the Laminar flow upper Reynolds number limit.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to either:\n\n\u2022 `Haaland correlation`\n\n\u2022 ```Tabulated data - Darcy friction factor vs. Reynolds number```\n\nNominal mass flow rate used for calculating the pressure loss coefficient for rigid and flexible pipes, specified as a scalar or a vector. All nominal values must be greater than 0 and have the same number of elements as the Nominal pressure drop parameter. When this parameter is supplied as a vector, the scalar value Kloss is determined as a least-squares fit of the vector elements.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Nominal pressure drop vs. nominal mass flow rate```.\n\nNominal pressure drop used for calculating the pressure loss coefficient for rigid and flexible pipes, specified as a scalar or vector. All nominal values must be greater than 0 and must have the same number of elements as the Nominal mass flow rate parameter. When this parameter is supplied as a vector, the scalar value Kloss is determined as a least-squares fit of the vector elements.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Nominal pressure drop vs. nominal mass flow rate```.\n\nMass flow rate threshold for reversed flow. A transition region is defined around 0 kg\/s between the positive and negative values of the mass flow rate threshold. Within this transition region, numerical smoothing is applied to the flow response. The threshold value must be greater than 0.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Nominal pressure drop vs. nominal mass flow rate```.\n\nVector of Reynolds numbers for the tabular parameterization of the Darcy friction factor. The vector elements form an independent axis with the Darcy friction factor vector parameter. The vector elements must be listed in ascending order. A positive Reynolds number corresponds to flow from port A to port B.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Tabulated data - Darcy friction factor vs. Reynolds number```.\n\nVector of Darcy friction factors for the tabular parameterization of the Darcy friction factor. The vector elements must correspond one-to-one with the elements in the Reynolds number vector for turbulent Darcy friction factor parameter, and must be unique and greater than or equal to 0.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to ```Tabulated data - Darcy friction factor vs. Reynolds number```.\n\nFriction constant for laminar flows. The Darcy friction factor captures the contribution of wall friction in pressure loss calculations. If Cross-sectional geometry is not set to `Custom`, this parameter is internally set to 64.\n\n#### Dependencies\n\nTo enable this parameter, set Viscous friction parameterization to either:\n\n\u2022 `Haaland correlation`\n\n\u2022 ```Tabulated data - Darcy friction factor vs. Reynolds number```\n\nand Cross-sectional geometry to `Custom`.\n\n### Pipe Wall\n\nSpecifies wall flexibility. This parameter is independent of pipe cross-sectional geometry. The `Flexible` setting preserves the initial pipe shape and applies equal expansion of the cross-sectional area. It may not be accurate for non-circular cross-sectional geometry under high deformation.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility.\n\nLinear expansion correlation. The settings correlate the new cross-sectional area or hydraulic diameter to the pipe pressure.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible`.\n\nCoefficient for calculating pipe deformation for the `Cross-sectional area vs. pressure` setting. The gain is multiplied by the pressure differential between the segment pressure and atmospheric pressure.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility, and set Pipe wall specification to `Flexible` and Volumetric expansion specification to ```Cross-sectional area vs. pressure```.\n\nVector that contains the gauge pressures. The block uses this vector in a table lookup to calculate the pipe cross-sectional area. The vector entries must be strictly positive and monotonically increasing and the vector must be the same length as the Cross sectional area gain vector parameter.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible` and Volumetric expansion specification to ```Cross-sectional area vs. pressure - Tabulated```.\n\nVector that contains the pipe cross-sectional areas. The block uses this vector in a table lookup to calculate the pipe cross sectional-area at other pressures. The vector entries must be strictly positive and monotonically increasing and the vector must be the same length as the Static gauge pressure vector parameter.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible` and Volumetric expansion specification to ```Cross-sectional area vs. pressure - Tabulated```.\n\nCoefficient for calculating pipe deformation for the `Hydraulic diameter vs. pressure` setting. The gain is multiplied by the pressure differential between the segment pressure and atmospheric pressure.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible` and Volumetric expansion specification to ```Hydraulic diameter vs. pressure```.\n\nMethod the block uses to calculate the material behavior.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible` and Volumetric expansion specification to `Based on material properties`.\n\nThickness of the pipe wall. The block uses this value to calculate stress.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible` and Volumetric expansion specification to `Based on material properties`.\n\nYoung's modulus of the material that makes up the pipe wall.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible`, Volumetric expansion specification to ```Based on material properties```, and Material behavior to ```Linear Elastic```.\n\nPoisson's ratio of the material that makes up the pipe wall.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible` and Volumetric expansion specification to `Based on material properties`.\n\nVector containing the stress values for the material that makes up the pipe wall.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible`, Volumetric expansion specification to `Based on material properties`, and Material behavior to `Multilinear Elastic`.\n\nVector containing the strain values for the material that makes up the pipe wall.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible`, Volumetric expansion specification to `Based on material properties`, and Material behavior to `Multilinear Elastic`.\n\nWhether the block does nothing, generates a warning, or generates an error when the stress is above the maximum stress specified by the Maximum allowable stress parameter.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible`, Volumetric expansion specification to `Based on material properties`, and Material behavior to `Multilinear Elastic`.\n\nMaximum stress the block allows on the pipe wall. Control what the block does if the stress exceeds this value with the Check if stress exceeds specified allowable level parameter.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible`, Volumetric expansion specification to ```Based on material properties```, Material behavior to ```Multilinear Elastic``` and Check if stress exceeds specified allowable level to `Warning` or `Error`.\n\nTime required for the wall to reach steady-state after pipe deformation. This parameter impacts the dynamic change in pipe volume.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and set Pipe wall specification to `Flexible`.\n\n### Initial Conditions\n\nInitial liquid pressure, specified as a scalar or vector. A vector n elements long defines the liquid pressure for each of n pipe segments. If the vector is two elements long, the pressure along the pipe is linearly distributed between the two element values. If the vector is three or more elements long, the initial pressure in the nth segment is set by the nth element of the vector.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility.\n\nInitial mass flow rate for pipes with simulated fluid inertia.\n\n#### Dependencies\n\nTo enable this parameter, select Fluid dynamic compressibility and Fluid inertia.\n\n## References\n\n[1] Budynas R. G. Nisbett J. K. & Shigley J. E. (2004). Shigley's mechanical engineering design (7th ed.). McGraw-Hill.\n\n[2] Ju Frederick D., Butler Thomas A., Review of Proposed Failure Criteria for Ductile Materials (1984) Los Alamos National Laboratory.\n\n[3] Hencky H (1924) Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen. Z Angew Math Mech 4:323\u2013335\n\n[4] Jahed H, \u201cA Variable Material Property Approach for Elastic-Plastic Analysis of Proportional and Non-proportional Loading, (1997) University of Waterloo\n\n## Version History\n\nIntroduced in R2020a\n\nexpand all","date":"2023-03-24 16:43:07","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 50, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.45337581634521484, \"perplexity\": 2363.7867269708468}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296945287.43\/warc\/CC-MAIN-20230324144746-20230324174746-00072.warc.gz\"}"}
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PROLOGUE
It all seems so long ago. I was only fourteen. I was a bright girl, very bright, and did really well at school, but I was still mixed up, a bit of a mess to tell the truth. My parents had divorced recently, my boyfriend couldn't keep his hands to himself, and I didn't even have a computer. Can anyone who wasn't there believe that? 1995 was a time when nice middle class households like ours usually still had only one phone, a landline of course, often in the hallway. No privacy. No texting. One phone!
But it turned out that our phone was special.
Cell phones—mobiles, we called them in Australia in those days—were just coming in. I remember the first one I saw: some guy was walking down the street talking to it. It was about the size of a small brick. And here was this guy in the street with a brick rammed up against his ear and he was talking to it, talking to a brick. He seemed only slightly embarrassed. I just stood and stared, trying not to laugh, as did most of the other pedestrians.
It was an innocent age. The Twin Towers in New York were as solid as concrete and steel could make them. If you wanted to find out a fact, you looked it up—in a book, unless you were a geek with a modem connection to an Internet that had hardly got started by today's standards. I don't think Google had even been launched back then, but I can't be bothered googling it to make sure. It took a solid week for a letter to get from Melbourne to San Francisco and another week for the reply to reach you. Hell, you could exchange two letters a month with your American pen friend. I might have been bright, but I had no idea where Iraq or Afghanistan were. Why should I? I mean, the world's greatest scientists didn't even know that the universe is expanding faster and faster. They thought it was all doomed, billions and billions of years from now, to collapse into a Big Crunch. They didn't know about dark matter and dark energy. They certainly didn't know about time zone resonances. Hey, I was only the second person in all of history to know about that.
So in this innocent time I arrived home one afternoon from the supermarket on my bike. I could hear a phone ringing in the hall instead of vibrating in my pocket, because they didn't do that yet....
MELBOURNE, AUSTRALIA: SATURDAY, 8 APRIL 1995, MIDDAY
The phone is ringing in the hallway. I drop my new mountain bike at the front gate, shove in the key, run inside balancing my bag of groceries, kick the door shut.
It keeps ringing.
Usually I'm there three seconds late so all I hear is David putting the phone down at his end. Maddy says I should call him back but I don't like to push. I have trouble imagining why he goes out with me.
"Hello?"
"Don't hang up," a man says urgently.
"I'm sorry?"
"You sound as if you've been running."
"Who did you wish to speak to? Whom." Youngish, but I don't recognize the voice.
"Sorry, I'll explain all that, just promise me you won't hang up until you've heard what I've got to say."
A charity drive. Or some slick scammer selling a set of Kitchen-ware made from a miracle space-age substance you can safely drop from a great height.
"Look, I nearly busted a carton of eggs getting to this phone. Can you please just tell me who you're trying to reach so I can go and unpack? Do you want my father?"
"Oh. Is that a child I'm speaking to?"
I fume. I'm fourteen, halfway to fifteen.
"Yes, this is a child you're talking to. Could I ask the name of the ill-mannered adult who's asking?"
After a long moment of silence I start to move the handset away from my ear.
"Don't hang up!" he yelps, guessing. "Look, I'm sorry, I'm really sorry, whatever it was I said. You're a teenager, is that right?"
"Dynamite."
"Oh hell, I truly do apologize, the last thing I want to do is upset you. Listen, what's your name?"
"Why should I tell you what my name is? I think you must have the wrong number."
"No," he says fiercely. "No, I have the only number this machine can access. It's not like I can just dial any old number I want."
"What are you talking about?"
"Sorry, look, this isn't just an ordinary phone—I'm using resonant circuits. The whole thing's touch and go. It's a miracle I reached anyone at all."
I'm starting to get the message. This guy is some sort of mobile phone freak. All this hot digital technology: it's breeding a race of try-hards and loonies. Any moment now he's going to tell me he's got his own uplink dish. Maybe his own personal satellite.
But all he adds is, "For God's sake don't hang up. Hear me out. If you like, go and put your carton away safely and then come back, but make sure no one hangs up this phone. I beg you. This is a matter of—"
I grunt, half laughing, and he breaks off. He's had me going, this jerk has actually started to reel me in.
I finish for him, snidely: "—of life and death, I suppose?"
He makes a coughing sound and I can't tell if he is laughing too or just embarrassed by his overstatement.
"Well, maybe not that important, but pretty damn important, believe me. Do you believe me? Have I convinced you, O nameless teenager?"
"Why should I believe you, O nameless telephone mugger? I don't know your name and you have a definite advantage, because obviously you already have this number, even if it is the only number your precious little toy can ring up. So you either know my parents' surname from the phone book, or you're calling at random and I really should hang up. What's it to be?"
"This is a miracle. It's more than a miracle. You've got a mind like a steel trap. What a stroke of incredible luck. I thought I'd have to try explaining all this to some thick-witted office clerk. What time is it at your end?"
I glance automatically at my digital watch. 12:27 in the afternoon. Then I do a double-take.
"At my end? You're telling me this is an international call?"
It can't be, I realize the moment I've spoken. Firstly, there'd been no International Subscriber Dialing bips or operator's instructions. Is it true that they bip at you with ISD calls? I can't remember. Certainly they do with interstate subscriber trunk calls. Second, I'm hearing his reactions too quickly. Speed of light. New York, say, or London, half the time you spend most of your buck garbling over the top of each other's sentences.
That isn't happening. So my invisible caller is not from outside Australia.
Even so, there are time zone differences between Western Australia, say, and Melbourne, over here on the East Coast, and then there's daylight saving which some States don't use though we do, so I decide to give him the benefit of the doubt.
"Half past twelve."
"In the afternoon?"
I start to say, "Of course in the afternoon," when he cuts back in, "Oh, sorry, yes, you'd hardly be able to go out at half past twelve at night and pick up a dozen eggs," and I say, "Well I could, of course, if I went to a 7-Eleven," and he falls silent.
I think about what we've just told each other and realize there is something majorly fishy afoot. I mean, he is saying he didn't know if he'd called someone in the day or night but the lack of lag in our conversation means he has to be within a few thousand kays of me. None of it adds up.
"My father will be getting home pretty soon," I say, a trifle nervously. "I have to start getting lunch ready, so I think—"
His scream nearly deafens me. "No, please, please, DON'T HANG UP! You'll kick yourself if you do. No you won't, because you'll never know what you missed. But if you did know you'd kick yourself. My God, you'd go out and find a thick length of rope and hang yourself."
He's starting to sound like the sort of sexual weirdo thrill seeker they warn us about in social-ethics classes, and I'd get absolutely crazy frenzied mad at him except that something in his tone sounds desperate but not warped desperate, if you know what I mean. Like a third grade boy I knew in Balmain before we shifted down here to Melbourne, where the weather's boiling hot one minute and drenching wet the next. This kid's father used to beat him with an old-fashioned leather shaving strap or strop or whatever it's called, a thing they used to sharpen their blades on in the days before electric razors and disposable Schicks, anyway this kid used to cop it whenever his old man was in a bad mood which seemed to be most of the time, and he really hated having to go home. The teachers had to shove him out the school gate. That's not such a hot example now that I think about it, but the point is I am starting to feel sympathetic towards this crackpot on the other end of the phone.
"I'll give you five minutes," I say. "Make it good. Any sleaze and I hang up fast, and then I dial the cops."
"What? You think I'm—" He laughs rather nicely. "No, if that was my game I'd find a less expensive way than this to go about it. Let me tell you something that might give you an appreciation of what's at stake here. How much do you suppose this call is costing me?"
"Assuming it's a local call, which I will for reasons too boring to go through," I say instantly, "thirty cents. Or less if you're ringing from a private phone. Or nothing if you're using one in an office."
"...Cents?" he says.
"It's more?" I'm skeptical.
"That's Australian cents, is it?"
"Look, what's wrong with you?" I yell, getting annoyed. "Do you think we use drachmas in Melbourne? Pesos? Rubles? Telstra was an Australian company last time I looked. Strangely enough, they ask you pay them in Australian cents."
It's just as well Poppa didn't hear this. He hates me talking back to grown-ups in that smart-aleck way, and he'd ground me for the night, which would break my heart because Davy has invited me over to his place to babysit his kid brother and, more to point, watch a video while his folks go to some dinner party.
"Thirty cents," he says as if he can hardly believe his ears. "That's inflation for you. All right, hold on to your hat, nameless teenager. And don't, please don't for the love of Harry, don't drop the phone in your amazement and cut me off."
"I never wear hats. I'm holding on with both hands."
"Fifteen thousand pounds a minute this call is costing. Um, that's about thirty thousand dollars."
"Not at today's exchange rate," I say nastily. Show-off. "So you're calling from England, are you? Why isn't there an orbital delay?"
"A what?"
"Come on, nameless Englishman, you know perfectly well that an international call has to go to the local exchange and then get bounced up to a satellite in fixed orbit forty thousand kays up and then down again the same distance plus the extra distance around the curve of the Earth, it all adds up. Unless it goes by co-ax cable or optical fiber."
There is a long pause. Then he says, "Is this a boy or a girl I'm talking to?"
That really makes my day.
"Sheesh! Didn't anyone ever tell you the difference? What do you think?"
"I'm just going to have to keep apologizing, I can tell that much. The difficulty is, I can't see what you look like through this fairly opaque earpiece. Now don't get angry and hang up the phone, but I thought...I think...you're a girl."
"Brilliant. I'll make it easier for you in future. There's a rule to apply to these cases, see? The girls have high voices and the boys have deep voices."
He laughs. "It doesn't always work that way. My voice didn't break until I was sixteen. I'm just surprised that a girl would know all that stuff about orbits."
This is insane. The man is trying to win the Blundering Sexist Jackass Award.
Very curtly, I say, "Mister, you still haven't said who you're trying to reach."
"I'm trying to reach the number in your house, which thank heavens I've done." He seems to be breathing rather heavily. "Listen, you said 'satellite,' didn't you? Are there people up there?"
"How should I know? Hang on, there are some Russians in the Mir space station, they seem to like long orbital missions, and that American guy they took up with them."
"Russians and Americans in the same space station!" he says incredulously. "What about the American space program?"
"I don't think there's been a shuttle mission for a few weeks. But they're all working on docking, so they can get Space Station Alpha started. Look, why ask me this? Can't you read the paper?"
"The Moon," he says urgently. "What about the Moon?"
"I think your five minutes must be up." My feet are getting numb because of the angle I'm leaning against the table that the phone sits on. "What do you mean, what about the Moon?"
"Are there people up there? A lunar settlement?"
"Are you nuts or something? There's nothing up there since they killed off Apollo before I was even born."
"They killed Apollo? Wait a minute, this is getting too much for me to take in. Apollo the Greek god?"
I hear Poppa's key in the door.
"Look, I don't find your line of repartee particularly amusing, nameless nerd, and your five minutes ran out at the third beep." Poppa hates me hanging off the phone, as he calls it. "So long, Charlie," I say, and put down the receiver. I think I hear a thin drawn-out scream of anguish and wonder what kind of loony creep the nameless nerd really is.
Poppa catches me taking my hand off the receiver but he doesn't take the chance to nag at me. He smiles, actually, and gives a quick hug as he goes by, loaded down with books and notepads and calculators and his Dictaphone and stuff.
"Hi, Jenny. Get to the supermarket in time?"
"Only just. I haven't unpacked yet."
"Is that your bike sprawled in the street?"
"Yeah, I'm just going."
"You should be more careful, pet. Bikes cost money."
"I had to answer the phone, I could hear it ringing."
I bring the bike into the hallway through the front door and nudge it shut with the heel of my sneaker.
"Not for me, I presume?" He's taking eggs from the carton and putting them one by one into the plastic slots in the top of the fridge door. I'll never understand why he bothers. Why not leave them in the carton? I suppose it conserves space, but we never have all that much food in the fridge now there's just the two of us.
"Don't think so."
"Don't be absurd, Jenny. Either the call was for me or it wasn't."
"It wasn't for either of us."
"Oh. We've been getting a few wrong numbers lately. It must have something to do with the road repairs."
I think of asking Poppa's opinion about the nameless phone freak or at least telling it all to him as a sort of entertaining story but then I notice the Science Show has been on for a quarter of an hour and run for the radio. I hate missing it.
SATURDAY, 8 APRIL, LUNCH
"That was delicious, sweetie. I must eat lunch with you more often."
"I cannot tell a lie," I say, cleaning away the plates. "Papa Giuseppe did it all."
Poppa wipes the last of the flan out of his beard. It's been going gray recently. Tall and rather thin and going gray, a nice person really, but quite vague. "Who?" he says vaguely. "Someone I know, I hope."
"It's a brand of frozen quiche, donkey."
"Rudeness is not attractive, Jenny. Are you saying you cheated?"
"Certainly not! I never told you I'd made it from scratch. That's why I had to rush out to the supermarket at the last minute and miss half the Science Show."
"I thought you went to get eggs."
"You can get eggs anywhere. You can get eggs at the milk bar around the corner. You can get eggs at the 7-Eleven store at half past midnight."
"I might be able to," my father says sharply, glancing up from his Awfully Official Papers that are spread out over a third of the kitchen table. Mum would never let him do that. "You, on the other hand, will be tucked up in bed and well asleep by that hour."
I sigh loudly. "Don't nag. You know I always get back before curfew."
"Hmph. Scraping in just under the clang of the witching hour. Speaking of which—"
"Ha, very funny."
"Pun unintended, I'm glad to say. Speaking of which, I repeat, whom are you going out with tonight, someone I know, I trust?"
"David. You know him, and you can trust him." Maybe.
"I know David?"
"Poppa, you've only lectured him on the theory of fiscal macro-dynamics or some damned thing every single time he drops in here to—"
"Ease up, Jenny. That David. Nice boy—I think. Does he know how to keep his hands to himself?"
"Poppady!" I'm shocked.
Actually I'm not terrifically shocked, because in fact I have to keep warning Davy to do exactly that whenever we sit next to each other in the movies or round at Louise's for a video like Drugstore Cowboy the other night, so who knows how I am going to keep him cool while we snuggle up alone together at his folks' place watching something gross? Do I really want to, for that matter? But it is always wise to sound as pure and outraged as possible when your father asks a question like that.
I think he sees through me, though.
"It's a reasonable thing for the parent of a daughter to ask, I believe, especially a daughter whose mother currently declines to sit at the same table with us. I have to do the work for both Hattie and me, after all. Mother and father in one horrible balding bundle." He smiles in self-mockery, which is always a happy thing to see in a grown-up.
"Currently?" I say, quick as a steel trap. The mysterious telephone mugger just won't get out of the back of my mind.
"You know I hope to re-establish cordial relations with Hattie, sweetie."
"Oh, don't be a stuffy old Prof, Prof," I tell him, feeling angry underneath my burst of fond love. "'Cordial'! You still love her, admit it."
"I admit it. But we are divorced, after all. Let's change the subject, Jenny. The topic's painful."
"We have to talk it through properly some—"
"Not now." He's avoiding my eye, suddenly. He looks meaningfully at his watch. "I really do have a lot of work to finish. I think I'll take all this stuff into the study. Leave the washing-up, I'll fix it later."
"Poppa!" I shout. I pound on the table. "How can you just stand there and say 'the topic's painful'? I'm part of the topic!"
"Later, Jenny. I mean it. I have too much on my plate right now to divert any emotional energy into this sort of draining row."
"I don't want a row, I want to—"
"You're yelling, Jenny. For somebody who doesn't wish to get into a row, you're—"
"Oh damn it," I yell, and slam back my chair and stomp to the front door, where the bell is buzzing.
"Madeleine," I grunt.
"Hi. Would you rather kill me now or should I come back later with witnesses?"
I glare at her. She's doing her retro-Madonna number. The kid's got no taste. For once I agree with my father. Socks in three different luminous colors. Lace around her breasts, which are getting pretty spectacular these days anyway. Ballet tights, dark bracelets from her elbow to her wrist, a wonder she can lift her arms. Metallic woven jacket with bits of silk and satin and leather hanging off it, a bunch of Catholic rosaries around her neck, urchin shoes. God, she looks like a reject from MTV. No, that's not fair. Standing there with the early afternoon autumn sunshine blasting through hair that seems to have exploded upwards after her brain went off, she looks like one of the success stories from MTV.
"My father will flip," I tell her, giggling.
"You got no style, Jenny," Madeleine says, coming in and slamming the door behind her. "Look at you. Worn out jeans, old school sweater, awful shoes, let's face it, and your hair hasn't changed since you were 10. Where's your class? 'Gonna dress you up,'" she sings in a thin little voice, like something out of 1985 or whenever it was, writhing as she bops down the hall. A trailing rosary catches on the handlebar of my bike and almost trips her on her face. She doesn't appreciate my snigger.
"Got any Pepsi?"
"Come upstairs to my room, I've got some in the fridge."
One of my father's lateral thinking breakthroughs was providing me with a small refrigerator of my own, the sort they have in hotel rooms. I keep Cokes and stuff in it, and ice cream and chocolate when it's hot, and he figures this stops me from making a mess in the kitchen. Considering that I am preparing half the food in the house these days, this is pushing his luck.
"Where's the olds? Sorry," she catches my look, "the old."
"Downstairs getting some report prepared. 'Nor shall my sword sleep in my hand,' that sort of thing."
"Huh?"
"William Blake or something."
"William who?"
I give up. "A poet."
"Uh. Does he play with a band?"
"Let's start again from the beginning, shall we? Hey, Madeleine, ah jest lahhhv yo' clothes."
"Whah, thank yo', babba dorl." She twirls, sending bits spinning outward. She throws herself backwards across my messy bed and tries hard to look like a frame from a video clip. "Music," she cries. "Play music. I'll go crazy if I don't hear music."
I switch on K-Rock but it's doing a retrospective on the era of the Beatles and the Stones or something. Not that I've got anything against John Lennon, or Julian for that matter. No, Julian wasn't one of the Beatles, was he? Anyway, it's Mick Jagger and the Stones who've just been here for their first tour in twenty-three years or whatever it is.
Madeleine finds a Yothu Yindi CD and starts bouncing around the room, humming and pulling faces. "What kind of reports?" she asks, popping a big bubble of gum.
"What kind of reports what?"
"Is he writing? I mean, I never thought about it until just now. What is your father?"
"Economist," I mumble. Maybe I'm jealous. That's what it feels like, a nasty little stab. But I couldn't tell you if I am jealous because she's paying attention to Poppa instead of to the fun time we are supposed to be having, or because I want to keep Poppa to myself. Having a mind like a steel trap isn't all good times. It hurts. Maybe I just shouldn't worry about it.
Madeleine stops dead and stares at me with her jaw hanging open and the blob of gum stuck to her front teeth.
"Jenny! Your father's a communist?"
I fall on the bed laughing, then fall off it laughing. I can't help it. She's such a jerk.
"What did I say?" She's giggling with me, and we are both snorting like fools and pounding our feet on the floor without really knowing why. There is a crabby shout from downstairs to please for the love of God get rid of those damned rhinos or leave me in peace. I choke and cover her mouth with a pillow. She fights me off and whispers hoarsely:
"Tell me true! Is he a communist or what? I won't hold it against him, Helen's father is a bus-driver."
"Economist," I hiss. "Money. You know, that paper stuff we wish we had some of so we could buy a— buy some—" I have to stop. I can't think of anything I want to buy.
"Clothes," Madeleine is saying dreamily, "records, great beads, get our hair done every day, cars, trips to Disneyland and see Braincase playing in New York or Las Vegas or wherever and—"
Downstairs, the phone rings. I think of going down to get it, but decide Poppa's closer. It keeps ringing. I get up and go to the door. By the time I hit the landing he's come out of his study and answers it. He glances up to me.
"Are you the teenager with the mind like a steel trap?"
I stare at him. I haven't told anybody, not even him over lunch.
"Is that Davy?"
"I shouldn't think so, unless his speech has improved markedly. Well come on, don't dawdle, my computer's probably having a melt-down while I loiter here."
I gallop down the stairs. He grimaces and mutters something about damned elephants should have been put out with the rhinos and hands me the receiver.
"Yes?"
"Don't hang up," the voice says.
"You again."
"Oh, if only you knew. If you realized how much sweat and pain and bloody trouble you put us to, doing what you—" His voice cuts off suddenly, as if someone had covered the mouthpiece. A few seconds later he says in a much more controlled tone, "I'm not getting off to a very good start this time either, am I?"
"I don't have the faintest idea." I see Madeleine peering down over the top banister with her eyebrows pushed up into her frizzy blonde hair, doing a question at me. I shrug back and wave my free hand in a circle. I add, "I suppose it depends what you're trying to say and who you think you're saying it to." Whom.
"Who am I saying it to? No, hang on, my turn. This is Rod Gianforte. You've never met me, but I guarantee that I'm of sound character and clean in mind and person. Please laugh, that was a friendly self-deprecatory joke."
"Ha ha," I say. I hold the receiver away from my face and stare at it. When I get it back to my ear he's saying, "...tremendously important." The voice takes a deep and shuddering breath. "Listen, nameless teenager, I would beg your indulgence for just three more questions. Think of this as some kind of intelligence test, or a quiz, yes, that's it, like a—"
"What's the prize?"
"The prize? Golly, the prize...it's just about anything you could ask for, I suppose, when you think about it."
He seems so enthralled with this thought that I start to hear a weird sound, in behind him, like a whole room of other people sitting and listening and holding their breaths. "Um, anyway, mysterious teenager, I really would be very grateful if you'd just give me the answers to these three—"
"Jenny," I say, on a sudden impulse.
There is a sound like a wave going out late at night, low tide, gentle but powerful, like a roomful of ghosts brushing through each other.
"Thank you, Jenny. Thank you very much. Now, this is the first question. You will think it sounds strange, crazy, nuts, but please just tell me the simple truth. What is the name of the president of the United States?"
What kind of quiz is this? A quiz for cretins? A test for people who don't know what day it is? Come to think of it, this guy sounds as if he doesn't know what day it is. He's already proved he doesn't know what time it is.
So I give up trying to analyze his motives and tell him, "Bill Clinton."
"Bill. The informal touch. Okay. Thank you, Jenny. That was great. Now, question two: who were the previous two presidents? Do you understand what I mean by that? In the four years before this president came into office, who was pres—"
I'm really pissed off by his presumption of my ignorance. One of Poppa's snide jokes comes into my head, and I say, "George Bush and before him Bing Crosby." Some sort of awful singer, that's all I know about him, but the reaction is spectacular. I hear this wheezing gasp, then a gulping snort.
"You're joking," the voice says weakly.
"It's Poppa's joke, not mine, but he says the real thing was just as silly."
Very patiently, the voice says, "And who was that, dear?"
"You know as well as I do," I snap. "Ronald Reagan, and what the hell is all this about?"
"Crosby," he says. "Movies. Reagan. Wasn't he in cowboy films? I really can't...." He sounds as if he is struggling with a hairball. "Thank you, Jenny. Here's the final question. I'd like you please not to hang up anyway, after you've told me this, but even if you do decide to, give me the answer first. Okay?"
"Fire away," I say. I am getting pretty bored, and Madeleine has gone back inside my bedroom and turned the sound up and she's dancing her disco aerobic steps, and I know Poppa will be out any minute to shout at us. I can do without that, because I want no trouble fouling up my date with David in a few hours.
"Was Kennedy or Nixon the President of the USA?"
"That's the question?"
"Yes. Do you want to hear it again?"
"No. What a dumb-ass question. Is this a trick or what?"
He sounds terribly worried and baffled. "No, Jenny, this is not a trick question. Just tell me, which one was president? Have you ever heard of John Fitzgerald Kennedy and Richard M. Nixon, the presidential candidates in—"
"You're driving me crazy," I say. "Of course I've heard of them. In fact I did a social-ethics essay on them last term, 'Camelot and Watergate, a comparison.'"
"Camelot and— Fascinating. My God. Apollo, Camelot, I feel as if I'd fallen into a mythological— Look, Jenny, if you did an essay on them, then think back carefully to this one point. Which one of them became President?" A sort of screech gets into his voice.
"Which one? Which one? What do you mean, which one?" I shout at him. "Both of them did. They were both President, you dumbo," and I hang up in his ear, hard.
SATURDAY, 8 APRIL, EVENING
In the middle of all this bizarre stuff, I start getting cramps. Oh great. Maddy's upstairs and I'm feeling weird and uncomfortable but I don't really feel like talking about it to her. Perfect timing for a romantic night with Davy. I was a late starter, Maddy's been getting periods since she was twelve, and it always gives me a lot more trouble than she ever has. Just what you need for a really terrific mood on a night in front of the video. Not that I have any intention of—
So I'm in the bathroom off the hallway when the doorbell buzzes. It could be anyone but since Maddy is already here and bopping around upstairs I know it just has to be David. The only time in his life he's ever been on time. We have one of those once-trendy 1970s' lavatories with pine slats in the door, not that you see in or anything but everyone can hear a good fart if you let rip, not to mention a good plop, and if everyone's halfway through their wine and coq au vin down the hallway in the dining room the idea is to pretend that nothing happened. It shows how relaxed you are about the physical reality of the body or something. I am unwrapping a tampon, and the wrapping makes a soft crumpling sound that nobody could hear unless they have their ear jammed up against the door, and I go bright red anyway and just crouch there on the edge of the toilet seat as Poppa opens the front door and lets David in.
So naturally they decide to have a little conversation at the far end of the hallway, while I wait to stop my life's precious fluids running out. From the sounds of traffic it seems like Poppa has the poor boy bailed up in the open doorway. I wish they were both dead, or at least a kilometer down the street.
"Oh, good evening...David," my father says, with that pause while he hunts through the huge list of my known boyfriends. Ha. It's the sort of thing that really puts David at his ease. To make things even better, Poppa adds, "Is it that late already?"
"Hi, Dr. Kanes. I'm not too early, am I?"
"Kane, dear boy," my father chides him. "Like the fellow who slew his brother because he had a birthmark. Or was it the other way about?"
This is not the sort of test David does well at. "Huh?"
"Actually, David, my name is Kane, not Keynes. Don't dawdle, come in. Jenny's upstairs."
I want to yell out "No I'm not, I'm three feet away dying of humiliation," but I would die of humiliation.
"Sorry," Davy says, deeply baffled. "I always thought it was 'Kanes'."
A diesel bus roars by. I smell the fumes. Poppa finally shuts the door. "Actually, no. Keynes was the celebrated economist."
"Aren't you an economist?"
Poppa sighs painfully. "Yes. Not, however, that one."
They lumber past into the kitchen. I flush, wash my hands, and come out calling cheerily, to cover the noisy cistern, "Oh hi. Is that you, Davy?"
None of it fazes that boy. He probably didn't notice. He looks gorgeous, as usual, like Matt Dillon in the video we saw last week at Louise's. I wish I looked like Kelly Lynch, that's all. But why bother trying when you don't? "Hi, Jenny," Davy yells. "Hey, they've got a great double bill on at the Valhalla.... Back to the Future III and Terminator II."
"Seen 'em. Bor-ing. Come on up. Maddy, stop giggling like a child." She's leaning over the top of the banister and starts down as we start up, after Davy gives me a little squeeze and a light smooch around the mouth that we both make a mess of.
"Hi Maddy."
"Hi David."
Poppa is back in his study. He calls, "I really must put on a turn of speed. Enjoy the film, you three. I'll be back from the lecture by eleven, Genevieve." He puts his head around the door. He's trying to look stern and parental. "Make sure you are too."
"Aw, Poppa, the movies aren't even out till then. Midnight?"
He pauses at the front door to muse on the reckless pace of modern life. I try to imagine what he'd been doing at midnight 20 or 30 years ago. Getting stoned, probably. Or arrested in a Vietnam demonstration outside some Embassy. Covered in hair. Wearing flares. Erk. "Eleven thirty and not a second later." I pull a face and nod, and he shuts the door behind him. David instantly puts his hand up the back of my sweater and I let it stay for about three seconds, then run up the stairs very fast away from him. I say, "Maddy was just leaving, weren't you Maddy?
Maddy looks baffled rather than crushed, which I would be. "Huh? I thought we were all going to the Valhalla."
"Nah," Davy says. "I'm babysitting. Jen and I thought we'd look at a video."
"Aw yeah." Madeleine can be very cynical. "I know what you're going to do, you're gunna—" I grab her and start to strangle her, but she says, "—fool around, aren't you. You filthy things, you're going to take off all your—"
"You hold her down," I say loudly to David, "and I'll put the pillow over her head till she's dead."
"Lively little thing, isn't she? Maybe we should take off all her—"
Indignant, we both cry, "Day-vid!"
He doesn't look very ashamed of himself. "Just messin' with ya. Hey, is there anything to eat around here?" He opens the fridge and finds my last Mars bar.
"Jenny's been getting these weird phone calls."
"Oh yeah? Prob'ly creepy Bertram from the chess club, breathing all his snot down the phone—"
Revolted, we both cry, "Er, yuck!"
"We could get a pizza and eat it while we—"
"No pizza," Maddy says, looking for another CD.
"No eating it," I add. "I mean, Maddy, shouldn't you be going home for tea? Your Mum'll be wondering where you are."
"No she won't. I told her I was coming over here to study."
Davy bugs his eyes. "Dressed like that?"
"What's wrong with the way I'm dressed, nerd-features? First they tell me to go, then they insult me."
"It's usually the other way round, I know. Hey, actually I like your, um, dress. Could we discuss it some other time? Like next winter?"
The poor girl sighs long-sufferingly. "I can take a hint. I know when I'm not wanted. I know blazing passion when I see it. Listen, I read this booklet the other day about safe sex, would you like me to—"
"Let me show you the way to the door, Maddy."
As she leaves, Madeleine sticks her nose in my ear and whispers, "Is this the night? Are you going to Do It?"
I push her onto the footpath. A kid on a skateboard nearly takes her left ankle with him. "Mad, I'm only fourteen," I whisper crossly. "You're only fourteen. Davy is only sixteen. Have you been watching too many episodes of Models, Inc. or what?"
"Well, Julie Blackford's Done It, and she's in the—"
"Good night, Maddy. Can I come over to your place tomorrow morning?"
"'Course ya can. In fact you hafta promise to, especially if you're gunna—"
"Hey Jenny," David yells down the stairs, "where's the Violator CD?"
"Under the bed. I'm sick of Braincase. Listen Mad, I've got to go."
"What will you do about those phone calls?"
"Dunno. Tell the phone people, I suppose. Anyway, he hasn't rung back so he's probably got bored. See ya."
"Bye." She bops away down Rathdowne Street, in her own instant movie, happy as a tick. I shake my head with admiration and go back inside. That girl and I have been through a lot together.
FLASHBACK
Mum and Poppa split up over a year ago. I'd just turned thirteen, and I didn't really know what was going on. Mum went to stay with her sister, my aunt Vicky. I told myself it was because something had gone wrong with Vicky's marriage. I thought Mum had driven up to Ballarat to help her poor older sister Vicky get over some crisis in her life. Ha! Well, anyway, that's what I wanted to believe, so that's what I did believe.
Mum and Poppa are great ones for being honest and up front about family matters. Full and frank disclosure and all that. But the truth is: they're not very good at it.
All that time Mum was at Vicky's I thought she was going to come back home. I took it for granted. I mean, wouldn't you? If Mum had gone storming out of the house after a screaming row, if she and Poppa had been throwing plates and glasses at each other, well, then, I'd have had a better idea what was going on. That's how they're supposed to do it. That's what happens on telly. But it was all so civilized that I missed it entirely. Didn't catch on for ages.
Being split-up isn't why I feel so awful though. There are stacks of other kids at school from single-parent families. Only it's mostly their dads who've run off, not their mothers. God, you ought to hear their stories, some of them. It'd curl your hair. Actually it hasn't curled mine, but then nothing ever seems to, despite hours down at the hair dresser three months ago when Mum wanted me to look beautiful for Aunt Vicky's twenty-fifth wedding anniversary party. Ha!
Mostly kids won't talk about it, but sometimes, when they know you come from a single-parent family yourself, they talk and talk. Fights, smashed-up furniture, the police at the door so you could die of embarrassment, women's refuges for the mothers and the kids, court orders, the lot. Even broken bones. Lots of bruises they can't hide very well.
Well, it wasn't like that round at our place. No, it was like skating on ice, beautiful and smooth and techno music in the air—and then in one hit you're flat down on the ice with your head buzzing and a nose full of blood. I got home from school one day and Mum was packing her bags, saying she had to go to stay at Vicky's for a few days. "To sort things out," she said. "Marriage is a funny business," she said. "It has its ups and downs," she said.
Poor old Aunt Vicky, I thought, she must be having trouble with uncle Bill. Mind you, the way Mum hugged me and kissed me and told me I was the most precious thing in her life.... I should have realized something was going on. It was as if she was heading off to spend a year in Antarctica.
But I thought she must be clinging to me like that because she was upset about her sister and that rotten no-good uncle Bill. Actually Bill is really an old sweetie and always gives good cash presents at Christmas and on my birthday, even if he is amazingly boring. He worked in provisioning for the Air Force or something equally dreary, never went near the jet fighters.
You can be a real dweeb-head when you don't want to look reality in the face.
But hey, I still don't want to think about the break-up. Maybe I'm a bit like the other kids at school after all, the ones from single-parent families, I hate thinking about it. Not that there's that much to think about, it was so boring, all that on-again off-again stuff for a year. All those visits. All that "talking it over." By the time Maddy and I first saw Mum and this Edward character in Bourke Street, I had come to accept that she and Dad aren't going to live in the same house any more. After a couple of months Mum had come back from Ballarat and moved into a nasty little brick apartment in North Fitzroy, so at least I could go and see her every week. It might seem unusual for the girl to stay behind with the father while the mother goes off by herself, but I was in the middle of exams and besides Mum said she just needed to be completely alone for a while. We assumed that meant a couple of weeks. Then it was a couple of months, including the Christmas holidays. Then a year had gone by. It wasn't as if I never saw her, of course. She wasn't living very far from me and Poppa. All by herself, except when I stayed over for the night. I thought. But I could hardly keep thinking that once she shifted to the creep's place in Kew.
The first time I met Edward the creep it was more or less by mistake.
At that stage, Mum hadn't quite got around to mentioning his name in conversation. So Poppa and I didn't know of his existence. I happened to be in the city with Maddy to see a movie. We were coming out of the cinema complex and there on the other side of the street, across the tram tracks, I see Mum and this guy in a dark suit carrying a briefcase covered in gold catches and combination locks and with this mobile phone in a leather holster clipped to his belt, although I didn't notice that right away. He was explaining something to Mum, who was listening intently, her face turned toward him in a way that made my flesh crawl.
Well, you have to deal with all sorts of people in this world, don't you? Lawyers and accountants and all sorts of creepy wheelers and dealers, especially when you're a woman living by herself because she's walked out on her family, so I didn't instantly think, God, who's Mum's repulsive friend? I just thought, Poor thing, she's stuck there having to listen to some wheeler-dealer and be nice to him.
I gave Maddy a nudge. "Hey, Mads, there's my Mum on the other side of the road."
Maddy never misses a chance, so she says, "Well, let's go and cadge a hot chocolate."
We're standing on the curb and yelling at her, but it's Bourke Street in the late afternoon, and even though the Swanston Mall blocks off most of the city through-traffic there's a tram and a romantic carriage pulled by a lovely old horse with incredibly hairy feet and a few cars that look lost, and Mum doesn't hear us. I still don't think there's anything weird about this. We skip across the road and get clanged at by the tram driver, and by the time we get to the other side Mum and the wheeler-dealer are a bit in front of us with other people getting in the way, and they're walking slowly towards the lights.
"Who's the guy?" Maddy asks. "He looks as if he's loaded."
"Dunno," I say, a bit out of breath. "Never saw him before."
We're hurrying to catch them up and you can tell, from the way Mum keeps leaning her head close to him, that she's having difficulty hearing what the wheeler-dealer's telling her, probably some doubtful scam with money, but her trouble hearing him is pretty much what you'd expect in the middle of the city at that hour, the traffic being what it is and all the other people swarming along, etc. I think to myself, What a nerd, why can't he wait until they're up in his expensive air-conditioned office before he starts explaining about stocks and shares or her income tax deductions, or whatever it is? Why does he have to give his client a hard time by trying to make her listen to this sort of complicated detail in the middle of the rush-hour traffic? All this goes through my head in a flash as we're hurrying to catch up with them, and then Maddy tugs at my arm and pulls me to a stop. I shake off her hand, but she hisses at me in a conspiratorial way.
"What?"
"Let's watch them for a minute."
Maddy's my best friend, but she has some really dumb ideas sometimes. Why do we want to watch the back of Mum's head in Bourke Street while she's consulting with some ill-mannered nerd? I just say impatiently, "Come on, Maddy...," and keep going.
We catch up with them at the corner when the lights go red. I arrive alongside and say, "G'day, Mum." And my mother sort of jumps, and takes a quick step away from the wheeler-dealer, and lets go his arm which I hadn't actually noticed she was holding, and is really surprised to see me.
"Jenny!" she squeaks. "Oh...er...hello, darling. What are you doing here?"
"Been to the movies" I tell her, sneaking a sidelong look at the nerd. "We thought we'd hit on you for a hot chocolate or something. That is, if you haven't got to do something else." It looks by now more as if they're on the way to the nerd's office, rather than having just left it. Anyway, his office would be in Collins Street, wouldn't it, or Williams Street? One of the business zones? But my mother says hello to Maddy, and then says to me, "Oh, what a good idea. Edward and I were just going to have a drink ourselves. I'm sure we can put off the alcohol for a bit. Let's go to The Coffee Place."
Unbelievable. She's been heading off to some bar with this nerd. First you go to see them in their office about something and then you have to go to the bar with them. I feel like I'm charging in here to the rescue, saving her from a long boring time with the boozy accountant. Maddy is making some sort of face at me and I don't get it. I grab Mum's left hand, which I never do, and clutch onto her. After a moment she pats my hand with her other hand, and smiles in a way that I can only describe as nervous. The light changes and we get swept across Swanston Street and into the Bourke Street bit of the Mall, and while we're getting tugged along by the crowd Mum does these funny formal introductions. Apparently the wheeler-dealer's name is Edward Thing, which is so ridiculous that I almost get a fit of giggles but actually I'm suddenly not all that sure it's funny.
"They keep changing the geography," Mum says brightly to Edward Thing, and he says something about the Mall being an improvement to civic tone and potentially a boost to small business in the CBD, whatever that is, and we end up in The Coffee Place sitting around a little table with black coffee and foamy chocolate and pieces of chocolate to nibble on, and it isn't anything like what I've had in mind—I mean, with this wheeler-dealer, this Thing person being there as well.
"How's your bike?" Mum asks me, so we start talking about this new U-shaped bike-lock I want that's made of duralumin or titanium or something and costs the earth but they keep your bike safely locked to the lamp post, rather than being ridden away by some rotten thief with a pair of bolt cutters. Poppa bought me the Malvern Star mountain bike, but he reckons any old chain and cheap K-Mart padlock is good enough to protect it. He's a bit simple, sometimes, old Poppa. He goes on about how when he was growing up everyone just leaned their bikes against shop windows and came back half a day later and they were still there, just sitting there. And they didn't used to lock the front door, either, just went out for the day and left the place wide open. Of course they didn't have computers or videos in those days to steal, or street junkies either. So he doesn't really understand about bike locks. He thinks if I've got to have one, I can make do with an old padlock and an iron chain. I reckon if I lean on Mum a bit, she might come good for the classy U-shaped unit.
While Mum and I are raving on about bike locks, poor Maddy is left to have a conversation with E. Thing. I can sort of hear them in the background, over Mum's insistence that she isn't at all sure Carlton and Brunswick are good places to ride a bike in the first place, and how Sydney Road and even Lygon Street are death traps even if you're in a car. She seems to be trying to convince me that I'll be run down by some huge interstate 18-wheeler if I so much as put my front wheel out into the traffic, which is true enough in some places; you'd need to be a suicidal maniac to try to ride a bike down Sydney Road.
"I know, Mum," I say, "but the cool thing about old Melbourne suburbs like Brunswick and Carlton is all the small side streets and back lanes." We've got this excellent networks of back lanes where I live, even if half of them are still cobbled with huge blocks of blue granite and shake you about if you ride fast. "If you know your way around you can avoid all the traffic."
But Mum is ignoring this and starting on about how I should avoid the lanes and only ride down proper streets because of the risk of muggers and perverts and junkies. In fact she's getting so worked up I expect her to start telling me to only ride down the tram tracks in the middle of Sydney Road. So I switch off and try to hear what Maddy and Edward Thing are saying to each other. I wouldn't have thought they'd find anything to say at all, but he's murmuring away in his posh accent and she's lapping it all up.
Edward must have asked Maddy what school she goes to. They always do, don't they, ask you what school you go to?
"North Carlton High," she says.
"Oh? And what's it like?"
What does he think it's like? It's like a school. But Maddy is really polite, for some reason. "It has a high ethnic component," she tells him. This is something the Principal's terribly proud of, and they put it in all the promotional leaflets. It doesn't make any difference, the funding in schools like ours keeps getting cut.
"Ah," says Edward, as if this is something very interesting indeed. "I think this is a desirable feature of well-rounded education that my boys have missed out on."
I'll bet they do, I think, the little private school dweebs.
"Although," Edward says carefully, "the place isn't nearly as homogeneous as it was when I was a boy there. There are a couple of very bright Chinese students in Tristan's form."
Maddy says, "Huh, that's nothing. Our form has more boat people than a Hong Kong ferry."
I nearly choke on my chocolate. Mum stops going on about riding down Sydney Road without a police escort and asks me if I'm all right. I say yes, I'm fine, but I do need a better bike lock and Mum says, "Oh, all right, what do they cost?" I tell her the exact price because I checked them out in Bike World the day before, and Mum fishes her check book out of her handbag and starts to write me a personal check. And a phone starts ringing in my ear.
E. Thing hauls his little mobile phone out of its holster and snaps the mouthpiece open and says, "Thring!" into it.
That's exactly what he says. Not "Hello." Not "Edward Thring here." Just "Thring!", like a word in a foreign language. Or as if his name was some famous trade-mark, like "Coke!"
I look at Maddy and Maddy looks at me, and we both have to look away to try to control ourselves. Mum hands me the check, and I'm strangling, trying not to laugh out loud. Mum is gazing at me, rather puzzled. I certainly don't want her to think I'm laughing at her, especially when she's being so nice and buying me a bike lock. I sort of nod my head in the direction of Thring! hoping she's heard him and know that's what's breaking us up. There's all this babble coming from his side of the table: "...don't move until it reaches four point two oh. And we can always cover the deal with the Brazilian perps—"
It's actually pretty bloody hysterical sitting in a coffee lounge at the same table as a tacky loon who's raving that sort of rubbish into a mobile phone. So I push myself away from the table and say, "Look, Mum, thanks for the chocolate and the money and everything, but Maddy and I have to get back to her place to babysit." This is true, but we don't have to be there for two hours. I can't stand to be here for another minute. Mum gives me a perfumey kiss, and says, "See you on the weekend, darling." And Thring! says, "Hold on a minute, Frank," and puts his hand over the mouthpiece on the phone, and turns to me and says, "Lovely meeting you, Jenny. And you, too, er...er...."
"Maddy," my mother says.
"Maddy," Thring! says confidently. Then he looks me in the eye and says, "Jenny, you must meet Tristan one day soon. I'm sure you have a lot in common."
I can barely keep a straight face, so I just wave goodbye and Maddy and I more or less run out of the shop.
Gasping for breath, Maddy and I fall about in the Bourke Street Mall, going, "You should meet Tristan one day" in a posh way. Then Maddy was being Tristan, talking with a stuck-up preppy voice: "Oh, hello, I'm Tristan son of Thring! and I've got these awfully frightfully bright Chinese chums in my class. They are called Fu Manchu and Ming the Merciless." I'm saying: "Oh, I say, we've got so much in common!" and "Things were far more homogeneous in my day."
And Maddy says, "We've got a homo genius in our form, he's an Eye-talian called Leonardo da Vinci." Which is pretty good for Maddy. I wouldn't have thought she's even heard of Leonardo da Vinci, let alone known he was gay and where he was from. She's more likely to think he's a turtle. So we're falling about and I'm holding on to Maddy to stop myself collapsing in the middle of the late-afternoon Mall when Maddy says, "Jeez, your Mum can pick them."
"Pick what?"
"Boyfriends."
Suddenly I'm cold all over and very, very angry at Maddy. "What are you talking about?"
"Oh, come on, Jen. She's got to have some fun."
"Fun? You're bloody mad, Maddy. That's a horrible thing to say."
I feel like bursting out crying. Then I am crying. In the middle of the Bourke Street bloody Mall. I'm just standing there with tears rolling down my face, and my chest heaving as if something solid is stuck in the middle of my lungs. There aren't any cars in this section of Bourke Street, which is just as well, but they let trams through—and one of them is clanging rudely at me to get out of the way. Maddy leads me to a brick bench, and a fat old Greek lady in heavy black shifts along to give us room. I wipe my eyes on my sleeves and say to Maddy, "Sorry. You're probably right. That creep probably is Mum's—"
I can't finish the sentence.
So I stopped being angry at Maddy and became very angry at Mum instead. How could she?
SATURDAY, 8 APRIL, NIGHT
Anyway, we go upstairs and hang out in my bedroom. Davy sits on the bed. That could be trouble, so I sit in the chair by my desk. Chair's probably not the word. It's more like an ejector seat. The thing is gas-powered and it's got all these controls: height, tilt, swivel, tension, everything. Poppa bought it for me when he started having trouble with his back. He said if only he'd had a proper chair when he was a boy, he wouldn't be in such pain now. All those long hours of study, bent over like a paper clip. Yeah, well....
Davy says, "Come over here, Jenny," and pats the bed beside him.
"I want to talk, Davy," I tell him carefully.
"Can't you talk over here?" he says and pats the bed again.
Well, why not? We can talk and kiss at the same time—well almost at the same time. So we lie there for a bit being friendly. And it is nice having Davy for a friend. Poor Maddy, she's got no one to kiss at the moment. She did have this hulk called Jem once, only he ditched her for a girl called Bo. We all say that Bo is short for Bimbo. Maybe it is. I push Davy away a little bit, not too much, not so he feels rejected, but enough to let me talk. I want to lie in his arms and talk. I feel like talking about true love and what it means. Not soppy true love, the real thing. I don't even know if the real thing exists. I don't even know if it's possible for two people to live happily together forever and ever. Mum and Poppa thought it was forever, and look what happened to them. So I try to ease into a conversation with Davy about relationships and love and commitment and all that.
"What do you think about monogamy?" I ask.
"Eh?" His mouth drops open. He's got a lovely mouth, but I don't really like it when he does that, it makes him look a bit...stupid?
"You know, only loving one person."
"Jeez, Jen, if you reckon I'm two-timing you, you want to think again."
"No, I don't think that," I say quickly.
"So why ask the question?"
"It's just a question."
"But why ask it? You've got to have a reason."
"No I don't. It's just something we can talk about."
"Eh?" says Davy, but this time closes his mouth.
"Stop saying Eh?" I snap, annoyed. "Tell me something about monogamy."
"About what?"
"What we're talking about: only loving one person."
"You're the only girl for me, Jen. Honest. I reckon you're heaps cool."
"Look, Davy," I say, "I'm trying to have a talk about an idea. It's just the idea of monogamy I want to discuss."
"Jenny, if you want to go out with some other guy, I think you ought to tell me straight. I don't want any bullshitting around the bush."
"Any what?"
"You heard, Jen. Now who's this new dude? It's not that creep Wilco, is it? 'Cause I'm telling you Jen, you can just forget it."
"Hey, Davy," I say, "I'm trying to talk about a, an abstract idea."
"Bloody Wilco's not what I'd call an abstract idea, Jenny. Do you know what he did with Inessa d'Acierno after the last school disco?"
"Oh, do shut up, Davy," I say. "It's just that not all societies use the monogamous model as the ideal for the man-woman relationship. You know, we are allowed to talk about polygamy and androgyny and that."
"I don't like the sound of those words, Jen. They don't sound like the sort of words I'd like to talk about."
"You don't know what they mean."
"Yes I do, Jenny. You've just told me what they mean. They mean two-timing. Cheating."
I give up. It is easier to kiss Davy than to talk to him. I have to admit it. I like kissing Davy, but I have this vision of sort of lying around and kissing and talking about stuff that really matters. Oh well, you can't have everything.
The phone rings.
"Oh shit."
I run downstairs and gingerly pick up the receiver. "Jenny Kane speaking."
"There's a reward," the man's voice says.
"What reward? You mean money? What for?"
"I mean big money. For you."
"Is this some kind of kidnap scam?" To my surprise, I find that I am suddenly quite scared, and I'm glad Davy is upstairs. "Listen," I say, and my hands actually start trembling, like they do in dumb horror stories, "listen, I've got a friend here, my Poppa'll be back soon, I mean he's here too, just don't—"
"Jenny, I thought we'd got past all this rubbish." the voice says briskly. "Have you got a pen or a pencil?"
What? "Of course I have. My mother always has a message pad next to the phone." No mother in the house, but her message pad's still here, very reliable.
"Write this down, Jenny, and everything will be explained. In a few minutes, God and Heisenberg willing, everything will become crystal clear."
Just to annoy him, I say, "You want me to write all that down?"
"No." He sighs the way Poppa sighs when David says something especially dorkish. But he's trying very hard. He keeps it under control. In fact now that I'm relaxing again I'm starting to develop quite a sense of power over him, whoever he is. "I want you to write some numbers down," he is saying, "then some words. A quotation. Okay?"
"Why?"
"Just do it, damn it!"
"You're shouting."
"I'm sorry. Please? Pick up your pen and—"
I snort loudly. "This had better be incredibly good."
"Hey Jenny," David shouts down the stairway, "come on." Loud hip-hop rap starts up behind him, Ice-T. I cover the mouthpiece and call back up the stairs, "It's another one of those calls. He wants me to write down a message."
"Wow." David peers over the banister at me. His hair is falling in one eye. He pounds down the stairs and whispers hoarsely, "Listen, you've got to keep him on the line."
I whisper back, "Why?"
"So they can trace his number and catch him at it."
"David, you nerd! Who can trace him? No one knows he's calling."
"Oh. Hey, I could go next door and ring the cops and get them to—"
"Shh." I put the receiver back against my ear just as the nameless mugger finishes saying something. He adds, "Did you get all that?"
"Sorry, I was talking to someone."
There's a pause. He's trying so hard not to be nasty again. "How much did you miss?"
"All of it. Say it again."
"We're going to lose the envelope." It sounds like real anxiety, almost panic, and I don't have the foggiest what he's on about. "All right, Jenny. Write this down: One two two, six two three. Got that?"
"122,623."
"Precisely. Now copy down this quote: 'But now she's in the creek again, that woman made of flame'." After a pause, he asks carefully, "Have you got that?"
"Yes. What's it mean?"
"With any luck you'll understand everything in about two minutes. Put the sheet of paper face down so you can't see what you've written. Okay?"
Davy is peering at my scribbles; I shoo him away. "This makes no sense, you know."
"I'm going to hang up, then you'll get another call. If it works. If Heisenberg is looking down upon us."
"Like atoms? Heisenberg's Principle?" This Rod guy is coming on like an encyclopedia salesman—bits of strange poetry, then bits of physics. It's all an offer on a set of Britannica, I suddenly decide, and the thought makes me feel horribly deflated. Then I discount that idea, because here's another one of his really gross sexist remarks:
"My gosh, you're a clever girl. How old did you say you are?"
But maybe it's not sexist. Maybe it's a compliment. I don't suppose David knows about Heisenberg, and he's two years older than me, almost. I decide to give Rod the benefit of the doubt. In fact, I'm beginning to think he's rather cute, in a weird way.
"Fourteen. We did it in Mrs. Levine's accelerated physics class. If you measure an atom's position, you can't tell its speed. Something like that."
"Close enough. Jenny, I think we're going to make history, you and I. My God, this is exciting. Right, I'm going to hang up. Don't go away."
And he does. He hangs up in my ear. The disconnect noise starts up, but I stupidly keep saying, "Hello? Hello?"
"What's he saying now?"
"He's hung up."
"Well, put the phone down and come back upstairs. We're wasting valuable time here."
I cradle the receiver, shaking my head and rolling my eyes.
The phone instantly begins ringing. I reach out, and Davy puts his hand over the top of mine, holding the hand piece down.
"Don't answer it. This guy's a whacko."
"He said he'd call back."
"He must be a whacko. Listen, let's just—"
I push his hand away. I hate it when people try to boss me about. "Hello, is that you again?"
"Hello, Jenny. Is this my third call to you or my fourth?"
"Oh, for heaven's sake!"
"Sorry, it was a stupid question. Let me put it another way. Um, that stuff you just wrote down for me.... You did write—?"
"Yes, the number and the—"
He yelps. "Don't look at it!"
"I haven't touched it. But I can remember the quote, it said—"
"Don't tell me! This is a test, Jenny. This is a way for me to prove my credentials to you."
"Uh huh." I roll my eyes some more. Davy is going off his face, trying to jam his ear up against the other side of the receiver.
"You're a smart girl, there's obviously some books about the place."
"Half the house is lined with them."
"Right. Great. Now look, this'll sound even crazier than anything I've said yet—"
"That'll be pretty hard to manage."
"Yes, but do it. Number One, get a book with some numbers in it. The telephone book will do, or a table of random numbers if you've got one, or—"
Is he an encyclopedia salesman? Instead of just challenging him, I say cunningly, "How about the Britannica Yearbook?"
"Fantastic! Ideal! Get the latest one that's there, and bring it back to the phone. Hang on. While you're there, get another book as well. Any book at all. I want this to be your choice. I want you to know that it's your choice. Okay?"
This still doesn't rule my theory out—he could be trying to find out how recent our set is, so he can pitch us a more up-to-date one—but I have to admit to myself that the idea is leaky. "Two books. Pure insanity, but okay."
When I put the phone down and start off along the hall, David turns into a dog with two bones. He snatches up the receiver and holds it to his ear, but presumably the guy isn't saying anything so he drops it and rushes after me into Poppa's study.
"What's he want you to do? This guy sounds dangerous, Jen, I really think I should go next door and ring the cops."
I'm rooting around on the lower shelves, breathing hard with pure delight. "Davy, this is getting quite exciting. I don't know what he wants, but it sounds like a sort of quiz. Maybe he works for some, I don't know, some special place that tests you to see if you're smart enough to join them, and then—"
"Oh yes. And then what?"
"I don't know! Get off my case, David. He rang me, not you."
"Hey, I'm just trying to help!" He's halfway between hurt and angry. He says petulantly, "Did I know you were gunna chuck a menstrual? I can piss off right now if that's how you feel."
I can feel my face going red. How did he know? Has he been keeping count? My body is betraying me. I'm even more shocked by that thought. No, it's not. There's nothing wrong with my body. I'm a girl becoming a woman. It's a proud thing to be. It's certainly nothing to be ashamed of. I'm so confused I don't know whether to shove him out the door or apologize for my crankiness. But why should I apologize? What have I done? Anyway, I realize abruptly, it's just a silly sexist pun, he probably doesn't have a clue. So I say, to placate him and me, "David, don't be like that. Pass me the Britannica Yearbook. Second shelf."
He's still sulking. "Get this guy to show you a video. You can read encyclopedias together."
"David, please." All of a sudden I can't be bothered arguing with him. Silly child pretending to be a man. I take two books down the hall, with David complaining along behind me.
"Hello? I've got them. Now what?"
"You found the Yearbook?"
"Right here."
"Which year?"
"The latest one Poppa bought. 1985. But I think all the stuff in it's about 1984, so it's eleven years out of date."
"Eleven years out of date! My aching bones! 1995. Thirty-five years. Oh my God they'll give me the Nobel Prize for this. Jenny."
Davy pulls the phone away from my ear, scowling. "What's he saying?"
I shove him away. "He's going to win the Nobel Prize in the twenty-first century or something. Yes, O Mugger, I can hear you."
"Call me Rod. Open the Yearbook anywhere there's statistics, tables of numbers, Gross National Product, that sort of thing."
"Got it. Argentine Employment and Labor, how's that?"
"Don't tell me! This has to be a blind test, or you'll never believe me. Close the book and open it again somewhere else, and find, let's say, the number on the top left-hand side of the page. Write it down on the back of the piece of paper you used before."
"You want me to find a number that you couldn't possibly known what it is, is that the test?"
"That's the proof."
"Gotcha. I'll make it the right-hand page in that case. Okay, page 901, um, communications, this runs across from the other page anyway, France is the top country, over to the right-hand side, international outgoing—122,623." I lose my voice for a moment, and something creepy happens to my skull and the skin down the back of my arms. Maybe this is what they mean when they talk about your hair standing on end. I clear my throat and say very faintly, "Holy smoke. Isn't that the—?"
"Don't turn the page over!" the guy called Rod bleats. He's having as much trouble breathing as I am, from the sound of it. I can barely see Davy jumping about like a blurry lunatic, wanting to know what's going on. "Open the next book at any page you like," Rod tells me. "No, wait! Is that other person still there? David, you called him?"
"Yes, David's here. How did you do that?"
"What do you mean, I'm here?" Davy shouts. He hates to be left out, but he hates to be brought in. "Does this guy know me? Jeez, Jen, maybe it is Creepy, I'll break his bloody—"
"Give him the book," Rod is saying. "Get him to open it at random and write down the line on the top of the left hand page."
"Davy, he says to open this at random."
For a change he stops babbling and grabs the paperback I found on Poppa's special shelf. "The Penguin Book of Australian Verse. Yuck, it smells foul. I hate old paperbacks. Is this your Dad's? Hang on, there's a dedication in it. Oh. It's a present from Hattie, 1965. Who's Hattie? One of your father's old girlfriends?"
My stomach jumps. Just more cramps, I tell myself angrily. "It's my mother. Give it back."
"No, just a moment, you want me to find you a random bit. Okay, page 178. Now what?"
"First line. Write it down."
He scribbles, and hands over the sheet. "There you go. Who's Douglas Stewart?"
"I don't know." I turn over my own sheet of memo pad, and put them next to each other, and the cramps really are there, like a jolt of electricity into my abdomen. "Oh my God, David, this is impossible. He told me to write that down before I even got the books out."
"Hey, that's what I just wrote down."
Into the phone, I say, "You knew."
"I don't yet." Rod's voice is so tense it could cut the wire to the handset. "Read it to me."
I'm really quite scared, all of a sudden. There's only one explanation for this, and that's crazy. "You can control our minds, can't you?"
He laughs, slightly shrill. "Of course I can't. Just tell me what David wrote down."
"What you read out to me before. 122,623. 'But now she's in the creek again, that woman made of flame.'"
"Sounds like poetry. Poetry to my ears." He's really laughing now, almost giggling. He catches his breath, and I can hear his pen scribbling, I think. "Oh Genevieve, Jenny, you little darling, do you know what we've just done? We've broken the time barrier, that's what we've done. Oh Stockholm, here I come. I'm off to get drunk."
"You sound drunk already. How did you do that? Are you a stage magician?"
"Actually I can't afford to get drunk, Jenny." I can almost see him brutally pulling himself together. In a tired, sober tone, he adds, "Hours of work still to be done tonight. I have to recalibrate the bloody machine so I can call you back fifteen minutes ago and read these lovely little items out to you so you'll write them down and be convinced."
"Convinced of what?"
"Be convinced, Jenny, that I've done what no one else in all the history of science has ever managed to do."
"Are you sure you're not drunk?"
"Drunk with success. Drunk with joy. Farewell, for the moment, young Jenny of 1995."
I go so cold I think I'm going to faint. I clutch at the hall table. "Oh shit. You said 'time barrier,' You wanted to know what year it was. I don't think you're a crazy kook after all. Rod, I think you're calling me from—"
"Thirty-five years distance, Jenny, that's how far away I am from you. Over a third of a century. We're in different time zones, and it's going to make us both rich and famous, even if I do have to cut Dr. McReady in on it."
I snatch at that to keep from falling over. "Who's this Dr. McReady anyway?"
"My supervisor. He's nominally in charge of the research, but he thinks it can't be done."
"I don't think it can be done either." My fright is turning into a fit of the giggles. "Time travel? By telephone?"
David grabs my arm and shakes it. His eyes are bugging again. "What? What are you saying to the crackpot, Jen?"
"I'm exhausted, kiddo," Rod tells me. I stifle my laughter, and he says, "I'll call back tomorrow, your time."
"All right." Then I remember, and I'm furious at myself for forgetting. "You can't, actually. I spend tomorrow with my mother. Sunday lunch and probably tea."
There's a pause while he takes that in. Fortunately he doesn't pry, or I'd hang up hard in his ear and he can twiddle his thumbs, wherever he is. When ever. Finally he says, "Oh. I'll try to tune it in to, say, five o'clock the day after that, will you be home then?"
"Monday. Probably." I don't know whether to take this seriously or not, but an idea occurs to me. God, wouldn't it be wonderful if it were true! "Listen, Rod, I think you're doing this all wrong. All you need to do is give me next week's Lotto numbers. Isn't that what you meant by 'big money'? We could make a million bucks if you really were from the future."
"The future!" David's voice cracks, and I realize he's still here. Disgusted, he says, "You've both flipped!" In almost the same moment Rod says, "The future! Jenny, you've got it completely wrong. I'm not ringing you from the future."
I shoosh Davy with my free hand. "You're not? Then what on earth have we been talking ab—"
"October 7, 1960, Jenny. That's when I am. You're the one in the future, kiddo. I'm here, stuck in the present." And he hangs up.
SUNDAY, 9 APRIL, MORNING
When the phone rings, I snatch it up. "Is this the time machine?"
A startled voice, backed by scratchy rap lyrics, says, "The what?"
"Oh." I am horribly disappointed, to my surprise. "Maddy."
"Well pardon me for breathing! But hey, don't keep me in suspense. Did you Do It last night?"
"You've got a one-track mind, Maddy. What is this, Doogie Howser, M.D.? No, we did not Do It. If you must know, David stormed off. He said— Can you believe this? It was really gross."
"What?"
"He said I was chucking a menstrual."
"Aw, what foul timing."
"That's not why he said it! How would he know, anyway?" I've heard girls talking and giggling about this in the school loo, and they reckon boys can smell it—but I think that's sexist crap. It's got to be. The very idea gives me sweaty armpits.
"Well, were you or weren't you?"
"As a matter of fact I was. Not chucking one, having one. But that's not—"
"So you didn't Do It?"
"No! But that's not why. It was that guy on the phone—you know, Rod."
"Jen!" She's agog. Maddy is a true romantic. "Have you met him yet? Have you set up a date? Are you going to Do It?"
I look at my watch instead of tearing my hair out, anything to distract her. "I have to go now, Maddy. I'm expecting him to call back any minute." In fact I can't believe he'll even phone me back on Monday. This is too weird.
"How devastating! My Mysterious Lover the Sex Fiend! You'll be in all the TV news reports. They'll show your mangled body on tomorrow's six o'clock—"
I can't resist that silly girl. Giggling, I say, "You idiot! Look, anyway, that's why I haven't come round. Sorry 'bout that."
"So you have to hang about there just in case he—"
My face is hot. I must learn to control this dumb blushing. "Aw, no, not really. You know. Anyway, I'm off to see Mum soon."
"Yeah. Well, see ya tomorrow at gym. When's your Mum coming over, I haven't seen her for ages?"
"Well, I don't suppose she ever will. I mean, they're divorced."
"Jeez. I wish my Dad would go away and not come back."
"You wouldn't if it happened." To my amazement and mortification, I start to cry all over again. "It's the worst thing. It's the very worst thing."
"Oh Jenny, I'm sorry, I didn't mean to—"
"It's okay. Got to go now. See ya." Super cheery. No worries.
"Hey, if you're really down you could smoke that joint you bought from Louise that time."
"Too late. I smoked it last week."
Maddy is indignant. So much for sympathy. "You rat! Without me?"
"I nearly hurled. You didn't miss nothing. It just made me feel worse."
"Oh. Well, see ya, then."
"Bye, Mads."
I hang up.
§
In the afternoon, I walk up Lygon St to the tram-stop, sniffing the pollution and the backyard barbecue odors. I love the autumn, it gives me a chance to crunch through beautiful fallen leaves. I change tram routes in the city, and when the tram to Kew finally arrives I sit staring out through the slightly dusty window and my mind goes into a dazed whiz. None of this can be real. What's my mother doing over here, over the river, among all these snooty brain surgeons and real estate moguls in their shiny expensive cars? Since Mum moved in with the creep I've been to see her every couple of weeks. I still hate going there.
His house looks empty when I trudge up the tasteful path. Just her little blue Honda, the BMW is missing from the garage. Inside the portico, the front door is ajar. When I ring the bell Mum comes brightly out and kisses me carefully, and I go stiff as a board, and we walk through the big house and out into the back garden for our solitary luncheon. There's a tennis court, and the swimming pool is covered so the leaves won't foul the blue, blue water, and trees and bushes everywhere, and some more water glimmering through the greenery.
I want to be a million kays away from here.
I want to be upstairs at home with Davy, pushing his groping hands away.
I want to be in the kitchen making up some fettuccine for Poppa's dinner.
I want my Mum back. It's so hard not to burst out crying. My mouth feels hard and tight.
Mum's feeling the strain, too. "Had enough cake, sweetheart?"
"Plenty."
"One slice! Are you going on a diet again?"
"I'm not an anorexic, Mum." I glare at her, turning the plate around and around. "And I'm not a junkie either." That's what they all think, judging from the telly programs. Stupid adults.
"Good grief, child!" Mum is shocked, or pretends to be. She takes the plate away from me, tidying up, and starts to lug everything inside but changes her mind, sits down opposite me again at the white iron table, knots her fingers. "Jenny, there is something we have to talk about."
I twist my mouth about and stare at the molting trees. "Where's What's-His-Face?"
"I wish you wouldn't be so hostile. Edward is visiting his eldest son this afternoon; he's taken Tris with him."
Bitterly, I mumble, "Musical children."
Her eyes are pale blue, and she stares at me. "Why, I don't think 'children' is exactly the word for his sons, except for Tristan, of course, and no, they don't play— Oh, very funny. Musical chairs." I turn away, kicking at the leg of the chair. In a funny voice she says, "No, it's not funny, is it? Not a bit funny." After a moment when we both get something stuck in our throats, she blurts out, "...Sweetheart, darling, please don't be like this. I love you very much, you know."
"How should I know that?"
"I'm your mother! I carried you in my body for nine months. I—"
Oh, really! "We did biology last year, Mum."
"You're upset. I— Now you've got me crying. Oh dear, Jenny, this is awful. I do love you, you know."
"I know you do. I love you, too, Mummy. Why don't you just come home!"
"It's simply not possible, darling. Not any longer."
"It is that simple. Just pack your stuff up, and we'll put it in the car, and drive home to Carlton. You and Poppa don't need to be married to live together." I stand up and grab all the plates and pots of jam and the teapot and stick them in a heap and start into the house, mumbling, "You don't even like Kew!"
I get stuck with the wire door, and Mum reaches past and opens it. "When I was your age, Jenny—"
"Aw no. Same old—"
When I look at her, sideways, she's giving this sly grin.
"—there was one thing I absolutely hated like poison," she says, "and that was some old fart telling me I wouldn't understand, because I was too young."
"Yeah."
"But it turned out to be true. Not my fault, sweetie, it's the way the world is. Perhaps if I'd never met Edward, or if I hadn't met him when I did, when things were so bad between— Well, who knows, perhaps your father and I might have patched things up. As it is— But there you are, you see, you've got your face all scrunched up like a gargoyle, you don't know about adult love, Jenny! Your...your hormones aren't old enough to understand."
That's true and not true, and beside the point, and I'm furious all over again. "Look, you don't know everything either! I mean, God, I'm just dying to tell you all about this ridiculous thing that happened on the phone yesterday, and Poppa's getting vaguer and vaguer and he's missing you so much, and all you can do is sit there wondering when bloody old boring Edward is going to get back from his nasty little rotten spoiled brats."
I burst into tears.
Mum takes the lunch things and places them on the bench beside the dishwasher and comes back to put her arms about me. Finally I stop sniveling and she pushes me off a little, gazing very seriously at me. I feel sick, and it's not my period. I know something really foul is going to be said. She says, "We're going to get married, Genevieve. Edward and I are announcing our engagement after Easter."
She didn't say it.
It can't be true.
Say she didn't say it.
Beside myself with fury, I shriek, "You've only just got divorced!"
I sob, and my mother holds me against her breast.
"Oh darling," she says. She's not crying. She can't even be bothered to cry. "Oh darling girl."
MONDAY, 10 APRIL, AFTERNOON
When the phone rings I'm at home alone, waiting right beside it.
"Hello?"
"Jenny?"
"Of course. Who else lives here with a high squeaky girl's voice?"
"Um, yes. Greeting again from 1960."
"I still can't believe it." I can't. Pulling out the extension cable a few inches, I slide down the wall and lounge with my legs straight out across the hall. I really can't.
"Are you free to talk? Getting this thing locked onto the future is like walking a high-wire with a rattlesnake in each hand."
"It's dangerous? You mean the phone line might blast fifty thousand amps down my ear or something?"
"Absolutely not." He uses the tone you'd try to calm a dangerous madman with. "I only mean it's very tricky to keep the resonance balanced. Have you worked out yet what I did with the numbers and the quote?"
"Well, unless this whole thing's a major hoax—"
"It's not."
"You'd say that anyway. But if it's not—well, I guess you rang me at like 6:30 the day before yesterday and got me to look up the books and stuff, then I read you what David and I'd written down, and then you—uh, then you hung up and rang me earlier, like at 6:15."
"Spot on, kiddo." In a sarcastic tone, he adds, "But isn't that impossible?"
I roll my eyes at an invisible audience. "The whole thing's impossible. But just s'pose it's true—well, after all, you're calling the future. I suppose there's no rule that says your first call can't go to 1995 and your second call to, I dunno, 1975."
I feel quite proud for thinking up this feat of mental gymnastics, but then he dashes it. "That's not strictly true, sadly. I tried that, and it doesn't work. The system crashes."
"What about this Heisenberg junk?" According to Mrs. Levine, it's something to do with, like, in physics you can get away with it but only if no one's looking.
He says it before I can. "See, Jenny, the thing about Heisenberg is that you can cheat a little bit. as long as you do so fast enough that the universe doesn't catch you at it—a small bit of energy cheating for a longish time, a huge bit for a much smaller time. That's quantum theory for you."
"I thought the thing about physics was that you can't cheat. It's not like business rip-offs, it's laws of Nature. That's what my science teacher says."
"A wise man."
"Woman, Nameless Chauvinist. Mrs. Levine."
I'm getting used to these pauses. "I always thought a chauvinist was someone who prized his country over all others."
"Male Chauvinist. Sexist. You know."
"I don't, you see." Rod sounds worn out and despairing. "That's just it. O Brave New World that has such terminological distinctions in it." As if he's muttering to himself. "There could be people with two heads for all I know."
They've been discussing that sort of thing in the papers, we did it in a social-ethics exercise. "Yuck. Transplants. Recombinant DNA."
"See? What's that mean? Oh, DNA—I suppose that's deoxyribonucleic acid, isn't it? What those guys Crick and Watson discovered a few years ago. The, um, Double Helix?"
"It's sort of the secret of life. Everything's coded into it."
"Just keep talking, Jenny." The despair's gone. He is jumping out of his skin, and it makes me buzzy too, just listening to his excitement. A feeling of power, somehow. "My God, this is like having a crystal ball that's focused on next century's textbooks. Have they discovered antigravity yet? Immortality? How about nuclear physics, is there anything smaller than neutrons and protons? Hell's bells, Jenny, I've turned into a babbling loon. You won't have the faintest idea what I'm talking about."
"Quarks."
"Say again? Corks?"
"Quarks. That's what protons and neutrons and mesons are made of."
"I've never heard of it. What's it mean?"
"I could go and get the Britannica and read it to you, I suppose."
"In a minute. My head's reeling. Do you know what this implies? We could short-circuit three decades of scientific research. No, wait a minute, we can't. I've thought all this through. It's not on. I have to calm down. Give me a moment, Jenny. My God. Quarks."
He's got me going now, and I'm talking even while I'm thinking. "There's no such thing as antigravity, but there are black holes, which is sort of the opposite."
"Supergravity? What would that be?"
I've vaguely heard Mrs. Levine talking about something called supergravity, but that's from the Theory of Everything, or something. "Well, if you mean nothing but gravity then that's sort of what black holes are, I think, but supergravity is actually something else in some other theory." But I can't start on that, Rod'll go bananas and expire of frustration. "And there isn't any immortality. My father says people are dying younger, of stress."
"I can understand that. I'm about to flake out on the lab floor myself."
"I saw these old Back to the Future movies, Michael J. Fox finds this time machine, it's built into a car, see, and he drives back and his mother falls in love with him. That's just the start, of course."
"They let children see films like that?"
"Sure. I mean, nothing gross happens."
"Oedipus Sex," Rod mumbles. "Dr. Freud meets H. G. Wells. Ye Gods."
"Anyway, he does this stuff back there in the nineteen-fifties, and his dad turns out different, and they change the future. Is that what you mean?"
It doesn't really sound like it, but Rod says, "Exactly. I've been reading all the science fiction I could get my hands on. They're the only crackpots crazy enough to have given this sort of thing any thought."
"I never read sci fi," I say dismissively. "It's just sexist male fantasies. Apart from Le Guin and a couple of others."
"I haven't heard of him."
Jesus on a stick! "Do you really want me to hang up in your ear? Ursula Le Guin is a woman, Bozo."
"Listen, do men do anything in your time?"
"Very funny. I don't think you're going to like it here, Nameless Masher, with your attitude."
"I'm not nameless, I'm Rod, remember? That's the big question, you see. Where am I in your time—and do I like it?"
"Well, you're not in the Melbourne phone book," I tell him carelessly, flicking the A-L out from its shelf under the table, nudging it back in.
"You already looked?" He sounds impressed, and rightly so.
"Of course I did. I'm the girl with the brain like a steel trap, remember? There's no R. Gianforte."
"Sorry, it'd be H. For Herodotus. Not my idea."
"Doesn't make any difference, there's no Gianforte in all of Melbourne, which is pretty amazing, since they reckon there's more Italians in Melbourne than in the whole of Rome."
"A slight exaggeration. Probably I'm in New York by the 1990s. After all, I'll be incredibly famous."
"Herodotus is Greek, isn't it? Not Italian?"
"They're all wogs, aren't they," he says with a surprising touch of bitterness. "My parents doted on the classics."
I'm embarrassed. "Why will you be famous, Rod?"
"Inventor of the Intertemporal Communicator, what do you think? And maybe the, what was it, the quark." The bitterness has vanished as quickly as it appeared.
It is getting quite dark outside in the street, despite the Monday evening home-from-work cars rushing past. Poppa must be due in any minute. I should get off the line and start some dinner. Rod is loony-tunes, let's face it. I should hang up. But it's a cute fantasy. "If you're the famous inventor of the time machine, how come I've never heard of it?"
That doesn't faze him for a moment. "Different future. That's what I reckon."
I've thought of that one too. "I don't really exist? Is that what you're trying to tell me? Like, you're having a conversation with a figment of your imagination who lives in the future, only it won't happen because I told you about quarks? Rod, I think you've been working too hard."
"I never said it was easy to understand. Look, time isn't just one vast network of links. It must be a sort of...of cascade. Every time we make a choice, the world splits into as many versions as there are choices, and—"
I snort. "They used that corny old idea in every third Star Trek classic episode."
"What's that?"
"Ancient telly show. They've started re-running it, the Trekkies just keep watching. Also Doctor Who. Parallel universes, that's what it's called."
"They stole it from ancient science fiction magazines. But it isn't just fantasy, Jenny. I looked it up. A couple of American physicists worked out all the math. Wheeler and, uh, Everett."
He's not going to give up. I blink, then frown. "So you're saying I live in one of the futures that branch off from yours—"
"Could be millions. Billions."
Slowly, I say, "But that means there's no point in asking me anything, doesn't it? It'll all turn out different anyway."
Again, to my great pleasure, Rod sounds impressed. "That's the risk, of course. We've just got to find a way around it. For example, I doubt that some future universe will suddenly turn out not to be made of quarks, whatever that is."
"I know just the person to ask," I tell him. There's a sizzling sound, and then dead air. Not even beeping. We've been cut off. Or maybe Rod's "lost the resonance." Whatever that means.
Extremely frustrating. I hang up the dead handset, feeling as though I'm stuck in a dream. But the phone doesn't ring again.
TUESDAY, 11 APRIL, AFTERNOON
Mrs. Levine, our science teacher, doesn't really look like a teacher. I don't just mean because she's not that old. Most of the teachers at North Carlton High are only about ten years older than us students, except for the Principal and even she isn't as old as Poppa. It's more the way Mrs. Levine looks and acts, which is a bit like Jennie Garth, you know, Kelly in Beverly Hills 90210, only with big boobs like Madeleine's going to have any day now.
And I certainly don't mean you can't have big boobs and still be clever, but Mrs. Levine wears a leather jacket and drives a little red Honda sports car as if she's in the Grand Prix. Plus she's a feminist but she uses her husband's name, which is weird, and she's got a Ph.D. in mathematics even though she just teaches high school science. Mum had an interview with her when I started accelerated physics, and she told Poppa that Mrs. Levine had tried to get a job at the university or in industry, but there just weren't any jobs around anymore because of the recession. So she ended up at North Carlton, which is how come I'm able to stay back after chemistry class and ask her about time travel by telephone.
"Jenny, you look distracted. Having trouble with your homework?"
"No, Mrs. Levine." I stand there in front of her desk while she shuffles assignments into a big shoulder bag made out of leather patches. How do you ask someone about such a crazy thing without sounding as if you're crazy?
"I'm in a bit of a rush, dear. By the way, I was very sorry to hear about your difficulties at home." She gets a sudden gleam in her eye. "Oh, I see. Is it something to do with that?"
"Huh?" I lose my train of thought completely. She is looking at me with sort of sentimental sympathy, and then I get it. Well, what happens at home really is none of her business, so I go sulky and cross. "If you mean my Mum moving to Kew, it's got nothing to do with that at all."
"I see." Mrs. Levine sits down again behind her desk, pushes her long blonde hair back and loops it into a ponytail, and pats the edge of the desk for me to hitch myself up on it. "Look, actually I do have a few moments spare, Jenny. Why don't you just tell me what's on your mind?"
By now I am wishing I'd never started. Outside in the corridor the other kids are banging about, getting their stuff out of the lockers and heading for home. Some jerk is bouncing a basketball off the wall of the corridor, and Mrs. Blakeley yells at him furiously to stop that racket and go home. "Uh, really, it's nothing, Mrs. Levine. Just an idea I had for a story." I stop and look at the open door, wanting to just slide inconspicuously out of it. I've decided to pretend it's a story I'm writing for a mid-term project, because I certainly can't just tell her straight out about the phone calls from Rod the mysterious time travelling mugger. "It's sort of a science fiction idea."
Mrs. Levine gazes at me as if she can see something deeper than I'm letting on.
"I see. Let me guess. Something like Mr. Data on Star Trek: The Next Generation, who can't really feel anything because he's an android rather than a regular person?"
"Huh?" Where do they get these ideas? "No, this is about time. Well, sort of. A way of reaching into the future. Um, well, that's not quite right either, because it's also a way to change the past."
"Ah!" Mrs. Levine looks pleased. "You'd like to alter the past so something that's happened turns out to have happened some other way. Something different and better."
"Yes!" Suddenly I'm glad that I took the risk of talking to her. This could be easier than I'd expected. "Only it looks as if you can't change the past without, um...." It's hard to keep this time-loop stuff straight in my brain, even if it is a brain like a steel trap.
"...without changing the present," Mrs. Levine finishes for me. "That's actually a very mature perception, Jenny. Even when we wish things had turned out otherwise, the fact is that we are the result of everything that's happened to us, even the bad and uncomfortable things. So if we could change the past we would be wiping out part of ourself."
She's gone off the track again, and she's looking ridiculously pleased with herself.
"No, that's not it," I say uneasily, hopping down off the edge of the desk and walking back and forth in little steps. Mr. Ironside the history teacher pauses at the open door, pokes his head in, sees us talking, waves to Mrs. Levine, wanders off. She glances at her wrist, then back to me. "See, in my story it doesn't just change," I explain, "it stops completely. I mean, it never happened."
"But it did happen, Jenny," Mrs. Levine tells me seriously. She leans forward and steeples her fingers. "It did happen whether we like it or not, and the only way forward is to confront that reality and deal with it emotionally. Bottling it up, what we call 'denial,' just makes things worse."
Suddenly I see what she's getting at, and it makes me really furious.
"I'm not talking about moldy old Edward Thing," I snap. "This isn't about my Mum leaving us. I'm talking about a real phone call!" Then I catch myself, and feel my face blushing. "I mean, a phone call in a real story I'm writing. Oh, look, Mrs. Levine, this is hopeless, I've got to go home and start getting the dinner ready, I'm sorry I've wasted your time," and I grab up my bag and books and head for the door, feeling like a complete fool.
Mrs. Levine buzzes across to the door like a sprinter and cuts me off.
"It's all right, dear, it really is," she says, and puts one arm around my shoulders. "Enjoy the Easter weekend, and come and see me whenever you wish to. I'd like very much to hear more about your story. It sounds extremely interesting. Just bear in mind, though, that even in a story we can't change the past. Not really."
"Thanks, Mrs. Levine." I scuttle into the empty corridor and bite at my lower lip. Can't change the past! Tell Rod Gianforte that! Then I start to feel a little buzz of excitement. Maybe he will have got his machine working right again by now. Maybe he'll give me another call through the time zones. Maybe I really will get a chance to change the past.
SATURDAY, 22 APRIL, AFTERNOON
The day Mum gets engaged looks like being a total downer. It's utterly tacky, really, getting engaged at their age. It isn't as if she and Edward haven't both been married before. I mean, you'd think they could just sneak off to the city registry office and quietly get married if they absolutely have to. But that isn't how it's happening. They've decided to get properly engaged, with engagement rings and all the rest of it.
All the rest of it is a party that both Poppa and me have been invited to.
Poppa hasn't been too consistent about the party. He'd actually known Mum was going to get engaged for weeks before she worked up the nerve to tell me about it. So getting the invitation shouldn't have been that much of a shock. But it was. I could see that when he opened the envelope. All the colour drained out of his face and he didn't say anything for a few moments.
"What's up, Poppa?'
He didn't reply, just handed the card to me. We were both invited to help Harriet and Edward celebrate blah blah blah yetch.
Poppa finally said, "Well, it's nice of her to ask me. But I really don't think it would be appropriate for the ex-husband to go to his ex-wife's engagement party.
I agreed with him there. But he said he thought it was necessary for me to go. I nearly hit the roof.
"Your mother would be terribly upset if you stayed away."
"Good," I said nastily.
"Now, Jenny," he said. "There's no quarrel between you and your mother. It was me she left. She didn't leave you."
"Then how come I don't live with her?"
"Because it is more convenient.... I mean it is probably better all round.... Look, you can't live with both of us at the same time. And we've lived in this house ever since we moved down from Sydney."
"And this is where I'm staying next Saturday afternoon. Here. In this house. How dare she? How dare she go and get engaged to that man?"
"I'm sure he's very nice."
"No he's not."
"It is hard to be objective in situations like this, but...."
"Look, if you think Edward bloody Thing is a nice man, you go to the engagement party. I'm not."
"Now, Jenny...."
"Don't you now Jenny me!"
I burst into tears and ran out of the room. I lay on my bed and wept. I'll say one thing for Poppa: he had enough sense not to try to comfort me until I felt like being comforted. After about an hour I was feeling all lonely and empty inside. He came upstairs then and sat on the end of my bed and we talked some more. He was right, really. Mum will be totally upset if I don't go to her awful engagement party. But I guess she really doesn't want Poppa to come to it. She probably only invited him to show she still cared about him.
In the end I said I'd go as long as I could take a friend. Poppa said he was sure there would be some children...er, um...people my own age. For example, he understood that Edward had a son called Triton or some such.
"Tristan," I said. "He goes to school with some incredibly bright Chinese boys called Fu Manchu and Ming the Merciless."
"Well, then. They might be there as well."
"So if Tristan is going to have his friends there, I'm going to take mine."
"I'm sure you can take a friend."
"I'm going to take a whole bunch."
"I don't think that would be very appropriate, but I'm sure Madeleine would be most welcome."
When I phone Maddy, she says she can't come. She has to go to some cousin's place this afternoon. So I decide to take Davy instead, and he moans a bit but finally settles down and says he wouldn't leave me to face the dragons by myself. I really do love that boy.
§
I realize we shouldn't have come the moment we walk in the door. Everyone is dressed up like something out of the Sunday newspaper fashion pages in all these up-themselves clothes. They're standing around sort of like polite zoo animals scoffing pink stuff with bubbles out of silly shaped glasses and jawing at each other. Blab blab blab. And there's a real animal somewhere, barking and bellowing, some huge dog. It sounds as if it's coming from the bowels of the earth, like a tormented spirit.
Mum appears, hugs me tightly and says, "Oh, Jenny I'm so glad you came." And she gives me a kiss and says to Davy, "And you too, sweetheart. It's very nice of you to escort Jenny." Her face is flushed. "I know this sort of do isn't very exciting for young people, but there are one or two others here you'll like. Tristan's around somewhere." She stops talking as if she knows she's fussing too much. "Anyway, Davy, it really is very nice of you to come."
"That's all right, Mrs. Kane," Davy says, and adds with his usual tact, "Jenny said she needed someone to stop her smashing the place up."
This is true, that's just what I did tell Davy, but he shouldn't have repeated it. Mum goes a couple of shades paler and laughs nervously.
"Oh, don't worry, Mum," I say. "I promise not to break anything really valuable." I stare around at Edward Thing's ridiculous living room. I suppose it is his living room. Maybe it is his reception area or something. There's an awful lot of stuff just asking to be broken: little china figures of milk maids with dopey-looking dudes in matador pants, and silly moo cows with crumpled horns, and a horrible clock with all its inner working parts showing but instead of a pendulum it's got a dweeby-looking girl on a swing bouncing up and down. Mum says, "Come on, then, let's introduce you to Tristan."
That's how Davy and I get dragged across the room to meet this private school nitwit.
He has a blazer and tie on, although it isn't his posh school blazer and tie, it's his engagement party blazer and tie. His hair is cut quite short at the back and sides, but flops down over his forehead at the front. And of course there's glasses perched on his nose, like Clark Kent's in Lois and Clark. He's standing in a not-really-relaxed way talking to this hunky looking adult.
"This is Tristan," Mum tells us, "and this is his brother, Alain." The hunky adult shakes hands with me and Davy. He is amazingly tanned, with fine lines all over his rather good-looking face, as if he has been left out in the sun all summer. What sort of name's 'Alain', anyway? French probably. He's nattering on in a beautiful voice, absolutely at home in this enormous house with its hideous knickknacks. In the background, like a strange echo, the huge dog is baying and booming. I want to go and look for it and let it out. Obviously it's trapped somewhere. They've probably got the wretched animal tied up for the occasion.
Something bizarre happens. Davy stops scowling at the Persian carpet and really looks at this Alain, and his jaw drops open. I can see his mind do a sort of somersault.
"Alain Thring? Weren't you the tactician on the Pretty Polly?"
"In the last challenge, yes. You follow the sport?"
I don't have the faintest idea what they're talking about. Mum is looking pleased as punch, obviously grateful that Davy hasn't turned out to be the social disaster she's expected.
"What kind of tactics were you a tactician of?" I ask in a dull voice. "The Gulf War?" Hearing about boys' sports is the last thing on my mind.
"Jenny, don't you get it? This is Alain Thring! He was at Rhode Island for the America's Cup challenge!"
"What's that?"
"The world's greatest yacht race! Hey, this is great! Um, could I have your autograph? Here, on this napkin will do."
I am furious and walk away, leaving them to their stupid boats. The room is crowded with over-dressed rich people I don't know, but it still looks half empty. Up on the walls are these big portraits that I'm sure Mr. Percival our arts teacher would condemn as worthless and without a scintilla of taste or life. Actually they're not so bad. At least you can recognize them as people. I mean, they don't have both eyes on the same side of their heads like some of the stuff old Percival loves to show us on his videos of the great museums of Europe.
One of them shows a young crewman being extremely macho and dashing with a spinnaker line or something on a yacht that's crashing through heaps of waves and foam and sunlight. It's Alain, of course. Another one a bit further along shows a serious young insect wearing a black gown and a square academic hat on his head, and Melbourne University's tower clock looming in the background. Further down there's the dweeb himself, looking about 10 years old. I nearly fall down laughing. An old bird in a pink floral hat looks at me disapprovingly, but I'm choking with laughter, because up there on the wall is little Tristan the wonder boy dressed in a blue satin sailor suit, with ridiculous little suede booties on his feet, tied up neatly with blue satin bows. I almost feel sorry for him. I mean, how would it be to have something as gruesome as that hanging over your head for the rest of your life? I bet he never brings his school friends in here.
"Pretty dreadful, isn't it," someone says. "Poor old Tris says he's going to sneak in here one night and burn it in the fireplace."
I stifle my laughter and look around. It's the young man in the graduation painting, except he's now a few years older. Unlike the sunburned yachting hero, this one is pale and indoorsy. Probably a great disappointment to moldy Edward.
"You must be Genevieve," he says. "I'm Carlos."
"That's Spanish for Charles," I blurt out. "How come none of you lot have ordinary Australian names?"
He takes a sip of orange juice and looks up at the awful picture of young dweebhead. "Mother and Dad travelled rather extensively during the early days of their marriage," he says. "She loved Europe."
"What, so you were born in Spain?"
"Exactly. Or something similar." He smiles to himself.
"And Alain was born in France, and Tristan in...what? Germany?"
"England, actually. Tristan is a very old and romantic name in certain parts of Britain. Tristan and Isolte, you know?"
I don't, but I'm not going to admit that to one of Edward's ghastly grown-up children. Davy is still blathering on to the prize-winning seaman, and Mum has disappeared. Carlos goes back to admiring the portrait of his baby brother. I say, "So where's your mother? I don't suppose she really wants to come and see your father get engaged to someone else."
He gives me a shocked look, then shakes his head slightly, as if he's angry but controlling himself. How dare he be angry about it? I'm the one who's losing her mother. "I don't find that particularly amusing, Genevieve."
"My name's Jenny. What do you mean, amusing? My Dad's not here either, and I don't think that's very funny either."
Putting down his glass, Carlos says, "Mother died when Tristan was eleven." He pauses and looks hard at me. "Three years ago. Do you mean you didn't know, or are you just naturally rude?"
I can feel myself blushing all the way from the top of my head and across my face and down my chest, and then going tingly. No one has ever said anything about Edward's wife being dead. I just assumed they were divorced, like everyone else. Well, most of the parents I know.
"Sorry," I mumble. "Mum doesn't talk about...you know."
"Her new life? Her husband to be? Her wealthy widower?" Carlos, I see, is extremely angry, and he's no longer making any attempt to disguise the fact. "No, I suppose not. People who trample on the memory of other people might very well not care to mention the details to their own children." He turns on his heel and barges away into the middle of the expensive Kew crowd, while I stand with my mouth open and stare after him.
Someone holds up a crystal glass and taps it with a spoon. Probably a silver spoon, for all I know. It gongs like a beautiful little bell, clear and distinct, cutting through the rhubarb of conversations. The distant dog keeps barking, like an echo from below the floorboards. Why doesn't someone do something about it? A man's voice says jovially, "Testing, testing, two, three. Well now, friends and colleagues, be upstanding, charge your glasses, it's that time of the year," and everyone starts milling about looking for champagne to stick in their long fluted glasses, and they're all smiling and murmuring encouraging things in their silly accents, and then Mum and bloody Edward come out from a side room and step up onto a raised platform covered with rose petals, and Mum is nearly crying with happiness, and hanging on Edward's arm, and I push blindly though the crowd and out the back door into the garden.
I can't stand it!
She's really going to do it.
She's really going to get engaged to this man with children called stupid things like Tristan and Carlos and Alain, and she's going to live here in this horrible big castle of a thing, Thring's Thing, and she won't be my mother any more. Just like Tristan's mother. She won't be there. It'll be like she's dead, only worse, because she's chosen to do it. She's walked away from Poppa and me.
I hate her!
I really hate her!
After a while I stop crying and realize that I'm lost. That's stupid, of course, because how can someone get lost in the back yard of a house in Kew? But there are huge trees and shrubs and stuff everywhere, and I almost fall into some ornamental pond that's got ducks swimming about on it. So I just stand there and look at the silly things and wish I had some bread to throw to them. There's a distant burst of clapping from behind the trees, then some laughter, then even louder clapping. I pick up a lump of wood that's fallen off a gum tree and toss it at the ducks, who kick their webbed feet under the surface and sail off to the other side of the pond.
People are singing "For they are jolly good fellows," and I really feel like throwing up. Where's Davy when I need him,? Inside drinking beer with the bloody yachting hero. I look around, stupidly hoping he might have come out to find me....
...And there's the dweeb, loitering gloomily next to an oak tree, gazing at the ducks—and ignoring my presence as if I'm some sort of unpleasant ghost.
We stand there like two store dummies for a bit. Then, to my absolute astonishment, Tristan reaches up with one hand, still acting as if I'm invisible, and sticks his index finger deep inside his left ear. I try to look as if I'm paying no attention, but it's really gross, he's digging around in his ear hole as if he's trying to scare out an earwig or a cockroach or something that's burrowing into his brain. Then he pulls his hand away, to my relief—and there's an egg between his fingers.
I mean, this is totally impossible. A hen's egg, large size, right out of a packet of twelve, white and perfect and drawn from his ear. It's the best conjuring trick I've ever seen done live. (You see better stuff than that on telly, of course, David Copperfield making the Statue of Liberty vanish, and stuff, but that's all special effects. This is happening in front of my very eyes, and in real time.)
Still not looking at me, or acknowledging my presence in any way, the dweeb crouches down and cracks the egg on an ornamental rock with a sun-dial set into it. I can hear the shell crack. Tristan stands up and starts peeling the shell off this hard-boiled egg that he has pulled out of his ear.
When he's finished peeling the egg he looks at it with satisfaction and eats it.
Just stuffs it in his mouth and chews it up.
What a pig!
By this time I'm staring blatantly at him without pretending not to, but he's ignoring me completely. When he's finished gobbling the huge boiled egg—I can see his lumpy Adams apple gulping and bobbing in his throat—he opens his hand and inspects the bits of eggshell. Then he closes his hand, passes the other hand over it, opens them both—and the eggshell is gone. He hasn't hidden the shell fragments up his sleeve, or dropped them on the ground, or stuck them back in his ear. Amazing! He rubs his empty hands together, shrugs, and still without giving me the slightest glance walks off silently into the shrubs and out of sight.
SATURDAY, 22 APRIL, LATE AFTERNOON
When I finally go back inside, the grown-ups are all thronging about half drunk, laughing and chuffing and hooting, and the dog is bellowing underneath the floorboards, though it's harder to hear with all the noise the human animals are making. Davy is still hanging about near the yachting legend. Disgusted, I slide in and grab his arm and give it a tug.
"Oh, hi, Jen. Hey, this is great!"
"You're a whole lot of help," I grumble. "I might as well be stuck here by myself."
The boy looks bashful for a moment, which he does rather nicely for such a macho kid. "Well...let's get a Coke and some of that amazing chocolate cake. Have you got an eyeful at the rest of the house yet?"
"Certainly not," I say haughtily. "I never intend to set foot inside this place again, ever, and I don't wish to deign to, um, I certainly won't, er—" but I'm completely lost in my indignant sentence, and Davy looks as if he's ready to burst out laughing but knows it wouldn't be worth his life, so I snort and start again. "And I'm certainly not eating their rotten cake. Look, come outside, that dweeb Tristan just did the most disgusting and amazing thing, and anyway I think we should find that dog and bring it inside to join the party."
The idea just jumps into my mind out of nowhere. But it's brilliant, and I get goosebumps with delight at the thought of letting some hell-hound loose among the posh show-offs and wheeler-dealers.
"What dog?" asks Davy. The boy is thrown, as he usually is when I change mental direction too fast for him.
"The one making all the racket."
"That's coming from next door, isn't it?"
"I don't think so," I say, dragging him toward the door to the garden. "I think it's tied up under the house somewhere. It's cruel, that's what it is. And it's up to us to set it right."
It doesn't take us long to find that around the side of the house, almost blocked by shrubbery, there's a door leading to the cellar. Davy and I go down half a dozen steps to the door. You can hear the poor dog much more clearly from here, going ape behind it.
"What if it bites?" Davy says nervously. He's usually quite brave. Maybe he's scared of dogs. Maybe he's got a phobia. "It's a guard dog, after all," he says. "It might be fierce."
"No it's not," I tell him, not really convinced myself. "It just wants to get out and join in the fun."
Davy cautiously opens the door and suddenly we're faced by this enormous black and brown Rottweiler in a sort of bunker. It starts frothing and slavering and barking its head off the moment it sees us. Luckily, it has a heavy steel chain attached to its studded collar, with the other end wrapped around the leg of a metal desk. Everywhere I look I see books piled up on shelves made of planks and bricks, piled on top of each other and falling down in heaps, old books with thick covers and hardcover books and stacks of dog-eared paperbacks. Well, they would be dog-eared, wouldn't they, if this is a kennel?
The walls are absolutely covered with heavy metal and grunge posters and basketball posters of truly huge black slam dunkers or whatever they're called, and David Copperfield the stage magician with two beautiful girls in glittery dresses, and a nice big picture of white-haired old Albert Einstein, my favorite scientist. On the desk, above the Rottweiler's huge head, there's a computer monitor with a silly screen saver flashing away on it. No wonder the animal is going ape—locked in a room with a lot of bubbles endlessly popping on a screen.
"I think it's hungry," Davy says, standing well back out of reach of its teeth.
"No reason why it should be. That dish must have half a sheep's carcass in it."
"It's tangled its chain," Davy says, edging toward the bowl full of chopped-up meat. Another bowl has tipped over, and water has spilled from it in a big wet stain on the old carpet. "If I can find a stick or something I might be able to push its lunch over to it. That might calm it down."
On the monitor screen, the bubbles turn into colorful flying toasters flapping their wings. It sounds a bit as if the room has filled up with a flock of military birds flying in formation. At the sound of toasters on the wing, the black and brown dog goes off its face again and drags at its chain, trying to eat the flapping machines on the screen.
"I don't think you should touch its food bowl," I start to say, but Davy has overcome his nervousness and reached forward with a fishing line that he's found in a corner of the den. He misses the edge of the metal bowl and by mistake hooks a lump of meat the size of my head. It flies across the room and lands near the killer captive dog, just out of its reach. I've never heard such a hullabaloo. You'd swear it hadn't eaten for a week. It's staring at the lump of meat and its fangs are gleaming in the fluorescent lights overhead, spit flying every which way, and it makes a mighty straining leap and gets halfway loose.
Unluckily for Davy, its leap sends it straight in his direction.
Davy takes off for the far corner of the room, white as a sheet. The Rottweiler lunges at him, howling with fury, even ignoring the lump of tasty carcass now right under its nose. "Get it away from me," Davy yells. "Help! Help! It's going to tear me to pieces!"
Then I do a really rotten thing. I can't help myself. This temporary kennel is obviously the dweeb's own special cubby-house, and he's left the computer running, so behind that screen saver display there's probably something extremely interesting and tacky. So I leave poor Davy bailed up by the killer dog and take advantage of its distraction. I lean across the desk and very, very carefully nudge the computer's mouse toward me, and hit the button.
The toasters vanish, and the screen fills with words.
"What are you doing?" Davy is screaming. "Jenny! Get help! It's going to kill me!"
"No it's not," I tell him reassuringly. "The chain's still caught. It can't reach you." I'm peering at the screen, which has a file headed TRISTAN'S CASEBOOK. A couple of words catch my eye: "Mother" and "Jenny." Davy is bellowing with panic, but I can't help myself, I desperately want to read this diary while I have the chance and I might never get another opportunity to sneak into the egg-conjuring dweeb's underground fortress. But it's hard to concentrate on the screen with all the barking and yelling, and surely someone will come down from the house any minute now. I peer closer and read.
I'm reading so fast I can't make much sense out of Tristan's words, but the general tone of the thing comes over loud and clear: this boy is deeply disturbed. He's as freaked out by his Dad getting engaged to my Mum as I am by Mum getting engaged to his Dad. And he doesn't like me—or he doesn't like the idea of me. Which is deeply unfair, since at the time when he wrote this stuff, he hadn't even met me. There's a bit about "...Hattie probably ran away to get clear of her idiot daughter...." For a minute I'm so angry I could spit. Who does the nerd think he is? Idiot daughter! That's me he's talking about....
"Jenny!" Davy is yelling from the corner of the room. "Do something! Get someone to come and shoot it." So I drag myself back to reality. It would bloody well serve Tristan right if someone did shoot his beastly dog. The animal is snarling and growling so much I can't think straight.
"You just stay there," I tell Davy, who is even more white-faced and ghostly and ghastly. "I'll get someone."
The room goes a bit darker for a moment, and I realize that Tristan has stepped into the open doorway. "Quiet, Lamb Chop," he says softly. Instantly, the Rottweiler stops barking and frothing at the mouth, and now it just sort of growls horribly at Davy—all low and menacing. This sounds even more scary than when it was barking its head off. "That'll do, Lamb Chop. Lie down."
Davy stays in the corner. He is not breathing very well; he's panting in time with the dog. For a moment the room is full of the sound of synchronized panting, but the dog does as it is told and lies down on the floor, pointing its snout at Davy. There is still no way Davy can get out of the corner without coming in range of the dog.
"That animal ought to be shot," Davy says to Tristan. "It should be put down. It's illegal to own animals that can kill."
"It's illegal to break into other people's private rooms," Tristan says. "And to read their private writing," he says to me. I look back at the screen, but it's full of flying toasters again.
"That's not writing," I say. "That's toasters. And anyway, who are you to call me an idiot? You don't even know me. You're the biggest private school dweeb I've ever seen. Just because you can pull eggs out of people's ears you think you're the ant's pants." I know while I'm talking that I'm sounding a bit hysterical, not cool at all. But I'm furious.
Tristan goes over to the metal desk, turns the computer off without deigning to look at either of us, and starts to untangle the dog's chain. "Don't let it go!" Davy yells.
"He won't eat you," Tristan says. "At least, not unless I tell him to. Come on, Lamb Chop, let's go for a walk." Tristan and the dog leave the bunker. Davy and I look at each other, we both feel the same mixture of fury and embarrassment.
"I'm not staying here any longer," Davy says, "This place sucks."
"Yeah, let's go," I agree.
A lot of guests are milling around on the lawns. Some of them are quite drunk by now. The noise level has risen still further and people are starting to shout at each other. Mum is deep in conversation with Alain and a couple of other people. I start to walk over to her to say goodbye, but then I think better of it. I grab Davy's arm and we leave by the front gate. While we are standing at the tram stop we see Tristan and the Rottweiler walking towards us on the other side of the road. I don't know if Tristan even sees us. He has his head down and might even be muttering to himself. The dog seems to be towing him along. Tristan doesn't look very happy.
"Jeez, I'd like to sock him one," Davy says.
For a couple of seconds I silently agree with Davy, but then the sight of Tristan mooching unhappily along suddenly drives all the anger out of me. "Oh, he's probably all right," I say.
"Aw, what?" Davy says. "He's a prize dork. If it wasn't for that damn dog...."
"He hates the engagement as much I do," I say. "He's in exactly the same position. He doesn't want his dad to marry someone else...."
"Jeez, Jenny. His dad is a real drag. Your Mum's one of the nicest people I know...."
"Yeah," I hear myself say, "That's what it looks like to us. But from Tristan's point of view...."
"You wouldn't want to see anything from that nerd's point of view."
But I can't help myself. All of a sudden, sad and lonely as I feel, I can see it all too easily from Tristan's point of view. And I suspect he sees it from mine.
TRISTAN'S CASEBOOK: April 22
The subject is a young woman of fourteen years of age. She manifests some of the uncertainties usual in adolescents of that age. An Intelligence Quotient considerably in excess of the statistical mean helps compensate for those gaucheries that occasionally limit her world view. The subject comes from a broken home, her father having proved incapable of retaining the affections of her mother Hattie. It can be assumed that this insecurity explains her choice of "boyfriend," a lumpen young man of considerably lesser IQ, who never-the-less provides a crude supportive friendship.
The present writer is involved with the subject because the subject's mother is about to marry his father. An interesting interaction took place at the "engagement party" that celebrated this upcoming union. The subject and her "boyfriend" were poking about in a reprehensible manner in the present writer's private domains and were "bailed up" by the present writer's faithful hound "Lamb Chop."
When the present writer's father heard of this event and the attendant "bad-feeling" that resulted, he insisted that a reconciliation take place and suggested a meeting on neutral ground—for instance a video arcade. It is a measure of the father's sincerity in this regard that he is prepared to bankroll the whole exercise and has already pressed a number of monetary funds on the present writer.
SUNDAY, 23 APRIL, AFTERNOON
The phone is ringing while I'm fumbling with the key. I think it must be Rod so I fumble harder. The phone keeps pulsing away behind the front door. I get it open and pounce on the phone.
"Rod?" I say, "Is that you?"
"Um, no," says a different voice, "I am afraid it's only me."
For a moment I'm completely confused. I know the voice but I can't picture its owner. Then I suddenly know only too well. "Oh, it's you, is it?" I say, quite coldly.
"Well, I'm sorry I'm not Rod," Tristan says. "Rod must be some hunk."
"Drop dead."
"Charming," Tristan says.
"Look, what is this? Have you just rung me up to tell me I'm charming? Because if you have—"
"Don't be like that, Jenny. We are going to be brother and sister, so we might as well learn to get along together."
"I don't see why. And as for this brother-sister thing, I believe it's got something to do with having the same parents, not just having a mother who's run away from home and shacked up with some no-hoper. Even if they do get engaged in some stupid ceremony with a lot of dead rose petals and people getting drunk all over the garden...." And then I'm crying. I simply can't believe it, but it's happening. I'm on the phone crying to Tristan.
"I know it hurts, Jenny," Tristan says. "It hurts me too. There's no point in fighting."
He's right, actually, but I still feel angry and upset. I stop crying and say, "Yeah, well, all right. Anyway, why did you ring me up? I don't think we've got anything to say to each other."
"Well, maybe we haven't. But we don't know that until we've talked to each other."
"We're talking now, aren't we?"
"I think we should meet somewhere. There are limits to what you can say on the phone."
But in fact we talk some more on the phone and I start to feel a bit less angry and then Tristan suggests we meet at the Time Zone arcade in the city. I've never been there. I don't think Poppa would consider it the sort of place I ought to go to. I'm sure he thinks it's full of dope peddlers. Maybe it is—but I wouldn't mind checking it out. I say, "Oh, all right, but I'm bringing a friend."
Tristan says, "Davy? Or Rod?"
I sort of giggle. "I couldn't bring Rod."
"Why not? You seemed eager enough to talk to him just now."
"Yeah," I say, "But he lives in 1960."
There's a moment of baffled silence. "I don't get you."
"It doesn't matter," I say. "I'll meet you at the Arcade tomorrow after school. I'll bring Davy and maybe my friend Maddy. See you."
I go off to the kitchen to grab a bowl of corn flakes. The funny thing is: I feel quite happy. I'm quite looking forward to meeting Tristan again. After I've finished the corn flakes I phone Maddy. She's really pleased at the idea of checking out Tristan, not to mention the Arcade. She's never been there either. Then I ring Davy. He's not so keen on meeting Tristan again, to say the least. But I tell him that Maddy and I are going anyway, so he says he'll come too, just to add a bit of support. Big deal.
MONDAY, 24 APRIL, AFTERNOON
After school, Maddy and Davy and I get the tram into town. Davy starts telling Maddy about Tristan. "He's got these real small piggy eyes," Davy says. "And these glasses made out of the ends of beer bottles. And he wears these ratty jackets with thirty five pens sticking out of the pockets and he's got braces on his teeth made out of paper clips."
"What about his really bright Chinese friends?" Maddy says.
"He hasn't got any friends," Davy says. "They don't even let him in the house. He has to live in the cellar with the dog."
Maddy is giggling and falling about and Davy is enjoying himself and has his arm around my shoulder. I shrug his arm off and say, "He doesn't live down there. That's just his den."
"How do you know?" Davy says.
"There was no bed in there, you dope."
Maddy says, "He probably sleeps on the floor with the dog."
Davy says, "The dog's got braces on its teeth as well, only they're made of barbed wire."
Maddy giggles. I say to Davy, "You weren't being such a smart-arse when the dog bailed you up." I'm getting really cross with my friends. In fact I'm half wishing I'd left them at home and arranged to meet Tristan by myself. I move Davy's hand off my leg. "This is our stop," I say, "and about time too."
"What's eating you?" Davy says. "Fallen for dweeb-head, have you?"
"He's going to be my brother. So shut up."
We jump down onto the road and the tram goes rattling off to St Kilda. Maddy says to Davy: "I bet he's wearing his school uniform."
Davy says, "St. Dweeb's Scottish Academy for Young Nerds."
I'm getting really pissed off with the pair of them. "Just shut up," I yell at them. "Or go away! I'll go and meet Tristan by myself."
"All right, Jenny," Davy says as we are crossing the road to the Arcade. "Lighten up a bit. We're just joking." He puts his arm around my waist but I do a side step and get free.
Maddy just says, "Sorry, Jenny.'
§
There's a security man on the door of the Arcade. A big guy with a huge stomach and a two-way radio hanging off his belt. We slink past him. Inside everything is flashing and techno music is blasting from the speakers. I suddenly realize this is hardly the place to have a conversation with Tristan or anybody else. But maybe that's a good thing—maybe we can sort of get to know each other a bit without too much talking. And given the way Maddy and Davy are carrying on, maybe a no-conversation rule would be a blessing. We're standing there, looking around the Arcade, wondering if Tristan is already here, inside one of the racing cars, perhaps. Or landing on the moon. Suddenly there's a tap on my shoulder and I feel a light kiss on my cheek.
"Hello, Jenny," Tristan says. "I'm glad you made it."
I shoot a quick glance at Davy. He looks like he's ready to start a fight. I don't think he thinks anybody but him is allowed to kiss me.
"Oh hello," I say to Tristan and give him a quick peck on his cheek. He's not wearing all his proper school uniform. He's got an old parachute jump-suit top on that says PROPERTY OF NEW YORK YANKEES on it. You can't see the shirt underneath, but his pants are the uniform pants from hell. At least he's taken his shiny brown school shoes off and put on a decent pair of high tops.
Tristan reaches into a pocket and pulls out a handful of tokens. He says, "Here, my Dad's bankrolling this. It's to make up for Lamb Chop."
"It's all right," I say. My pride is hurt. "We've got the odd dollar between us."
Tristan insists. "You can buy us all an iced coffee later, if you want to. But we might as well use up Dad's money in here."
"Too right," says Davy. "After what that animal did to me."
"It just growled at you," I tell him sharply. "But, okay, we use up Edward's tokens in here and I'm paying for the coffee." I'm not too keen on the idea of accepting Edward bloody Thring's dough, but Tristan has all ready gone and bought the tokens. So we might as well use them up.
I start playing Virtua Fighter with Davy. On another machine, Maddy plays the same thing with Tristan. Davy's too good for me. After a couple of rounds I collapse in a heap. We both wander over to where Maddy and Tristan are still hard at it.
They've attracted a small group of onlookers—boys mainly, all wearing their baseball caps the wrong way round. It would make Poppa freak. Maddy is being Wanda the girl ninja. She's beating the stuffing out of Tristan's character.
On the big screen, Wanda goes twirling through the air, kicking and punching and somersaulting all at once. Maddy's fingers are thrashing the controls like a drum soloist cracking a psycho. Wanda hurtles through space and kicks Tristan's character in the head. The sound is like a thick piece of timber cracking. He goes spinning backwards, smashes flat on the ground. The ground vibrates, and not just on the screen. There's a sound like a train crash as Wanda lands on top of her opponent and stomps his face. She leaps back and stands like a traffic cop with one arm outstretched. She's got her hair in a pony tail but with a red head band covered in Japanese writing. Wanda wears a black bra, baggy pants and big lace-up boots, and I have this sudden strong picture of what Madeleine's next outfit will be.
Tristan rattles his controls and his character comes flying straight off the ground, throws a vicious kick at Wanda, but Wanda is no longer there, Maddy has already dropped her to the ground and rolled her away, cool as a cucumber. Tristan's character kicks air. I cheer. Tristan mutters something and hits his controls even harder. Wanda bounds up and knocks her opponent flat. Tristan goes ape, but it is too late. The screen announces that Wanda is the winner with 5,897,876 more points than her opponent.
They chose new characters and play each other again while Davy and I watch. In this game Maddy is a fire-breathing robot with almost no head. But the lack of brains is no problem. The contest is still hopelessly uneven. Maddy flattens Tristan. I watch Maddy's face as she plays. It's hard to recognize the girl. She's all concentration. Tristan flails around hopelessly. I try to judge what he's thinking, but it is impossible. The game finishes with Maddy winning by more than seven million points.
Tristan shrugs, and turns away from the board. "Let's see who's the better shot." He points at a video machine with a couple of hand guns attached to it.
"Sure," Maddy says.
Davy and I watch from a distance as Tristan and Maddy push through the crowd to the machine. Tristan starts to show Maddy what to do. She positions herself like a telly cop, holding the gun two-handed, pointing at the screen, while Tristan sort of stands close behind her with one arm over her shoulder, showing her some of the finer points to the art of pulling a trigger. With his other hand he waves his own gun around. He says something, his mouth about two centimeters from Maddy's ear. Maddy laughs.
Beside me, Davy says in amazement, "Jeez, Jen, that guy's coming on all heavy with Mad."
I look at him with wide eyes. "No kidding?"
"Do you reckon we should rescue her?"
"Get real, Davy," I say. "Does she look like she wants to be rescued?"
Tristan sticks a token in the machine and the pair of them stand there side by side like two tough but sensitive cops in the Blue, firing at the screen, except this isn't brutal New York, it's desert warfare. Great waves of tanks are careening towards them over hectares of sand dunes. Every time one of the shooters hits a tank, it explodes with a roar. Davy and I shove through, stand just behind Maddy and Tristan. It's a bit hard to tell who's destroying the most tanks just by looking at the fire-fight, but in the top corners of the screen the scores go rolling up.
We wander around the different machines, play a bit more. There's one last epic struggle between Maddy and Tristan, driving racing cars on a dangerous circuit. Maddy loses. Tristan is overjoyed, his face flushed. I'm furious with Maddy, because I suspect she lost on purpose. I'm sure she lost on purpose. She did it just to butter-up Tristan's ego. But I don't say anything.
It's getting dark when we leave the arcade and straggle down the street to a deli with a few tables. Sitting there drinking iced coffee through a straw, it seems to me that the result of this little exercise in reconciliation is a beautiful friendship between Tristan and Maddy. There they are, on the other side of the table from me and Davy, slurping away through their straws with their shoulders almost touching. They're doing a move-by-move analysis of one of the games they've just played.
You could put the pair of them in a couple of matching blazers and put them on telly. If it was football they were discussing rather than Virtua Fighter, they'd be just right for Football Inquest or Match of the Day. Davy tries to talk to me about the games we played, but I can't remember them. I like playing computer games every now and then. But afterwards they're just a blur. They're not something you need to discuss. So I try to get a conversation going about something interesting.
"Have you ever taken Lamb Chop to an obedience school?" I say to Tristan. He doesn't answer, he just keeps on yakking to Maddy. "Hey! Tristan, about your dog," I say a bit louder, "have you thought of getting him trained?"
"He is trained," Tristan says without taking his eyes off Maddy. She was looking at him, too.
"Trained to kill," Davy says with feeling.
"Only on command," says Tristan. "Would you like to meet my dog?" he says to Maddy.
"I'm told it's got barbed wire teeth," Maddy says.
"It's as meek as a lamb...."
"...Chop!" says Davy, making a karate chop with his hand.
For Davy, this is a pretty good joke. I laugh and lean on his shoulder a bit. Davy lets his arm slide round my waist and under my sweater. I let him keep it there, on my bare skin, for at least ten seconds. Over the other side of the table Maddy and Tristan have started to discuss their favorite films. I groan inwardly. When people start to discuss movies like that, they usually end up going to see one together. I get the impression me and Davy aren't going to be invited to go along too.
§
On the tram home, I say to Maddy, "Get his number?"
"What number?"
"Tristan's telephone number, you idiot."
"Jeez," Davy says, "what would Mad want with Dweeb-head's phone number?" He can be a bit thick at times, Davy.
Maddy blushes. She doesn't usually blush, my friend Maddy, but she does now. "He said to get it off you," she says.
"Haven't got it," I say. "And it's not in the book. You'll never see him again."
"Yes you have, Jen," says Davy. "It's the number you use to ring up your Mum now she's moved in." Davy is a big help at times. Suddenly I'm reminded that Mum is now living in the same house as Edward Thring. She's living in the same house as Tristan. When Mum gets up in the morning, it's Tristan she has breakfast with. Not me. It's Tristan she sees off to school. Not me. Suddenly I feel angry at Tristan and Maddy. I don't feel like teasing Maddy anymore. I sit there on the rocking, clattering tram wishing I'd never agreed to Tristan's big reconciliation scene. All that happens is Tristan and Maddy start behaving like soggy biscuits and I end up feeling miserable about Mum. Davy puts his arm round me. I lean on his shoulder and close my eyes.
WEDNESDAY, 26 APRIL, AFTERNOON
When Rod finally "retrieves the resonance envelope" and gets through to me again, I hit him straight off with my great new theory of what to do with time travel by phone and how to make pots of money without damaging his system. Even though Mrs. Levine was a complete washout, I've been figuring this out for more than two weeks, including the Easter school break. Rod's not impressed, though, and I try hard to work out why he doesn't think my plan would work.
"So you figure even if I gave you all last Saturday's Lotto numbers it wouldn't mean a thing, because I'm living in a future where you didn't win?"
"No, that's not the problem," he says wearily. "Look, suppose time is actually very conservative—" He pauses, lost for words.
"You mean it's always locked on to pretty much the same track?"
"Exactly. Maybe time has immense inertia, like a massive boulder that's thundering down a hill. Once it starts, it's very hard to stop. You can't even divert its path without applying a huge sideways force. And if you stand in the way, you'll just get crushed."
"You mean we can't change what's going to happen? That's a horrible idea!"
"I agree," Rod says bleakly. "It's even got a name—'predestination.' But that's not quite it. Here's a better way to picture it: suppose time is like a vast elastic band. You can deform it, even stretch it a bit, but sooner or later it's going to bounce back to where it was. And crush you like a bug."
I'm horrified by all this doom and gloom and bug-crushing. "Look, lighten up, Rod. That's just a theory, isn't it? We'll never know unless we try it."
He sighs. "Okay, you give me the winner of the Melbourne Cup for 1960, which is going to be run in about a month from now. I place a bet on it. What happens?"
"You win a fortune and go to New York." And, I think happily, I take half.
"No, I've worked this through carefully. Even if some long-shot wins at 100 to one, I can't win a million quid without putting down ten thousand pounds. How can I get my hands on that sort of money?"
"All right." It doesn't seem such a lot, but I suppose there's inflation. And anyway lots of people run up huge debts. Couldn't he harass his bank manager or something? "What about this? I could tell you the Melbourne Cup winners for ten years. Then you just keep putting your winnings back on each time. Wouldn't that grow by compound interest or whatever it's called without anyone noticing?"
"Forget the Melbourne Cup. There are races every week." Rod doesn't sound as enthusiastic as I'd expected.
"I'll help," I tell him. "I could probably research the results in the State Library where they keep all the old newspapers. Or just use a search engine of Dad's computer—although he hates me touching it."
"Your father has a computer? Oh, you mean at work."
"No, here at home. I keep asking him to get me one, but he says it will stunt my mental growth."
Another one of those pauses. "Okay. Forget I asked. But anyway, look. I start off betting ten pounds, say, or 100 pounds. Hell, I'll get a double mortgage and put a thousand down. You're right, it wouldn't take all that long to build up a decent stake. But Jenny, then what?"
Huh? "You're incredibly rich and you send half to me," I say, shaking my head at his slowness, "and you go off to New York so your name isn't in the book."
"Jenny, I'd be in all the papers. Believe me. The fabulous gambler who never goes wrong. The mysterious punter with the Italian surname. They'd arrest me for mopery and dopery. Gangsters who fix horse races would bump me off in the dark of the night. You would already know my name for sure, kiddo. Famous mysterious Mafia victim of the early nineteen-sixties."
"But that didn't happen. As far as I know." But after all, it would've been years ago. How many dead gangsters do I know of? Or victims.
"Precisely. Why not? Because it didn't work. Or I didn't do it."
"You were smarter than that," I suggest, thinking fast. "You got all your friends to place the bets for you. You set up a company to do it. You waited until Lotto started up and made a fortune in one go during a Golden Lotto draw."
"What is this Lotto you keep talking about?"
I've never bought a ticket, because Poppa says the odds are ludicrous and who am I to disagree with an economist who has all the official results in a official State government computer file? Maddy lives for the Saturday draw, but she's never even won a minor division. "You tell them which six numbers out of forty-five. If you get a first division prize, you win millions. Well, unless twenty other people share it that week."
"Hmm." The line hums distantly while he muses. "Same problem. Why haven't I been heard of? Or have I?"
"No. I checked. Unless you won under another name."
"You checked?"
"This is Miss Smarty Pants here, Rod. Poppa did some sort of audit for the government a while back so he has all the official records in his desktop computer. I sneaked a look this morning. He doesn't know I know his password. No Gianforte."
"I knew it. I really knew it." He doesn't sound very happy at being right all the time. "It's built into the theory. I was just trying to hide the grim truth from myself."
"What grim truth? You don't know we can't use this thing."
"'We'? You're getting awfully pushy suddenly."
I smirk, but he can't see through the phone. "So sorry. I'll just hang up and let you get back to your—"
"Don't hang up! If you had any idea what I have to go through to get this system into resonance...."
"My ear is getting sore." But of course I don't hang up. I'd rather die at this point. I'm starting to get worried that Poppa will march in and trip over my legs and make me hang up.
"Can you check for Dr. McReady's number?"
"He's not in the book either." Of course that was the second thing I searched for, after his own name. "But look, Rod, if I give you this address, you could leave a message for me, something with your own 1995 address."
"No, no, no. Don't you see? That's the basic paradox. We don't know how much information can be sent back and forth through time without compromising the resonance. If I know the exact address where you live, I might inadvertently do something in the next twenty-five years that prevents your family from living there. Even knowing your phone number might destroy the—"
"You have my number. How else could you ring this phone?"
"Oh Jenny, it's so complicated. I don't have your number. That's not how this thing works. See, the mathematics of electromagnetism gives two solutions to each equation, what we call the 'retarded' wave and the 'advanced' wave."
"I'll be the advanced wave. You can be the retarded one."
"Ha ha. In physics it's the other way round. Look, toss a pebble into a pool—"
"I'd get the carpet wet." I stand up and wiggle my toes. It's quite dark outside now.
"There's a splash. The ripples go out to the edge. Then they bounce off the sides of the pool and flow inwards. Think of the inwards ripples as going backwards in time. They're 'advanced' waves."
Suddenly I see it! It's beautiful, like a moiré laser experiment. "And you get interference patterns where they meet? Pretty crisscrosses."
"Right."
"Like holograms."
"Like what?"
"Three-dimensional pictures. You use the interference patterns of laser light—"
"I don't think I want to hear this. It makes me feel like a caveman peering through a crack at an atomic pile."
"A what?"
He's incredulous. "You don't have atomic power anymore?"
"Oh. A nuclear reactor?"
"Nuclear reactions are what happen inside a pile, so I suppose so."
"We don't use power reactors in Australia. There's too much radioactive waste, and they're way too dangerous. Didn't they know that in your time?"
"No, sweetheart," Rod says sadly, "there's a lot we don't know in my time."
SATURDAY, 29 APRIL, AFTERNOON
I get off the tram and make my way to Tristan's house. This will be the first time I've been alone with him. Mum and Edward have gone away for the weekend, they've booked themselves into an old done-up, deconsecrated church in the bush. You get to stay in this church and eat and drink and sleep and listen to the bell-birds and apparently you become spiritually renewed. Tristan is all by himself for two days. Mum said on the phone that he'd insisted he was old enough to look after himself. I suppose he is. I'm not sure what to expect from my visit. I don't any longer think that Tristan's the nerd he makes himself out to be in company. I'm interested to see if I can talk to him by myself. When he answers the doorbell, it seems he's surprised I'm alone.
"Where's Maddy?" he asks, a bit grumpily.
"I don't go everywhere with Maddy," I say. "I am allowed out by myself sometimes.
"Oh, I just thought Maddy was coming too."
"Well, she isn't. I didn't ask her."
"Oh, well, come in then."
We go into the house, but I say, "Let's keep Lamb Chop company."
"Why? He's around somewhere."
"I thought he lived under the house. In that room."
"He was only in there because of the party. Normally he just roams around."
"Well, let's go down to your room, anyway."
"That's my private space."
"Yeah, I know," I say, "that's why I want to go down there. It will make getting to know you easier."
"Nobody but me normally goes down there."
"Well, if I'm meant to be your new sister, I think you'd better show me your den properly. Without Lamb Chop trying to eat me."
"It was Davy he didn't like."
"Yeah, well, whatever. Let's go and check the place out."
When we get to the downstairs room, Tristan unlocks it with a old fashioned key and we enter the gloom. The gloom is dimly lit by the computer screen, which is now infested with fish slowly swimming around and eating each other.
"Don't you ever turn that thing off?" I ask.
"It's bad for computers to be turned on and off all the time. It's much better to just let them run."
Tristan sits in the chair in front of the computer. He swivels it to face me. There is no other chair in the room, so I move a pile of books off the top of a big wooden box and sit on it. It's one of those huge wooden boxes with metal fittings at the corners and a fancy wrought iron lock.
"What do you keep in here?" I ask.
"Magic," Tristan says.
"Like hard boiled eggs?"
"That sort of thing," Tristan agrees, cagily.
"What else?" I ask.
"Severed limbs," Tristan says. "Bits of bodies."
"Yuk. Show me."
"Not now," Tristan says. "You'd freak. I'll show you sometime, though."
"Oh yeah."
We sit there in the semi-darkness for a couple of minutes. We don't say anything, but there's no strain. Then I say, "Are all these books yours?"
"They are now." Tristan gets up and starts flicking through them. "Most of them used to belong to my grandfather. He was a famous psychoanalyst. I'm going to be one myself after I qualify in medicine."
"A shrink?" I say, incredulously. "You're going to be a shrink?"
"I wouldn't use that word. I find it rather silly. All the really great mysteries are in the mind. I often read Grandfather's old books. I've learnt lots from them. After I qualify as a doctor I'll have a head-start on the other trainee psychiatrists because of my reading."
"Most shrinks are madder than their patients," I tell him. "It's a well-known fact."
"That's just popular opinion. It's a defense mechanism. People don't like the idea that other people can see into their minds."
"Can you see into mine?"
"It would be unprofessional to tell you."
"Tell me what?"
"What is going on in your mind," Tristan says. He is getting quite agitated, but I feel I'm getting to see a side of him that he normally keeps hidden. He goes on, "You might not be able to handle the insight. Freud warned against wild analysis...that's when—"
"It's when some poor shrink's brain gets overheated and he starts making up stories. You're better off making up real stories. Proper novels and plays and poetry," I say. "I've been thinking of writing a science fiction story myself."
"What about?"
"Oh, telephones and all that. The past." I know it sounds a bit silly saying this, but probably not as silly as if I started to talk about Rod Gianforte straight out. I'd just be giving Tristan ammunition for his crazy psychiatric theories. Anyway, Tristan doesn't seem to think I'm silly.
"Tell me about this story," he says, all very calm and reasonable. Like a psychiatrist on telly, actually. Except that they usually turn out to have murdered their beautiful patients and taken to dressing up in their high heels.
"Well," I say, "in my story, the one I'm working on, I haven't actually written anything down yet, well, there's this guy who rings up from the past. Like there's this girl and the telephone rings and the caller is in another time."
"When? The Middle Ages? The Age of the Enlightenment?"
"Don't be a twit," I say. "They didn't have phones in those days."
"Well, maybe the caller could be talking into a magic conch shell or something like that and—"
"No. The caller is talking on a normal telephone. Only he's in 1960."
"That's too boring, Jenny. Hardly any time ago at all. Besides, my Dad says the early nineteen-sixties were very boring years. It didn't start to get controversial until about 1967. Why don't you put the caller on another planet and have—"
"Look, Tristan, this is my story. And the caller is in 1960. And he's in Sydney, okay?"
"All right. All right. I was only trying to be helpful."
"Yes. Well. Thanks. But Rod, this guy on the other end of the telephone, calls me up...calls up the girl in my story...and he tells her—"
I'm sitting in Tristan's bunker describing Rod and the telephone and he is listening in an interested sort of way. He doesn't make any more suggestions. I think he realizes that this is my story and I'm not looking for editorial help. It occurs to me as I'm talking to him that I'm beginning to like him a bit more. I mean, he is listening to me, which is a bit more than I could expect Davy or Mum or even Poppa to do.
When I finish my "story," Tristan asks, "How does it all end?"
"I don't know," I say. "We'll have to wait and see."
"I'll have to wait and see," Tristan says. "You can end it any way you want to."
"Yeah," I say without conviction, "I suppose I can."
There is a moment's silence. I decide to tell Tristan that it isn't really a "story," that it's real. Before I can speak, he says, "Anyway, tell me about Maddy."
"What's Maddy got to do with anything?"
"She's your best friend. So tell me about her. We're meant to be getting to know each other, so we'd better know about each other's friends."
He's right, of course. But at the moment I don't really want to talk about Maddy. Still, I suppose I ought to be polite, so I tell him a thing or two. I tell him about how Maddy isn't all that good at school work. I tell him that Maddy used to have a boyfriend called Jem, but he ditched her for an air-head called Bo which is short for Bimbo. Tristan listens intently, probably more intently than when he was listening to my story.
"Maddy's got beautiful eyes," he says.
I nearly die laughing. Tristan is annoyed.
"What's so funny?" he asks me.
"They're just ordinary old eyes, Tristan. You know: pupil, iris, cornea, cataract, eye lashes, focal point, contact lenses, bloodshot veins...."
"That's not funny, Jenny."
"Are you sure it's not her tits?" I say sarcastically. "I think what you really think is beautiful about Maddy is—"
I don't get to finish my sentence. Tristan leaps out of his chair and stands glowering at me. It looks like he is going to chuck a real mental. Even in the bad light of the bunker I can see that his face is all red.
"All right, Tristan," I say. "Only joking. Keep your wool on."
Slowly Tristan sits down again. The poor kid. He's in love with Maddy. Well, I suppose things could be worse, my new brother in love with my best friend.
After a bit more chat about nothing very important, I say I've got to go.
"I'll walk with you to the tram."
"That'd be good. Listen, why don't we all go skating next weekend?"
"Who, you and me and Davy?"
I wait a moment to tease him. "And Maddy."
Tristan shrugs. "Fine. Call me with the details."
When the tram comes, I'm half way up when I turn around. "I'll give your love to Maddy," I yell at Tristan, "You know, the one with the great tits...." But this time he doesn't blush.
"I know," Tristan yells from the curb.
The tram driver looks at me as if I'm a delinquent. He probably thinks I'm carrying a spray can. "No, it's true," I say to the tram driver, showing him my ticket. "My friend Maddy has perfect breasts."
"Just sit down, girlie," says the driver and starts the tram. I sit looking out of the window at all the nice houses and silly boutiques as they pass. When the tram finally rattles over the bridge, I look down on the muddy waters of the Yarra and suddenly think to myself that I'm completely happy. I'm probably happier than I've been at any time since Mum left home.
TRISTAN'S CASEBOOK: April 29
The subject paid the present writer a visit. During the course of the interview she managed to contrive a fictional account of a series of telephone calls from someone in the past. It is obviously no accident that the caller from the past is represented as an older man. One feels that this man—to whom, no doubt significantly, she gave the name "Rod"—represents an idealized version of her inadequate father (who, we must remember, has proved himself wholly incapable of retaining the affections of his wife; the poor woman having been forced to seek the companionship of the present writer's own father). All attempts by the present writer to convince the subject that she should provide her "story" with a definitive ending failed. She became confused and evasive when asked to do so. The present writer interprets this inability to bring things to a proper conclusion as evidence of the subject's ambivalence in regard to her father.
The subject's relations with her girlfriend, the delightful Madeleine, are also a matter for some concern. When asked why she hadn't brought her friend with her, the subject became quite aggressive. That an enquiry as eminently reasonable as this one should produce such a reaction can only be seen as evidence of acute insecurity. Although the subject eventually relented slightly and talked about her friend Madeleine, it was only to make slighting remarks about her exam results. As she took her leave of the present writer, the subject went so far as to conjecture that the present writer's interest in the charming Madeleine—with whom an afternoon of skating is to be arranged—was the result of an infantile infatuation with certain parts of her anatomy. One can only think of the common phrase: "sour grapes."
SUNDAY, 30 APRIL, AFTERNOON
We stand around outside the Ice Arena waiting for Tristan. Maddy and I have been here before, but Davy has only ever used roller blades. He says he thinks ice skating is for English dorks in silly frocks. I think he's seen too much Torvil and Dean on the telly. He's being a bit silly if he thinks the scene inside the Ice Arena is going to be like that, but I don't say anything.
Davy mutters, "I hope Dweeb-Head doesn't try anything stupid. It would be a total bummer if we had to spend the afternoon carting him off to casualty."
I say, "Stop calling Tristan that."
Davy is surprised and offended. "You used to call him that yourself."
"Yeah, well I've changed."
"I don't know about you, Jenny."
"Oh do shut up, you two," Maddy says. "Here he comes now." and there's Tristan walking towards us with a tote bag swinging in his right hand. I wonder if he is going to give me a quick kiss like he did in the Time Zone Arcade. I half wish he would, just to get up Davy's nose. But he doesn't.
"Hello, Maddy," he says. "Nice to see you." It actually looks as if it's Maddy he wants to kiss, but doesn't quite dare to.
"Hello," says Maddy, suddenly all smiles. I feel a rush of jealousy, but don't want to admit it.
"Come on," Davy says. "We can't stand around all day."
We pay our money at the cash register and the girl says, "Skate hire?"
"Yes," I say.
"Not for me," Tristan says and waves his tote bag merrily at the girl. The bag is quite heavy. He's got his own skates in it. The rest of us pay $1.50 extra and the girl gives us little plastic tokens.
While we are at the counter exchanging the tokens for skates Davy says, "Oh God, he's got little bed-socks for them." I glance across to where Tristan is sitting on a bench putting on his skates. His skates are brilliant black and gold. You can't see the blades because they've got these pink protective plastic covers. Tristan slips the covers off, and the blades are very bright stainless steel, as if they've never seen the ice.
"These should do youse," says the boy at the skate counter and dumps a pile of scuffed blue plastic hire skates in front of us. "If they don't fit, give us a yell and I'll get youse a new pair."
We sit on the bench next to Tristan and start taking off our shoes. Bad pop music is being played too loud, but it grinds to a halt and the DJ starts on about a cheerio to all the Kevins on the ice. A couple of girls further down the bench giggle. Tristan has just taken off the crappiest pair of old Dunlop Volleys I've ever seen. Both shoes have holes over the big toes and the laces are broken and tied together again. They are the color of dish-water. Davy sees them as well.
"Nice shoes," Davy says.
"You want to wear old shoes to the ice," Tristan says. "Then no one will steal them."
"I'd reckon," says Davy.
"We've hired a locker," says Maddy.
"It's all right," says Tristan, and pushes his crappy old shoes under the bench.
"No, really," says Maddy, "you can put your shoes in our locker."
"Phew!" says Davy.
"Oh do grow up," I snap.
In the end we all put our shoes in the locker, stuffing in Tristan's tote bag and the pink blade-preservers as well, then stagger across the rubber matting to the ice. It's not too crowded. The air is as cold as a fridge, but then we are in a fridge. They have to keep the ice from melting. Natch. We all push off from the wooden retaining wall and glide across the ice.
To my surprise, we're not too bad at this. Davy wobbles a bit, but all that roller-blading has left him knowing what to do. We circle around the arena, at first together, then we start to get split up. The other skaters keep cutting across and getting between us. Besides, it's cool to just be on your own for a bit, whirling round, being blasted by the bad rock music.
Davy shoots past me. "Watch this, Jenny," he shouts and does a mad 180. Suddenly he's up in the air and twisting. Then he's gliding backwards. He teeters a bit, regains his balance and collides with this kid in a green bomber jacket. Neither of them falls over.
"Watch it, mate," says the kid.
"Sorry, mate," says Davy.
Then Tristan starts performing, and he's shockingly good. He skates backwards like Davy—but he does it on one leg, sticking the other leg out horizontally behind him. Or perhaps it's in front of him, considering that he is going backwards. Tristan doesn't wobble one little bit. He sails round in a graceful curve and suddenly spins to face forwards again. He zooms away.
"Try-hards," Maddy says, suddenly appearing beside me, "the pair of them." But she sounds secretly impressed to me.
Then Davy and Tristan are racing each other. Tristan is faster, so Davy does a method. Something I've seen him do on roller blades: jumping into the air and catching hold of the skates with his hands. I've only ever seen him do it by jumping off something, like steps or a low concrete wall. But the ice is all flat, there's nothing to jump off. He doesn't get very far into the air and crashes down in a heap. Tristan circles round and offers Davy a hand up. Davy says something I can't catch, but it sounds aggressive to me. He pushes Tristan's hand away and gets to his feet. He shoots off and I lose sight of him.
Minutes later Maddy and I are fooling about trying to skate in unison with our arms round each other's waists. Tristan and Davy flash past. They are deliberately trying to bump one another.
"Heav-vy...," Maddy says.
Next time the boys pass us they are going at top speed. Davy bumps Tristan. Tristan wobbles, regains his balance and manages to get in front of Davy. They collide. Tristan is down on the ice.
Davy's skate goes straight over Tristan's hand, cutting one of his fingers off.
Tristan screams and clutches his maimed hand to his stomach. The severed finger lies on the ice in a small splotch of blood.
I can't believe it. I can't believe what I've just seen. Davy is unaware of what he has done. He keeps skating, disappears into the crowd. But other people have seen what happened. There is a shocked group of skaters around Tristan. His finger lies on the ice—horrible to look at. The severed end is all bloody, with a bit of white bone showing through the red tattered flesh.
Tristan lies on the ice, eyes tightly shut. His injured hand is still held tightly to his stomach. Someone asks him if he is all right. It's the most ridiculous question I've ever heard. A couple of the younger skaters are sobbing and gasping. One little kid is as white as a ghost. Another one looks like he is going to throw up.
Beside me Maddy starts to giggle. She gets completely hysterical.
"Shut up, Maddy," I tell her, aghast. But it's no good. She keeps giggling. Tears are running down her face, ruining her eye makeup. I leave her and go over to Tristan. His face is contorted in pain. I kneel down beside him and put a tentative hand on his shoulder. Before I can say anything to him, he jack-knifes into a sitting position, scrambles to his feet and swoops on his severed finger. Still holding his injured hand to his stomach, he hurtles off after Davy, waving the severed finger in the air with his other hand.
"You bastard!" I hear him yell. "You cut my best finger off."
I think I'm going to be sick. I get to my feet. Maddy is hopelessly hysterical, she's laughing like a drain. I might have to slap her face. That's what you do with hysterical people—it jolts them back to reality. But I just say, "Please shut up, Maddy."
Maddy says through the laughter, "That's better than an egg." She's obviously unhinged. She's making no sense at all.
"Maddy, I'll have to slap your face."
"Oh Gawd," says Maddy. "You believe it! Oh, Jenny, Jenny, you think it's real." She's almost convulsed with laughter.
I look wildly around. The expressions on the faces of the other skaters are a mixture of shock and bewilderment. But some of them are starting to grin. They think it's a joke. Maddy thinks it's a joke. Davy and Tristan come screaming past. Tristan is still holding one hand to his stomach and waving the severed finger around with the other. "You'll pay for this...," he yells.
There's a blur as a big guy, Ice Arena—Staff embroidered on his jacket, takes off in pursuit of Davy and Tristan. It doesn't take him very long to catch the pair of them. He shoves them both towards the exit, holding onto their collars. Tristan takes his hand away from his stomach. There's nothing wrong with his hand: all five fingers are alive and wriggling. Tristan puts the severed finger into his pocket. Just outside the exit, standing on the rubber matting, is a red-haired guy in a suit. He must be the manager, and he doesn't look pleased. I'm not pleased myself. Maddy seems to think life is a total hoot.
"You buy them in joke shops," she says to me. "You know, you can get hideous wounds and fake puke and rubber dog poop."
"It's not funny, Maddy," I snap at her, "I thought it was real."
I look to where the guy in the suit is heavying the two boys. I can't hear what he is saying, but the boys are standing looking down at their skates. The man demands something. Tristan puts his hand in his pocket and produces the severed finger. The man in the suit stands there, contemptuously turning the thing over in his hand. He turns and walks away, taking the finger with him. Davy and Tristan make their way back onto the ice. They look pretty low. Slowly they skate over to Maddy and me.
Davy says to Tristan, "There was no need to call that sleezebag 'Sir' all the time."
"Well, you didn't call him anything. You didn't say anything at all."
"It wasn't my finger," Davy says.
"Wasn't mine either. Look." Tristan displays his hands, wriggling all ten fingers. "You must have cut someone else's finger off. You want to look where you're going."
"I'll bet you don't dare go and get that rubber finger back when we leave," Davy says. "You won't have the guts to go along to the manager's office and say, 'Please Sir, I'm leaving, Sir, can I have my finger back, Sir.' That guy'll take your finger home with him and play tricks on his kids."
"What about your ear?" Tristan says.
"What about my ear?"
Tristan reaches across and pulls something out of Davy's ear. This time it's not an egg. It's another ear—all covered in blood.
Davy slaps his hand up to his ear. And looks foolish for a second. Then he pushes Tristan hard in the chest. "You bum," he says, "you've cut off my best ear." Tristan skates away. Davy zooms off after him. "Give me back my ear," he yells. I see the bouncer in the Staff jacket eyeing the boys coldly.
"Let's pretend we don't know them," I say to Maddy.
"Lighten up, Jenny," Maddy says. "It's like that painter, what's-his-name."
"Van Gogh," I tell her.
"Yeah, him," Maddy says. "He cut off his ear for love. He sent it to his one true love. I saw this video. Maybe the boys love us."
"Help," I say and start skating. Maddy comes up beside me and soon we are skating in unison again, our arms round each others' waists. Maddy, I can feel, is starting to giggle again. Suddenly I am too. "Greater love hath no boy," I say, "than he pull a plastic ear off another boy's face."
"See," Maddy says. "You have got a sense of humor, Jenny. You're just a bit slow."
§
We end up eating hamburgers in a fast food outlet. At least the others are all eating hamburgers. I don't feel like one myself, so I just eat fries out of Davy's paper bucket. It's funny how boys make friends. Tristan and Davy are now the best of mates—all because they both copped an earful from the Ice Arena manager. They fool about, getting more stupid by the minute.
"What about a whole leg?" Davy proposes. "Just lying there on the ice. Cut off at the knee. Or the hip." In a deep and gravelly voice, like a horror movie, he moans: "The Severed Leg."
"It's no joke, you can buy them," Tristan says. "They use them for training ambulance crews. Totally lifelike. But they'd be expensive."
"We could make one," suggests Davy, really getting into it. "We could get some raw meat. You know, a leg of beef or something...."
"And we could dress it up in an old track-suit. With, say, an old skate at one end and then all the meat sticking out of the torn-off top bit."
"We'd need a lot of blood...."
"Easy. Tomato sauce."
"Speaking of which," says Davy, reaching for the ketchup bottle, "have you got any more fingers?"
"Sure," says Tristan, "What do you want? Little finger? Thumb? Finger with wedding ring?"
"Just an ordinary finger," Davy says.
Tristan leans down and rummages in his tote bag. He produces a new plastic finger in its own little pool of plastic blood and passes it over. Davy takes the top bun off his half-eaten hamburger and arranges the severed finger on the meat. It really is a sickening sight. To complete the effect, he picks up the plastic ketchup container, shaped like a red tomato, and squeezes a bit more "blood" onto the finger.
"Gross-out!" shrieks Maddy, like it's the wildest thing she's ever seen.
Davy takes the hamburger over to the counter. The boy behind the counter is wearing a red baseball cap with the fast food outlet's logo on its brim. He can't be much older than me. Fifteen maybe.
"Hey, mate," Davy says. "I think you ought to check the kitchen staff. There's been a bit of an accident."
The kid glances without much interest at the half-eaten hamburger. Then does a double-take. It looks as if he is going to spew straight over the counter. From out in the kitchen, somehow making the whole scene much worse, there's the sudden hiss of somebody squashing more hamburger meat onto the hot plate. Two girls standing by the counter, waiting to order, peer over at where Davy is waving the hamburger about.
"Aw, yuckoh," says one girl.
The other girl goes green, and her cheeks bulge, but she doesn't say anything.
"How much of it did you eat?" says the first girl.
"Most of it," says Davy.
The kid in the baseball hat lurches away from the counter and staggers out into the kitchen. The talkative girl says, "What did it taste like?"
"Real tasty," says Davy. "I think I'll have the rest." He picks the finger off the hamburger and pops it into his mouth. The green girl goes even greener. Her friend lets out a hoot of laughter.
"Far out!" she yells.
Across the table from me, Maddy falls in a giggling heap. Her giggles turn to chokes and gurgles as the hamburger she's eating goes down the wrong way. Tristan starts to thump her on the back with one hand while putting his other arm right round her.
"Maddy, darling," Tristan says, "Don't leave me now. You are too young and fair of face to die!"
He collapses all over Maddy, convulsed by his own wit. Maddy is choking and laughing at the same time. A bit of half-eaten hamburger flies out of her mouth and hits the green-faced girl on the bare leg. The girl squeals and jumps back in horror.
Maddy and Tristan are a gibbering heap. It's the most disgusting scene I've ever witnessed. Over by the counter Davy is standing with his mouth closed over the plastic finger, looking like a goldfish that's swallowed a cat. The kid in the baseball cap comes out of the kitchen accompanied by a big guy of about thirty wearing a dirty apron over a pair of football shorts. His blue singlet leaves his arms bare. His arms are long and hairy and covered in ferocious tats. He takes one look at Davy. He takes one look at Tristan and Maddy. I try to look as if I don't know these people. The big guy raises one arm and points with the greasy stainless steel spatula he's holding. First he points at Davy. Then he points at our table. Davy spits the finger into his hand and holds it up like a trophy.
"You arseholes," the cook says quietly. "Out! Now!"
He points the spatula at the door, and it's obvious that he's very, very angry. Next thing I know I'm halfway out of the door with Maddy. Close behind us surge Tristan and Davy. The last sound I hear before we are all reach the cool night air of the street is the green-faced girl puking like a fire hydrant. We set off down the street at an extremely rapid pace—just in case the guy with the spatula decides to follow us.
"Where do we go now?" Davy says. I get the idea he wants to go some place where he can repeat his trick.
"Madeleine and I are thinking of going to the pictures," says Tristan.
"We are?" says Maddy.
"Aren't we?" asks Tristan.
Maddy giggles and says, "Sure we are."
I say, "I'm going home."
"Jeez, Jen." Davy pulls a face. "You don't have to be home for hours. Let's go to the movies with Mad and Tristan."
"I don't feel like the movies," I tell them. "I feel like going home. You can come too if you like."
"Aw, all right, Jenny." Davy says, "We can watch a video."
"I was thinking of doing my homework. I'll help you with yours too, if you'd like me to."
"Hey, really?" says Davy. He's always trying to get people to help him with his homework. Usually it's me.
"Well, we'll see you party-poopers later," says Maddy. "Come on, Tris."
§
Davy and I walk over to the nearest tram stop. I lean against the safety rail. In the distance I can see Maddy and Tristan walking towards the Cinema Complex. They have their arms around each other's waists.
"Tristan's not a bad guy," Davy says. "For a dweeb."
TRISTAN'S CASEBOOK: April 30
The present writer had an interesting and informative time at an ice skating rink and fast food outlet yesterday. The subject and her lumpen friend were accompanied by their charming companion, Madeleine. After some high jinks on the ice, during which the present writer amused the crowd with witty severed-digit jests, the jolly foursome retired to Harry's Hamburger Heaven where further escapades took place. The lumpen young man showed a surprising ability at employing the severed-digit joke in the novel guise of a hamburger insert. The delightful Madeleine showed her appreciation of these larks in free-spirited and uninhibited merriment. Alas, the same cannot be said for the subject who remained tight-lipped and disapproving throughout. The present writer must confess to feeling a little relieved when the subject took her lumpen friend away to attend to their studies. This left the beautiful Madeleine free to give her undivided attention to the present writer during the viewing of Rogue Cop III at the Cinema Complex. A most pleasant interlude followed the viewing of the film. Madeleine, oh Madeleine, Maddy. Mad mad Madeleine your kisses are sweeter than wine.
The present writer here records and acknowledges his growing infatuation with the subject's friend, Ms. Madeleine Smith.
TUESDAY, 2 MAY, AFTERNOON
Everyone is packing up after physics and I'm keen to get out of the place and go home. It's been a long day. Mrs. Levine comes over to me as everyone's crashing and banging their way out of the room. "Jenny, could we have a little chat?"
"Huh? Sure."
We wander over to her desk and she goes on for a while about resolving vectors, which I know all about anyway. It seems to me that she's just waffling, waiting for everyone else to leave the room. I'm not sure I want this little "chat." A couple of kids are still mucking about with Bunsen burners and Mrs. Levine says to them, "Leave that stuff. I'll put it away later."
This is the first time in my life I've heard a teacher say she'll tidy up after her students. The other kids are pretty amazed as well. They look at each other and shrug and grab their school bags and leave the room. So there's just me and Mrs. Levine. She clears her throat and says, "How is your story coming along?"
Huh? Oh—she means that science fiction "story" I told her I was writing about getting a phone call from the past. When I'd told her, she'd got it all wrong—she'd thought my "story" was really about Mum leaving us and going to live with Edward. I decide I don't want to have any more of this sort of discussion. So I say, "Oh, I've given that up. I'm not writing it any more. All that stuff about changing the past is too difficult."
Mrs. Levine says, "Yes, I think we have to accept that there is nothing we can do about things that have already happened. We just have to work at making the present as satisfactory as possible and plan for the best conceivable future."
Poor woman, she's still on about my home life. I start to bring the interview to a close by telling her that absolutely everything is wonderful at home, when she says, "You've been doing really well at school, Jenny. At least in science."
"Yeah, I know," I say, "I'm crash-hot at science." This is true: I'm extremely good at physics and chemistry. I'm a legend. Mrs. Levine looks just a little taken aback. I think she thinks a bit of false modesty might be appropriate. Then she seems to get a grip on herself—she's meant to be encouraging girls to do science, to have a strong self-image of themselves as scientists. And here I am: Ms. Positive Self-Image herself. So Mrs. Levine says, "Well, I'm glad you are so confident, Jenny."
"Come the final exams, I think I'll top the State."
"Well, you never know, but...."
Suddenly I'm starting to enjoy this little "chat." So I say, "That'll stick it up the Vietnamese."
"Jenny!" Mrs. Levine, shocked, is on firmer ground here. She's not meant to be encouraging ethnic conflict. "I wouldn't have expected that sort of remark from you, of all people!"
Actually the poor thing does look pretty staggered. But to keep the gag going, I say, "Well, they can't be the only ones getting perfect scores every year."
"Jenny, while it is true that many of the top students are Vietnamese, it is also true that they work very hard indeed. If you had come to Australia on a leaky boat...."
"No, Mrs. Levine," I say earnestly, "it's got nothing to do with leaky old boats. It's because they are more intelligent than us. The Vietnamese have got more brains. Well, more brains than most of us. But me, Mrs. Levine, I'm different. I'm a legend. I work very hard too, and I'm as bright as a Vietnamese."
Mrs. Levine can't think of anything to say. I start giggling then, which gives it away. And Mrs. Levine suddenly catches on.
"Jenny!" she says crossly, but she's relieved all the same. "I take it that you are being satirical? I take it that you are sending up what you see as stuffy, middle-class liberal values?"
"Could be," I say, looking at the floor.
"Well, just be careful, my girl. It is very easy to be misunderstood."
"Like you misunderstood my story about telephones working across time," I say.
"How did I misunderstand that?" Mrs. Levine asks, puzzled.
"You thought it was about my home situation. About Mum moving out and getting engaged to that creep."
"Oh, and it isn't?"
"No. It's about what I said it was about: someone in the past ringing up someone in the present."
"Well, it's your story, Jenny. So I suppose you know what it is about." Mrs. Levine looks almost embarrassed. I can tell that she isn't too keen to abandon her theory about my "story." She adds, "But...er.... Anyway, Jenny. Do you mind if I talk to you personally for a minute?"
This is truly weird. The poor thing must be going off her rocker. First she tells a couple of students she'll put their equipment away, then she asks me if I mind if she talks to me—personally. Who ever heard of a teacher asking for permission to talk to you? I'm starting to get worried. I'm also a bit intrigued: I want to know what she's on about.
"Yeah, sure, Mrs. Levine. Feel free to speak."
"Jenny. You used to be so neat," she says and then stops.
"Uh, neat?" She must be talking about my handwriting. "You can still read my homework, can't you?" I say. "Anyway, I print most of it on the computer. Just because I don't write like a primary school kid anymore...."
"No," Mrs. Levine says, cutting in, "I don't mean your handwriting—although that could do with a bit more care and attention. There was a time, Jenny, when you would never have worn jeans like that to school."
She's looking down at my jeans, which do have these ragged cuffs. We're allowed to wear jeans to school, only they have to be "school jeans." The authorities can't get away from the idea that it's their job to make you wear a uniform, but they know they have to be "responsive to the needs and aspirations of today's youth"—so they try to turn proper clothes, like jeans, into a sort of uniform. Except that the type of proper clothes they decide you are allowed to wear are all up the nerd end of the spectrum. The whole thing sucks. When I'd bought the jeans, they had been too long. I was going to take them up properly with the sewing machine. But then I thought, screw it, and I just cut them down to size with a pair of scissors. Now they've got these wicked gross-out cuffs: all frayed.
"That's deliberate, Mrs. Levine. I like them like this."
"Oh, I'm sure you do, Jenny. Tell me, why didn't you iron your shirt?"
I wouldn't have expected this. I really wouldn't have expected anybody as cool as Mrs. Levine to start cracking on about my clothes. I'm about to go into a major fit of quiet sulks but I remember that she asked me if she could speak personally and I've gone and given her permission. So I tell her, "Look, I didn't think it was going to get so hot today. So I ironed the collar and I ironed the cuffs. See, I thought I was going to wear my sweater all day. There's no point in wearing ironed clothes under other clothes. And anyway," I go on, "I'm not the only one. There were a couple of teachers I noticed at lunchtime looking just like me: nice smooth collar and cuffs, all scrumpled in the middle. Look at Mr. Ironside!"
"Some of my colleagues, I admit, are a bit untidy."
"Some of your colleagues, Mrs. Levine, are total bums."
"Jenny! I really can't tolerate—"
"You said you wanted to talk personally. It was you who started on about my clothes."
For a moment Mrs. Levine is silent. I look at her, sitting behind her desk. She really is very pretty. She's my favorite teacher by miles, except that I can't understand why she calls herself "Mrs. Levine" instead of "Dr. Levine', unless it's to save the Principal the embarrassment of not having that sort of qualification. I'm also beginning to think I must be her favorite student. She's wearing this real cool gray silk shirt with a rose embroidered on the tip of one collar. The shirt shows off her boobs nicely. The shirt is very well ironed. She's got a silver chain round her neck. It might have a locket or a cross or something at the lowest point. But the lowest point is hidden by the gray silk. She smiles at me and says, "Look, Jenny, all I really wanted to say was that you can be a good scientist and look neat and tidy at the same time."
"Albert Einstein didn't seem to think so. He didn't even wear socks."
Mrs. Levine laughs.
"That's very good, Jenny. But there's no real need to look like Einstein. It's just that the clothes we wear often reflect our inner selves. You've been looking so...er...dowdy lately that I can't help wondering—"
Mrs. Levine doesn't finish the sentence, but I know what she means: she's worried about me. And maybe I am her favorite student. So I just say, "Not to worry, Mrs. Levine, I'm not going to get an ear-ring through my eyelid."
She shudders. "I hope not. I can't imagine anything more...er...uncomfortable."
"Neither can I," I say as I grab my bag and hit the track. "We agree on the really important issues. See you."
"Good afternoon, Jenny," Mrs. Levine says with a slightly sad note in her voice as I zip out the door. Teachers are weird.
SATURDAY, 6 MAY, AFTERNOON
Tristan phones me after the Science Show and suggests that we go for a bike ride together.
"It's too far for me to ride to Kew," I tell him.
"No, I'll come over to your place by tram."
"How can you take a bike on the tram?"
Tristan laughs. "You great dill, don't you remember? Your mother said I could borrow hers. How about you get it out of the shed and pump up the tires for me, and I'll whiz over right now. We could go down along the Merri creek bike path."
"Won't you be embarrassed, riding a girl's bike?"
"It's a trail bike, your mum said. Who would know the difference?" He sounds a bit exasperated. "Anyway, that's a pretty sexist remark, coming from you. I mean, what's the difference?"
I feel quite nettled by this, because it's a sensitive spot of mine. Usually I'm the one to complain about people making distinctions based on sex and gender when they're irrelevant. "Well, some boys wouldn't, that's all. Some boys are afraid of being laughed at."
He grunts. "Davy might be, I suppose. Surely you've noticed by now that I don't worry what people think of me."
That's true, but I try to wiggle out of it. "I bet you'd feel pretty stupid if you had to wear a dress! Or, I dunno, a pink woolen cardigan."
"You can keep your cardigan," Tristan says. "But I've worn a kilt, and that's like a dress. Anyway, didn't you ever see the clothes Greek soldiers wear when they're feeling sentimental? Little frilly skirts and pom-poms on their boots."
I burst out laughing. He's right—it's in an Encarta history file. Weird. "Okay, come on over. Poppa's at the university, but he'll be back for tea—I'll have to be home by six. Anyway, I don't think we've got any batteries for Mum's bike lights."
Tris is wearing perfectly ordinary clothes when he rings the door bell, which is a relief. I've hauled Mum's old trail bike in from the back yard and cleaned it a bit, plus pumped up its fat tires. Tristan throws one leg over the seat and jigs up and down for a moment.
"Hey, this is just the right height. Thought I might have to adjust it." He digs out a small tool kit from his tote bag, which he's thrown in the wire basket mounted over the back wheel, and waves it at me.
"Always prepared for everything, aren't you, Tristan? You must have been a boy scout."
"Not me," he says disdainfully. "Carlos either. We left that kind of macho nonsense to our big brother Alain."
"Come on." I slam the door behind us. The sun is out and the day is autumny but nice. The air is lovely. "Let's go. There's this place I want to show you."
Rathdowne Street is too busy for good cycling, so I lead Tris down to Canning Street, which also has a green median strip but much less traffic. We pedal without saying much up to Park Street, at the boundary with Brunswick, which is a much poorer suburb. Park turns one-way after a bit, but there's a cute pathway that you can use to get almost all the way to Rushall railway station, which is perched high over the Merri Creek. We're puffing a bit by the time we go down through the creepy underpass beneath the station, and I'm glad Tristan is with me because I always have a little fear that some horrible man will jump out of the shadows and grab me. There's no one there, luckily, except a tiny foreign lady from the old folks' home next to the railway, and she waves happily to us as we get off our bikes and push up the slope to the narrow bridge leading from Carlton to yet another suburb, Northcote. All the suburbs come together at this one point. It's a hub, this place. Four suburbs stretching away in four different directions. Here you can go from one to the other in a few steps. Maybe time works the same way. All you need to do is find the hub and you can step from one time zone to another. Hell, they tell us space and time can't really be separated.
"Space zones," I mutter. "Spacetime zones."
"What?"
"Oh, nothing. It's just, this place reminds me of me and Rod, this guy who—" I stop. The sun doesn't reach the water flowing below us in a deep cutting. "Well, it's in my science fiction story."
Tristan gazes into my eyes like a doctor with a wild new theory. "Wow, you're really obsessing about this story, Jenny. I sometimes get the feeling that you think it's real."
I hesitate for a long moment. I'd love to tell him that it is real, and that it's about to change history, but he'd just think I'm crazy. "Sometimes it feels real," I say. "I've been thinking about it for days. Anyway, it's about these two people in different time zones, this girl now and this old guy in the past. Well, he's not that old, but he is by now." I stop in confusion. "If you see what I mean."
Tristan, to my surprise, is looking rather impressed. "You really are a very interesting person, Jenny Kane. I'm glad we've become friends. I'm even glad we're going to become brother and sister." He grins and looks away shyly. "It's a pity we didn't bring Maddy with us, though."
"Oh, you're the one who's obsessed!" I push him on the shoulder, and get back on my bike. "Come on, let's go across the bridge as fast as we can. It's a real buzz!"
The narrow bridge dips slightly in the middle, and it rattles like a thousand old bones. Down below, vegetation is green and brown, and the water gurgles through rock. My bike's wheels thump and bump.
"Hey, that was great." Tristan jumps off when we reach the far side, and returns to peer into the creek bed. "I love bridges. How did you know?" Beneath his borrowed safety helmet, his face is flushed.
"I didn't. But if you like bridges, you'll love the place we're going next."
You have to zig and zag along the side of the Merri creek before you get to the main street, and eventually there's this big steel bridge that carries the railway lines across the Merri. A Reservoir train rumbles overhead, tremendously noisy, as if the whole world is shaking, as we get off and lock our bikes together to a NO PARKING sign with my fabulous new bike lock. The bridge that spans the Merri is edged by waste land full of bushes and broken stone and rusting old car bodies. I know it's probably even more dangerous than going under the Rushall station underpass, but it's great—a place that's right in the middle of town and yet it looks like a piece of the country, or Mad Max territory, or something.
"You want us to go down there?" Tristan asks. "Doesn't look very interesting. Anyway, there could be snakes, you know."
"There are," I tell him. "There's warning signs. I've never seen one, though." I point to the rock wall of the railway bridge. "Look up there."
"Oh." Tristan's eyes gleam. "Fabulous! A pedestrian walkway!"
"Come on, I'll race you to the middle."
We run up the steps and then belt along this really narrow metal pathway that's hanging suspended under one side of the rails. The barrier to our right is just metal and wire, you can see right through it, and when you run it seems to disappear. It's as if you're running in the sky. The sound is really strange, banging and echoing. We stop halfway across, right over the creek far below. Tristan sucks at his mouth and builds up a huge spitball and lets fly straight down, but the breeze grabs his little drop of gleaming spit and carries it away to the rocks.
"You must be a genius, Jenny," he says. His glasses catch the light of the afternoon sun. "This is exactly what I love."
"Of course I'm a genius," I say modestly, leaning back to stare up at the train tracks. "The really terrific thing is when a train goes over. There should be one any minute—"
I hear, then, from up above me, "Fantastic!" and my blood sort of runs cold. I turn around, and start to scream Tristan's name, and stop myself in the nick of time because I don't want to scare him or throw him off balance, because the bloody idiot has climbed up on to the handrail of the pedestrian walkway and is standing in the sky, one foot behind the other, arms outstretched like a circus acrobat.
He takes one step, foot out into space, then back in front. And another step.
My heart literally stops.
It starts again, with a bang surely loud enough to scare Tristan off his perch. But in fact I'm the only one who hears it. Tristan is singing! Tristan is cavorting along in the pale light, swaying slightly, twenty or forty meters above a cold brown creek and smashed rocks and hard tree branches, and the idiot is humming and crooning to himself like a happy child with a brand new Christmas present!
"Tristan!" I try to say, but nothing comes out. My throat is totally dry. For the first time in my life, I'm actually, literally terrified. I haven't got a clue what to say to get him down. Out of my mouth come words that seem to appear from nowhere:
"I'm starving."
Tristan looks down at me, over his shoulder, and sways slightly. I go rigid with terror.
"Me too," he says amiably, and reaches into his shirt pocket. "Luckily, I have a Mars Bar." He pulls it out, tears the foil open with his teeth.
"Tristan, please come down," I wheeze in a tiny voice.
"Can't hear you, why don't you hop up here with me, the view's terrific."
At first I think it's my heart pounding like a machine in my chest, but it's not, it's an electric train rumbling toward us around the curve of the track from the northern stations, thumping and thundering toward the bridge. I press myself back against a steel stanchion and try not to scream. Tristan swivels on one foot and spins in midair, standing now on the aerobic heels of his hightops with his back to the endless fall behind him, staring up toward the approaching train. Its yellow headlights reflect from his glasses. I wonder if I'll have the slightest chance of rushing forward with my hand outstretched when he slips and tumbles into the gulf.
"I'm glad you've got a Mars Bar," I squawk. "But what about me? I said I was hungry first."
"You can have it," Tristan yells through the roar of the train. Lights from its windows flash and shadow, flash and shadow as it crashes above us. Everything shakes. "I've got a little treat of my own." Tristan reaches into his ear, pulls out an egg, crouches down on his haunches, whacks the egg on the vibrating handrail under his feet, breaks it open, scattering shell everywhere, pops the cold boiled egg into his mouth, and tosses the Mars Bar to me. I put out my numb hand. Too late. The confection sails through my grasp, hits the metal grid under my equally numb feet, bounces once, sails through a wire gap into the open sky. Horrified, I watch its dark chocolate tumble away in the vague light.
I can't stand up any longer. My legs give way, and I subside on to the cold metal surface. It's painted white, but the paint is crackled from the weather. Tristan, whose right cheek is bulging with boiled egg, looks at me with stricken eyes. He chews hard, once, twice, and swallows the egg. Then he jumps down lightly on to the pedestrian bridge, and grabs my hand.
"Jenny, are you all right?"
Angrily, I shake him off. "You bloody idiot!"
"Look, I'm sorry, okay?"
"You could have been killed." There are tears in my eyes. "Come on, we've got to get back, it's getting late, Poppa will be furious."
"It's not that late," Tris says sulkily. "Anyway, it wasn't dangerous, I've been doing it for years." He tries to grin at me, and it's not very convincing. "You should have seen your face!"
I stomp back along the bridge and down the metal stairs at the end and unlock the bikes and push mine on to the street, flicking on the headlight and the blinking red tail light. "You scared me, you stupid thing."
"Jenny." When I look around, he's just standing there, looking downcast, hands in his pockets. His voice is dejected. "Hang on a bit. I want to explain."
"You don't have to explain it to me, I'm just the cowardly girl you just got a thrill out of by scaring her half out of her mind." But I wait, holding the handlebars, until he lifts his eyes and meets my gaze.
"You're not cowardly, Jenny," he says, "and you're not half out of your mind. I was, though, a few years ago." He stops, and I can see him screwing up his courage, so I give him a little smile of encouragement. It's hard to stay angry at Tristan.
"What, literally out of your mind?"
"That's right. Literally. I'm still seeing a shrink, you know."
"A psychiatrist?"
"A Freudian psychoanalyst, actually. Twice a week."
I stare at him. "Is that why you're so interested in all that mental stuff? In your diary."
Tristan gives me a very suspicious look, then shrugs. "My CASEBOOK. Partly. As I said the other day, it's part of my family background—but yeah, I suppose it's transference."
"What's that?"
"Never mind." He pushes his bike into the grass to let a young yuppie couple jog past with their German Pointers, and then props it on its fold-down leg. He digs into his tote bag and pulls out another Mars Bar. "Go you halves."
"Okay." I prop my own bike, and we sit down on a patch of short grass. Another train clanks past overhead, this one coming home from the city. People are silhouetted in the windows, staring out into the early twilight, reading newspapers, talking or just sitting.
"I sort of went mad for a couple of years after my mother killed herself," Tristan tells me.
My skin goes cold all over. Suicide! This really is freaky. It's nothing like having your mum go and live with someone else. I mean: I've still got Mum, even if I don't live with her. Tristan's mother has left him forever.
"Sorry," I stammer, "I didn't know."
"That's all right," Tristan says. "I'm over it now. Well, sort of."
"Look, if you go fooling around on bridges like that, you can't be all that...er...."
"Sane?"
"Well, er," I say, searching for the right word, "you know, stable."
"Oh, I'm very stable, Jenny. You saw me, I didn't fall off."
"I don't mean that sort of stable."
"Oh, I see, you mean stable!" Very seriously, like a worried teacher, Tristan says, "I'm not a horse, Jenny."
"I don't mean...," I start to say, but Tristan suddenly packs up. "You bum!" I yell at him, "you just love playing word games, don't you? You knew what I meant."
And then both of us are lying next to our bikes on the grass and all the discarded cigarette packets and the dried lumps of dog poop, convulsed. It seems to be the funniest thing either of us has ever heard. We're lying there laughing and crying and spluttering words like horse and stable and cracked and oats. I know that these words really aren't all that funny—but it's just the relief. After being scared out of my wits and then learning that Tristan's Mum committed suicide, it's good to able to laugh at something ridiculous.
"Look, we'd better go home," I say at last. "You can tell me about this psychoanalyst on the way."
We get back on our bikes and start home. The sun's definitely getting low and red in the sky, and the wind is rather cold. Tristan is silent for a while and then he says, "After Mum died, I went quite loopy. I sort of, you know, crawled away inside myself. I didn't want to know about the outside world. I didn't like it. I'm still a bit like that. That's why I go and see Dr. Grogan twice a week."
I'm not sure if I should say anything, so I don't. Tristan goes on, "When Mum died I started having all these fantasies. I'd make up stories about myself. And I'd believe them."
"We all do that," I say with a shrug that makes my bike bell tingle. "Everybody makes up stories about themselves."
"Yeah, but I really believed mine," Tristan says. "I didn't know where my mind stopped and the real world began. In my mind I was a super-hero, I could do anything. Fly, almost. I nearly tried it a couple of times."
"Flying?"
"Yeah, like off a building or a high cliff."
"But you didn't?" I say.
He shoots me a sarcastic glance. "Well, no, as you see I'm still in one piece."
I can be just as sarcastic back. "No, you just dance around on bridges."
"Yeah," Tristan says, "that was a bit silly wasn't it?"
"It was bloody madness."
"See, it's just that sometimes I feel completely invincible. Nothing can happen to me. I am in total control. If I say I won't fall off the bridge, then I won't."
"One day you might," I say.
"I hope not. Part of me knows that doing things like that is just dumbo, real stupid, destructive. But when I'm doing it, I'm such a super-hero that the other part of me takes over completely."
We pedal along the bike path in silence for a while. Then Tristan says, "I'm like that about people as well."
"What do you mean?" I say, "about people...?"
"I feel superior to everyone. I can see inside their minds. I can look down from a great height and watch everybody scurrying around like ants. They think they're free and independent—but really I understand them better than they understand themselves. They've got no free will."
"Is that what your CASEBOOK is all about?" I ask.
Tristan goes ballistic this time. "Look, how did you find out about my CASEBOOK?" he yells.
"Take it easy, Tristan," I say. "You'll fall off your bike."
"No one's meant to know about my CASEBOOK, it's mine. It's private."
"Maybe you're the ant," I suggest, feeling rather clumsy and nervous but not wanting to admit it, "and I'm looking down from a great height on you and seeing everything that goes on in your mind."
But Tristan is right off his rocker. I'm really sorry now that I teased him like that, but it's too late for regrets.
"You can't!" he shouts like a loon. "You're lying, Jenny! Nobody sees inside my mind. Even Dr. Grogan can't see inside my mind. She only knows what I choose to tell her."
"It's all right, Tristan," I say, getting off and pushing my bike up on to the Rathdowne St footpath. "Take a chill pill. I don't really know what's in your CASEBOOK. I just saw a little bit of it. Remember? When Davy and me were being monstered by your dog. I shouldn't have done it, but I did. Sorry."
We've arrived outside our front door. Without saying anything we push our bikes into the hallway. It will be terrible if Tristan goes home still angry with me, so I force myself to say, "Come in the kitchen, why don't you eat with us? Poppa won't be home for another half hour, but I've got to start cooking."
For a moment it looks as if Tristan is going to refuse my offer. He's never met Poppa, but he has to, sometime. Instead of refusing, to my surprise, he takes off his jacket and says, "Sure, why not?" We go into the kitchen and I organize him into making chocolate thickshakes in the blender while I peel some spuds. When he's finished flailing the thickshake mixture to an aerated sludge, he says, "Anyway, I'm not really very proud of what I write in my CASEBOOK. I don't treat people very nicely. I've written some stuff about you, Jenny. It's sort of true, but it's all, you know, cold."
"So why do you write it?" I ask.
"Sometimes, when I'm feeling angry or insecure or something, then it makes me feel better. But it's just fantasy. It's just a way of making myself feel powerful. It's like the fantasy of flying, of being invincible." He brings the thickshake over to where I'm standing at the sink and sits on the kitchen bench next to me. He says, "When I'm alone and thinking about the way your Mum has taken the place of my Mum, then sometimes I get angry with you, Jenny. I know it's got nothing to do with you. But just knowing something like that doesn't always help. Then I write in my CASEBOOK: cold stuff about you and your Mum."
Tristan is silent for a while, staring into his thickshake as if all the answers to all the questions in the universe are to be found in a glass of chocolate milk. Then he says, "When I'm with you, Jenny—like now—I don't feel that way at all. I feel ashamed of what I've written. You're, you know, warm and human."
"Thanks," I say, feeling uncomfortable but pleased.
"But you get these fantasies too, Jenny."
"Well, not quite like yours," I say sharply.
"That story you were telling me—the one about the guy calling you from another time. That's the same sort of thing. It's a fantasy about having secret friends, about power, about controlling the present and the past."
"Crap," I say. A bit of potato flies across the room.
"It is, Jenny. I've read lots of books about this sort of thing. I discussed it endlessly with Dr. Grogan—you know, my analyst, my shrink as you'd call her. There's nothing wrong with having fantasies—but you've got to learn from them. You've got to face the real-life problems that the fantasies are compensating for—"
"That's a load of crap, Tristan. I'm sorry to tell you this, but you're raving."
"Jenny," he says patiently, "believe me, there's this phenomenon called resistance."
"I know all about resistance, thank you very much, you measure it in Ohms."
"Not electrical resistance. Psychological resistance. It is a bit similar, I suppose. You are refusing to see that all this telephone stuff is really about...."
"Look, smartarse, I get all this crap from my science teacher, Mrs. Levine. She thinks my telephone story is really about me wanting to change history so that my Mum doesn't go off and marry your Dad. You think my telephone story is about me wanting to be all-powerful and have secret friends who can control the universe. Well, you're both wrong. The point about my telephone story is that it isn't a story. It's true."
"I see. It's true."
"Very, very true. I've got this mate called Rod Gianforte and he calls me up from 1960. Regularly. So there."
There's silence in the kitchen for a while. I realize I've been almost shouting at Tristan. But it is a real relief to have told somebody openly about Rod. It was all getting bottled up inside. I look at Tristan to see if he believes me. He doesn't. He thinks I'm a fruitcake.
"Jenny," he says very quietly, pronouncing every word very clearly, "I know about this trip. I've been there. When I first cracked up I really believed my own fantasies. Just like you now believe...."
"Don't talk to me like that!" I yell at him. "You're talking like I was an imbecile or someone who can't speak English very well. Talk normally."
"Sorry," he says, and returns to his usual rate. "But what I'm saying is true. It is impossible to call the past."
"It's not the past, it's the future."
"I thought you said this guy Rod was in 1960."
"He is. So when he rings me up, he's ringing up the future—see?"
"And he's a real person? Not just someone you've made up?"
"Absolutely. It might sound weird. It is weird. But it's true."
"So let's ring him up. Now. I'd love to talk to this guy myself; ask him a few questions."
"We can't. He has to ring me."
"Ah, I see," says Tristan, like he's humoring a particularly difficult child. "You haven't got quite enough control over this all-powerful device to be able to demonstrate it to a third party?"
"It needs a bloody great machine," I shout. "A resonance generator. Rod's invented it. Not me. He's got the machine at his end, in his time. And it won't be in resonance again until tomorrow afternoon."
"Ah, yes. It figures. Tell me, Jenny, how do you know that this isn't all a delusion on your part? How do you know it's true?"
"Because it bloody well is!"
"But you've got no proof?"
"Rod tells me stuff he only knows because I tell it to him after he's told it to me. Davy was there too. See?" It doesn't sound very sensible as it comes out of my mouth, but that's the trouble with time loops.
"No, I really don't see," Tris says sadly. "This doesn't sound very convincing, Jenny. If you think about it, it sounds a bit mad. How do you know you're not imagining all this?"
I don't say anything. There is nothing I can say. If I try to tell him anything, he'll just say that there is no way of knowing that I'm not stark raving bonkers. I just go on peeling potatoes. I discover that I've peeled enough potatoes to feed ten people. I feel a bit of a fool.
"You haven't drunk your thickshake," Tristan says.
It's true. I've peeled a thousand potatoes without drinking a drop. I down the thickshake in three big gulps. I'm beginning to feel a bit vulnerable. After all, how do I actually know that Rod is real? How do I know that the whole thing isn't just a figment of my imagination?
Then an idea occurs to me. It's so obvious I wonder why I haven't done it already. "Look," I say, "I'll tell you what I'll do. I'll record the next conversation I have with Rod. Okay?"
"That would be very interesting, Jenny. I'd love to hear a tape of someone talking in 1960—a tape that was made in 1995. Although it'd be more impressive the other way around."
Tristan is still talking to me as if I'm mad. I know what he's thinking: he's thinking that the tape will confirm his loony theories about me being in the grip of a fantasy that I can't distinguish from reality. I suppose he thinks I'm going to concoct the tape myself: put on a gruff voice and pretend to be a man when I'm acting out Rod's part of the conversation. Well, Tristan's got another think coming. Rod sounds like Rod. He certainly doesn't sound like a fourteen year old girl pretending to be a man.
Suddenly I want to be alone for a bit. I start to regret asking Tristan to stay for tea. He and Poppa will have to meet one day—but I'm feeling a bit worn out. Just at the moment, I could do without the emotional strain of playing hostess at a step-brother-meets-step-sister's-father tea-party.
Maybe Tristan feels the same thing. He actually is quite a sensitive boy. "Look, I think I'd actually better go, Jenny. I've got stacks of homework—mathematics, English, Society and the Environment, you name it."
"Yeah, all right," I say. "I'll see you to the door."
As he disappears into the early evening, Tristan says, "Don't forget to make that tape."
"I won't, buster," I yell at his retreating back.
I shut the door. Actually, I think to myself, it would be great to have a recording of Rod—something real and tangible that I could play over and over—not just a voice that comes out of nowhere on the phone. It'd be great to have a recording for all sorts of reasons, not just because Tristan needs convincing. I go into Poppa's study and get his Dictaphone. When Poppa arrives home a few minutes later I'm in the hall doing a practice recording: holding the Dictaphone up to a 005 number I've rung.
"Jenny dear, what are you doing?"
"Recording Dial-a-Prayer," I explain.
"Sweetie, what on earth for?"
"Homework. Society and Environment. Other people's beliefs."
"It wouldn't have happened in my day." Poppa goes through into the kitchen, shaking his head. Half a minute later he yells, "What in tarnation are all these potatoes doing?"
"We're having potato soup," I call back as I'm putting down the phone.
"There's enough to feed an army."
"That's why we've got a deep-freeze. We can have potato soup once a week for months."
In my hand the tape starts to issue its orders to God: "Dear Lord, help us to grow in spirit and in wisdom. Give us the courage to overcome adversity. Make us...."
SUNDAY, 7 MAY, AFTERNOON
Really, there's only one way I'm going to convince Tristan that I'm not hallucinating, or inventing some wild story to make myself sound interesting. I do need to tape-record my next conversation with Rod. Poppa doesn't want me to use his Dictaphone because he depends on it for work, not as if I'd be likely to break it or anything, but that's the way he thinks. So I search through an old Tandy catalogue to see if they sell those magnetic resonance things you see undercover detectives using on cop shows to bug calls. You clip it on the phone line near the handset, then run a wire back to your tape recorder. It's probably illegal. I can't find any ads for it, anyway, and in any case I wouldn't be able to get one until the shops open on Monday but Rod's due to call me back this afternoon. Any minute, in fact. I try propping the tape deck next to the ear-piece, because it's got its own miniature built-in mike, but the rotten thing keeps tipping over or I slip and drop the phone. What I need is a separate microphone with a cord and a jack on the end. I ring Davy.
"Hi, Jen. Watcha doing?"
"Hi, David. Your Dad's got a classy reel-to-reel tape machine, doesn't he?"
"Huh?"
"You know, the one he uses to record his old cronies when they get together to play jazz." Oomp-pa, oomp-pa. I hate trad jazz, and so does Davy, which is one reason we mostly see each other around here instead of at his folks' place.
"Yeah. Oh, yeah, the stereo mike. Do you want to borrow it? He'll go off his face."
"Can you sneak it out and bring it over?"
"I never knew you were musical, Jen."
"This is to record off the phone."
Davy draws in his breath suspiciously. "Is that creep still ringing you? I thought it must have been Tristan, mucking around. It's not, is it?"
"What? Of course not. Don't be ridiculous. Can you get it or not?"
"Okay. I thought you were pissed off at me."
"That's silly. Look, hurry, can you?" Rod could call any time.
"Five minutes."
Luckily Poppa is off at one of his dreary weekend conferences (unless he's got a new girlfriend, ha ha) so Davy gets in the front door without a lengthy and painful attempt at conversation. He's got this big fat mike in a plastic bag. I prop it on the table where we keep the phone and the message pad and plug it into my Sanyo.
"Testing, testing."
Amazingly, it works when we talk into it, but that doesn't mean it will be able to pick up Rod's voice from the phone. I tie it on to the handset with a length of string and punch Maddy's number. Her mother answers, sighs at my name, calls down the hallway for her daughter. "She's doing her geography assignment, Genevieve, so please don't distract the girl. It's hard enough to get her to do any work at home. I don't know how you kids ever get any homework done, you're always on the phone or out mucking around." But she says it with a smile in her voice. I like Mrs. Smith a lot.
"You forgot to turn it on," Davy hisses. He's right, damn it. I push the REC button and the PLAY button together, and the cassette starts to turn. The microphone is heavy, industrial strength, and keeps sliding down the handset away from the ear-piece.
"—your bike ride with Tristan yesterday?" Maddy is babbling when I get it back to my ear.
"What?"
"I thought you were going to invite me as well." She really sounds disappointed.
"Are you soft on Tris?" I ask teasingly. "Are you going to go all mooshy and clucky when you see him? Are you always going to let him win when you play on the machines at the Arcade?"
"I did not!" Maddy cries indignantly, but I don't believe her. I'm trying to keep one eye on the recording indicator, which is flickering in a suspicious fashion.
"Look, I'm recording this, just hang on for a mo while I check it out." I put down the handset and stop the tape and run it back and then hit PLAY. My own voice comes booming out, but Madeleine's is scratchy and distant and missing bits. This isn't going to work.
"It's not working," I say to Maddy when I pick up again. We have the usual confused exchange and finally I get through to her what I'm trying to do. That girl can be quite thick sometimes.
"Oh, is that all you're doing," she says. "What's wrong with the answering machine?"
Davy is mooching around, bored out of his mind. I stare at him, or through him, astonished at what I've just heard. I stare at the stupid arrangement I've got tied to the handset. Maddy's not the slow one. I am.
"—or does it use some special cheapo cassettes?" Maddy is saying.
"No," I say, flipping up the lid and peering inside the old black answering machine that Poppa is too mean to replace with a call-waiting system. "There's a fifteen-second loop-tape that answers your call, and an ordinary thirty-minute cassette for the messages. I think. Hang on." Amazingly, the tape's the right size for my Sanyo. I pop the lid closed on the answering machine. Unfortunately, I can't get it to go without hanging up and waiting for someone to phone in.
"You're a smart girl, Mads. When I hang up, can you call me straight back? This is really important."
"I suppose. Mum's staring at me something fierce, but. It'll have to be quick."
"Just to test the system. Half a sec, okay?"
"Listen, when you do, take out the answer loop cassette and swap it with the message tape. Otherwise you'll get the usual stuff about 'This is Dr. Kane's residence.'"
"But how do I get it to record?"
"Aw, Jen, come on. When the phone rings and you pick up, just flip it straight into RECORD MESSAGE mode."
"But it'll turn itself off after fifteen seconds."
"No, it won't! That only happens with the loop tape. It should just keep running."
"God." I'm incredibly impressed. "Madeleine Smith, you're a genius."
"Yeah, sure. Look, hurry up, okay? Mum's gunna kill me. I'll call you straight back." The phone clicks.
Davy has gone out to the kitchen by this time, and I can hear him digging around in the cookie jars. The boy has a sweet tooth. I hang up the handset, flip cassettes, switch on the answering machine which lights up its little green light, and untie the stupid string holding Davy's dad's stupid stereo music microphone to the handset. The phone rings. I flip to RECORD and press the start-up button. The red light comes on.
"Maddy?"
"Herodotus. It's an hour later for me. What about you? It should be eleven days."
"Um, the Wednesday before last. That's right, eleven days. This is Sunday the 7th. How can that equal one hour of your time?"
"I'll show you the equations some day when you've got a higher degree. Anyway, let's get back to something simple, like how to change the past. Maybe we can still work out how to use this link without short-circuiting the whole universe."
The red light stays on. As far as I can see, the tape is working fine. Running the call through the answering machine gives Rod's voice an extra distant and eerie quality, but I can understand him without any trouble.
"Last time you said it was like ripples in time."
"Right. Cause and effect work on one another like interfering waves. Ripples passing through each other. Effects ripple out into infinity, for billions of years, and finally they sort of bounce back off the end of the universe and set up an interference with their causes. Of course they're extremely weakened by then."
"That's the silliest thing I ever heard. The universe hasn't got an end. Unless you mean the Big Bang. Or the Big Crunch, when everything collapses into a huge black hole."
"The Big Bang. My aching head. That's probably exactly what I mean, Jenny. Anyway—"
The man is easily distracted. We'll get nowhere fast if I don't keep him on the straight and narrow. "You're saying your machine sets up these ripples in the phone network."
"Thank you. Precisely."
It's logical and beautiful. I see why Mrs. Levine calls science "elegant." Happily, guessing how it works, I tell Rod smugly, "And they don't leak out. So they don't get weaker and fade out."
He is impressed. "I'll give you a job in my lab. Forget about the higher degree, you're hired without one."
I like anyone who likes a pun, so I snigger. "'Highered,' ha ha. So anyway, these, um, ripples, they go backwards and forwards in time and that's why we can talk to each other?"
"You now know as much about it as I do, kiddo."
"So where's the big problem?"
"The big problem, my bright but not all-knowing pupil, is that we can't afford to mess around with the network. Add or subtract one link in the net and the resonance changes. It's like snapping a string on a violin. Screeches and no music."
"Like, if I help you win Lotto and you build a giant mansion by the sea and get them to put in a new phone so you can talk to all your new friends on it—"
"—the network would be busted, the bubble burst, the ripples ripped. And we would not now be conversing on such an elevated level of speculative physics."
"Oh." That stumps me. How can you do anything if you're not allowed to do anything? After a while I see a sort of possible answer, and say carefully, "What if you just didn't do anything that affected the phone system?"
"But how could I be sure?"
"You'll have to be very, very sneaky, I guess. Would you like me to look up some racing results from the end of 1960? And a list of all the Melbourne Cup winners. Might take a few days."
"Why not? I'll try a modest wager or two, shouldn't do any harm. In the meantime, I have to find out how one delivers a message to someone who won't be born for another two decades or so. Speak to you soon, kiddo." He hangs up, and I turn off the answering machine.
While we've been talking, Davy has slouched past in a bad mood and gone upstairs to my room. He puts on the Braincase CD I don't like any more, and sings along loudly to it. I decide to just ignore this pitiful bid for attention, and flip the cassette out, switch it to the Sanyo recorder, run it back to the start, and play it back. It's perfect. Well, as perfect as a cheap answering machine can make it, which isn't very, but hearing Rod's voice come out of a tape makes a shiver go down my back. It's hard to explain, but it seems different somehow from just talking to someone who's stuck more than thirty years in the past. Hearing his words locked into magnetic tape is awesome, and scary, and almost impossible to believe.
"Hey, Davy, turn it down a bit," I yell up the stairs. I run the tape back and start listening to it again, all about ripples in time. David comes clumping angrily down stairs and grabs his father's microphone off the table and stuffs it into his plastic K-Mart bag.
"You're no fun sometimes, Jen," he says accusingly. "If it's not nerd-features and his new girlfriend, it's this bloody weirdo on the phone. I don't know why you even bothered to get me to come over."
"I asked you to come over to do me a favor," I say, rather coldly. "Don't you remember? It's not all that long ago. You lent me that microphone you're holding in your hand."
"Yeah, well I didn't know you'd be using it to record Creepy the phone freak." He grabs up the Sanyo with Rod's voice in it, and I go off my face.
"Give that back!" I shriek. "It's important! Sometimes you're so mean, Davy." I wrestle the machine out of his hand and put it behind my back. "Sometimes," I add hurtfully, "you're just so stupid." The moment the words are out of my mouth I wish I'd cut my tongue off, but it's way too late.
Davy just stands there like a sick dog. "Yeah, I know. Not you, though. You're a legend," he says slowly, "you've got a mind like a steel trap. Well, at least I don't spend all day hanging around waiting to talk on the phone to some bent weirdo who pretends he's from another planet or something."
"Another time, you idiot," I yell at his retreating back, and when he closes the front door he doesn't even bang it like I would. Before I have a chance to work out if I'm going to have a screaming fit in the privacy of my own hallway, or run upstairs for a good cry, the phone rings.
"Dr. Kane's residence," I say in a very tense voice.
"Well, did you get his voice on tape?" asks Tristan, highly skeptical.
I brighten up instantly. "Yes! Listen to this, Tris! I'll just play you the tape, hang on."
Then we both sit there, me in Carlton and him in Kew, and listen to the recorded words of a man speaking to me from another time zone.
TRISTAN'S CASEBOOK: May 7
The present writer has just heard a most extraordinary recorded phone conversation between the subject and the unknown man she insists upon calling "Rod" or "Herodotus." This was a very unsettling experience, as the nature of the exchange makes it apparent that this "story" is not a complete fabrication after all.
It has been the theory of the present writer that the subject's "story" is no more than a delusionary compensation for certain traumatic incidents in her recent life, especially her mother's impending marriage to the present writer's father. This interpretation follows the accepted doctrine of psychoanalysts of the school of Dr. Sigmund Freud, who believed that most claims of abuse and conspiracy were fantasies "covering up" deep sexual problems and anxieties in his patients. However, it has come to the notice of the present writer that this line of thought is being called into question by many contemporary feminists and experts in "recovered memory." These alternative specialists maintain that many such incidents, most too horrible to record here, are not "fantasies" but actually refer to real events in the past and present lives of patients or "clients."
While the present writer is not yet in a position to evaluate such controversies, it does begin to look at if the subject's intriguing case might be based more extensively in "actual events" than has been supposed. This interpretation would clarify a number of odd remarks made to the present writer during the last several weeks. For example, the subject lapsed into discussing her "story" as if it were actually real during the daring bridge-climbing episode shared with the writer.
In regard to that event: it seems to the present writer that a closer and indeed a warmer bond was established with the subject on that occasion. Even though my analyst was furious when I told her that I had, as she put it, "risked my neck in a suicidal gesture," I do not believe that I was trying to kill myself. On the contrary, as I explained to Dr. Grogan, I was merely "showing off" in a typical macho fashion, as my brother Alain might have done. God, I hate being the youngest one in this family. I know that Mother did not kill herself because she was ashamed of me, but it is so hard to believe it, deep down. No wonder I'm such a nerd. No wonder Davy calls me "Dweeb-head," Oh, yes, I've heard him mumbling to Jenny. But the lovely Maddy doesn't seem to think I'm such a hopeless case. She is beautiful and feisty. I think I must be in love with her. I can't get her out of my mind. I dream about her every night. Maybe Jenny and her telephone accomplice "Rod" are as mad as meat axes, but they have brought me into contact with the delicious Madeleine Smith, and for that I shall be eternally grateful.
The present writer notes that he has been "babbling on the screen" for the last five minutes, and will decide later whether or not to delete this file.
MONDAY, 8 MAY, EVENING-A
The TV news is telling us all about the New Europe, and then about the plans the Russian and American Presidents are setting up to deal with joint defense arrangements. "A further round of massive strategic arms reductions appears imminent," says Mary Kostakidis, who's done something weird to her hair. Poppa comes clunking down the hall and drops a mess of files on the kitchen table where I'm finishing off my algebra homework. He gives me a kiss on the back of the head.
"Evening, honey. How'd you like to go out for dinner?"
"I already made a curry, Poppa, it'll be ready in half an hour. Wanna help me slice up some side dishes? You can make the pappadums, too." I close my own folder. My father pours himself a glass of Morris Blanc Superior from the cask in the fridge and throws in some ice.
"You're a good girl, Genevieve. I wish to God your parents had been as thoughtful."
"Um, Poppa, has Mum said anything to you?"
"About what, princess?" He's got his nose in the curry pot. "Hmm, smells wonderful. Have you got a cucumber?"
"Bottom tray of the fridge. I got some of that creamy yoghurt. Um, after the wedding, about her and—" Just keep pushing. What else can I do?
"Jenny, I spent half the morning on the phone to her lawyer. I'm afraid she's decided that she wants to change the custody arrangements."
All over my chest the skin feels cold and horrible. "She wants me to live there with that creep?"
"It seems so. Only part of the time, mind you. It seems a quite equitable arrangement, in all truth. Ouch! Damn it, now I've cut my— Jenny, speaking of talking all day on the phone, I tried to ring you for nearly an hour this afternoon. No, no, don't fuss, it's just a small cut." It seems to be bleeding all over the cucumber, but he puts his hand under the cold tap while I get out a Band-Aid, tear off the cover, start its ends, and pass it to him. He hates anyone fussing about pain. "You really have to stop using the phone as your private line to your friend David."
"It wasn't David. We've had an argument."
"Well, whomever. I needed to speak to you."
"Here I am," I say grumpily.
"Hmm. So you are. Genevieve, I received a most extraordinary document in the mail today."
Instantly, in a flash of delight that burns through my whole body and pushes out all the sick feelings about Mum's impending marriage, I realize what it means. I can't believe it, but I know it's got to be true. "Oh shit," I blurt. "It really worked."
Poppa doesn't notice. "I've got it here in my coat. I must say I've never heard of these people. A firm of solicitors in New York, evidently, representing something called the Ripple Corporation."
"A million dollars," I breath. Ripple. Oh my God.
"Eh?" He looks up sharply. "Don't be absurd, child. Still, it's nearly as impressive. I really don't understand it. I've spoken to your Principal and she doesn't understand it either."
The real world intrudes with a jolt. "Huh? What's old Blakers got to do with it?"
"Genevieve, show some respect. In fact, Mrs. Blakeley knows nothing about it."
"About what? Tell me, Poppady, or I'll give your curry to the cat."
"We don't have a cat. It's a scholarship, evidently. Your excellent marks have attracted the attention of an educational foundation in the United States. A bursarship has been granted which will see you through any university in the world, assuming your final marks are up to scratch. There's a most generous living allowance. In the meantime, you are allotted two thousand dollars a year toward science research materials. Jenny, have you decided to go into science?"
"Poppa, I've been in the advanced phys/maths stream for two years." I can hardly get any air into my lungs. "Oh boy. Oh wow. New York, here I come!"
"Slow down, princess." But he's smiling too, grinning with shared delight. "Not for a few years yet."
"What's a few years?" I grab up the letter and dance around the kitchen, school heels clattering on the tiles. "What's time? It's just...just ripples, Poppa!"
§
The phone rings once, and I've got it.
"Dr. Kane's residence."
"If all my planning worked out," Rod says in a tautly controlled voice, "you should now be a few pounds better off—dollars, I mean."
"Rod, thank you. You're wonderful! I believe every word!"
"I don't see why you should. I could still be a wealthy nameless telephone mugger with a confederate in Sydney."
"Why Sydney? The Ripple Corporation is in New York."
"Oh? Things must be going to work out really well. I set it up with a lawyer who was at Sydney University with me back in the Dark Ages. That's just a start, Jenny. We'll be placing your half of the earnings in an investment portfolio to be delivered into your hands when you turn twenty-one. I think you should be mature enough by then to know how to handle, uh, how should I put it, he-he, incredible wealth."
But I don't giggle along. I can feel my mood shifting as his becomes more manic. "Rod," I say, and stop, sucking at my lower lip.
After a moment he says back, "Jenny."
"Rod, I've been wondering about this. We shouldn't use it just for ourselves. This is too important."
"Well, think of it as an experimental test. Normally you'd use strings of random numbers. So why not use horse races and make some money on the side?"
"I think we should save those poor people in the Shuttle."
"The what?"
"There was a mini-series on TV. Seven astronauts got killed when the space shuttle blew up in 1986. It was a fault in the O-rings. I mean, the technicians knew there was a problem, but no one listened to them. But if you sent them a letter in, say, 1984 or 1985, they'd have to investigate it, wouldn't they? You could stop the Challenger taking off."
"The O-...? Jenny, hang on. I don't even know what this shuttle thing is—"
"It's a space ship! There were two women on board! I mean, one of them was just a school teacher, and they—"
Rod cuts over me. "I'm sorry to hear that, kiddo. Tragic. But Jenny, why stop there? There must have been worse disasters in the last thirty-five years."
He's right. I keep forgetting how far back he's talking from. They didn't even have shuttles. My God, they hadn't even landed on the Moon. No wonder he got weird when I mentioned the Apollo program. And there were those nutty questions about Kennedy and Nixon— "Oh golly. When did you say you were ringing from?"
"It's October 12, 1960."
"In about three years, President Kennedy is going to be shot."
"Jesus! Assassinated?" He's shocked into silence. "Is that how Nixon—?"
"No, that was later. You've got to stop it happening, Rod. Maybe we could stop the Vietnam War before it starts."
"Jenny, Jenny, that's the whole problem!" I hear anguish in his voice, real adult horror and suddenly I feel like a silly kid, and I hate it. "How could I? How long do you think I'd stay out of jail if I phoned the American Embassy and said, "Hey, chaps, President Kennedy's going to be killed in 1963'? He's not even president yet!"
In a sulky tone I say, "So what? You haven't even put any money on those horses yet, but my father's already got the scholarship from your lawyers. I haven't even looked up the winners, for heaven's sake!"
"Hmm. But don't you see, that won't happen if I stop Kennedy's murder. In your world, Kennedy's dead. I have to leave it that way, or the resonance is destroyed. The link is broken. None of this will have ever happened. Not even our first phone conversation."
"I don't care. Poppa has enough money, I don't need your scholarship. I think we should—"
"Jenny, calm down." He doesn't sound very calm himself. "I don't say I disagree with you. But why stop with one man's death? Haven't there been other disasters?"
My mind goes blank. All I can think about is TV news broadcasts. "Uh, there was that earthquake in Afghanistan, and, um, the famine in Rwanda because of the war—"
"We can't stop an earthquake or a war, kiddo. I don't think anyone would believe us anyway, so we couldn't even get the place evacuated."
"Three Mile Island! It was a nuclear accident in the States."
"An atomic accident! My God! How many killed? Hundreds of thousands, I suppose."
"I don't think anyone was killed, exactly. But it nearly melted-down, like Chernobyl."
"Where's that?"
"Some part of what used to be the Soviet Union."
"Used to be?" Rod is utterly incredulous. "Are you saying that communism isn't— God, the far right are going to love that. No one, I mean no one, will believe any of this! I mean it. Who would believe us, Jenny?"
"Bhopal! That was really awful! We could stop that."
"Somewhere in India?"
"Just a tick, I've got the Yearbooks here. Capital of Madhya Pradesh, however you pronounce it. December the third—"
"1994?"
"No, way back, 1985, I must have still been in kindergarten but Mrs. Levine goes on and on about it, it's stuck in my memory. Methyl iso-kyan-ate...."
"Iso-sigh-an-ate."
"...a deadly gas used for making pesticides, leaked out of a...Union Carbide.... Many residents died in their sleep, 2,500 dead, many thousands more blinded. Rod, it was really horrible! We could stop that, couldn't we? All we have to do is tell them to check their storage tanks. Rod, there were babies!"
His voice is absolutely flat. "We can't."
"Why not?" I'm literally hopping up and down, and the phone cord is banging on the wall. "It's our duty!"
He sighs bleakly. "Look, think this through, kiddo. Sure we can change your past, my future, whatever you want to call it—but we can only do it once! One shot. Then the resonance is disrupted, and our time zones drift off in different directions."
For some reason I think of my mother, sitting there in the leafy garden of Edward's house in Kew with only Tristan the dweeb and Lamb Chop the killer dog for company, instead of her own daughter. "We'll never talk to other again?"
"Worse. None of this will have ever happened. We never did speak to each other."
It makes me feel sick as well as disoriented. Flippantly, to hide it from him and me, I say, "There goes your Nobel Prize. Not to mention all the millions."
"We've already established that I'm not going to get a Nobel Prize. Not in the next thirty-five years, anyway."
"Well, you've certainly become some kind of big shot." I'm starting to feel desperate and sad. I pick up the brochure from the table, I haven't even read it properly yet. "Listen, here's this thing they sent along with my scholarship letter, it probably lists you as chairman of the board."
"I don't think so. I'm planning to be very discreet." After I've been silent for a time, he says, "Well?"
I'm such a baby. I feel as if I'm going to burst into tears again. And I've never even met this guy, and by now he'd probably be old enough to be my grandfather. "Oh gee. Oh Rod, I'm so sorry.... I didn't have time to read it before—"
"What's wrong?"
"Oh, it's nothing. I was looking at the wrong bit. Hey, this is interesting, there are no phone numbers listed for the Corporation, just an address and a box number in New York—"
I don't fool him. Forcefully he says, "Tell me, Jenny. It's something about me, isn't it?"
"You don't want to know." I don't want to know. "You've just said you can't change time."
"Of course we can change time. You would never have got that bloody letter if we couldn't change time. Read it to me. You owe me that much."
"Oh, Rod!" The tears are leaking down my chin. "It says, 'The Ripple Corporation is a non-profit organization established under the laws of New Jersey as an educational and research fund.'"
I'm reading very clumsily, getting everything tangled with my thick tongue. I stop, swallow, try again. "'It rewards accomplishment in many fields of science and the arts. What is more, in keeping with the founder's far-sighted belief in the future, the Ripple Corporation seeks out bright young talent and encourages—' Rod, I can't read this to you."
"The founder? That's me? God, they make me sound like I'm a thousand years old. Or as if I'm—" He stops dead.
"That's what it says here, Rod. 'His own painful search for truth, which cost his life.' There's something about synchrotron radiation. Do you know what that is?"
"Oh Jenny." His voice is a thousand kays away, and right in my ear. His voice sounds gray. "I feel sick. I think I'm going to be sick. Just a moment.... My own obituary. God, I feel as if I'd been smashed in the guts." I hear him take a deep breath. "When do I die?"
"They don't say. No, here it is. 1935-1963. Oh Rod, you're going to die the same year as President Kennedy."
"A macabre note of distinction, Jenny. My God, three years. No, it's not true. I can't believe it." It's as if I can hear his brain roaring, a motor for thinking impossible ideas. Then he says, "It's the resonance. It must be. But I don't feel sick. 1963. McReady and I have only been using the machine for a few weeks. If I shut it down right now...."
"You have to, Rod! It's killing you! Do it, turn it off."
"You haven't researched the race winners yet, Jenny. If I shut the machine down I'll never win that money and never start the Ripple Corporation and you'll never have got that brochure.... This is crazy. We really are talking about altering the future. The past."
Hotly, I say, "Well, if you think I'm gonna go ahead and tell you those race results, now I know it'll kill you—then you're the one that's crazy!"
"Jenny, you're right. Unless I can find some way to shield the machine."
Neither of us says anything for a while. I realize suddenly how dark it is in the hallway, and reach over to switch on the light.
"If you do," I say at last, "you know how to reach me."
"If you're still in the same future, Miss Steel Trap." Another pause which neither of us can fill. "You know, I've really got quite fond of you. I wish I had a sister like you. A daughter."
"Are you married?"
"Not yet."
"I'm going to hang up now, Rod," I say very definitely. "I hope you don't die."
"Thank you, kiddo." His voice is faint, and choked. "This is like two ghosts saying goodbye to each other. Look after yourself."
"Bye, Rod."
I cradle the phone before he does. Then I just sit there for a long time, hunched over the useless thing, sobbing like a baby.
MONDAY, 8 MAY, EVENING-B (REVISED WORLD)
The TV news is telling us all about the New Europe, and then about the plans the Russian and American Presidents are setting up to deal with nuclear defense arrangements. "A further round of massive strategic arms reductions appears imminent," says Mary Kostakidis, who's done something weird to her hair.
"I want all this junk off the table pronto, young lady."
"It's not junk, Mum, it's my science project."
"I know, sweetie, but we have to get the table set. What's wrong with your own desk?"
"It's covered in junk. Gosh, a lace table-cloth? We are getting fancy."
"Oh, your father wants to make a big impression," my mother says, shooing me away. "Now go and get ready, I want you on your best behavior tonight."
"Aw, yack yack yack about economics and balance of payments all night."
"Actually, you might even learn something. Our guest is a physicist from the States. Your father was on the debating team with him at Sydney University."
"I thought physicists were the Enemy of the Department?"
"This one is the biggest Enemy of them all, which I think is why your father is hoping to butter him up, aulde acquaintance and so on."
"Oh. Is he the one all the fuss was—"
"Little pitchers have big ears. Not a word about that. The University was very lucky to get Professor Kanthamani. Berkeley was quite eager to keep him, apparently, but he wanted to come back to Australia. God knows why he chose Melbourne."
I pick at the shiny black olives piled in a bowl. "Poppa won't be in a very good mood, then. I can remember him ranting on about—"
"Genevieve! Your father never rants. He might sulk a little...."
She's always criticizing. I butt in, "So what happened to what's-his-name, the last guy we had to dinner?"
Mum is snide, and I don't know why. "I greatly admire the precision which a mathematical education brings to the mind of the young."
"Oh, that distinguished-looking man, you know, from Deakin's Business Administration. You and him were laughing all night."
My mother's eyes narrow. There is a clatter of silverware. "Money's tight, sweetie, especially in universities. It's something you won't understand until you're a few years older. If one wishes to acquire a certain tasty plum, according to the Vice Chancellor, one has to forego another. It's a matter of balance, Jenny, a matter of juggling and compromise."
She's getting very snaky these days. In a sudden bad mood, I tell her, "I don't care if he is a physicist, I'd rather go over to Maddy's for tea. We can finish our homework together."
Mum seems more pleased with this idea than I'd wish, somehow. I think she enjoys getting a bit soused at dinner parties and flirting with the guests, but feels it's a bad influence on her suggestible teenage daughter. "Oh, I suppose we can spare you," she says carelessly. "Just this once. But you'd better call her mother first and check."
I grab up my text books, drop the pile on the hall table, punch the number. A lot of noisy headbanger stuff comes through the line when it's finally answered.
"Hi, Maddy. Listen, can you ask your Mum—" Behind me, competing with the heavy metal in my ear, Mum is calling firmly, "Just don't hang on the phone for hours, Jenny. You spend far too much time hogging that instrument." I just grin, and get down to the serious business of quizzing Madeleine about her hunky boyfriend David. Then it turns out they're already booked for the night, so I'm stuck at home.
§
Dinner starts off as a nightmare, a real pain. This Professor Kanthamani is about Poppa's age, but he looks younger. He's chubby and dark, with thick waving hair that looks as if he's poured oil all over it, and he is rather lofty and dignified. Mum is put out because he's brought a bottle of some awful red wine and insists that she open it, even though she's serving chilled Chablis with the chicken. He and Poppa stumble through dry conversations about economic rationalism and the terrible things the Vice Chancellors are doing to academic freedom, but I can tell neither of them has his heart in it. Mum just seethes.
And then something wonderful happens. Prof Kanthamani starts telling us about an amazing quantum theory experiment that's just been done at the University of California at Berkeley, in the USA. It's all about time. Somehow, it seems that what we do now, at this very moment, can change things in the past. I listen to this with my eyes bulging and my mouth open.
"Genevieve, close your mouth," Mum says, "a fly will get in."
"There are no flies on Jenny," Poppa says. "She's just dazzled by science."
I gulp, and a bit of chicken goes down the wrong way, and then I'm coughing and spluttering. The scientist leaps up and pours me a glass of water and everyone looks very concerned, and I say, "Do you really mean that we can change the past, Dr. Kanthamani?"
Maybe my interest in science cheers him up, because he smiles warmly at me for the first time all night.
"Call me Ram, Jenny, everyone does eventually. Short for Rambo, because I'm named after a famous movie star, which is why I went into physics. Just joking." Strange sense of humor if you ask me, but I give him a careful grin. He takes back the glass and asks, "Feeling better?"
I cough one last time, and find that I can breathe again.
"Yeah, thanks. Is that right, though, about time?"
"Not exactly," Ram says. He glances at my parents. Mum shrugs, Poppa nods interestedly. "What Raymond Chiao's experiments have shown is that bits of the past aren't totally completed until the present moment occurs—or even until the future happens. Oh dear, I've made it worse. It's hard to talk about this kind of thing in ordinary English, our language isn't built for temporal paradoxes."
Poppa pours another glass of Ram's cheap claret and sips it without wrinkling his nose at the taste. "But Ram, how can this quantum experiment be a paradox if you can test it in the laboratory? A paradox is an error of language, like asking who shaves the barber if the barber only shaves those who can't shave themselves."
Barber who what? I think.
"Ms. Barber," Mum says snidely, "she does it." Both the men laugh.
"That's cheating," Ram tells her. "The logical trick—it's called Russell's Paradox, as I recall—depends on the barber being a man with his own shaving problems. So who shaves him, if he can only shave those who can't shave themselves? And no, Jenny, he doesn't nip out of town to get it done somewhere else, and he isn't allowed to grow a beard."
My head spins a bit as I try to think it through. "I dunno, Ram. Sounds impossible."
"It's a trick of words," Poppa declares. "Don't the philosophers call that 'self-reference'? One part of the puzzle looping back to undermine an earlier part? Really, valid logic doesn't allow you to do that. It's like lifting yourself into the air by tugging at the soles of your shoes." I almost see what he means, but Mum is just shrugging her shoulders at the stupid games men play. She heads out into the kitchen to prepare dessert. I get up to collect the plates.
"The quantum eraser experiments aren't like that, though," Ram says. Now that he's on his own topic he's happy as a lark, relaxed and ready to talk all night. I grab his empty plate and put it on top of Poppa's, and then loiter in the doorway to the kitchen because I don't want to miss any of this. "Actually, if you want the full low-down on this kind of caper, you should chase up my old mate Rod Gianforte—if you can find him. He was heavily into quantum weirdness twenty or thirty years before it became fashionable."
"Rod Gianforte?" Poppa says, scratching his head. "Wasn't he at Sydney university in the early sixties? Some terrible scandal about a ruined computer?"
"Yeah. Went out with a bang—I don't think they've ever forgiven him. Lucky to get a job in some small sheep college in New Zealand. Actually I gather he's back in Australia these days—lurking somewhere in Newtown, I imagine."
There's the weirdest buzzing in the top of my head, as if I'm going to faint, or lift off my feet into the air even without tugging at the soles of my shoes, or something else totally impossible, I don't know. Suddenly I get the most awesome feeling that I already know this guy Prof Ram. Or maybe the one he just mentioned, Rod something-or-other. I'm absolutely convinced that we've talked about all this before, and that—
What? I just don't know. It's called déjà-vu, I think—the sensation that something has happened before, exactly like this moment now. You walk into a room where you've never been before and instantly recognize all the furniture, and the paintings on the walls, and you know in your bones that outside in the yard there's a huge oak tree with a rubber tire for kids to swing on hanging from a chain, and a brown bantam hen scratching and...
Only that's not it, not precisely. I don't think this exact same dinner has happened before, or that it's actually Ram Kanthamani I'm remembering. Mum calls crabbily to me to bring the plates and cutlery in to the dishwasher, and I'm standing here in the doorway numb from the neck down, wondering if I'm going to barf. This has happened before! No! No, something else—
"In Ray Chiao's experiment," Prof Ram is saying, "single photons are sent through a beam-splitter—"
"Photons?" asks Poppa. He knows all about running the economy, but physics is just a black hole for him and Mum.
"Particles of light," says Ram. I put the plates into the open dishwasher without bothering to rinse them, and shoot back into the room. I don't want to miss any of this.
"Particles? I thought light was made of waves," Poppa says, even more confused. "Light-waves."
Ram looks very pleased with himself. He pounces.
"Exactly! Sometimes it's a wave, but at other times it looks like a stream of little hard pellets."
"Don't be ridiculous, Ram," Poppa says crossly. "That really is a paradox." He takes a piece of fruit out of the bowl in the middle of the table and brandishes it in the air. "It's like saying this apple is red and green at the same time."
"Dear, it is," Mum tells him, coming back into the room with several plates of apple cream flan balanced along her arm like a waiter. "Look more closely. It's red on the top where it's ripest, and green underneath."
"No, no," cries Prof Ram excitedly. "Dr. Kane is right, quantum effects are paradoxical, by ordinary standards—as if that apple were both all green and all red at one and the same time." Poppa opens his mouth to interrupt, but Ram wags a finger under his nose. "Let me tell you about Chiao's experiment. You see, they send a single photon through a— No, wait on, let me try my little 'quantum eraser' story on you. That's where you rub out the past and then get it back again by changing your mind later."
Now we're all staring at him with our mouths open. "Colored lines will make it easier," he adds. "This is a parable I dreamed up for my students." He grabs a piece of paper from the sideboard, digs out one of the five or six felt-tipped pens jutting from his inside suit pocket, and starts drawing diverging lines in different colors.
"I told you science had become the new religion," Mum says snidely. "'Parables,' indeed."
Ram isn't put off. "Imagine there's a huge bunch of football players, and just before they run on to the field they're randomly divided into two teams with distinctive colors."
"Ah," says Mum, "a male chauvinist parable!"
"Not at all!" He laughs in a lilting, Indian way. "The womenfolk are welcome, for these are non-sexist teams! Men and women in equal numbers."
I can see Mum about to go ballistic when she hears such a vile term as "womenfolk" but she catches herself in time, realizing that Ram is pulling her leg.
"Could we just have colors by themselves, without the allegorical football players?"
Ram shrugs. "Very well. I do not know any women footballers anyway." He loses his pens and grab frantically for them as they roll off the table. "Let us say that a single photon or light particle is divided into two by a device called, amazingly enough, a 'beam-splitter.' Now you must bear in mind that these colors I am going to draw really aren't colors at all, but just a way of keeping track of what's happening."
He peers at us doubtfully. Poppa nods even more doubtfully. My mother shakes her head in despair, and says, "Clear as mud."
Ram has drawn one line splitting into two thin black lines that spread apart until each of them enters a separate little box, marked TOP and BOTTOM. When they emerge from their boxes, they split once again, but now there are four colors. Coming out of the TOP box is a yellow line heading upwards and an orange line heading downwards, slowly getting further apart from each other. Down below, coming out of the BOTTOM box, there's an upward-heading blue line and a downward purple line. Plus there's a spot where the yellow line at the very top bounces off a mirror and starts heading down again. Is this craziness supposed to make sense?
"What a mess," I say.
"Jenny," Mum says, "that is a rather rude comment. And you haven't touched your pudding."
Ram looks abashed, and takes a quick taste himself. "I'm sorry, Harriet, this sweet is wonderful, the cinnamon is a touch of genius. Am I ruining your excellent meal with my allegory?"
After a long moment's silence, when it becomes obvious that Mum is not going to let him off the hook, Poppa says, "Not at all, Ram, I for one am intrigued. It's not often we have anyone from the sciences here to dinner. Usually the conversation is about funding for the arts—deathly boring." Mum's lips tighten, but Professor Ram has put his spoon aside to go back to his diagram, and starts on again about his quantum splitter or whatever it is.
"Okay, now the Yellow and Blue lines merge." They're the two that were both running toward the top of the page, except the Yellow line bounces off a mirror there and runs down again to cross over the Blue line. "Imagine the Blue and Yellow lines pass under a camera at the intersection."
"A traffic camera," I say, grinning.
"What about the Orange and Purple lines?" Poppa asks.
"Forget them for a moment. They're both running south. Eventually they meet up and merge together, and we never hear from them again. Maybe they run down the page until they fall off the edge of the world." I laugh, because physicists aren't supposed to talk about the world having an edge. But this is just a parable, after all.
"This traffic camera," Mum says. "Presumably it's going to take a picture of the Yellow and Blue lines, which will join together at the intersection, and this will prove that light is either a wave or a particle. Or have I missed something?"
"No, Harriet, you're ahead of me. The camera snaps a single, shot of the two overlapping lines. When it's developed, it shows only a Green blur."
"Because," Poppa says, nodding, "the yellow and blue colors get mixed together on the exposed film, and that creates this green streak."
"Exactly. Think of that case as light behaving like a wave. Instead of our split photon travelling through the detector in the form of one distinct color or the other, it sort of gets smeared into a blurry wave."
Mum looks up suddenly with her spoon in her mouth. "I remember this now," she says, "atoms and electrons and so forth look like waves or particles depending on how you choose to observe them."
"Correct. So let's change the way we're observing these lines. Suppose we'd blocked one of the two lines running away down the south-bound roads, the Orange and Purple ones. Now we have a way of telling these two lines apart, which we were unable to do before. Say the Purple line is blocked." Ram pauses, and stares at each of us with a strange, mischievous excitement. "This is where it gets bizarre. Instantly, way over here on the other side of the page and it might as well be hundreds of kilometers away, the Yellow and Blue lines mysteriously thin out a little. Now the camera can only manage to take a shot of one colored line or the other, not both at once."
Poppa blinks. "As if they stop being spread out like waves and turn into particles?"
Ram scribbles frantically on his diagram, but at this point it looks as if he needs a computer animation to make it clear. "Give the economist a prize. So, let's say, the camera records only the Yellow line."
"You're cheating!" I cry in outrage. "How can blocking one of the Blue or Purple lines influence the Yellow and Orange ones? Are they all staying in touch somehow?"
"Nope. Absolutely no contact allowed between the Yellow-Orange pair and the Blue-Purple pair after they separate. That's the mystery of it. But wait! There's more!" he cries, like the advertising guy on telly. "If we re-open the road block now so the Blue and Purple lines do mix together after all," scribble, scribble, "the Yellow and Orange lines instantly blend back together. Now, as they cross at that intersection, the camera is again recording a green blur."
"This is making my eyeballs dance," Poppa says sadly.
Mum stares hard at the diagram. "Ram, if I follow you, you're saying that the top photons—the yellowish pair, I mean—stay spread out like waves only so long as nobody can tell one of the bottom photons—the bluish pair—from the other?"
"Precisely. What happens to the yellowish lines all depends on whether you make a particular kind of observation about the bluish lines, which are completely out of touch with them."
Mum snorts. "Well, that's sounds more like your original football teams. It's always the men who count in the end, and they're always completely out of touch."
Ram shakes his head, and smiles. "This isn't a parable about feminism, Harriet. But look, now it gets really weird. Say we re-run the ride once again, but this time we snap the photo of the Yellow and Orange lines crossing before anyone has decided whether or not to throw up a roadblock on one of the BOTTOM pair."
I say: "You mean the yellowish lines get photographed while the bluish lines are still running down the page on parallel tracks."
Ram nods. "Right. Then, if you later choose to leave the Blue and Purple lines separated, that film you've already taken—without looking at it yet—will show only one of the top colors, either Yellow or Orange. Remember, my dear, the shot is exposed before you decide what to do with the lower colors, but it's developed after you carry out that plan. It's as if your decision now in the present has influenced which of the two possibilities the camera recorded in the past."
I stare at him, trembling a little bit. "That's nuts!"
"In the words of my Adelaide colleague Paul Davies," Ram says, not taking offence, "the record of the past remains undecided—until we choose later to let the Blue and Purple lines merge, or keep them apart."
The dizziness I felt earlier returns. I'm whirling and buzzing. What the professor is saying sounds completely insane, but he said it's been done in a laboratory experiment and it works. Changing the past.
Mum has gone quite pale, and I wonder if she's as shocked as I am. "Ram, are you telling me that we can select reality after the event? That something I do today can affect what the picture shows even though the camera took it yesterday?"
"Yes, but only if you don't look. Because the past remains undecided until the whole experiment is completed."
I don't know why, but now I really do feel as if I'm going to faint. Or throw up. In a squeaky voice, I ask Ram, "Does that mean we can change the past?"
"Not quite—but the actions we take in the present moment help to determine the reality that was the case at a past moment. You see, in situations like Ray Chiao's experiment, the present is a kind of double exposure. The past only comes into focus when we—"
But I am losing his voice, which seems to echo and boom at the end of a long corridor. I feel myself slumping back into the chair, sliding gracelessly down on to the floor under the lace table cloth, and the world really has become an overlapping set of different movie frames. Mum is darting around the table to grab my hand, but at the same time she's not even there, not in the room, not even in the house, and Dr. Ram isn't there either, and some nerdish looking boy is holding up something disgusting, I think it's a human finger, yuck, cut off at the knuckle, and Maddy's boyfriend Davy is leaning across to kiss me, and Poppa is complaining about me hanging on the phone all the time, and—
TUESDAY, 9 MAY, MORNING (REVISED WORLD)
I'm having this terrible nightmare. My dear old friend has died, and there's nothing I can do about it. Blood everywhere. Ears and fingers cut off, it's horrible. Somehow, in the ridiculous way of dreams, there's a carton of eggs toppling off a bridge and falling down into rocks, and the shells crack open, and I see suddenly that the eggs haven't smashed into runny whites and yellow yolks because they're all hard-boiled, like blind eyes bouncing and jouncing into the water, and there's nothing funny about this, not one little scrap of humor—
I wake up sobbing. My bedroom door opens in the dim light of early morning and Mum bustles in from her upstairs study, where she's been sleeping in the spare bed for the last couple of months. Her warm perfume reaches toward me, and I sit up in bed with tears running down my face and hold out my arms to her like a little scared kid.
"Oh, darling, pet, whatever is the matter?" she murmurs in my ear, hugging me close and stroking my tangled hair. "It's just a bad dream, Jenny, that's all it is."
"I was talking on the telephone," I mumble into her hair, "and then he died."
"It's all right, sweetheart, it's just your imagination playing tricks on you. Nobody's been hurt. There, there."
I realize that I haven't got the faintest idea what I meant. The vague last memories of my dream drain away, and I give myself a shake. Mum sits back and looks at me carefully in the dim light from the shaded window. She pulls out a Kleenex from the pack on the dressing table beside the bed and dabs at my eyes.
"That's better, darling. Now try and go back to sleep, you can still get in another hour's rest before school."
Without quite knowing what I'm about to say, I blurt out: "Mum, are you and Poppa going to get a divorce?"
My mother shoots up off the edge of the bed as if I've jabbed her with a pin, and gazes down at me. "Why, Jenny, whatever gives you such a strange idea? Is that what your dream was about?"
I feel cold all of a sudden, and hunch down under the quilt. "Don't think so. It was about a boy who— I mean a man who—" I stop, my thoughts all tangled. "Well, are you?"
There's a long pause. Then Mum sits down again on the bed and puts her hand on top of the quilt, pressing my shoulder. "It's true that your father and I have been going through a rough patch lately, darling. But—"
I feel a lump in the middle of my chest, and a whiny little snivel comes out my mouth.
"—that doesn't mean we're going to split up," Mum adds firmly. "I know that's happened to a lot of your friends' parents, but it's not going to happen to this marriage. God willing." She leans over, kisses me on the forehead, and stands up again. "Try to get a bit more sleep, darling. You'll see, everything will look a hundred times better when the sun's properly up."
After a while I do drift off to sleep, and when the clock-radio rocks me awake at 7:30 all I recall is waking up from a bad dream, and Mum coming in to comfort me.
§
At lunch, I get a sudden great idea.
"Hey, Mads?"
"You can't have any," she says, greedily holding on to her last slice of pepperoni pizza. "Anyway, I thought you were going on a diet."
"You're the anorexic," I say derisively. "No, look, how about you and Davy and me go skating after school? You know, at the ice rink."
Madeleine looks vague for a moment, almost cross-eyed, chewing up her last bit of lunch, and then gives me a big grin. "Absolutely fabulous," she screams like Joanna Lumley on that telly show. "Only one problem—I can't skate."
We fall about laughing. "No troubles, sweetie darling," I shriek back. "There's absolutely nothing to it. Go and tell lover-boy, I'm sure he's got two left feet, he can stop you from falling over and cutting your fingers off." As the words come out of my mouth, a sick jolt of horror goes through the lump of pizza in my guts. Maddy doesn't notice. She just jumps up and zooms across the playground to where the boys are tearing around like great apes.
§
We wobble about on the ice. None of us is particularly good. Maddy has done a bit of roller blading and she reckons ice skating can't be that different, but she still falls over the moment she tries to go fast. Davy wobbles over to help Maddy. She grabs hold of his hand to pull herself up, but only succeeds in pulling Davy down on top of her. They lie on the ice in a giggling heap. I take it easy. I move with little shuffling steps, getting the hang of it, speeding up as I get more confident.
After half an hour all three of us are moving round the ice fairly fast. I dodge between two boys and collide with a third boy who's been catching my eye for some reason. I can't explain it, it's not as if he's especially good looking, or anything. Not like Maddy's boyfriend Davy.
"Sorry," we both say together.
"Snap," says the boy.
I try to think of something witty to say in return. But I can't think of anything. I'm getting these weird feelings again. I feel just like I did when I fainted during Professor Ram's quantum eraser story, or like when I woke up from the nightmare; I feel as if I've been here before, on the ice-rink with this boy. I look at the boy while trying to pretend that I'm not. He's a bit nerdish, wearing a bomber jacket with Property of the New York Yankees written on it. I've got this terrible urge to look at his fingers. I'm sure there is something wrong with his fingers, that he's missing one or two. I force myself look at his hands—and there's nothing wrong with them at all.
"Are you okay?" the boy asks. "You look traumatized."
"I'm fine, I'm really fine," I stammer. "Tristan."
His eyes bug and his mouth drops open. "How do you know my name?"
I'm covered in confusion. "I don't know. I just said it. I wasn't meaning to call you anything. Is that really your name? Are you called Tristan?"
"Yeah, that's my name. Have we met before?"
"I don't know," I say. "I suppose we must have. I sort of feel that we've met. But maybe we haven't. Do you know my name?"
The boy stands there on the ice, thinking. His skates, I notice suddenly, are very expensive, but they look as if he's used them a lot. And his hair's nice. Around us, the other skaters go whirling past. The rock music suddenly stops, and the echoey voice of the disk jockey says, "No throwing snowballs on the ice. Anyone throwing snowballs will be banned from the Ice Arena for the rest of the day." The music starts as suddenly as it stopped. I look around. A couple of kids are discreetly dropping the snowballs they'd made out of the ice-shavings around the edge of the rink. I look back at the boy. He is staring at me hard. I get the impression that he has the same funny feeling that I have. Very seriously he says, "I think you're mad."
I'm grossly insulted. I might be feeling a bit odd, but I'm perfectly sane. I snap back at him, "I'm not remotely mad, thank you very much."
"No, no," the boy says, flustered. "I didn't mean that you are mad. I meant that your name is Mad. I just had this weird sensation: I've met you before and your name is Mad or Maddy or something."
I gulp. This is truly crazy. "No," I tell the boy, "I'm Jenny. That's Mad over there. The one with the luminous yellow scarf—she's Mad. Madeleine."
The boy looks at Maddy and Davy, who are trying to skate with their arms around each other's waists. Then he looks back at me. "Of course," he says, "you're Jenny. She's Mad. I dunno how I could have mixed you up. But where have we met?"
"Look," I say, "This might sound a crazy question, but have you ever had any trouble with your fingers?"
Tristan stares at me. "No, never. Why?"
"I don't know," I say wretchedly. "I just had this feeling that you'd once lost a finger."
Tristan wriggles his fingers and grins. "All present and correct," he says. I notice that he's tucked his thumb away just to tease me.
"Never had microsurgery?"
"Nope," he says.
And then without thinking, I blurt out. "What about eggs?"
Tristan does a double take. "Eggs?!" he says, "Oh, eggs. Well, yeah, I'm not bad with eggs."
He seems to know exactly what I'm talking about, although I don't have a clue what I'm talking about myself. The question just leapt out of my mouth without me knowing what I was asking.
"Look," says Tristan, "Do you want a coffee or something?"
"Yeah, sure," I say.
We both skate over to the rink's exit, stumble in our skates across the rubber matting and through the glass doors into the coffee shop. When we've got our drinks and sit down beside each other at a table, we try to remember where we've met before. We get nowhere. Tristan lives in Kew and goes to some preppy private school. One of his brothers is a famous yachtsman, which just makes me yawn. It doesn't look as if our paths have ever crossed. So I say, "Anyway, about eggs. What are you good at with eggs?"
"You must know," says Tristan. "You asked me about them in the first place."
"Yeah, but I don't know why I asked you. I just did."
"Hang on," says Tristan, "Don't go away."
I watch him disappear in the direction of the lockers. A minute later he comes back with his hands in his pockets. He sits down again at the table, opposite me this time. His right hand goes up to the side of his head as he's reaching for his cooling coffee with his left, and he pulls an egg out of his ear. I smile, but in fact it's pretty easy to see how he does it. He had the egg in his hand all the time, only with the back of his hand turned towards me. It's a pretty amateur performance. He'll have to practice a bit if he wants a job as a magician. But, to be nice, I say, "Great trick. Can you pull one from my ear?"
"Anything to please a lady." Tristan turns around quickly in his seat so that I can't see what he is doing, turns back instantly to face me, making a great show of waving his right hand in the air. It's true that nothing appears to be in it. He's genuinely empty-handed. I'm a bit more impressed than I was before. With a flourish he brings his empty hand up to my left ear. But I see what he is up to. I turn my head to get a better look at the egg he is sneaking up to my right ear with his other hand.
Smash. The side of my face goes wet and crunchy. Yuck.
This is really gross. There's raw egg sliding down my face and neck and into the collar of my jumper. My hair is sticking to my ear. A few people at the other tables have witnessed this great feat of the conjurer's art, and there are some cheers and whistles.
Tristan says, "Oops!"
A guy with Ice Arena—Staff on his jacket comes over to our table and says to me, "Are you all right?"
"Yeah. Sure. I'm fine. Just fine," I say, seething.
"Well, just watch it, fella," the guy says menacingly to Tristan.
"It was a mistake," Tristan says to the guy. "I thought it was hardboiled. I've got a couple of hardboiled ones in my bag. I must have grabbed the wrong egg."
"Just watch it," the guy says again, but his heart isn't in it, and he wanders back behind the counter.
I go off to the Ladies and clean myself up as best I can. While I'm looking at myself in the mirror, trying to sponge myself down with a wet paper towel, I mutter, "I thought he was better at it than that—a real smooth operator." But why do I think that? I just know I do—I've got this really strong "memory" of Tristan effortlessly producing eggs from people's ears. Hardboiled eggs. Which he then eats. There's a duck floating on a pond. Oh, help! He's balancing on a railing over a massive gorge. Eating an egg. I know where it is: it's Merri Creek. I'm on the pedestrian bridge with him, scared out of my wits. Then I'm back in the Ladies at the Ice Arena. Just standing in front of a mirror with bits of soggy wet paper-towel stuck to my cheek.
When I get back to the Coffee Shop, I'm shaking a bit. Davy and Maddy are just stumbling through the glass doors, wobbly on their hired skates. They see me and I drag them over to meet Tristan. Maddy says something like how Tristan looks familiar, but she doesn't seem to be freaked by the fact: you meet people you vaguely remember all the time, Tristan's no different from the rest. We all drink another round of coffee in styrofoam cups, then go back to the ice.
For the rest of the session the four of us skate around, sometimes as a group, sometimes in pairs, sometimes alone. I decide I want to see more of Tristan, I need to find out what's going on. Before we leave the Ice Arena we exchange addresses and phone numbers.
§
I'd have preferred it if Maddy and David hadn't seen me exchanging addresses with Tristan. They take a keen interest in my love life, Mad and Davy. They are always on about it—or, rather, they are always on about my lack of it. Maddy can get a bit patronizing sometimes. Just because she's got this great hunk David putting his arms round her all the time, she thinks she can lecture me about lurve and passion and commitment and stuff like that. She thinks she's a bit of an expert, truth be told. (To borrow an expression from Poppa.)
David's not much help. He thinks he's god's gift to teenage girls. He thinks he's the reason Maddy thinks she's such an expert. So after we said goodbye to Tristan and got on the train, I know I'm in for a bit of teasing. We are rattling up Swanston Street, past the University, when Maddy says, "Why was your hair all wet in the coffee shop, Jenny? You looked like a drowned rat sitting there without that Tristan guy."
I have half a mind not to tell her. But I want to know if she's been getting these déjà-vu feelings as well. So I say, "He bungled the egg trick."
"What egg trick?" David says.
"The one where he pulls a hard-boiled egg from someone's ear and then peels it and eats it."
"Aw yucko," Mandy says. "That's gross."
"Not as gross as when the egg's raw," I say. "And it breaks."
"Is that what he did?"
"The guy's a sicko," David says. "I'd stay clear of him, Jen."
"I rather like him," I say.
"I've heard about getting egg on your face on your first date," Maddy says, "but not before the first date. I reckon if you're still going to go out with a guy after he's carried on in such a fowl way—" She winks at me, and I roll my eyes back at her—"well then, it must be true love at first sight. What do you reckon, Davy?"
"Aw, come on Mad. We can find Jen a better specimen than that. There are some cool dudes around. What about—"
"I'm not going out with him," I say.
"Yeah, right," Maddy and David say together. Then Maddy says, "No, of course you're not going to go out with him, Jenny Kane. You just gave him your address and telephone number in case he wanted to consult you about his homework, you being such a genius and all that. I mean you wouldn't be interested in going to the movie, or a rage or anything. You just want to talk to him about Fu Manchu and Ming the Merciless."
"What?" Davy says. "What's this Fu Manchu?"
"I don't know," Maddy says. "It's what Jenny talks to boys about."
"She only talks about science, don't you, Jen? Subterranean particles and stuff?"
I'm getting this weird feeling. I say, "Listen, Maddy. Why did you say Fu Manchu and Ming the Merciless? Why did you say I talk about them?"
Maddy looks confused. "It just sort of popped into my head. I reckon that's the sort of thing you and Tristan would talk about. You know, Chinese history. Or maybe it's Japanese."
David says, "Jenny doesn't know anything about Chinese history, do you, Jen?"
"No," I say. "But listen, you two...have we ever met Tristan before?"
"Yeah, right," David says. "Down the loony bin. On the funny farm."
"Come on, be serious," I say. "I've got this sort of memory as being on a bridge with him. I think it's the Merri Creek Bridge. He's fooling around standing on the railing. There's a train rattling past...."
Maddy and David look at each other. David makes a face that says, Jenny's gone bonkers. But Maddy looks a bit more worried. I think she knows I'm talking about something serious. She doesn't say anything, just leans across from where she's sitting and puts her hand on my shoulder and squeezes. I know what she means. She means: Let's talk about this when David's not around.
For a moment there's a bit of commotion when a group of Japanese tourists start taking pictures of each other in the aisle of the tram. I start telling Maddy and David about Ray Chiao's experiment. I try to explain it using Dr. Ram's analogy.
I haven't got very far when David says, "Color gangs are all into organized crime in Los Angeles. I saw it on 60 Minutes. They have shootouts in car parks outside some sleazy bar. Bodies all over the place. And they make half the drugs on the street. Speed and that."
"It's only an analogy about photons, the different colors," I say.
"It's not analogy," David says. "It's analgesic."
He looks really pleased with his use of a big word, even if he has pronounced it wrong. I tell them that analgesic is another word for aspirin. "But photons," David goes on. "That's a new one. Probably worse than Grievous Bodily Harm. Some of these new drugs—no one knows what's in them. There was this nightclub in Queensland. Everyone was dead by morning."
Maddy just looks out of the window of the tram. I could tell David that photons are actually subatomic particles of light, but somehow, I don't think it's worth the effort. When we get to our stop we all get off the tram and scuttle across to the pavement. I'm meant to go one way and David and Maddy are meant to go the other. But Maddy says, "I'll go home with Jenny."
"Jeez, Mad," David says. "I thought we were both going to your place."
"Yeah, well, I reckon I'd better see Jenny home. She's not feeling well."
"Aren't you, Jen?" David says. He is very concerned. "You should've said. Because I'd of got you an analgesic at the Ice Arena. They're sold in the coffee shop."
"No, it's all right. I haven't got a headache," I say.
"Well, I'll come back to her place, too," David announces. "Then I can walk Maddy back to her place."
"Look, Davy," Maddy says, and puts her arms around him and whispers in his ear. Then she kisses him.
David suddenly seems a bit embarrassed. His face just goes slightly red.
"Oh, um, errr...all right then," he says. "Um, see you later, Jenny."
Maddy kisses him again for about 10 seconds. The pair of them just stand there on the pavement with cars and trucks roaring past and a couple of pedestrians have to walk around them. I exchange a shrug with one of the pedestrians—a woman carrying three plastic bags of shopping and a baby. Then David is disappearing in one direction and Maddy and I are taking the shortcut to my house in the other direction.
"What did you tell him, Mad?"
"What do you reckon?"
"I suppose you told him I had women's troubles."
"Actually, I said girl troubles."
"Same diff," I say.
And then Maddy and I are giggling like kindergarten kids walking along with our arms around each other. Poor David. He's a nice boy and I'm really glad he and Maddy are an item, but the truth is, he's a bit thick. And he'd run a mile from girl troubles.
"So what's it all about?" Maddy says as we approach my place. "What's all this about hard-boiled eggs and bridges?"
"Look," I say. "It's just that I've been having these funny flashes."
"Flashes?"
"Here, you know, where one thing remind you of another, and the first thing seems familiar, but it isn't."
"That's just because you forget stuff," Maddy says. "I forget stuff all the time and then maybe I half remember it. School crap especially. Your trouble is that you have a mind like a steel trap. You never forget things. Except now you're starting to. Welcome to the real world."
"No, it's not like that," I say. "I have this feeling I've met Tristan before and he was fooling around on the Merri Creek Bridge. If I'd ever actually had that experience, I couldn't possibly just forget it. Or even half forget it."
"Well, I don't know," Maddy says. "Tristan did sort of seem familiar. And what I said about Fu Manchu—I've got this feeling that Fu Manchu is really the name of Tristan's friend."
"But that's silly," I say. "Nobody is actually called Fu Manchu."
"Must be a nickname."
We've reached our house and we go inside. Nobody is at home. We climb the stairs and sit on my bed.
"Don't worry about it, Jenny," Maddy says. I'm sure there's an explanation. Are you going to go out with the guy?"
"I think I'll go around to his place and see him. Have a talk. See if we can work out what's going on."
"I'd do more than that," Maddy says. "If I were you, Jenny, I'd do a lot more than just talk to the boy."
"I know you would."
"It's about time you expanded your horizons."
"Expanded my horizons," I say, all innocent. "Why, Madeleine dear, what can you mean?"
"You'll have to find out for yourself."
"No I won't," I say. "You're going to tell me."
And I suddenly turn to where she's sitting beside me on the bed and I grab her under both armpits and tickle her for all I'm worth. Maddy fights back. We roll around giggling for a bit and then she says, "All right, all right, Jenny Kane. I surrender. I'll tell you how to expand your horizons."
And for the next half hour she does just that.
TRISTAN'S CASEBOOK: May 9
I take up my pen to write in this most sacred of notebooks with less than my usual composure. God, that sounds pretentious. I'm beginning to think that a lot of the crap I write in this notebook is pretentious bilge. I'll try to write sensibly.
My brain is out of control. I've met this girl. Jenny. At the Ice Arena. Perhaps Jennifer. But no, I don't think so. I think Genevieve. I'm sure it's Genevieve. I know it's Genevieve. But the question is: why do I know it's Genevieve? She didn't tell me, she just said that her name is Jenny. At first I thought it was Madeleine, but that was her friend. It was weird. And she knew my name straight away. I didn't have to tell her.
I made a fool of myself, though. The egg trick went all wrong. Poor girl. She had yolk and albumen running all down the side of her face and in her hair and everything. I could've crawled under the table I was so embarrassed. She was nice about it, though. And afterwards we were skating together and she was laughing, and, well, when she laughs as she was quite pretty. That's a bit mean, saying she looks "quite pretty." She looked pretty. Full stop. She gave me her phone number and address. Maybe she'll ring me. But if she doesn't, I'll damn well call her.
But the funny thing is, I think I already know her. But maybe that's just because she's so nice, intelligent, and when she laughs it's like all the world is suddenly new and exciting.
I like writing this way: just letting the words say what I'm really feeling. It's better than all of psychoanalytic rubbish I normally write. I think I'll give up writing psychoanalytic rubbish.
Sigmund Freud, you're a long-dead duck.
SATURDAY, 13 MAY, AFTERNOON (REVISED WORLD)
Tristan lives in this expensive house in Kew. He meets me at the front door, but instead of showing me in he leads me around the side of the house. "Dad's got some important international clients with him," he explains, "Arabs, I think." A short flight of steps leads downwards to a sort of half-submerged cellar. I step inside, and the creepy feeling is back. I've been here before. Visions of mad dogs barking.
"I have this incredibly strong feeling," I say to Tristan, hesitating in the open doorway. "I've been here before and there was a pack of fierce dogs in here."
"Could only have been one dog," Tristan says. "Lamb Chop."
"That's its name," I say, excited. "Lamb Chop. It was tied up, really fierce. The computer was, was showing toasters."
"He couldn't have been very fierce," Tristan says, looking at me strangely. "He got run over when he was still a puppy. Dad wouldn't have another one, he said his death made me too upset. It did, too."
"That's not what I remember," I say stubbornly, even though I feel stupid. "I remember it as huge, snarling. A, a Rottweiler."
"That's the right breed. Your Mum and Dad must have brought you here when you were about four or five."
That thought also makes me go queasy, and I can't imagine why. The thought of my Mum being here just makes me want to throw up. I say nothing, because there's nothing sensible to say. I sit down on an old couch with the stuffing coming out of one arm, and Tristan perches on a swivel stool in front of his computer. "Tell me everything you can remember," Tristan instructs me.
This seems a bit one-sided. "You've got to tell me everything you remember as well."
He nods. "Sure. It's a deal."
"Look, you know how when we met on the ice you told me I was mad?"
"Yeah," says Tristan, "an unintentional pun."
"Well, look, forgive me for saying this. But I've got memories of you saying you were seeing a shrink."
Tristan blushes a deep red, and doesn't say anything for a minute. I'm a bit worried I've touched a raw nerve. Eventually he says in a low, controlled voice, "A psychoanalyst. Her name's Dr. Grogan. I see her twice a week. Tell me more, Jenny. Tell me all you can remember."
"This has got nothing to do with you," I say, "but I've been having these dreams of being rung up on the phone by someone called Rod. He tells me he isn't in our time. He's in 1960."
"I had the same dream," Tristan says wonderingly. "You recorded him on a little tape-recorder and played the tape to me. I remember now. But this is nuts. People can't have the same fantasies in their dreams. That Jungian, not Freudian."
I don't know what he's talking about. "It was real, though, it wasn't a dream. When did it happen? It can't have been very recent, we'd remember it better if it was. But it can't have been years ago either—we'd both have just been tiny."
"Listen, Jenny," Tristan says. He's staring at me as if the most amazing thought he's ever had has just gone off with a bang inside his head. "I think we might be dealing with parallel universes here."
"With what? Get a life, Tristan! That only happens on telly."
"No, no, this is serious. There was this Science Show I heard a couple of weeks ago. Paul Davies was yacking on to Michio Kaku about hyperspace and Many-Worlds cosmology. You know, parallel realities."
"Yeah, I heard that one."
"Davies said you'd go bonkers if you tried to live your life thinking that the universe is branching into stacks of other universes all the time. We have to go around behaving as if it's all so simple and straightforward. But really space and time are breeding like rabbits."
"He didn't say breeding like rabbits."
"No, but that's what he meant. It's the same with psychology. We can't go around all day long knowing our innermost thoughts are just a chunk of the collective unconscious. We want our thoughts to be our own. But really—"
"Yeah, yeah," I say, shrugging. "Poppa says people don't put much faith in Freud any longer."
"The collective unconscious is Carl Jung, not Sigmund Freud."
He's about to go off on one his favourite rants again. Hastily, I say, "What do you think these different universes have got to do with our funny memories? Aren't they supposed to be in, like, different universes?"
"Our memories are leaking over from one world to the other," he insists. "That Rod guy must have something to do with it."
"This is spooky, Tristan," I say, shivering. What he's suggesting is mad, but....
It's actually quite warm in Tristan's secret room under his father's house, but I feel chilly anyway. I'm beginning to believe him. "This is more like something out of Time Trax or The X-Files than anything Mrs. Levine teaches us about physics."
"But it's interesting, it's exciting," Tristan says. "Can you remember that Rod guy's surname?"
"Why?"
"Because we might be able to track him down, see what he has to say."
"But he was in 1960," I say.
"There are people still alive who were alive in 1960. He'll just be incredibly old, that's all. He might be sixty or something. Think, Jenny. What was his surname?"
"I don't know," I say miserably.
"Think!"
"You think! If I played some tape-recording to you, I must have told you his name."
We both sit in the cellar, thinking. It is an untidy place, full of old books and posters for heavy metal bands. On the computer, a screen saver is endlessly producing bubbles.
"Shouldn't you turn that thing off?" I suggest.
"It's bad for a computer to be turned on and off all the time," Tristan says. "It's better just to let them run."
"Sorry," I mutter, "you've told me that before."
"Have I?"
"Yeah."
"I can't remember," Tristan says.
"I can," I say, "I've got this really strong memory of you saying just that. Really strong."
"Strong!" yells Tristan.
"Not that strong," I say.
"No, no, you maroon. The guy on the phone!" Tristan is jumping up and down and swiveling about in his seat.
"How would I know if he's strong or not, I've never seen him," I mumble. I don't like being called a maroon.
"No. That was his name. Rod Strong. Rod Strong!"
"No, it wasn't," I say, feeling quite sure of this even if I don't know his real name. "He had an Italian name. He didn't sound Italian, but his parents must have come from there."
"Got it!" yells Tristan. "Forte! The Italian for strong. Rod Forte, that's gotta be it." The kid is going ape, and I'm starting to get excited myself. Although I know we are not there yet.
"No," I say, "It had more syllables, it was a longer name."
"Well, what else was he called?"
"I'm thinking."
"Well, don't, don't think!"
"What do you mean? Don't think? What stupid advice! Don't you want to know his name?"
"Of course I do," Tristan cries. "But it's an old Freudian trick. If you want to uncover a blocked memory you don't think about the thing itself! You think about something else and the unconscious mind sneaks past the block and gotcha! It's all in the Psychopathology of Everyday Life. Chapter...er...chapter...I think Three."
"What Mrs. Levine says is," I say, "she says Freud couldn't think straight to save his soul. All his ideas are patriarchal waffle from middle class Vienna before the First World War. She says—"
"Stop raving, girl!" yells Tristan. "How can I think with you going on about this Mrs. Vine and her idiot ideas?"
"Levine...and you're not meant to be thinking about Rod's surname, you said so yourself. So stop cracking on at me about stopping you thinking because...."
"Piano-Forte!"
"What's that got to do with anything?" It's just the proper name for a piano. It means soft-strong, from before they had peddles on musical instruments.
"It's his name!" Tristan shrieks. "That's what he was called. Rod Piano-Forte."
"He wasn't a piano," I say, "he had a proper surname, not something stupid."
"Well, what was it?"
I think for a bit, then I say, "You're right, it was very close to Pianoforte, but it was...."
"Go on."
"Go-on! That's it!" I yell and suddenly I'm up off the old sofa I'm sitting on and I've embraced Tristan where he's sitting in his chair and I've kissed him and I'm yelling, "Go-on Forte! Go-on Forte! No, that's not right, I remember now, Professor Ram told us about him last weekend at dinner and I didn't even know it was him, God maybe that's why I fainted, I suppose I could just telephone Ram and ask him for the name but that's no good because Ram's gone back to Sydney and I'd have to ask Poppa for his number and how could I explain why I wanted to, hang on, hang on, he said this Rod had been a student at Sydney university when him and Poppa had been students and he got into some terrible trouble and his name was...Gianforte, Gianforte, Gianforte, Gianforte." I'm giggling like a lunatic. "Quick," I say, "let's go upstairs and get a phone book."
"On the floor next to you." I get the listings open at G and race through them. Giancaspro, Giandzis, Giang Thong, Gianni.
"It's no good," I say, "it would have to be between Giandzis and Giang Thong. He's not in the book. Maybe he's already dead."
"Or moved away," Tristan says.
"We can't go through every phone book in the world, looking for the place he's moved to."
"Internet," Tristan says. To my amazement, he reaches around behind the computer and hooks out a handset. There's a tangle of wires linking it to a jack running into a box that's also connected to the computer.
"You've got a modem?" I cry with strangled envy. This kid has his own line to the Internet! Poppa and Mum would have a cow if I asked for something like that in my room.
"We have to," Tristan says vaguely, holding the phone. "It's a requirement of the school."
"Oh, very class-y," I say sarcastically, but really I'd die for a modem. "What are you doing?"
"We could at least try the capital cities of Australia," Tristan says. "Start with Canberra and then try Sydney."
"That's it, Sydney, he lives in Sydney, Ram said he'd just come back from New Zealand or something. Does the Internet have a Sydney phone book?"
"Probably."
Tristan is keying away like a professional typist. He mutters, "Okay. Sydney area...Gianforte...initial R. Damn, it'd help if we knew his address. Even his suburb. Nope, no R—"
"H!" I gasp, "Initial H. His proper name is Herod or Hotrod or something!"
"Let's try initial H." Tristan clicks, then sends me a smug glance. "Newtown." He is scribbling a number down on a yellow Post-It pad, hands the pad to me. "There you are, Jenny," he says. "Try that."
My fingers are trembling so much that twice I make a hash of punching in the numbers. Finally I do it right, and in my ear I can hear H. Gianforte's phone ringing in New South Wales.
SATURDAY, 13 MAY, AFTERNOON (REVISED WORLD)
Someone picks up the phone and through the STD pips a petulant man's voice says, "Well, what is it this time?"
I'm instantly paralyzed. I peer at Tris, who stares back at me and waves his hands in a questioning way, and I don't know what to say. Is this bad-tempered old man the mysterious "Rod" who's been haunting my dreams? "For heaven's sake," the voice says angrily, "just leave me alone," and I realize with a cold, sinking feeling that he's about to put the phone down in my ear.
"Don't hang up!" I squeal.
"What? Who is this?"
"Please don't hang up," I say, and then my voice gets caught in my throat again.
Tristan is pulling the most hideous faces of frustration at me, as if to say that he would have made a far better fist of this than I'm doing, and it makes me so confused and irritable that I have to turn away from him.
"Why shouldn't I hang up?" the angry old man snaps. "Do I know you? Are you from Foundations of Physics?"
"No," I manage to say. "Excuse me, is this Mr. Rod, uh, Gianforte?"
"Doctor, damn it, doctor! I'll ask you for the last time, who is this?"
"Sir, doctor, please don't hang up, this is very important."
"Is this a child I'm speaking to?" He is intensely suspicious. I've never met anyone as crabby and bad-tempered as this man at the other end of the thousand-kilometer wire between Kew and Newtown. "What's a child doing phoning this number?"
"My name is Genevieve Kane, Dr. Gianforte," I say very carefully and crisply. "Yes, I am a child, well, a teenager, but I'm in the accelerated physics class." I don't know why I've said this, and out of the corner of my eye I see Tristan cover his head with his hands and fall over sideways off the sofa on to the floor. It's enough to give me the giggles, but I clamp down on the merriment because I really don't want to make a mess of this. If I don't find out what's going on with our lives right this moment, the mad scientist will surely never answer another phone call from me as long as he lives.
"Very impressive," Dr. Gianforte is saying sarcastically. "And what possible concern could that be of mine? Besides, how did you obtain my telephone, it's not in the book yet, I've just moved in to this flat. I could sue Telstra for such a lapse of security. Breach of contract!"
"Um, um," I say intelligently, "um, Professor Ram told me you were back in Australia, so I used the Internet directory."
"That's not good enough, I thought I made it plain that I wished the service to be unlisted. Why does nobody pay any attention these days? Ram, you say?" he asks suddenly, interrupting his moaning about the state of the world, "are you referring to Ram Kanthamani?"
"Yes sir," I say, "we had dinner with him the other night."
"But he's at Sydney University," the man says suspiciously. "And you're not, I heard the STD beeps. What sort of game is this?"
I'm getting quite scared by now. The guy sounds like a certified whacko. Tristan has picked himself up off the floor and clunked his stool over beside me, where he's perched with his ear up against the back of the handset. I nudge him away, but he just cozies right back up.
"Actually Professor Ram's recently moved to Melbourne University," I say. "That's why my father invited him to dinner, we often do that with important people who've just come to Melbourne to work."
"Important? Harrumph!" Dr. Gianforte is indignant. "I don't know how anyone could regard Ram Kanthamani's tedious and derivative work as 'important,' I anticipated everything he's done with quantum theory back in the 1960s, and little good it's done me. Why, if the proper credit had been granted to—"
I take the chance of butting in. "That's just what Professor Ram was saying to my Poppa the other night."
That stops him in his tracks. Still with a suspicious note in his voice, but interested for the first time, the man says, "Oh, is that right? Kanthamani said that?"
I rack my brains, trying to recall just what Ram had said. There was that "quantum eraser" parable that seemed to mean that you could change the past, or rather that the past was blurry until it wasn't, or something, but I seem to remember something positive about Rod Gianforte. Oh, yes; it comes back to me.
"He said you knew more about quantum experiments with time than anyone else in this country. He said you could explain Raymond Chiao's recent experiments with, um, with—"
"Yes, yes," the man says impatiently, "delayed quantal photon indeterminacy measures. How old did you say you were?"
"Nearly fifteen."
"Good God, and they teach children this sort of theory at that age?"
"No, sir, not exactly. I was just having dinner with—"
And in the middle of my sentence, everything drops into my brain like a load of soggy cold pasta bursting through a brown paper bag. I gasp. I can't breathe. I drop the phone. Everything spins. I topple off the chair. Ripples. Time like ripples. Causes and effects in the wrong order. Changing the past, and changing the future. My brain seems to exist in two worlds at once, like a double exposure. Tristan is leaning over me, helping me sit up, concerned, and I wave him away. He has the phone in his hand, and is speaking with confident clarity to the man at the far end. I crouch in the middle of the old carpet, and tears are running down my cheeks. Oh, Rod. Poor Rod. I cried when I knew you were going to die, but look what's happened to you now. You didn't die, but you've changed. Time has spared you, and you have ruined your life. You've become a horrible old suspicious meany.
"I don't think she can speak to you just now, sir," Tristan is saying. "She's just had a nasty turn, it might be something she ate. Can we call you back later this—"
I snatch the phone out of his hand and say to the bad-tempered man in Sydney, "Listen, in 1960, thirty-five years ago, you tried to place a call to the future. You built a resonance machine that was connected to the telephone network. Am I right?"
There is a long, appalled silence. "How do you know that? How could anyone— Is Kanthamani spreading this sort of outrageous rumor, after all these years, I simply will not put up with—"
"You got through to me," I tell him.
There is another long pause. The emotion seems to be drained from his voice when he says, "No. Impossible. The machine didn't work. The valves overloaded and caught fire. There was a huge synchrotron surge through the hardware."
"And the computer burned to the ground?" I say, guessing.
"Not just the computer," Rod Gianforte says sadly. "The entire building. It cost half a million pounds to repair the damage."
"In this world," I say, and hold my breath.
His voice regains its abrasive hostility. "What other world is there, you stupid child?"
"The world where you got through to 1995," I explain, holding my temper back, "and you got through to Genevieve Kane, who's me, and we worked out how to make a million dollars through gambling and you set up the Ripple Corporation, and then you—" I can't go on. My head seems full of worms and old, lost grief.
"I what?"
"...You died."
Tristan is staring at me as if I've gone stark, staring mad. But I'm used to that reaction. Maybe it's true.
"The resonance radiation," Rod Gianforte says in a thin, terrible voice. "It would have been massively carcinogenic if I'd kept the original machine running for any length of time. Cancer. How did you know that? How could anyone? Good God, child, even Ram Kanthamani couldn't know that. I've never published...." The wire hums. I hear him grunt, loudly, as if he's been struck a blow to the belly. "Oh God, Genevieve," he says then, "I'm remembering. It's coming across to me. Oh dear Lord, it killed me. It gave me cancer, and it killed me. My double."
I'm sniffling softly as I hear the man at the other end of the phone line weeping for a lost life that never happened because somehow we changed it. Tristan just stands next to me without saying a word, for a change, quietly holding my spare hand very tightly.
Dr. Gianforte sighs, at last, and I can hear him blowing his nose.
"So, it worked. Well. And I'd thought my career had been ruined, when actually I'd avoided dying of cancer. Well."
I whimper, "How come we can remember all this if it didn't happen?"
The man gives a hollow laugh. "A quirk of the quantum universe, Genevieve Kane. I don't suppose you'll understand this yet, not until you've studied the field at university—"
"I want to," I say urgently. "That's what I want to do when I get out of high school. I want to be a physicist."
"Good for you, girlie. It's so strange, I can half remember talking with you...before. I was just a boy myself in those day. Twenty-four, twenty-five."
That doesn't seem too young to me, but I guess for someone who's sixty it must look like that. "Me too," I say. "It's very blurry, though." I glance at Tristan, and suddenly a whole lot of new stuff comes plopping like a heap of poisoned toads into my mind. I jerk away from him and almost drop the phone.
"What, Jenny?"
"Your father!" I spit out at Tristan, feeling really scared and rotten. "Your father and my mother."
I watch it hit him, as if he's recalling something that's repressed from memory, like that Freud stuff he was talking about earlier. He shivers, and looks away from me, embarrassed.
"Well, that hasn't happened, has it?"
"No," I say coldly, "and it's not going to. Your father busted up my parents' marriage."
Tristan is looking awful and sick, but then he stares up at the right-hand corner of the ceiling like you do when you're trying hard to remember something, and after a moment he gives me a snaky look.
"No he didn't, Jenny. I mean, that's a whole different world we're talking about, but he didn't anyway."
"Yes he did," I snarl. I've let the phone drop to my lap, and I'm hunched up in misery. "They got married. Or anyway they were going to."
"But I can remember him telling me, telling that other me, that your Mum had split up with your Dad a year ago. It wasn't his fault, Jen."
I sit absolutely still. It comes back to me like a lesson you've learned and forgotten until the exam, and I cringe even tighter. Tristan's telling the truth. In that other history, my mother hadn't just moved out of their bedroom and upstairs into the spare room. She'd left us completely. She'd gone off and rented her own flat. Tears are leaking down my face again. I pick up the phone and Dr. Gianforte is talking as if he hasn't even noticed I wasn't listening.
"...in a condition of superposition," he says. "I know this is difficult for you to understand, Genevieve, but those two histories haven't properly separated and decohered yet."
"What?" I say, flummoxed. "What?"
"Every time we make an important choice, the quantum universe splits into all the alternatives that would follow from that choice. Say if you came to an intersection and went one way and got hit by a truck, well, in that history you'd be killed. But if you took the other road you'd be all right."
"Like the yellowish photons and bluish photons," I say tiredly.
"I don't follow you."
"It's a parable that Professor Ram told us the other night. You don't know what's happened even after it's happened until after." That doesn't sound right, but I'm too tired and sad and scared to care much.
"Well, that's a very vague way to put it, Genevieve," Rod Gianforte says, "but you're on the right track. You see, we've done something very peculiar here. In a way, we've short-circuited the universe. Correction: the universes."
"There's more than one universe?" I raise my eyebrows at Tristan, who's trying with great difficulty to overhear our conversation.
"There is now. In that other history, I opened up a resonance pathway from 1960 to 1995. But it killed me, which sort of cross-wired everything and all the fuses of that spacetime loop burned out. It's as if history started again from some point before I made contact with you. But the different quantum states stayed entangled. Somehow we've welded the two together. There's been some discussion about this possibility by a British physicist called David Deutsch. He believes that—"
"Excuse me," I say. "I don't understand much of this. Could you try to keep it real simple?"
Some of his bad temper comes back. "Oh. Very well. I thought you were a clever child."
"Yes," I tell him, "I've got a mind like a steel trap." A new shiver runs down my spine.
Tristan says, "Ask him if he's built a replacement machine."
"Okay. Uh, doctor, did you try it again after the machine blew up?"
He laughs harshly. "Hardly. I was lucky to escape with any of my professional reputation intact. Besides, I concluded that it couldn't be done with the available technology."
I look at the neat little Apple computer on the desk. Toasters have started flapping across its screen. "That was then," I tell him. "What about now?"
"Don't think I haven't thought about it. It's all I've worked on for the last thirty years—in my spare time, of course, after I'd corrected a hundred stupid essays every night." He sounds exasperated, and I guess I can't blame him. "In fact, with today's micro-technology, and Deutsch's advances in theory, I suspect we're only a decade or so away from a safe, functioning temporal resonance system."
"Oh." I'm disappointed. "You reckon if you tried to build a resonator now it'd just blow up again?"
"No, I imagine we've got that under control with micro-circuitry. It's the radiation effects I'm thinking of. Give it ten years and we could have a shielded machine that dials back in time to a specific number—and then we'd really see some fancy effects."
I stare at Tristan with my mouth open. "He says he could get one that sends messages backwards as well as forwards."
Tris jumps up, rubbing his hands together. "That way you could win the lottery every week! You could change history!"
"Listen, Dr. Gianforte, why don't you get in touch with Professor Kanthamani and tell him about all this? He might get you a lab to work in, and—"
"I'm too damned old," says the voice from Sydney. He really does sound old, too, even though he's not all that much older than Poppa, now that I stop to think about it. "Too old and bitter and twisted, child. I've had my innings, and my score has not been impressive." I hear a thin, angry laugh come down the line. "In either history. Dead in one, a disappointed old misanthrope in the other. I shall leave it to someone else to carry on my work, Genevieve."
"I could do it!" I blurt. Suddenly I don't want him just to hang up and go out of my life. I can't really recall that other life in any detail, but there's a distant warm memory of a bright, caring man who died thirty-five years ago, and somehow this poor sad man is all I have left of that memory. Besides, I can't bear to imagine that his work will simply be lost, even if it is rediscovered by some nameless researcher in the twenty-first century. "I'll go to university and carry on your work," I tell him urgently.
There is another long silence, but I don't get any angry vibes down the line. After a time, Dr. Gianforte says in a pleased voice, "Well, perhaps you could, young Genevieve. I have all my research material stored here in my computer—"
"Print it out and mail it to me," I suggest. "I could hang on to it until I know enough physics to pick up your trail, and then—"
"Print what?" Tristan says. "Mail what?"
"He could send me everything he's got in his computer."
"Just put it on disk," Tristan says.
I'm crushed. "Oh, of course." I speak into the phone. "You could send me a Mac computer disk. For that matter, you could email your files to my father's computer. Do you want his number?"
"That's possible in principle," Dr. Gianforte muses, "except that we're talking about a couple of megabytes of text files and twenty or thirty megs of instrument data, so he'd need access to a Syquest drive. Hmm. In any case, of course, I'd have to ring him first and ask his permission, and that would lead to endless complications, and I'd have to get Ram to vouch for me.... No, really, it's just too much trouble. Let's forget the whole thing. I'm sick of it. Sick of it."
Tristan is pulling at my arm. "Use my modem right now. Ask him if he's got an Internet site. If he'll tell us his Net address—"
"Brilliant," I squeal. Eagerly, I explain our idea.
"You have a computer there? Why didn't you say so? Are you on the Net?"
Tristan nods. "I have a CompuServe account."
"Very well," Dr. Gianforte says. "You can find my research material under the name 'quanttime,' I've arranged it for anybody in the physics community who cares to study my findings and attempt a replication. Not that anyone with a brain in their head has bothered accessing it." He pauses. "Er, look, I know I was rather gruff with you when you first called...."
"That's all right," I tell him. The memory of that other, younger Rod helps to ease the sting of how rude he was.
"Well, it's not really all right. I'm a bad-tempered old stick, and my personal unhappiness is no excuse. I just want to thank you for taking the trouble to call me. You've given me a new lease on life. Who knows, perhaps I'll get back to this resonance research after all. If not, I expect you to finish it for me in the fullness of time. Is that a deal?"
"Deal," I say, grinning. "It's been a pleasure doing business with you." My voice drops, and I say quietly, "I'm glad you didn't die, Dr. Gianforte."
"Perhaps I am, too. And by the way, girlie?"
I hate the expression "girlie," it makes my scalp itch. But I can tell he's trying to be nice.
"Yes?"
"Call me Rod."
"Thanks, Rod. Call me Jenny."
I hang up. Tris starts scrolling through directory menus. Dr. Gianforte's Home Page comes up on the screen. It's the bare minimum, no fancy graphics or user-friendly icons, but it looks as if we should be able to find our way through it with a bit of effort. He finds a folder called "quanttime," utters a little cry of triumph, and clicks on it. After a few minutes, we realize that it's all heavy philosophy and even heavier mathematics that neither of us can understand—yet. Dr. Rod is right, this is going to be a long-term project. Tristan puts an electronic bookmark on Dr. Gianforte's site, so we can get back to it easily next time, logs off, and we get up and stretch and go out into the garden.
The ornamental pond is just where I "remember" it. A tall man is standing near a weeping willow, tearing up bread crusts and throwing them to the birds. He turns as we walk on to the grass, and my heart turns over. Thring!
"Hello, Tris," he says in quite a nice posh voice. "And who is your friend?"
"Dad." Tristan clearly likes his father. He touches his arm and gestures to me. "Jenny Kane, meet my father. Her dad's an economist at the university."
"Oh yes, Dr. Kane, we've met once or twice. And your charming mother Harriet. I hope they're well?"
My stomach sinks even further at the mention of my mother's name. But the man does not seem to be hiding any deep dark secrets. That was a different history, I tell myself, and we're going to keep it that way.
"Yes, sir," I say uncomfortably. Looking for something neutral to say, I mumble, "I like your garden."
"Beautiful, isn't it?" He glances in a rather touching way at the autumn landscape, the birds moving slowly on the blue-gray surface of the water. "My late wife designed all this. She had a special eye for beauty." He gives himself a shake, and I decide he's not such a bad old stick. "Well, very nice to meet you, Jenny. Perhaps Tristan will invite you to join us for tea, if your parents will allow that?"
I nod without saying anything, and a phone rings loudly. Both Tris and I look in surprise back toward the den, but the ringing is coming from his father's belt. Snatching up his mobile phone, and waving farewell to us with his other hand, Tristan's father turns toward the house, barking into the phone: "Thring!"
I just break up. I can't help myself.
Everything collapses in on itself. I'm almost paralyzed with laughter, red-faced and humiliated, laughing like a nut case. Edward Thring pays no attention, disappearing into the big house. Tristan stares at me in astonishment, and I gasp and shriek with mirth. And I can't explain it to him. I can't scream out, "Thring! Thring!" And I don't really know why I wish to. It's just all so incredibly funny.
Through my laughter, I hear a phone ringing. It sets me laughing even harder, and then after a while Tristan is shaking my arm.
"Pull yourself together, Jenny, there's a phone call for you."
"What? What? Where?"
"My phone."
"Rod again? Maybe he wants to know if we found his site—"
"No. This is someone else."
How could it be? Nobody even knows I'm here. Poppa and Mum certainly don't. Anyway, wouldn't they ring the main house? Maybe Maddy copied it down when we all swapped numbers at the skating rink. But why should she phone me at Tris's? Unless she's after him. Maybe she's sick of David. I give him a dark scowl as we trot back down the path to his den. The phone is lying on his desk beside the computer.
"Hello?"
A woman's voice says, "Don't hang up!"
Another little jolt, like electricity, goes through me, making my hands and feet prickle. What does that remind me of? I don't know the young woman's voice, but strangely enough it sounds a bit like Poppa. His accent, I mean; he's got quite a deep voice. Or maybe it's Mum's voice I'm reminded of.
"I won't hang up," I say. "Why should I?"
"Just don't. You might not believe this."
I start to get it, then. And I find this big huge grin spreading across my face.
"It worked?"
There's a gust of happy laughter at the other end of the phone. "It sure did! Only took eighteen years, too."
Tristan is jittering from one foot to the other, like a little kid who has to go urgently and needs the teacher's permission to leave the room. Except I'm sure that leaving the room is the last thing Tris has on his mind.
"Who is it?" he hisses. "What worked?"
"It's a person called...Jenny," I tell him, grinning fit to bust.
There's another gust of laughter from the other end. "Show some respect for your elders, Jenny! It's doctor, as our friend Rod Gianforte insists. Dr. Genevieve Kane speaking."
Tristan is no slouch. He's gazing at me and at the phone in astonished delight. "It's...you?"
"Yep," I say. "In 19— Uh, Genevieve, what year is that?"
"2013, Jenny," the confident voice tells me. "Ask Tris if he'd be so kind as to buzz off and make you both a hot chocolate, then pull up a chair. We have some catching up to do, kiddo."
"I'll leave you two alone," Tristan says, rolling his eyes heaven-ward. "If there's one thing I can't stand, it's a long session of girl-talk." Then that mad boy reaches across in front of me, pulls an egg from my ear, snaps it on the desk, peels it, and is popping it in his mouth as he closes the cellar door behind him.
ABOUT THE AUTHORS
Damien Broderick met up with Rory Barnes (who'd learned to walk and talk in a tribal mud hut in Northern Rhodesia) more than forty years ago at Australia's Monash University. They shared various student houses with a motley crew of would-be writers who did what students did in the '60s: got pissed, screwed around, smoked some pot, engaged in a small amount of semi-violent protest and wrote a lot of essays. Broderick sold some stories and books and eventually got a Ph.D., Barnes did some teaching then wandered around Southeast Asia and the Middle East. Since 1983, they have co-authored seven novels. Barnes and his two sons live in Adelaide, South Australia. Broderick shares several houses with his American wife Barbara in San Antonio, Texas. They are both far more law-abiding than their raffish hero, to their regret.
BORGO PRESS BOOKS BY DAMIEN BRODERICK
Chained to the Alien: The Best of ASFR: Australian SF Review (Second Series) [Editor]
Climbing Mount Implausible: The Evolution of a Science Fiction Writer
Embarrass My Dog: The Way We Were, the Things We Thought
Ferocious Minds: Polymathy and the New Enlightenment
Human's Burden: A Science Fiction Novel (with Rory Barnes)
I'm Dying Here: A Comedy of Bad Manners (with Rory Barnes)
Post Mortal Syndrome: A Science Fiction Novel (with Barbara Lamar)
Skiffy and Mimesis: More Best of ASFR: Australian SF Review (Second Series) [Editor]
Unleashing the Strange: Twenty-First Century Science Fiction Literature
Warriors of the Tao: The Best of Science Fiction: A Review of Speculative Literature [Editor with Van Ikin]
x, y, z, t: Dimensions of Science Fiction
Zones: A Science Fiction Novel (with Rory Barnes)
Borgo Press Books by Rory Barnes
The Dragon Raft: A Young Adult Novel
Human's Burden: A Science Fiction Novel (with Damien Broderick)
I'm Dying Here: A Comedy of Bad Manners (with Damien Broderick)
Space Junk: A Science Fiction Novel
Zones: A Science Fiction Novel (with Damien Broderick)
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 9,528
|
Saxifraga cortusifolia es una especie de planta fanerógama perteneciente a la familia Saxifragaceae, es nativa de Japón.
Taxonomía
Saxifraga cortusifolia fue descrita por Siebold & Zucc. y publicado en Abhandlungen der Mathematisch-Physikalischen Classe der Königlich Bayerischen Akademie der Wissenschaften 4(2): 190. 1843.
Etimología
Saxifraga: nombre genérico que viene del latín saxum, ("piedra") y frangere, ("romper, quebrar"). Estas plantas se llaman así por su capacidad, según los antiguos, de romper las piedras con sus fuertes raíces. Así lo afirmaba Plinio, por ejemplo.
cortusifolia: epíteto compuesto latino que significa "con las hojas de Cortusa"
Sinonimia
Saxifraga crispa hort. ?
Saxifraga jotanii Honda
Saxifraga madida (Maxim.) Makino
Cultivares
Saxifraga cortusifolia 'Rosea'
Saxifraga cortusifolia 'Ruby Wedding'
Saxifraga cortusifolia SILVER VELVET
Saxifraga cortusifolia VELVET
Referencias
Enlaces externos
cortusifolia
Flora de Japón
Plantas descritas en 1843
Plantas descritas por Siebold
Plantas descritas por Zuccarini
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,406
|
Q: How to watch post data I have implemented paypal button in my asp.net app. When buttons redirect me to paypal and when I pay service paypal redirect me to one of my pages where I need to get data retrived from paypal. I tried to se that data in firebug but I can't find anything. Is there any way to watch received data?
A: Check out Fiddler. It allows you to view HTTP traffic including headers.
Edit
Description from the website:
Fiddler is a Web Debugging Proxy which
logs all HTTP(S) traffic between your
computer and the Internet. Fiddler
allows you to inspect all HTTP(S)
traffic, set breakpoints, and "fiddle"
with incoming or outgoing data.
Fiddler includes a powerful
event-based scripting subsystem, and
can be extended using any .NET
language.
Fiddler is freeware and can debug
traffic from virtually any
application, including Internet
Explorer, Mozilla Firefox, Opera, and
thousands more.
A: When all else fails use wireshark. I'm also a fan of Tamper Data and Paros.
A: Somethimes I've used the Developer Toolbar of IE... it's very simple...
Press F12 and go to the Tab Networking then Start Capturing and when finished you have all data in the Result View. double click on a single request and you get it!
Otherwise the FireBug tools it's quite good!
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,344
|
Earth Observation Data
Adding New Data
Open Data Policies
Common Metadata Repository (CMR)
Global Imagery Browse Services (GIBS)
LANCE: Land, Atmosphere Near Real-Time Capability for EOS
NASA Earthdata provides a number of ways for viewing imagery and creating visualizations of data, whether you are interested in natural disasters, land surfaces, water resources, or our oceans. Many of these tools provide access to near real-time imagery from some of NASA's Earth observation missions, allowing for near-real time response to natural and man-made events.
Interactively browse and download full-resolution, global satellite imagery from over 900 data products from NASA's Land, Atmosphere Near real-time Capability for EOS (LANCE) and other NASA data providers. Showing the entire Earth as it looks "right now"—or at least as it has looked within the past few hours—Worldview supports time-critical application areas such as wildfire management, air quality measurements, and weather forecasting. Geostationary imagery layers are also now available. These are provided in ten minute increments for the last 30 days. These full disk hemispheric views allow for almost real-time viewing of changes occurring around most of the world. Worldview is supported by NASA's Global Imagery Browse Services (GIBS).
Worldview Snapshots
Worldview Snapshots is a lightweight tool for creating image snapshots from a selection of popular NASA satellite imagery layers. Users can preview and download imagery in different band combinations and add overlays on the imagery of active fire detections, coastlines, borders, and roads. Worldview Snapshots is ideal for users with low/limited bandwidth access or for users who want to rapidly retrieve georeferenced satellite imagery of the same area each day.
Fire Information for Resource Management System (FIRMS)
FIRMS was developed to provide near real-time active fire data to natural resource managers who face challenges obtaining timely satellite-derived fire information. Active fire data are made available within three hours of satellite observation from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument aboard the Aqua and Terra satellites and the Visible Infrared Imaging Radiometer Suite (VIIRS) instrument aboard the joint NASA/NOAA Suomi National Polar-orbiting Partnership (Suomi-NPP) satellite and the NOAA-20 satellite via LANCE.
Near Real-Time Data
LANCE provides access to near real-time (NRT) data products from a number of instruments in fewer than three hours from data acquisition. The system supports application users who are interested in monitoring and analyzing a wide variety of natural and man-made phenomena. If you are unsure which data set best meets your needs, you can browse the NRT data by topic on the Hazards and Disasters page.
Access global, full-resolution imagery from over 900 satellite imagery products via a variety of standards-based set of web services, such as Web Map Tile Services (WMTS), Tiled Web Map Service (TWMS), Web Map Services (WMS), and Keyhole Markup Language (KML).
Rapid Response was the precursor to Global Imagery Browse Services (GIBS), Worldview and Worldview Snapshots. Rapid Response has been providing subset and global swath imagery from the Moderate Resolution Imaging Spectroradiometer (MODIS) since 2001 but is now being phased out.
There are many other ways to access individual data collections. If you are unsure which tools meet your needs, see the Getting Started page.
Page Last Updated: Sep 11, 2020 at 3:34 PM EDT
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 9,219
|
{"url":"https:\/\/plainmath.net\/6588\/comparison-between-broiler-chickens-chickens-positive-illness-bacteria","text":"# In a comparison between two. major brands of broiler chickens, 70 of 160 Perdue chickens in a SRS tested positive for food-borne illness bacteria. In\n\nIn a comparison between two. major brands of broiler chickens, 70 of 160 Perdue chickens in a SRS tested positive for food-borne illness bacteria. In a SRS of 160 Tyson chickens, 132 tested positive. Wed\nYou can still ask an expert for help\n\n\u2022 Questions are typically answered in as fast as 30 minutes\n\nSolve your problem for the price of one coffee\n\n\u2022 Math expert for every subject\n\u2022 Pay only if we can solve it\n\nirwchh\n\nSolution:\nGiven: - For Perdue chikens,\n\nFor Tyson chickens,\nThe problem is to test\n\nVs\nwhere are population props of posotove results in Perdue and Tyson chikens respectively.\nHence it is the problem of generalition inference method and can be solved using two ${\\propto }^{n}$ z method.\nBecause sample size of 160 is large.","date":"2022-06-26 14:29:50","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 2, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.529735267162323, \"perplexity\": 8739.025103770995}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656103269583.13\/warc\/CC-MAIN-20220626131545-20220626161545-00161.warc.gz\"}"}
| null | null |
The Pros and Cons of UV Light
Normally in this space you'd expect to find a list of explanations of the harmful effects of Ultraviolet (UV) light. There would be admonitions against tanning (either outside or in tanning salons), lectures about using daily SPF, especially on your face and hands, piles of information on how UV rays increase cellular aging and are responsible for everything from age spots and wrinkles to deadly skin cancer. And that is all still very true! But today we are going to talk about one way that UV light is used to your benefit: as an air purifier.
The sun is a source of the full spectrum of UV radiation, which is commonly subdivided into UV-A, UV-B, and UV-C. Although UV waves are invisible to the human eye, some insects, such as bumblebees, can see them. Unprotected exposure to UV-A and UV-B damages the DNA in skin cells, producing genetic defects, or mutations, which can lead to skin cancer.
UV-C rays are the most harmful, but are almost completely absorbed by our atmosphere, luckily for us. These rays consists of a shorter, more energetic wavelengths of light, and they are particularly good at destroying genetic material – whether in humans or viral particles. Since this discovery in 1878, artificially produced UVC has become a standard method of sterilization – used in hospitals, airplanes, offices, and factories. Though there hasn't yet been research looking at how UV-C affects Covid-19 specifically, studies have shown that it can be used against other coronaviruses, such as Sars. The UV radiation warps the structure of their genetic material and prevents the viral particles from making more copies of themselves. So clearly, the benefits of UV-C sterilization need to happen nowhere near the human body! One ideal way to do that is using a ventilation system, such as an HVAC system. By installing a UV air purifier, UV irradiation can be used to destroy harmful organisms in the very air that circulates around you in a building.
At Privy Skin Care, UV air purification has been one of the many safety precautions we've taken over the years. Long before this current situation, our office was outfitted with a CaluTech UV Air Purifier, ensuring the cleanest, safest, and most allergen free environment possible for our customers.
Rest assured that when the Governor allows us to reopen, we will do so with open arms, and with a space that is as clean, sterilized, and as welcoming as possible. Until then, stay safe, take care of yourselves and each other! Online booking available, schedule now.
www.privyskincare.com
Know Your Products: Alpha Hydroxy Acids (AHA's)
Stress and Your Skin
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,043
|
Devon Montano, if you are reading this, can you explain what is the latest update is saying on Kickstarter, or perhaps copy/paste it here? Because Caputer is not sending emails to the rest of the funders outside of kickstarter campaign.
What is the latest update on kickstarter? I still havent receive the email.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,206
|
package cz.auderis.test.rule;
import java.io.InputStream;
/**
* Defines a generic provider of initial file contents
*/
public interface InitialContentsProvider {
InputStream getContents();
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 7,846
|
using System.ComponentModel.Composition;
using System.IO;
using System.Windows.Media;
using System.Windows.Media.Imaging;
namespace GameRes.Formats.Jikkenshitsu
{
internal class GrcMetaData : ImageMetaData
{
public int BitsOffset;
public int BitsLength;
public int DataOffset;
public int DataLength;
public int AlphaOffset;
public int AlphaLength;
}
[Export(typeof(ImageFormat))]
public class GrcFormat : ImageFormat
{
public override string Tag { get { return "GRC"; } }
public override string Description { get { return "Studio Jikkenshitsu image format"; } }
public override uint Signature { get { return 0x08; } }
public override ImageMetaData ReadMetaData (IBinaryStream file)
{
if (!file.Name.HasExtension (".grc"))
return null;
var header = file.ReadHeader (0x20);
int bpp = header.ToInt32 (0);
if (bpp != 8)
return null;
return new GrcMetaData {
Width = header.ToUInt16 (4),
Height = header.ToUInt16 (6),
BPP = bpp,
BitsOffset = header.ToInt32 (8),
BitsLength = header.ToInt32 (12),
DataOffset = header.ToInt32 (16),
DataLength = header.ToInt32 (20),
AlphaOffset = header.ToInt32 (24),
AlphaLength = header.ToInt32 (28),
};
}
public override ImageData Read (IBinaryStream file, ImageMetaData info)
{
var reader = new GrcReader (file, (GrcMetaData)info);
return reader.Unpack();
}
public override void Write (Stream file, ImageData image)
{
throw new System.NotImplementedException ("GrcFormat.Write not implemented");
}
}
internal class GrcReader
{
IBinaryStream m_input;
GrcMetaData m_info;
int m_stride;
byte[] m_output;
public BitmapPalette Palette { get; private set; }
public PixelFormat Format { get; private set; }
public GrcReader (IBinaryStream input, GrcMetaData info)
{
m_input = input;
m_info = info;
m_stride = m_info.iWidth * m_info.BPP / 8;
m_output = new byte[m_stride * m_info.iHeight];
}
public ImageData Unpack ()
{
m_input.Position = 0x20;
Format = PixelFormats.Indexed8;
if (8 == m_info.BPP)
Palette = ImageFormat.ReadPalette (m_input.AsStream);
var rowsCtl = m_input.ReadBytes (m_info.iHeight);
m_input.Position = m_info.BitsOffset;
var ctlBits = m_input.ReadBytes (m_info.BitsLength);
m_input.Position = m_info.DataOffset;
int src1 = 0;
int dst = 0;
var coord = new int[4,4] {
{ 0, -1, -m_stride, -m_stride - 1 },
{ 0, -1, -2, -3 },
{ 0, -m_stride, -2 * m_stride, -3 * m_stride },
{ 0, -m_stride - 1, -m_stride, -m_stride + 1 }
};
int blocks = m_info.iWidth / 4;
for (int y = 0; y < m_info.iHeight; ++y)
{
int ctl = rowsCtl[y];
if (ctl > 3)
throw new InvalidFormatException();
for (int x = 0; x < blocks; ++x)
{
int bits = ctlBits[src1++];
for (int i = 6; i >= 0; i -= 2)
{
int p = (bits >> i) & 3;
byte px;
if (p != 0)
px = m_output[dst + coord[ctl,p]];
else
px = m_input.ReadUInt8();
m_output[dst++] = px;
}
}
}
return ImageData.CreateFlipped (m_info, Format, Palette, m_output, m_stride);
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,379
|
Maxis promotes COO Gökhan Ogut to CEO
Ogut will take over from Robert Nason, who is currently the interim CEO
Was previously the CEO of Vodafone Turkey; appointed Maxis COO on Sept 1, 2018
MAXIS Bhd has appointed Gökhan Ogut as chief executive officer (CEO) of the group effective May 1, 2019.
In a statement on May 18, Maxis said Ogut, who was appointed as the chief operating officer of Maxis on Sept 1, 2018, will take over from Robert Nason, who is currently the interim CEO of Maxis. Ogut will report to the chairman and the board.
"We are pleased to welcome Ogut as CEO of Maxis. We are confident that with his vast experience and focus on innovation and growth, he is the right person to drive our new strategy," Maxis chairman Raja Arshad Raja Uda said.
Ogut was previously the CEO of Vodafone Turkey. Before Vodafone, Ogut was in senior marketing as well as general management roles with a number of large companies such as Danone and Procter & Gamble, holding positions that had domestic as well as global responsibilities in Turkey, US and France.
He holds a Bachelor of Science in Industrial Engineering from Bogaziçi University, Istanbul, Turkey and a Master in Business Administration from University of Illinois, Chicago.
Nason will remain on the board as a non independent non executive director, and will be appointed as chairman of the Business and IT Transformation Committee and a member of the Audit Committee.
The board has provided for a smooth transition period between Ogut and Nason which will expire at the conclusion of Nason's contract as the interim CEO of Maxis on April 30.
At 4.50pm, Maxis shares were down 8 sen or 1.42% at RM5.55, with 658,600 shares done, bringing market capitalisation to RM43.38 billion.
Maxis, Sacofa to bring fibre broadband to more Sarawakians
Maxis launches ONERetail
Maxis introduces affordable high speed fibre broadband plans
Gökhan Ogut
Robert Nason
Raja Arshad Raja Uda
Vodafone Turkey
ST Engineering's electronics arm secures US$258mil contract wins in 4Q18
Whither data and data analytics in 2019?
By Dan Sommer December 5, 2018
Cisco launches Webex in Indonesia
MYEG invests in China-based Jingle Magic
IMDA collaborates with industry to strengthen telecom cyber-security
Two hundred petabytes in a single gramme of DNA
By Dzof Azmi May 24, 2019
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,478
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{"url":"https:\/\/math.stackexchange.com\/questions\/2690301\/related-rates-question-rectangle-under-normal-curve","text":"Related Rates Question (Rectangle Under Normal Curve)\n\nI'm solving the following related rates problem (formatted as an image).\n\nPart (a) is easily found to be $A = A(x) = 2xe^{-x^2\/2}$.\n\nPart (b), I thought, would be easy, too, but my answer is differing from the textbook. Let me share my findings.\n\n$\\frac{dA}{dt} = 2 \\frac{dx}{dt}e^{-x^2\/2} + 2x e^{-x^2\/2}(-x)\\frac{dx}{dt}$. Cleaning this up a bit, we have $\\frac{dA}{dt} = 2e^{-x^2\/2}(1-x^2)\\frac{dx}{dt}.$ Then, evaluating at $x = 4$ and $\\frac{dx}{dt} = 4$, we have $\\frac{dA}{dt} = -120e^{-8} \\approx -0.04026$ cm$^2$\/sec.\n\nHowever, the textbook claims the answer to be $-3.25$ cm$^2$\/sec. Am I doing something wrong in my solution?\n\nAlmost everything you did looks good. Remember that $$\\frac{dx}{dt}=4$$ centimeters per minute, not per second, so the answer should be $$-2e^{-8}\\:\\mathrm{cm^2\/sec}\\approx-6.709\\times10^{-4}\\:\\mathrm{cm^2\/sec}$$, which, unfortunately, is even further away from the book's answer.\nYou can be pretty confident that the book is wrong, though, because when $$x=4$$, the height of the rectangle is already so small that the rectangle is nearly impossible to see, so there's no way its area could be decreasing at a rate anywhere near even $$-1\\:\\mathrm{cm^2\/sec}$$.","date":"2020-02-27 18:37:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 4, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8591439723968506, \"perplexity\": 142.17646099403558}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-10\/segments\/1581875146744.74\/warc\/CC-MAIN-20200227160355-20200227190355-00104.warc.gz\"}"}
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UR complainants vs. Seligman: War of words heats up
Back-and-forth dialogue surrounds an Equal Employment Opportunity Commission complaint against UR professor.
UR complainants vs. Seligman: War of words heats up Back-and-forth dialogue surrounds an Equal Employment Opportunity Commission complaint against UR professor. Check out this story on DemocratandChronicle.com: http://on.rocne.ws/2y2Q8eX
Victoria E. Freile and James Goodman, Democrat and Chronicle Published 10:09 a.m. ET Sept. 12, 2017 | Updated 3:23 p.m. ET Sept. 12, 2017
University of Rochester.(Photo: CARLOS ORTIZ/@cfortiz_dandc/File photo 2011)Buy Photo
Days after University of Rochester officials responded to a federal complaint surrounding a professor and allegations of inappropriate actions in the workplace, UR student government and past and present faculty members have fired back.
The group of eight current and former faculty and graduate students noted their disappointment in UR President Joel Seligman and the university's investigation into accusations of wrongdoing by a colleague in a written statement issued Sunday.
"The university is doubling down on the fundamental errors of understanding that have brought it to this unhappy place," the statement reads.
More: UR's clearing of prof accused of sexual harassment becomes focus of faculty complaint
The back-and-forth dialogue and controversy surrounds an Equal Employment Opportunity Commission complaint, which claims that professor Florian Jaeger has "turned out to be a narcissistic and manipulative sexual predator," harassing female students.
Jaeger, who joined the UR faculty in 2007, is a professor in UR's department of Brain and Cognitive Sciences. The complaint was filed by faculty who worked with Jaeger or came to the department as graduate students.
The allegations drew national attention in recent days following an article published in Mother Jones magazine.
Over the weekend, Seligman issued a statement saying that the university conducted "two comprehensive and careful investigations" that "resulted in findings of no substantiation of the complainants' allegations."
He also said: "I would urge you not to reach any conclusions about what may have occurred based on the allegations in the complaint itself or in media reports. Allegations are not facts, and as we saw in Rolling Stone's withdrawn story about sexual assault at the University of Virginia, even established media outlets can get it wrong."
One investigation concerned the harassment charge against Jaeger. The other was about claims of retaliation against those who complained about Jaeger's behavior.
Florian Jaeger (Photo: University of Rochester)
"The complaint itself has already demonstrated how those investigations were deeply flawed: they failed to consult important witnesses; they dismissed a major witness...they truncated the conversations with witnesses to avoid difficult facts," the statement read. The complainants also said the university's investigation focused on whether Jaeger's actions violated a specific university policy, rather than considering whether "his recurring actions has led to a hostile work environment for students in his department."
Jaeger was accused of having sexual relations with students and, according to the complaint, "made it clear that students who wanted to excel needed to please him, socially and sometimes sexually."
Joel Seligman (Photo: file)
At least 11 female students and post-doctoral scholars actively avoided working with Jaeger, said the complaint, "because of his constant sexual innuendos, pressure to sleep with students, power plays and other unprofessional behavior."
More: University of Rochester responds to sexual harassment complaint against professor
"If the university's investigations were as thorough as (Seligman) maintains, they would have easily found all of the things we detail in our complaint," the letter read. The complainants also said they were disappointed that Seligman did not address concerns about claims of retaliation for faculty who voiced concerns about Jaeger.
Several hundred UR students are planning to protest Jaeger and the UR administration Wednesday afternoon. Also, more than 5,400 people have signed a change.org petition requesting UR officials to remove Jaeger from the university and to further evaluate the university's sexual harassment policy.
"We implore the University, and President Seligman, to reconsider their response to this complaint," says the statement posted on the Students' Association Government Facebook page. It is signed by Students' Association President Jordan Smith and Vice President Rebecca Mooney.
The Students' Association statement, posted Monday, says: "We are deeply disappointed that President Seligman expressed an understanding that sexual harassment in academia has been fully addressed, despite present circumstances demonstrating otherwise."
In the past, says the statement, Seligman has demonstrated "impressive thoughtfulness and consideration while dealing with such matters."
But the statement faults Seligman for being "both dismissive and belittling; it is offensive and inaccurate to compare the situation at hand to the case at the University of Virginia, which occurred several years ago and involved one anonymous complaint."
UR spokeswoman Sara Miller declined to comment on the Students' Association statement and, in response to a question about Seligman's familiarity with the EEOC report, she said that he twice read the entire report before issuing his statements about it.
Noting that the complaint against Jaeger involves multiple allegations, the Students' Association noted that "it is a gross abuse of authority" for faculty members "to manipulate the power with which they are entrusted by our graduate and undergraduate student bodies."
The Students' Association statement says that since this story has broken, it's team has made it a priority to address the concerns and questions of the students.
"We have met with several University administrators, including President Seligman, and will continue to do so until we have reached a clear understanding on the severity of this matter and the impact that this has had on our community."
VFREILE@Gannett.com
JGoodman@Gannett.com
Read or Share this story: http://on.rocne.ws/2y2Q8eX
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"redpajama_set_name": "RedPajamaCommonCrawl"
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During her time with the X-Men, the mysterious young woman known as Rogue has been many things. Soldier, friend, student...and daughter. But when a mission brings her back to her childhood home in Mississippi, Rogue comes face-to-face with the demons in her past - and a terrible secret that has haunted her family since her birth! With Gambit on hand to help out, Rogue must discover her parents' fate! Then, when a photograph surfaces of Rogue and Mystique during their time in the Brotherhood of Evil Mutants - a photograph that Rogue has no memory of - her search for the truth takes her all the way to Japan! And during clashes with Sunfire and Lady Deathstrike, a traumatic encounter will leave Rogue drastically changed! Who is Blindspot - and is she Rogue's best friend, or greatest foe? Collecting ROGUE (2004) #1-12.
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Cami Dalton is an American author of contemporary romance novels. Dalton's debut novel, Her Private Dancer, was published by Harlequin's Temptation line of category romances in April 2004. In a review of the novel, Romantic Times remarked on the "sizzling sensuality and strong writing" of Dalton's novel, while The Road to Romance described the book as having "an exciting storyline, endearing and charming characters, laugh out loud scenarios and pure romance from the heart." Dalton was a finalist for the 2004 Reviewers International Organization Award for Debut Romance and was nominated by Romantic Times BookReviews for Best First Series Romance.
Cami's second book, published by Harlequiin's Blaze line, is called Pleasure to the Max! and is set to be released on August 1, 2008. In early 2008, Cami signed a three-book deal with Harlequiin to follow up her first two books.
References
External links
Official website
American romantic fiction writers
Living people
Year of birth missing (living people)
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Melodifestivalen 2015 var den 55:e upplagan av musiktävlingen Melodifestivalen och samtidigt Sveriges uttagning till Eurovision Song Contest 2015.
Finalen ägde rum i Friends Arena den 14 mars 2015, där bidraget Heroes, framfört av Måns Zelmerlöw, vann. Inför finalen skedde en turnering om fyra deltävlingar samt ett uppsamlingsheat ("Andra chansen") med totalt 28 tävlingsbidrag. Sveriges Television gjorde en rad förändringar i årets tävling, som att minska antalet tävlingsbidrag från 32 stycken till 28 stycken samt att fyra bidrag istället för tidigare två gick vidare från uppsamlingsheatet till finalen. Likt tidigare år var det tittarna som hade makten att bestämma resultatet i programmen även om de i finalen delade makten med elva europeiska jurygrupper. Christer Björkman var programmets producent och Christel Tholse Willers var chef över produktionen av Melodifestivalen 2015.
Heroes representerade Sverige i ESC 2015, som ägde rum i Wien den 19, 21 och 23 maj 2015. I finalen segrade bidraget med totalt 365 poäng.
Tävlingsupplägg
För fjortonde året i rad genomfördes Melodifestivalen med deltävlingar på olika håll i Sverige innan en final arrangerades. I deltävlingarna, vilka sändes från Göteborg, Malmö, Östersund och Örebro, tävlade totalt 28 bidrag, där tittarna röstade vidare åtta av dessa till finalen. Därefter arrangerades ett uppsamlingsheat (kallat Andra chansen) för de bidrag som placerade sig på tredje och fjärde plats i deltävlingarna, där totalt fyra av dessa bidrag röstades vidare av tittarna. Detta program sändes från Helsingborg. Finalen, som innehöll totalt 12 bidrag, sändes från Solna. Sanna Nielsen och Robin Paulsson var programledare medan Filippa Bark var bisittare.
Jämfört med de tidigare åren med deltävlingsupplägget (2002-2014) gjorde Sveriges Television en rad större förändringar det här året. En sådan förändring var att ändra upplägget för Andra chansen som nu endast hade en enda tävlingsomgång med fyra dueller och därmed också fyra vinnare. Tidigare år har endast två bidrag gått vidare från Andra chansen. Detta gjorde i sin tur att antalet bidrag i finalen ökade från tidigare 10 till 12 stycken. Dessutom infördes en röstningsbegränsning för telefon- och SMS-röstningen i programmen, samtidigt som en mobilapplikation infördes som ett nytt röstningsverktyg. En ytterligare förändring var att karantänsreglerna för Andra chansens bidrag slopades.
Bidragsuttagningen
Tävlingsbidragen till det här årets tävling valdes ut genom tre olika delar:
13 bidrag (av totalt 1 733 inskickade) kom från ett nationellt inskickande av bidrag.
13 bidrag som Sveriges Television själva valde ut från specialinbjudningar.
2 bidrag som var allmänhetens jokrar i tävlingen.
Under september 2014 fanns möjlighet för låtskrivare och artister att skicka in tävlingsbidrag via Melodifestivalens hemsida. Efter att inskicket hade stängts tog Sveriges Television ut ett mindre antal som gick vidare till en urvalsjury. Denna jury fick sedan lyssna igenom bidragen och välja ut startfältets 13 första bidrag samt ett av jokerbidragen. Sedan tog Sveriges Television vid och valde ut den andra halvan med 13 bidrag, som sedan kompletterades med det andra jokerbidraget och artister till samtliga uttagna bidrag. Hela startfältet, inklusive jokrarna, presenterades vid två presskonferenser i november 2014.
De två jokerbidragen i tävlingen valdes ut genom Svensktoppen nästa och Allmänhetens tävling. Dessa två moment skilde sig åt då Svensktoppen nästa från början tog ut en artist, men låten valdes ut av Sveriges Television, medan Allmänhetens tävling var en låtskrivartävling där Sveriges Televisions jury fick välja ut ett vinnarbidrag, varpå Sveriges Television tillsatte artisten. De två jokrarna blev Kalle Johansson, och Emelie Irewald.
För att få skicka in bidrag till tävlingen behövde man vara folkbokförd i Sverige (senast den 1 september 2014) eller samarbeta med minst en svensk medborgare. De personer som förbjöds skicka in bidrag var personer som var anställda vid Sveriges Television under hösten 2014 och våren 2015. Tävlingsbidragen skulle vara nyskrivna låtar som aldrig tidigare hade offentliggjorts, och de skulle vara 2-3 minuter långa. Bidragen fick framföras på vilket språk som helst, men Sveriges Television satte upp en gräns att minst 30 procent av de uttagna tävlingsbidragen skulle framföras på svenska. För att vara tävlande artist skulle man vara minst 16 år gammal. Varje framförande fick ha max 8 personer på scenen och förinspelad körsång var tillåten (all huvudsång skulle dock göras live). Ett liveinstrument fick man ha med på scenen. Dock ställde Sveriges Television som krav att om vinnarlåten innehöll hela eller delar av de tre sistnämnda sakerna så skulle låten behöva arrangeras om till Eurovision Song Contest.
Återkommande artister till startfälten
Nedan listas namnen på de artister som tävlat tidigare år i festivalen och som återkom i tävlan det här året.
1 2010 deltog Daniel Gildenlöw som sångare i musikgruppen Pain of Salvation.
2 2003 och 2004 tävlade Jessica Andersson tillsammans med Magnus Bäcklund som duon Fame.
3 2000, 2001 och 2002 tävlade Magnus Carlsson med musikgruppen Barbados.
4 2003 och 2005 tävlade Magnus Carlsson med musikgruppen Alcazar.
5 1971 och 1972 tävlade Marie Bergman i musikgruppen Family Four.
6 1971 anordnades fem semifinaler inför finalen där artisterna Family Four, Sylvia Vrethammar och Tommy Körberg tävlade med fem bidrag vardera om fem finalplatser. Samtliga fem finalbidrag kom från Family Four som därmed också intog samtliga fem slutplaceringar i finalen.
7 1994 tävlade Marie Bergman i duett med Roger Pontare.
8 2013 deltog artisterna Oscar Zia och Loulou Lamotte i Behrangs nummer, även om det bara var Behrang som krediterades.
9 2008 tävlade Andreas Johnson i duett med Carola.
10 I Andra chansen deltog operasångaren Malena Ernman som en del av kören i Behrang Miris & Victor Crones framträdande.
Övrigt
Låtskrivarna
Totalt sett var det 75 låtskrivare som stod bakom de 28 bidragen i det här årets tävling. Av dessa var 41 debutanter medan resterande 34 hade haft med bidrag i tävlingen vid minst ett tidigare tillfälle. Av låtskrivarna var 19 kvinnor och 56 män. Flest bidrag fick Thomas G:son och Anton Hård af Segerstad med, de fick med fyra bidrag vardera. Fredrik Kempe och Karl-Ola Kjellholm fick med tre bidrag var, och Aleena Gibson, Jimmy Jansson, David Kreuger, Sharon Vaughn och Anders Wrethov fick med två bidrag var. Siffrorna räknas även med låtskrivarsamarbeten.
Marcel Bezençon Award 2015
Marcel Bezençon Award är ett pris som delas ut i tre kategorier vid varje års Melodifestivalsfinal. I varje kategori har en viss grupp fått avgöra resultatet: i den första kategorin avgör presskåren, i den andra avgör upphovsmän och i den tredje avgör tidigare Melodifestivalsvinnare. Priset instiftades av Christer Björkman och Richard Herrey och har fått sitt namn efter Eurovision Song Contests grundare, Marcel Bezençon. De bidrag som tog hem priserna var "Don't Stop" (artisternas pris), Heroes (pressens pris) och "Don't Stop Believing" (upphovsmännens pris).
Pausunderhållning
I varje program arrangerades pausunderhållning i form av sketcher och musikinslag. I finalen bjöds 2014 års Eurovisionsvinnare Conchita Wurst in att framföra 2014 års ESC-vinnarlåt Rise Like A Phoenix. Efter att alla finalens bidrag var framförde gjorde den norska humorgruppen Ylvis pausnumret "Stonehenge" och musikgruppen Dirty Loops gjorde en tolkning av 2014 års Melodifestivalsvinnarbidrag Undo.
Datum och händelser
Melodifestivalens turnéplan 2015
Lördag 7 februari 2015 - Deltävling 1, Scandinavium, Göteborg
Lördag 14 februari 2015 - Deltävling 2, Malmö Arena, Malmö
Lördag 21 februari 2015 - Deltävling 3, Östersund Arena, Östersund
Lördag 28 februari 2015 - Deltävling 4, Conventum Arena, Örebro
Lördag 7 mars 2015 - Andra chansen, Helsingborg Arena, Helsingborg
Lördag 14 mars 2015 - Final, Friends Arena, Solna
Inför Melodifestivalen
Den 11 maj 2014 meddelade Melodifestivalens producent Christer Björkman att planeringsarbetet för Melodifestivalen 2015 skulle vara klart i juni 2014.
Den 20 maj 2014 bekräftade Sveriges Television Sveriges medverkan i Eurovision Song Contest 2015.
Den 24 juni 2014 presenterade Sveriges Television regelverket för Melodifestivalen 2015.
Den 31 augusti 2014 presenterades Kalle Johansson som den första artisten till Melodifestivalen 2015. Detta efter att han stått segrare av Svensktoppen nästa 2014.
Mellan den 1 och 16 september 2014 var inskickningen av bidrag till både Ordinarie tävling och Allmänhetens tävling öppen.
Den 16 september 2014 stängdes antagningen till inskickningen av bidrag till tävlingen. Totalt skickades det in 2 177 bidrag, vilket var en minskning med 451 bidrag jämfört med 2014 års tävling.
Den 22 september 2014 presenterade Sveriges Television det nya tävlingsupplägget inom formen för det tidigare tävlingsupplägget.
Den 25 september 2014 presenterade Sveriges Television de städer som besöktes under turneringen.
Den 29 september 2014 presenterade Sveriges Television programledarna för Melodifestivalen 2015.
Den 24 oktober 2014 startade försäljningen av biljetter till deltävlingarna, Andra chansen och finalen. Likt tidigare år med detta upplägg bestod varje veckas stopp av tre föreställningar: två genrep (varav ett som bandades som eventuell reservsändning och ett matinégenrep) och därefter en direktsändning.
Mellan september och november gjorde Sveriges Television sitt urval av artister och bidrag till tävlingen.
Den 21 november 2014 presenterade Sveriges Television en ytterligare förändring i röstningsbegränsningarna i de framtida tv-sändningarna.
Den 24 november 2014 presenterade Sveriges Television tävlingsbidragen (med tillhörande artister) som skulle tävla i den första och andra deltävlingen. Utöver detta meddelades också vinnaren av Allmänhetens tävling.
Den 25 november 2014 presenterade Sveriges Television tävlingsbidragen (med tillhörande artister) som skulle tävla i den tredje och fjärde deltävlingen.
Den 4 december 2014 offentliggjordes namnen på de 16 personer som suttit med i urvalsjuryn.
Den 10 januari 2015 sände Sveriges Television en årskrönika om Melodifestivalen och Eurovision Song Contest 2014, som en bakom kulisserna-dokumentär men även med fokus på 2015.
Den 14 januari 2015 presenterade Sveriges Television startordningen för deltävlingarna.
Den 19 januari 2015 presenterade Sveriges Television tävlingens bisittare Filippa Bark (spelad av Sissela Benn).
Den 22 januari 2015 presenterade Sveriges Television en regeländring för de bidrag som skulle gå vidare till Andra chansen.
Den 27 januari 2015 presenterades webbprogramledarna.
Den 29 januari 2015 presenterade Sveriges Television bilder och information om scenografin.
Den 30 januari 2015 presenterade Sveriges Television vilka personer som ingick i husensemblen (körsång och dansare).
Den 4 februari 2015 släppte Sveriges Television en mobilapplikation som användes som ett av tre möjliga röstningsverktyg i programmen.
Deltävlingarna
I varje deltävling tävlade totalt sju bidrag. Först framfördes bidragen samtidigt som tittarna kunde avlägga röster. Efter framförandena hölls en kortare snabbgenomgång innan telefonslussarna stängdes och resultatet lästes av. De två bidrag som vid tillfället hade fått minst antal röster fick lämna tävlingen omedelbart. Efter detta påbörjades en andra röstningsomgång, utan att nollställa de tidigare resultaten, som nu enbart pågick i ett antal minuter. Efter att telefonslussarna stängdes en andra gång slogs rösterna för bägge omgångarna samman. De två bidragen som totalt hade fått flest röster gick direkt till finalen, medan bidragen som hamnat på tredje och fjärde plats gick till Andra chansen. Bidraget som hamnat på femte plats åkte ut.
Tittarnas röster bestod i deltävlingarna av telefon- och SMS-röstning. Vid röstningen fanns det möjlighet att välja mellan två olika telefon/SMS-nummer som bestod av att antingen bara ge en röst (utan att skänka pengar) eller att rösta och dessutom skänka en del av samtalskostnaden för varje röst till Radiohjälpen. Under varje bidrags liveframträdande fanns dessutom möjligheten att rösta genom en mobilapplikation, som i programmen kallades för hjärtröster. Dessa röster var till skillnad från telefon/SMS-rösterna kostnadsfria men vägde lika tungt som övriga röster.
Samtliga individuella bidragsresultat hölls hemliga fram tills finalen hade avgjorts, eftersom Sveriges Television inte ville påverka tittarna eller jurygrupperna.
Deltävling 1: Göteborg
Deltävlingen sändes från Scandinavium i Göteborg den 7 februari 2015.Bidragen presenteras i startordning.
Telefon-, SMS- och applikationsröster: 1 222 692 röster (nytt rekord för en deltävling).
Till Radiohjälpen: 609 463 kronor.
TV-tittare: 3 383 000 tittare.
Deltävling 2: Malmö
Deltävlingen sändes från Malmö Arena i Malmö den 14 februari 2015.Bidragen presenteras i startordning.
Telefon-, SMS- och applikationsröster: 2 380 213 röster (nytt rekord för en deltävling).
Till Radiohjälpen: 659 055 kronor.
TV-tittare: 3 332 000 tittare.
Deltävling 3: Östersund
Deltävlingen sändes från Östersund Arena i Östersund den 21 februari 2015.Bidragen presenteras i startordning.
Telefon-, SMS- och applikationsröster: 2 863 269 röster (nytt rekord för en deltävling/final).
Till Radiohjälpen: 818 793 kronor.
TV-tittare: 3 145 000 tittare.
Deltävling 4: Örebro
Deltävlingen sändes från Conventum Arena i Örebro den 28 februari 2015.Bidragen presenteras i startordning.
Telefon-, SMS- och applikationsröster: 2 571 081 röster.
Till Radiohjälpen: 764 932 kronor.
TV-tittare: 3 111 000 tittare.
Andra chansen: Helsingborg
Andra chansen sändes från Helsingborg Arena i Helsingborg den 7 mars 2015.
I Andra chansen tävlade de åtta bidrag som hade placerat sig på tredje respektive fjärde plats i deltävlingarna om de fyra sista platserna i finalen. I likhet med de tidigare åtta årens Melodifestivaler tog momentet plats i en arena lördagen mellan fjärde deltävlingen och finalen, och bidragen framfördes live istället för att bandade inslag visades. Till skillnad mot deltävlingarna möttes bidragen denna gång i dueller, där vinnaren i varje duell gick direkt till finalen. Duellmomentet har funnits med i Andra chansen sedan 2007 men har använts på olika sätt genom åren. Precis som i deltävlingarna avgjorde tittarna alla resultat vilket skedde genom telefon-, SMS- och applikationsröstning.
Startfältet
Vilka bidrag som möttes i respektive duell avgjordes helt och hållet av Sveriges Television själva. Den enda regeln som sattes upp inför bestämmandet var att i varje duell skulle ett tredjeplacerat och ett fjärdeplacerat bidrag mötas. Startfältet redovisas i första hand efter deltävlingsordningen och i andra hand i bokstavsordning efter bidragstitel.
1 Operasångaren Malena Ernman medverkade som en del av kören i Behrang Miris & Victor Crones framträdande.
Dueller
Siffror
Telefon-, SMS- och applikationsröster: 3 829 977 röster (nytt rekord för en deltävling/final).
Till Radiohjälpen: 712 062 kronor.
TV-tittare: 3 030 000 tittare.
Final: Solna
Finalen sändes från Friends Arena i Solna den 14 mars 2015.
Finalen avgjordes genom kombinerad tittar- och juryröstning. Från början framfördes de 12 finalbidragen samtidigt som tittarröstningen (genom telefon- och SMS-röstning) pågick. Därefter hölls en snabbgenomgång följt av jurygruppernas röstavläggning. Medan detta pågick var tittarröstningen öppen vilket gjorde att tittarna kunde påverka juryns dom. Efter juryöverläggningen hölls en ny snabbgenomgång av bidragen innan telefonslussarna stängdes och resultatet räknades av. Sedan adderades tittarnas poäng till jurypoängen och därmed korades en vinnare.
Tittarna respektive jurygrupperna delade ut 473 poäng vardera till bidragen. Var och en av de totalt 11 jurygrupperna, vilka representerade tävlande länder i Eurovision Song Contest 2015, delade ut 12 poäng till favoritlåten, 10 poäng till sin tvåa, 8 poäng till sin trea och därefter 6, 4, 2 och 1 poäng. Totalt gav varje jurygrupp således sju bidrag poäng medan fem blev utan. Tittarnas poäng delades istället ut procentuellt utifrån hur många röster varje bidrag hade fått. Således kunde alla bidrag få poäng och summorna representerade tittarnas röstning istället för fasta poängsummor som jurypoängen.
På grund av tekniska problem med applikationsröstningen fanns för tittarna enbart möjlighet att telefon- och SMS-rösta.
Startlista
Bidragen listas nedan i startordning.
Poäng och placeringar
Siffror
Telefon- och SMS-röster: 1 555 557 röster.
Till Radiohjälpen: 2 984 896 kronor.
TV-tittare: 3 736 000 tittare.
Källor
Fotnoter
Externa länkar
2015 i Sverige
Sverige
2015
Musikevenemang i Göteborg
Musikevenemang i Malmö
Musikevenemang i Östersund
Musikevenemang i Örebro
Musikevenemang i Helsingborg
Musikevenemang i Solna
Malmö under 2010-talet
Göteborg under 2010-talet
Evenemang i Solna
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{"url":"https:\/\/cas-events.mpe.mpg.de\/indico\/event\/0\/session\/11\/contribution\/12","text":"# From clouds to protoplanetary disks: the astrochemical link\n\n4-8 October 2015\nHans Harnack Haus\nEurope\/Berlin timezone\nHome > Timetable > Session details > Contribution details\n\n# Contribution Contributed Talk\n\nHans Harnack Haus -\nPROTOPLANETARY DISK EVOLUTION AND SOLAR SYSTEM 1\n\n# Chemical footprint of a nascent planet\n\n## Speakers\n\n\u2022 Dr. Asunci\u00f3n FUENTE\n\n## Content\n\nThe formation of planetesimals requires that primordial dust grains grow from micron- to km-sized bodies. As dust grains grow, they start to decouple from the gas and drift radially towards the central star. Therefore, planetesimal formation has to happen in time-scales shorter than radial drift. One way to halt the inward drift is by developing a local maximum in the radial surface density of the gas that would act as a dust trap. Dust traps have been identified in transitional disks using the dust continuum emission at longer wavelengths (mm). However their detection remains difficult in molecular lines. Our data show the chemical footprint of the presence of a dust trap in a transitional disk. Sulfur monoxide has been imaged in the transitional disk around the Herbig Ae star, AB Auriga. This species presents an odd spatial distribution with a hole towards the dust trap. This hole is the consequence of the enhanced gas densities within the trap and it is so far the best example of how the gas dynamics, the grain growth and the gas chemistry are coupled. Hydrodynamical simulations couple to a time-dependent chemical model are able to explain the observed trend and prove that the sulphur chemistry can be used as a tool to investigate the planet formation process. SO is the second S-bearing molecule detected in a PPD (the first was CS) and opens the possibility to study the sulphur chemistry in a proto-solar nebula analog. Besides the high level of sulfur in the Sun (S\/Si $\\sim$0.5), sulfur is widespread in the Earth, the Venusian atmosphere, in the Martian regolith, it is present in Jupiter and Saturn, and is specially abundant in Io. The comprehension of the sulfur chemistry is of paramount importance to understand the formation of our own planetary system.","date":"2018-02-24 02:30:12","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5099225044250488, \"perplexity\": 3282.8585954432465}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-09\/segments\/1518891815034.13\/warc\/CC-MAIN-20180224013638-20180224033638-00748.warc.gz\"}"}
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Home/ Technology/What is New in Google Chrome 69?
What is New in Google Chrome 69?
Vivek September 7, 2018
The Internet has come a long way in technological advancements and user's preference in the recent decades. It is not long ago Google introduced their browser called Chrome that revolutionised the internet usage to a greater level. It is a decade now chrome has recently celebrated its 10th birthday with some improved features that would make you go Wow! The complete details of such advanced features of google chrome 69 updates are discussed in detail below.
Google chrome is one of the most commonly used internet browsers on a global level though there are many competitors in the market, its simple design and improved speed of access make it much more preferable. However, the internet gets improved with modern technological advancements in order to be on the race. This calls for frequent updates to simplify their search and also to retain their trust among people. This new Chrome 69 update is filled with surprises including increased speedy web access and improves search bars and their design features.
It is easy; one could easily download the whole new Chrome 69 with a few clicks. The desktop version of chrome update involves following steps.
Open your chrome browser
Click on the three-dot icons on the rightmost corner
Select Menu bar
Choose About Chrome
Update to latest version (Chrome 69)
In the case of the Mobile phones, one could get this latest update from the Google play store (for Android) or Apple App store for IoS mobiles.
Improved Design features
Chrome 69 has undergone greater changes in terms of user interface. In other words, it has adapted to its Material Design 2 philosophy to provide whole new looks and features. People now could enjoy easy surfing with stylish icons and improved color palette. In case of the IoS platforms, the toolbar has been moved to the bottom for easy access.
In addition to all such features, Chrome 69 also involves other customizable options. Now people could enjoy their desired background in terms of New Tabs. Also, it involves adding a new shortcut to the sites you visit. Though in the previous cases it would be recently visited pages here one could choose the particular site to be accessed quickly.
Improved Omni box
Chrome search box simplifies the idea of internet surfing, it provides numerous suggestions that helps one to pick rather than typing it. Well with the improved Chrome 69 this search box (often referred to as Omni box) has surely updated to work more efficient and simple. This smart Omni box displays information on the Translations, Weather, public figures, and other related answers to your search questions.
It is also said that people could access their Google drive files from the Search bars in the Foreseeable future.
Easy Signups
Chrome 69 reduces the burden of people in terms of logging into their desired web pages. This is made possible with the help of the newly improved password manager. When an individual sign up on any of the websites the login credentials will be auto saved onto their Google account. So when the particular individual visits the particular site again there is no need for him/her to go through the login process once again. This saves quite a time. In addition, as such login credentials are stored in the Google account; one could enjoy these features in terms of both the computers and the mobile platforms.
Advanced AI & Machine learning
Google has made real impressive work in terms of their AI and Machine learning in the recent years. And this development is ongoing. With latest google chrome 69 browser update, it mainly focuses on simplifying the information search and presenting it in much simpler terms that one desires. One could witness these changes in the Google translate features.
Well, other than AI developments they also focus on machine learning to ensure the secured internet access. This involves finding the Phishing and the malware sites and in the recent times, it has extended its operation in terms of other malicious extensions as well.
Sources: Chrome 69 latest update
Google chrome new design features
AdvancedAI chrome 69 design chrome browser google chrome 69 google update Machine learning Omnibox
Vivek is a Content Executive & Outreach specialist for Blogs. He is also a writing enthusiast fond of healthy and happy living. He believes Knowledge gets better when shared. So he founded The Mindful Bytes as a platform for people who love to read and write anything that has to do with Health, Tech, Business, Finance, and Lifestyle.
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What Makes the iPad Better Than the iPhone?
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Gladys Fornell Biography
Montel
TEI Encoded Manuscript
Narrative Overview
The Gladys Fornell Project
Visual Analysis
This project utilizes several feminist theorists to provide a framework for analysis of Montel. In considering representations of femininity, we can begin with Simone de Beauvoir's 1949 claim that "one is not born, but rather becomes a woman," which revolutionized feminist literary criticism as it reemerged in the twentieth century (301). With her assertion that one becomes a woman, de Beauvoir suggests that the notion of "woman" (and possibly all genders, although this is not as extensively addressed in her writing) is societally constructed and, moreover, a mechanism for men to establish their own agency in society while regulating women to the position of inessential "other" (301). Under de Beauvoir's argument, characterizing women limits females' identities and therefore strips them of agency.
One "becom[ing] a woman" without agency raises the possibility that females can be pressured to embody particular identities and behaviors in order to be socially accepted as a model of femininity. Judith Butler reinforces this notion with her argument that gender is performative and only exists when it is staged by actors. In her 1988 "Performative Acts and Gender Constitution: An Essay in Phenomenology and Feminist Theory," Butler declares that different gender expressions are reinforced by the "stylized repetition of acts through time, and not a seemingly seamless identity" (520). As actors repeat similar actions, coded as masculine, feminine, or an amalgam of the two, they reconstitute and reinforce a societal understanding of male and female genders. Importantly, these actions are performative, acted out for others to watch, mimic, and recast. Butler identifies that repeated gendered performances result in a "script" with consequences when actors deviate from it:
Gender is a basically innovative affair, although it is quite clear that there are strict punishments for contesting the script by performing out of turn or through unwarranted improvisations…Gender is what is put on, invariably, under constraint, daily and incessantly, with anxiety and pleasure, but if this continuous act is mistaken for a natural or linguistic given, power is relinquished to expand the cultural field bodily through subversive performances of various kinds. (531)
Butler emphasizes that gender is not natural or a product of biology, but is constructed and "put on" under "constraint," suggesting that there are limitations or a perceived artificiality; however, when gender is "mistaken for a natural or linguistic given, power is relinquished" to continue with "subversive performances." When society assumes that the gender "script" is no longer contestable, formerly hegemonic performances of gender become the only acceptable performances. Thus, as gender is performed, actors must accept that their actions are unnatural and changeable in order to preserve their individual autonomy.
In a literary context, the restriction of women's identities can be considered in relationship to both women writers and the female characters they create. Sandra Gilbert and Susan Gubar reflect on female characters as archetypes in their 1979 collection The Madwoman in the Attic, famously asserting: "The images of 'angel' and 'monster' have been so ubiquitous through literature by men that they have also pervaded women's writing to such an extent that few women have definitively 'killed' either figure" (812). Although their criticism is focused on the work of nineteenth century women writers, Gilbert and Gubar point to an important dichotomy between the "angel" and the "monster" that, considering their historical focus, can be traced into literature informed by movements like surrealism and imagism of the twentieth century. They describe the archetypes as extremes, suggesting that few depictions of female figures through nineteenth century literature existed in the liminal space between "angel" and "monster." Shifting their emphasis to the author, Gilbert and Gubar pronounce, "a woman writer must examine, assimilate, and transcend the extreme images of 'angel' and 'monster' which male authors have generated for her" because neither "angel" nor "monster" truly captures the breadth and complexity of female characters or the women authors behind them (812).
Using this angel/monster dichotomy as the fundamental lens for this critical examination of Montel, we can consider Gilbert and Gubar's call to arms for women writers to "transcend" the images of "angel" and "monster" to be Gladys Fornell's call to the typewriter. As a woman writer following the tradition of authors including the Brontës, Austen, Barrett Browning, and Shelley, Fornell is innately tasked with the need to create more heterogeneous female representation in literature, regardless of whether she considered this while writing. Focusing on two female characters, Alice Montel and Ingeborg Sondegaard, this project contends that Alice and Ingeborg exist as variants of Gilbert and Gubar's "angel" and "monster" and consequently do not "transcend" images originally generated by male authors. Fornell's employment of these archetypes, however, is ultimately subversive: the "angel" and the "monster" of Montel are not presented in earnest, but are instead hyperbolic, satiric constructions of each archetype that reinforce the problematic literary and authorial confinement of women.
Further, we can consider these hyperbolic representations of femininity in conjunction with Montel's emphasis on place and nature. Theorist Stacy Alaimo's "The Undomesticated Nature of Feminism: Mary Austin and the Progressive Women Conservationists" describes the writings of Mary Austin, a contemporary to Gladys Fornell, and points to a shift in early twentieth century literary representations of nature which began "contesting discourses that position women and nature as resources for exploitation… and [offering] women a figure of identification outside the law by depicting nature as a force that exceeds and resists mastery" (73). Alaimo suggests that representations of femininity "outside the law," or societally accepted standards for appropriate feminine behavior, can be viewed as indomitable in connection with more transgressive, undomesticated versions of nature.
In connection with Montel, Alaimo's conception of nature as a "potentially feminist space" can be recognized most clearly in connection with Ingeborg, a variation of Gilbert and Gubar's archetypal "monster," who is notably unruly and associated with nature imagery (73). It is important, however, to also consider Alice, a variant of the "angel," as an inhabitant of this nature space: she frequently transgresses the boundaries between the Montel home and the land of Lone Pine before finally, in her most extreme form, emerging on a stage in the woods and sailing away on the nearby lake. This thesis considers both Alice and Ingeborg in connection with an undomesticated, feminized representation nature within the broader context of place in the novel.
Following the mention of satire, it is necessary to pause briefly at a letter that Gladys Fornell received from publisher Mark Paterson, dated August 17, 1962, addressing her manuscript for Montel. With a mention of the hesitancy for British publishers to consider American novels — although he affirms that Fornell has a "better than even chance" — Paterson fleetingly states: "we are a little puzzled by your description of the novel as a 'quiet satire'. Could it be that this is lost on the reader unfamiliar with today's Wisconsin life?"[2] (Paterson). In her correspondence, Fornell did not explain what she intended to be "quiet satire." Paterson's tone does not seem intentionally condescending or patronizing, like he was attempting to diminish Fornell's authorial intent; rather, I surmise that his position as a male publisher prevented him from fully recognizing Fornell's satirical representation of women in Montel. Specific descriptions of "Wisconsin life" that might have prompted Paterson's comment are not overt, as "Wisconsin" elements are more interconnected with descriptions of nature and the people residing on this landscape. Reading the text in light of this mention of "quiet satire" therefore does not fundamentally alter the argument that Fornell's extreme portrayal of women is satirical, but rather enhances it and historically substantiates the possibility that Montel's emphasis on gender is a purposeful undercurrent.
Below, you can view visual representations of this feminist analysis as rendered by Voyant. For further analysis on Alice and Ingeborg, readers can view the written component to this project on Wooster's Open Works.
[1] Due to the scope of this project, I have limited my focus to two representations of femininity in order to thoroughly explore their nuances and interactions throughout Montel. In particular, Alice and Ingeborg seem to be the most extreme, hyperbolic variations of femininity. There are a number of other engaging characters, however, that would warrant further study given the theoretical framework of my analysis, including: Jane Montel, Lucie Montel, and Grandma Sondegaard.
[2] The spelling from Mark Paterson's letter, originally "Wisconcin," has since been corrected to Wisconsin in this project.
The images below provide examples of the ways in which we can use digital tools (for these images,Voyant) to analyze Montel. In the future, this project will expand analysis to address thematic elements more specifically.
The image below traces the themes from my encoding schema, which can be viewed on the Montel page of this site and or the downloadable TEI Encoded Manuscript, over the course of the manuscript.
The image below maps the frequency of the characters Alice, Philip, Jane, Thorvald, and Ingeborg over the course of the manuscript.
Copyright © 2020 — Made with ♥ and intention by Codestag
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{"url":"http:\/\/mathhelpforum.com\/algebra\/54194-word-problem-dont-know-were-start-print.html","text":"# word problem dont know were to start\n\n\u2022 Oct 17th 2008, 05:20 AM\nTweety\nword problem dont know were to start\nHi, I am really stuck on this question ,\n\nfig.19.2 shows a template whose area is 50 square centimetres. find the total length of the template.\n\nI have drawn the image on paint and have attached it, but its not a very good drawing. sorry if it does not make much sense to you!\n\nI would be able to work this out if it was just the square but because there\u2019s also this semi-circle shape attached to the square i don't really know how to calculate the length of it.\n\u2022 Oct 17th 2008, 06:24 AM\nPeritus\n$\n\\begin{gathered}\nArea_{template} = x^2 + \\frac{{\\pi \\left( {\\frac{x}\n{2}} \\right)^2 }}\n{2} = 50 \\\\\nLength_{template} = 3x + \\frac{{\\pi x}}\n{2} \\hfill \\\\\n\\end{gathered}\n$\n\ngood luck...\n\u2022 Oct 17th 2008, 06:43 AM\nTweety\nQuote:\n\nOriginally Posted by Peritus\n$\n\\begin{gathered}\nArea_{template} = x^2 + \\pi \\left( {\\frac{x}\n{2}} \\right)^2 = 50 \\hfill \\\\\nLength_{template} = 3x + \\frac{{\\pi x}}\n{2} \\hfill \\\\\n\\end{gathered}\n$\n\ngood luck...\n\nI don't really understand how you got to your final 2 equations(Worried) could you please explain it step my step? please\n\nthanks!\n\np.s. what do I do with the length of the square? which is 6cm? where am I suppose to use that?\n\u2022 Oct 17th 2008, 06:55 AM\nPeritus\nlet us denote the side of the square by x.\nThe area of the square is $x^2$.\nFrom your drawing I understand that there's a half circle on the rightmost side of the square, so basically the diameter of the circle equals the side of the square (x). We know that the area of a circle is:\n$\n\\pi r^2$\n\nwhere r is the radius of the circle (the diameter is twice the radius).\nSo we can express the area of the half circle using x, like so:\n\n$\n\\frac{{\\pi \\left( {\\frac{x}\n{2}} \\right)^2 }}\n{2}$\n\nthe area of the template is the sum of the square area and the half circle area, and that's how we get the first equation, I hope that you can figure out the second equation now.\n\u2022 Oct 17th 2008, 09:15 AM\nTweety\nI kind of understand the first equation, but i am still not sure how to calculate the total length of the template, would I just add all the sides up together?\n\nand isn't the area of the square 36cm^2 ?\n\u2022 Oct 17th 2008, 11:39 AM\nTweety\ncan someone please show me how to calculate the total length , please. maths is not my best subject (Doh)","date":"2017-12-16 09:20:28","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 5, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7997063398361206, \"perplexity\": 347.2536150831824}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-51\/segments\/1512948587496.62\/warc\/CC-MAIN-20171216084601-20171216110601-00456.warc.gz\"}"}
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Никола́й Ильич Пота́нин (род. 1801, ум. 1860) — сибирский казак, есаул Сибирского казачьего войска, , топограф, исследователь Центральной Азии; отец известного российского путешественника, исследователя Сибири и Центральной Азии Г. Н. Потанина.
Биография
Родился в 1801 году в семье сибирского казака, служившего в редуте Островном Пресновской крепости — сторожевого укрепления Тоболо-Ишимской линии Западной Сибири. Окончив Омское казачье училище в 1816 году (в возрасте 15 лет), вступил в службу казаком конно-артиллерийской бригады. В 1821 году за проявленное усердие в службе произведён офицерский воинский чин прапорщика, с переводом с января 1822 года во 2-й конный полк Сибирского Линейного казачьего войска, и назначением в Пресновскую крепость; в 1828 году произведён в очередной офицерский чин — хорунжего.
В 1829 году получил «особое поручение» генерал-губернатора Западной Сибири И. А. Вельяминова, назначен командиром казачьего конвоя для сопровождения кокандского посольства, возвращавшегося из Санкт-Петербурга в Коканд. Перед отправлением в Коканд прошёл дополнительное обучение маршрутной съемке местности. Пройдя подготовку в Омске, отправляется вдоль Иртыша в Семипалатинск, куда прибыл 12 августа (по старому стилю) 1829 г. и 10 сентября, и возглавив отряд из 13 казаков, 12 членов свиты посольства и 15 членов купеческого каравана, начал многодневный поход в Коканд. В пути следования конвоя произвёл топографическую съёмку местности, составил маршрутную карту и описал путешествие в путевых заметках, озаглавленных при опубликовании «Записки о Кокандском ханстве хорунжего Н. И. Потанина», впоследствии напечатанных в «Военном журнале» (№№ 4,5: 1831 г.) и позднее — в Известиях Русского географического общества (1856 г.).
В 1830 году произведён в обер-офицерский чин казачьих войск сотника. В 1834 году произведён в очередной казачий воинский чин есаула, с одновременным назначением на должность начальника Баянаульского внешнего округа и командира окружного военного гарнизона в Баянауле.
В 1836 году вступился за подчинённого ему казака, и за то, что публично поссорился с пехотным офицером, и "за превышение полномочий" попал под следствие, и приказом командующего Сибирского военного округа генерала Горчакова, был осуждён и разжалован в рядовые казаки. Через 12 лет службы произведён в чин урядника (См.: дело РГВИА, 1848 год).
В продолжение службы — рядовым казаком принимал участие в четырёх походах в Киргизскую степь. В их числе в составе научной экспедиции генерала Сильвергельма в Туркестан — через село Сузак, расположенное в сухой, безводной степи, до Чимкента, — во время которой произвёл топографическую съёмку от гор Улы-Тау вдоль долины реки Сарысу, до её впадения в Сырдарью; результаты съёмок в 1849 году опубликовало «Военно-статистическое обозрение Томской губернии», а в 1852 году «Военно-статистическое обозрение Киргизской степи Западной Сибири» (обозрения сопровождались картами). Cделанная Николаем Потаниным топографическая съемка, описание местности вдоль реки Сарысу стали одним из основных источников для составления третьей части (Киргизская степь Западной Сибири. 1852 г.) XVII-го тома фундаментальной энциклопедической работы «Военно-статистическое обозрение Российской империи». Отмечая деловой вклад казака Н. И. Потанина в успешном выполнении задач экспедиции, генерал Г. А. Сильвергельм направил генерал-губернатору Западной Сибири представление о награждении и восстановлении в офицерском чине Н. И. Потанина, однако, непреклонный генерал-губернатор Горчаков отказал в удовлетворении прошения.
В 1855 году, когда он по выслуге лет числился в запасе, по особому представлению, высочайшим указом императора Александра II ему было даровано воинское звание казачьего офицера — хорунжий. О последних годах его жизни пока сведений не найдено. Сведения о том, что с мая 1854 по декабрь 1857 г., он служил на золотых приисках дальнего свойственника, известного сибирского золотопромышленника Ф. А. Горохова, не подтверждены документально.
Семья
Брат: Дмитрий Ильич Потанин (род. 1792 – ум. 1842), есаул – командир казачьего полка Сибирского линейного войска. Его жена: Павла Александровна Горохова (род. 1808 – ум. 1858) – родная сестра коллежского асессора,томского купца и золотопромышленника Философа Александровича Горохова (1796 - после 1856).
Жена: Варвара Филипповна, урождённая Трунина (род. 1811 — ум. 24.02.1839, кр. Пресновская), дочь командира артиллерии гарнизона Ямышевской крепости штабс-капитана Филиппа Львовича Трунина (род. 1775 — ум. 1841) и его жены Матрёны Степановой дочери .
Сын: Григорий Николаевич Потанин (род.1835 — ум. 1920) — географ, ботаник, этнограф, фольклорист, публицист — исследователь Центральной Азии.
Источники, ссылки
Катанаев Г. Е. Н. И. Потанин и его русские предшественники по разведкам в киргизских степям и Средней Азии // Записки ЗСОРГО. 1916. Т. 38. С. 192-202.
Потанин Г. Н. Воспоминания / Сост., вступ. ст. и коммент. Н. Н. Яновского // Литературное наследство Сибири. Т.6. —Новосибирск: Зап.-Сиб. кн. изд-во, 1983. — 332, [4]: 6 л. ил., портр.
Примечания
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{"url":"https:\/\/www.physicsforums.com\/threads\/deriving-convolution.886469\/","text":"# I Deriving convolution\n\n1. Sep 24, 2016\n\n### rabbed\n\nHi\n\nCan I derive the expression for Z_PDF(z) where:\nZ = t(X,Y) = X + Y\nBy starting with:\nZ_PDF(z)*|dz| = X_PDF(x)*|dx| * Y_PDF(y)*|dy|\nZ_PDF(z) = X_PDF(x) * Y_PDF(y) * |dx|*|dy|\/|dz|\n\nand then substitute the deltas with derivatives and x and y with expressions of z?\n\nLast edited: Sep 24, 2016\n2. Sep 24, 2016\n\n### Stephen Tashi\n\nAre you asking whether you can \"derive\" in the sense of giving a proof? Or are you just asking whether you can get a result by doing some formal algebraic manipulations ?\n\nI see no reason why that would be true - even using \"infinitesimal reasoning\" upon \"dx,dy,dz\".\n\nInutuitively, the value of Z_PDF(z) dz is the probability that Z is in the interval (z - dz, z + dz). For that to happen, the probabilities of X and Y can't be chosen arbitrarily. You have incorporate some relationship between x and y and the value of z.\n\nI think the basic idea is that to approximate Z_PDF(z) dz you must integrate the joint PDF of x and y over the region where x + y is in (z - dz, z + dz). (If you are assuming X and Y are independent, you need to say so.)\n\n3. Sep 25, 2016\n\n### rabbed\n\nThe latter.\n\nOk, I have to do the substitution of x and y before I state the equality of probabilities (otherwise it's not true), and since X and Y are just any numbers picked at random (either does not affect the probability of the other), they are independent giving P(X=z-y AND Y=z-x) = P(X=z-y) * P(Y=z-x | X=z-y) = P(X=z-y) * P(Y=z-x), so:\nZ_PDF(z)*|dz| = X_PDF(z-y)*|dx| * Y_PDF(z-x)*|dy|\n\nIs this first step OK?\n\n4. Sep 25, 2016\n\n### Stephen Tashi\n\nNo. For example, suppose x = 100 and y = 1. You're claiming the value of Z_PDF(101) is approximately the probability that X is near 100 and Y is near 1. But Z_PDF(101) must also account for other possibilities. For example X might be near 50 and Y might be near 51.\n\n5. Sep 25, 2016\n\n### rabbed\n\nZ_PDF(z)*|dz| = X_PDF(x)*|dx| * Y_PDF(z-x)*|dy|\n\nBetter? :)\n\n6. Sep 25, 2016\n\n### Stephen Tashi\n\nSuppose z = 101 and x = 1. You're saying the probability that Z is near 101 is approximately the probability that X is near 1 and Y is near 100. But the probability that Z is near 101 must also include other possibilities - for example that X is near 50 and Y is near 51.\n\n7. Sep 25, 2016\n\n### rabbed\n\nBut if Z=101,\nI can set x = 1 and get y = 101-1 = 100\nZ_PDF(101)*|dz| = X_PDF(1)*|dx| * Y_PDF(101-1)*|dy|\n\nOr I can set x = 50 and get y = 101-50 = 51\nZ_PDF(101)*|dz| = X_PDF(50)*|dx| * Y_PDF(101-50)*|dy|\n\n8. Sep 25, 2016\n\n### Stephen Tashi\n\nYou can only do that if you assume the equation you are using is correct. You might get two different answers for Z_PDF(101) if you do those two different computations.\n\n9. Sep 25, 2016\n\n### rabbed\n\nBut am I not \"setting\" the unknown Z_PDF(101) to be the same no matter if x=1 and y=100 or x=50 and y=51?\nThey will become the same because of the different deltas?\n\n10. Sep 25, 2016\n\n### rabbed\n\nMaybe I'm lost..\nBut it would be good to have a 'derivation' starting from the probability approximations using the PDF's. And it should be possible because that's what's actually being used to get the destination RV's PDF? Any advice?\n\n11. Sep 25, 2016\n\n### Stephen Tashi\n\nYou are going to have to do something involving a summation. The value of Z_PDF( z) doesn't depend only on one particular pair of values for X and Y, so Z_PDF(z) is not going to be a function of X_PDF(x) and Y_PDF(y) for one particular pair of values x,y. The value of Z_PDF(z) depends on the values of X_PDF and Y_PDF at all possible combinations of x,y that sum to z. You have to sum over all those possible combinations.\n\nMost dx-dy-dz arguments explicitly or implicitly express a differential equation. I don't know whether there is a dx-dy-dz way to derive the convolution formula. My suggestion is to start with the answer and try to express it as a differential or partial differential equation. Try taking the formula for the cumulative distribution of the convolution of X and Y and differentiate both sides of it. (You might have to use Leibnitz's formula for differentiating an integral where variables appear in the limits of integration. See the \"Formal statement\" section of https:\/\/en.wikipedia.org\/wiki\/Leibniz_integral_rule )\n\n12. Sep 26, 2016\n\n### rabbed\n\nSo since the transformation function is describing a plane, The PDF formula of the destination RV needs to account for the probability of each point on that plane (or rather the infinite line of constant z)?\nLike for example a n-to-1 transformation function, where the PDF formula of the destination RV needs to account for the probability of n source RV values for each destination RV value?\n(The first case having two (dimensional) source RV's and the second case having one source RV)\n\nLast edited: Sep 26, 2016\n13. Sep 26, 2016\n\n### rabbed\n\nZ_PDF(z)*|dz| = integral wrt x from -inf to inf of X_PDF(x)*|dx| * Y_PDF(z-x)*|dy|\n\nLooks better?\n\n14. Sep 26, 2016\n\n### Stephen Tashi\n\nYes.\n\nYes, it's a similar situation. The convolution is a special case of a many-to-one transformation. The transformation Z = X + Y maps many points (x,y) to one point z.\n\nThe convolution of independent random variables is a even more special case where the joint PDF of X and Y is the product of their individual PDFs.\n\n15. Sep 26, 2016\n\n### Stephen Tashi\n\nIt looks better, but your integration isn't defined. You say \"wrt x\" but you also have a \"dy\" in the integrand.\n\nIn general, if you were asked to integrate a function f(x,) of two variables over the line x + y = 2, how would you write this integration ?\n\n16. Sep 26, 2016\n\n### rabbed\n\nI was thinking I could divide both sides by |dz| and change |dy\/dz| into it's derivative.. If y=z-x, then dy\/dz = 1?\n\nIt was a long time since I did much integrating, but maybe you mean a double integral?\nOr setting the integration limits according to that relation..\n\nLast edited: Sep 26, 2016\n17. Sep 26, 2016\n\n### Stephen Tashi\n\nYou can divide both sides of an equation by something once you have an equation. But what you wrote isn't an actual equation because the integration on the right hand side isn't completely defined.\n\nMy use of the terminology \"integrating over\" was not good. If we integrate g(x,y) over an area, then we use a double integral and, yes, one of the limits would involve a variable - since given a value of x, we can vary y and still have (x,y) be inside an area. However, we try to integrate g(x,y) \"over a line\" by using a double integral, we get zero since a line has no area. If we set a value of x, we have no choice about the value of y.\n\nWhat I mean to say is that we want the integral $h(z) = \\int_{-\\infty}^{\\infty} g(x,z-x) dx$, which doesn't involve any \"dy\".\n\n18. Sep 27, 2016\n\n### rabbed\n\nIn programming terms I see the integral sign as a summing for-loop:\nfor (v=a, result=0; v<b; v+=dv) result += f(parameters)\nwhere you can choose the limits a and b and which of the parameters that should be substituted by the value of v in some expression f.\n(Same with sigma, where the only difference being the increment 1 instead of the infinitesimal dv)\nAlthough, we can only do integration if the expression contains dx (in the case where the parameter x was chosen).\n\nShouldn't the right hand side also mathematically just be a sum in\nZ_PDF(z)*|dz| = integral wrt x from -inf to inf of X_PDF(x)*|dx| * Y_PDF(z-x)*|dy|\nand it shouldn't matter if some factor is infinitesimal.\n\nHow does this extend to n source RV's? Would I let n-1 variables not be substituted in terms of the other variables and be integrated, while one of the source variables is expressed in terms of the other?\n\nFor example:\nQ = X + Y + Z + W\nQ_PDF(q)*|dq| = integral wrt x from -inf to inf of integral wrt y from -inf to inf of integral wrt z from -inf to inf of X_PDF(x)*|dx| * Y_PDF(y)*|dy| * Z_PDF(z)*|dz| * W_PDF(q-x-y-z)*|dw|\n\nLast edited: Sep 27, 2016\n19. Sep 27, 2016\n\n### Stephen Tashi\n\nIf we are approximating the integral of a function \"f\", the code would be:\nresult += f(v)*dv\n\nThe sum we are approximating doesn't involve any factor of dy. The function being integrated is: f(x) = X_PDF(x)*Y_PDF(z-x) where z is a constant since we do this approximation when we are given a specific value of z in order to find Z_PDF(z).\n\nIf that were true then for X,Y independent and Z = X + Y we would have the convolution formula\n$Z\\_PDF(z) = \\int_{-\\infty}^{\\infty} \\ ( \\int_{-\\infty}^{\\infty} X\\_PFF(x) Y\\_PDF(z-y) dy)\\ dx$\n$= \\int_{-\\infty}^{\\infty} \\ ( X\\_PDF(x) \\int_{-\\infty}^{\\infty} Y\\_PDF(z-y) dy)\\ dx$\n$= \\int_{-\\infty}^{\\infty} X\\_PDF(x) (1) dx$\n$= 1$\n\n20. Sep 27, 2016\n\n### rabbed\n\nBut if I keep |dz| on the left side, the products on the right hand side will have a factor |dy| in their sum? And afterwards I divide both sides with |dz| to get rid of the |dy|.\n\nIf I have n independent source RV's and n=2 (Z=X+Y), I assign an integral sign for n-1 of them, for example x, and the remaining one, y, I substitute with the expression z-x.\nSo I will always have n-1 integral signs and 1 change of variable. Will this not work for n>2?\n\n21. Sep 28, 2016\n\n### Stephen Tashi\n\nIf you are going to begin the derivation with the assertion $Z_{pdf}(z) dz = \\int_{-\\infty}^{\\infty} X_{pdf}(x) dx Y_{pdf}(y) dy$ then you need to justify that equation before proceeding. For example, is that equation correct even in a simple case such as when X and Y are each uniformly distributed on [0,1] ?\n\nA derivation beginning with the assertion $Z_{pdf} dz = \\int_{-\\infty}^{\\infty} X_{pdf}(x) dx Y_{pdf}(y) dy$ is apparently claiming that an appropriate dy can be chosen to make the two sides of the equation equal, because there is no other stipulation on what dy represents.\n\nHowever, by a similar technique, we can begin by assuming the equation $1 dz = 2 dy$. Dividing both sides of that equation by dz doesn't prove 1 = 2. An equation like $1 dz = 2 dy$ only holds when there is particular relationship between dz and dy.\n\nSo you if attempt to derive the general convolution formula by assuming a special realationship between Y and Z, you must show that this relationship is not actually \"special\". It must always hold between Y and Z regardless of how X is distributed.\n\n22. Sep 28, 2016\n\n### rabbed\n\nI'm just trying (for my own sake) to explain the change of variables\/PDF method and have done this by:\n- first explain the PDF formula for one-to-one transformation functions\n- then explain how to use that in the PDF formula for many-to-one transformation functions (using OR-logic with the probability approximations:\nY_PDF(y)*|dy| = X_PDF(t1^-1(y)) * dx + X_PDF(t2^-1(y)) * dx + ..\nwhere t1^-1(y), t2^1(y) .. are the different solutions of the inverse transformation function)\n\nNow I want to learn how to treat the probabilities in the case of multidimensional transformation functions, starting with convolutions.\nSo as long as the reasoning makes sense probability-wise (using AND\/OR logic and some change of variables), I'm happy :)\n\nSince, before I started with the change of variables method-explanation I already explained how the AND\/OR-'formulas' hold for probabilities and that the probability of a specific outcome value for a continuous random variable can be approximated by multiplying its PDF with the infinitesimal outcome size, if I can explain how to treat the probabilities for the separate transformation cases above in a way that makes sense intuitively and mathematically it's feels like proof enough for me.\n\nLast edited: Sep 28, 2016\n23. Sep 28, 2016\n\n### Stephen Tashi\n\nThat's an interesting approach. I don't recall ever seeing convolution presented as special case of a more general theorem - a theorem for a general \"function of several random variables\".\n\nOk, but what you've presented so far doesn't make sense. If we are doing to do a dx,dy,dz type of argument it has to make sense to a dx,dy,dz type of thinker.\n\nIf we accept Z_PDF(z) dz as an approximation for the probabilty of z - dz < Z < z + dz then there is some area in the X,Y plane that corresponds to this event. How do we integrate the joint density g(x,y) of X and Y over that area? The area isn't simply a rectangle of dimensions dx by dy with sides parallel to the respective coordinate axes.\n\nFor $g(X,Y) = X + Y$, I think the area looks like two \"infinite triangles\" with a common vertex at (0,0). Every line that satisfies the equation x + y = k for z-dz < k < z+dz is within the area.\n\nSo I think the integration we need is $\\int_{-\\infty}^{\\infty} \\int_{ymin}^{ymax} g(x,y) dy dx$ where\n$ymin = MIN( z - dz - x, z + dz - x)$ and $ymax = MAX(z - dz - x, z + dz - x)$.\n\n24. Sep 29, 2016\n\n### rabbed\n\nI think the case of Z = X + Y does make sense:\nZ_PDF(z)*|dz| = integral wrt x from -inf to inf of X_PDF(x)*|dx| * Y_PDF(z-x)*|dy|\nThis would produce the right hand side sum:\n\nX_PDF(-inf)*|dx| * Y_PDF(z-(-inf))*|dy| +\nX_PDF(-inf+dx)*|dx| * Y_PDF(z-(-inf+dx))*|dy|\nX_PDF(-inf+2*dx)*|dx| * Y_PDF(z-(-inf+2*dx))*|dy| +\n...\nX_PDF(inf)*|dx| * Y_PDF(z-(inf))*|dy|\n\nWe get the sum of the probabilities of each infinitesimal point on that infinite line where z is some constant c and the result is Z_PDF(c)*|dz| (the probability that any point OR the others on that line will be the outcome).\n\nWouldn't the same reasoning work for another dimension of source RV, giving us a plane of points we need to sum the probabilities for? Maybe we don't need to look at the area\/volume etc. of the shape, just the probabilities of the points? So we only use the integral signs to produce the coordinates of those points and make sure that the change of the last variable (y = z-x in the above 2D case) keeps the coordinates on that line\/place etc.\n\n2D: z = x + y => (x, z-x) are the points on the 1D line where z is constant\n3D: w = x + y + z => (x, y, w-x-y) are points on the 2D plane where w is constant\n4D: q = x + y + z + w => (x, y, z, q-x-y-z) are points in the 3D volume where q is constant\n\nHm, is that correct?\n\nThen maybe the area\/volume element comes in automatically when dividing the right hand side substituted variable's delta by the left hand side delta. but yes, it feels too speculative.. so maybe we need a more analytic solution that you propose.\n\nLast edited: Sep 29, 2016\n25. Sep 29, 2016\n\n### Stephen Tashi\n\nIf you think that makes sense as an approximation, try coding it for a specific example and see if you can approximate Z_PDF(z) that way for various values of z.\n\nThe problem I see is that you are integrating the joint density over a line of uniform thickness, but the bundle of lines that define the probability that z - dz < Z < z + dz is not of uniform thickness.","date":"2018-07-23 18:19:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8993788361549377, \"perplexity\": 684.9069669662566}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-30\/segments\/1531676599291.24\/warc\/CC-MAIN-20180723164955-20180723184955-00543.warc.gz\"}"}
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I get a few requests a week to review various software, hardware, and service products. (Sadly, not many of these are aviation-related but maybe my luck will change). Inspired by DCRainmaker, who sets a super high standard for thorough and transparent reviews, I decided to set out my policy so I can just reply to those queries with a link to this page.
If you have something you want me to review, feel free to contact me.
If I think it's interesting or cool, I may decide to review it. This review may be anything from a mention on Twitter to a full-blown magazine article, depending on how interesting or cool the product proves to be once I try it.
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If the review item is an NFR software license or access to a cloud-based service, I will use it for the review. If I decide I want to keep using it after the review period, I'll buy it.
If the review item is a book, depending on the genre, format, and quality, I may keep it or give it away.
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I don't accept payment for reviews.
I'm Nancy with Colasoft. Sorry, I didn't find your contact information so I leave a message here.
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Whispers and Warnings
Amazon's Book Availability Problems Now Affecting Even MORE Publishers?! IS YOUR BOOK AFFECTED?? – Whispers and Warnings – 08/23/18
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Amazon Damaging Sales of Small Press Books
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#Metoo Hits The Comic Publishing Industry
A comics publisher is taking cartoonists to court for accusing him of rape
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"Royalty-on-sale" compensation vs. "Relative Use" Lawsuit
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Liberty University: Censorship of the Student Newspaper or Editorial Control?
"It's one thing for a private entity to exercise editorial control over what gets published and what doesn't. It's another thing altogether to exert control outside of the bounds of the paper, not to mention changing the words of the writers in published pieces."
This is NOT the way to keep the media honest…
NY Times Reporter Receives Threatening Voicemail: 'The Pen is Not Mightier Than the AK-47'
"You're the problem. You are the enemy of the people. And although the pen might be mightier than the sword, the pen is not mightier than the AK-47…"
Backpage.com founders claim victimhood. Uh huh…
Backpage.com's Founders Speak for the First Time
"The story of their arrest, then, is better understood as one of near-religious fervor, government greed, and political retribution, in which an escalating panic over commercial sex coincided with a booming online publishing platform."
33 Worst Mistakes Writers Make About Blind Characters
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lost soul skateboards — The Internet is Still Busy... Coffee Cup.
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| 683
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\section{ Introduction }
\label{sec:intro}
Among numerous new ideas and concepts that have been put forward to
explain the unusual properties the high temperature superconductors
(HTS), which go beyond the conventional Fermi liquid theory,\cite{Lee06}
the staggered flux (SF) phase \cite{sfp} attracts much attention as a
candidate for the pseudogap normal phase of the underdoped cuprates.
\cite{Iva03} Such a state is characterized by a checkerboard pattern
of plaquette currents circulating clockwise and anticlockwise on two
different sublattices so that the corresponding flux flowing through
each plaquette alternates in sign.
On the one hand, using the SU(2) gauge invariance of the Heisenberg
model one can show that at half-filling the SF phase is equivalent
to the $d$-wave superconducting wave function \cite{Aff88} which has
correctly reproduced several key experimental properties of the HTS.
\cite{And04} Moreover, its Gutzwiller-projected energy is in a very
good agreement with the best estimate for the ground-state energy of
the two-dimensional undoped Heisenberg antiferromagnet.\cite{Lee06}
On the other hand, even though a finite doping removes this degeneracy
and stabilizes $d$-wave superconductivity in the ground state,
\cite{dwave} the SF phase is the lowest-energy Gutzwiller-projected
nonsuperconducting state that has been constructed so far,\cite{Iva04}
and its energy spectrum remains similar to the $d$-wave superconductor.
Signatures of the SF pattern in the current-current correlation have
been seen in the Gutzwiller-projected $d$-wave superconducting phase
\cite{Iva00} and in the exact ground-state wave-function of the
$t$--$J$ model.\cite{Leu00} It has also been proposed that the hidden
$d$-density wave (DDW) order of the doped SF phase could be the origin
of the mysterious pseudogap behavior.\cite{DDW} Finally, it has been
shown that under some circumstances the SF phase can coexist with
$d$-wave superconductivity in the underdoped regime.\cite{coex}
However, the physics of the hole-doped cuprates seems to be even more
involved as the competition between the superexchange interaction which
stabilizes the antiferromagnetic (AF) long-range order in the parent
Mott insulator, and the kinetic energy of doped holes, might lead to
the formation of stripe phases with hole-rich regions and locally
suppressed magnetic order, which was suggested in early Hartree-Fock
studies.\cite{Zaa89} In a stripe phase two neighboring AF domains are
separated by a one-dimensional domain wall (DW), where a phase shift of
$\pi$ occurs in the AF order parameter. Later on, experimental
confirmation of the stripe phases has triggered a large number of
studies devoted to their properties within a number of methods which go
beyond the Hartree-Fock approach.\cite{stripe} Moreover, even though
static charge and spin orders have only been observed in layered
cuprates, e.g., in
La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO) (see Ref. \onlinecite{Tra95})
and La$_{2-x}$Ba$_x$CuO$_4$ (see Ref. \onlinecite{Fuj04}), while in
bilayered YBa$_{2}$Cu$_{3}$O$_{6+\delta}$ (YBCO) only a stripe-like
charge order and incommensurate spin fluctuations have been
reported,\cite{Moo02} stripe phases quickly joined the list of
candidates for the pseudogap phase in the cuprates as they are
compatible with many experimental results.\cite{Kiv03}
Although numerical simulations of microscopic models of correlated
fermions, such as the $t$--$J$ model (see later), are especially
difficult, various signatures consistent with
(i) DDW states, and
(ii) stripe phases
have been detected. In particular, the emergence of strong staggered
current correlations under doping the Mott insulator has been reported
in exact diagonalizations by Leung,\cite{Leu00} and attributed to the
formation of spin bipolarons.\cite{Wro01} These findings are consistent
with an early observation of staggered spin chirality\cite{Poi91} since
charge degrees of freedom strongly couple to spin {\it scalar\/}
chirality. Interestingly, spin chirality/charge currents seem to
compete with hole pairing,\cite{Mas03} and this issue requires a
further careful consideration. Simultaneously with those findings, the
observation of stripes and checkerboard patterns (which also include
some form of charge ordering) has also been confirmed by density matrix
renormalization group (DMRG) computations for some boundary conditions.
\cite{DMRG}
We also note that an exotic SF phase with long-range orbital current
order {\it at half-filling\/} (in contrast to the fully projected SF
phase, see Ref. \onlinecite{Iva03}) was stabilized in various extended
Hubbard-like models (which include some form of charge fluctuations not
present in the simpler model discussed above) within ladder \cite{Mar02}
or bilayer \cite{Cap04} geometries.
It was also shown that such a long-range DDW order could survive with
the emergence of stripe-like features under doping.\cite{Sch03}
Unfortunately, even though stripe phases seem to play important role in
the physics of HTS, it is still not clear how the stripes are connected,
as a competing state, to $d$-wave superconductivity. Therefore,
in this paper we introduce a new class of wave functions with composite
order in a form of {\it filled domain flux\/} (FDF) phases, with one
doped hole per one DW atom. In addition to capturing essential
properties of the SF phases, the FDF structure accounts for the
incommensurate \emph{diagonal} spin peaks observed in lightly ($x<0.06$)
doped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) \cite{Wak99} and Nd-LSCO.
\cite{Wak01} Thus, our phase should allow one to obtain a smooth
transition from the insulating state at half-filling to the $d$-wave
superconductor above a critical doping $x_c$, with a concomitant change
of the DW orientation into \emph{vertical} stripes just at $x_c$,
as observed experimentally in LSCO.\cite{Fuj02} The existence of such
phases is suggested by recent variational Monte-Carlo calculations
which show an instability of the SF states towards phase separation,
\cite{Iva04} and we argue that self-organization into flux domains
separated by DWs is generic in the doped $t$--$J$ model. Most pronounced
features of these phases shown in Fig. \ref{fig:cart}(a,b) are:
(i) doped holes self-organize into diagonal DWs,
(ii) DWs separate weakly doped SF domains with a smoothly
modulated magnitude of the flux within them,
(iii) DWs introduce a phase shift of $\pi$ in the flux
phase and the SF domains alternate, and finally
(iv) in contrast to the so-called commensurate flux (CF) phases,
the total flux vanishes, and therefore no asymmetry of the
magnetic response is expected when reversing the direction of
an applied magnetic field.
In fact, these FDF phases have strong similarities with the solution
obtained in Ref.~\onlinecite{cfp} using uniform (i.e., site independent)
Gutzwiller factors.
The paper is organized as follows. The $t$-$J$ model and its treatment
in the Gutzwiller approximation are introduced in Sec. \ref{sec:model}.
The properties of locally stable domain flux phases with either
bond-centered or site-centered domain walls are presented in Sec.
\ref{sec:dom}. The paper is concluded in Sec. \ref{sec:summa} by
pointing out certain possibilities of experimental verification of the
suggested type of order and by a short summary of main results.
\section{ Model and Formalism }
\label{sec:model}
We consider the $t$-$J$ model,\cite{Cha77}
\begin{equation}
{\cal H}= - \sum_{\langle ij\rangle,\sigma}
t_{ij} ({\tilde c}^{\dag}_{i\sigma}{\tilde c}^{}_{j\sigma} + h.c.)
+ J\sum_{\langle ij\rangle} {\bf S}_i \cdot {\bf S}_j,
\label{eq:H}
\end{equation}
which is believed to describe the physics of the HTS. \cite{And04}
Here the summations include each bond $\langle ij\rangle$ only once.
Next, the local constraints that restrict the hopping processes
$\propto {\tilde c}^{\dag}_{i\sigma}{\tilde c}^{}_{j\sigma}$ to the
subspace with no doubly occupied sites are replaced by statistical
Gutzwiller weights,\cite{Gut63} while decoupling in the particle-hole
channel yields the following mean field (MF) Hamiltonian,
\begin{align}
\label{eq:H_MF}
{\cal H}_{\rm MF}=&- \sum_{\langle ij\rangle,\sigma} t_{ij}g_{ij}^t
(c^{\dagger}_{i\sigma}c^{}_{j\sigma}+h.c.)
-\mu\sum_{i\sigma}n_{i\sigma}\nonumber \\
&-\frac{3}{4} J \sum_{\langle ij\rangle,\sigma}g_{ij}^J
(\chi_{ji}c^{\dagger}_{i\sigma}c_{j\sigma} + h.c. -|\chi_{ij}|^2),
\end{align}
with the self-consistency conditions for the bond-order parameters
\begin{equation}
\label{eq:bond}
\chi_{ji}=\langle c^\dagger_{j\sigma}c^{}_{i\sigma}\rangle.
\end{equation}
\begin{figure*}[t!]
\begin{center}
\unitlength=0.01\textwidth
\begin{picture}(100,39)
\put(10,26){\includegraphics*[width=15.4cm]{BC.eps}}
\put(10,13){\includegraphics*[width=15.4cm]{SC.eps}}
\put(10, 0){\includegraphics*[width=15.4cm]{CFP.eps}}
\put(5,36){ {\Large (a)} }
\put(5,23){ {\Large (b)} }
\put(5,10){ {\Large (c)} }
\end{picture}
\end{center}
\caption {(color online)
Spatial modulation of the hole density $n_{hi}$ (circles), bond-order
parameter $\chi_{ij}$ (lines with arrows indicating the direction of
charge currents), and flux $\Phi_{\Box}$ defined by Eq. (\ref{eq:plaq})
(positive/negative flux indicated by symbols $+/-$) distribution found
in two FDF phases at hole doping $x=1/8$ and $t/J=3$.
Circle diameters are proportional to the doped hole densities; widths
of bond lines connecting them are proportional to the magnitudes of the
bond-order parameters $\chi_{ij}$, while the magnitude of flux flowing
through each plaquette is represented by the size of $+/-$ symbol.
Two distinct phases are:
(a) {\it bond-centered\/} FDF phase with a vanishing current
(dashed lines) at the DW bonds;
(b) {\it site-centered\/} FDF phase with a vanishing flux
(indicated by 0) at the DW plaquettes.
Panel (c) shows the self-consistent CF phase ($t=0$) characterized by
the uniform fictitious flux $\Phi_{\Box}=\tfrac{1}{2}(1-x)$, as well as
by homogeneous charge distribution.
}
\label{fig:cart}
\end{figure*}
In principle, simultaneous decoupling in the particle-particle channel
is also possible,\cite{Poi05} but since we are interested in the
diagonal DWs similar to the ones observed in the underdoped LSCO family,
\cite{Wak99,Wak01} we focus here on nonsuperconducting solutions.
In particular we choose $x=1/16$, one of the magic doping fractions at
which low-temperature in-plane resistivity of LSCO is weakly enhanced
suggesting a tendency towards charge order.\cite{Kom05} Here, to allow
for small non-uniform charge modulations, the Gutzwiller weights have
been expressed in terms of local doped hole densities
\begin{equation}
n_{hi}=1-\sum_{\sigma}\langle
c^{\dagger}_{i\sigma}c^{}_{i\sigma}\rangle
\label{eq:ni}
\end{equation}
as follows:\cite{Zha03}
\begin{equation}
g_{ij}^t=\sqrt{z_i z_j}, \hskip .7cm g_{ij}^J=(2-z_i)(2-z_j),
\label{eq:bothg}
\end{equation}
with $z_i=2n_{hi}/(1+n_{hi})$. For simplicity, results
shown below correspond to nearest neighbor hopping $t_{ij}=t$ only.
\cite{Marcin2} Thanks to developing an efficient reciprocal space
scheme by making use of the symmetry,\cite{Rac06} the calculations
were carried out on a large $256\times 256$ cluster at low temperature
$\beta J=500$, which eliminates the finite size effects.
Our starting point is the CF phase,
a wave function which, away from half-filling, displays remarkable
commensurability effects at special fillings and fulfills the
self-consistency condition at $t=0$. \cite{cfp} Indeed, in the limit
$xt/J\to 0$, the magnetic (superexchange) energy in the CF phase
exhibits a minimum when the fictitious flux (in unit of the flux
quantum), flowing through each plaquette and defined by a sum over
the four bonds of the plaquette
\begin{equation}
\Phi_{\Box}=\frac{1}{2\pi}\sum_{\langle ij\rangle\in\Box}\Theta_{ij},
\label{eq:plaq}
\end{equation}
where $\Theta_{ij}$ is the phase of $\chi_{ij}$, follows exactly the
filling fraction, i.e., $\Phi_{\Box}=\tfrac{1}{2}(1-x)$.
In this case, Hamiltonian (\ref{eq:H_MF}) reduces to the Hofstadter
Hamiltonian describing the motion of an electron in a uniform magnetic
flux assumed to be rational $\Phi_{\Box}=p/q$. \cite{Hof76} Therefore,
the peculiar property of the superexchange energy follows from the CF
phase band structure with $q$ bands and the Fermi level lying in the
largest gap above the $p$th subband. As a result, the modulus of the
bond-order parameter $\chi_{ij}$ (\ref{eq:bond}), the spin correlation
and the hole density are all spatially uniform
[see Fig. \ref{fig:cart}(c)].
However, infinitesimally small $xt/J$ selects a special arrangement of
the phases $\{\Theta_{ij}\}$ so as to optimize the kinetic energy term
$\propto \sum_{ij}\cos\Theta_{ij}$ and should produce an inhomogeneous
structure.\cite{cfp}
Within this class of singlet (nonmagnetic) wave functions, competing
with possible inhomogeneous solutions (see later), the uniform SF phase
also offers a very good compromise between the magnetic ($E_J$) and
kinetic ($E_t$) energy. For small $t$ and $x$, the kinetic energy is
minimized (within the MF approach) when all phases of $\chi_{ij}$ are
set to a constant $\Theta_{ij}=\pm\pi/4$, corresponding to alternating
fluxes $\Phi_{\Box}=\pm 0.5$ (SF phase). Increasing $xt/J$ gradually
reduces $|\Phi_{\Box}|$ and drives the system towards a Fermi liquid
state (with real $\chi_{ij}$) in a continuous way.
\section{ domain flux phases }
\label{sec:dom}
Starting with initial parameters corresponding to a uniform CF phase,
the self-consistent procedure leads to new FDF solutions which could
explain a diagonal spin modulation observed experimentally in the
insulating regime of LSCO \cite{Wak99} and Nd-LSCO,\cite{Wak01} usually
interpreted in terms of diagonal stripes, even though no signatures of
any charge modulation were observed yet. This conjecture is also
supported by the recent neutron scattering studies of the Ni impurity
effect on the diagonal incommensurability in LSCO. \cite{Mat06} Indeed,
doping by Ni quickly suppresses the incommensurability and restores the
N\'eel state. This indicates a strong effect on hole localization and
thus favors the presence of charge stripes with mobile holes rather
than the spiral order with localized hole spins.
Interestingly, we found two types of topologically different but nearly
degenerate solutions which both have the same size of the unit cell
(see Fig. \ref{fig:cart}):
(i) a {\it bond-centered\/} FDF phase, very similar to the original
CF one, where each DW is characterized by a {\it zero current\/}
staircase and by a maximum of the hole density spread over the
related bonds [Fig. \ref{fig:cart}(a)], as well as
(ii) a {\it site-centered\/} FDF phase, where the DWs are characterized
by {\it zero flux\/} plaquettes ordered along a diagonal line and
by a maximum of the hole density centered at two of their corner
sites [Fig. \ref{fig:cart}(b)].
Apart from local doped hole densities $\{n_{hi}\}$, bond quantities
are needed for a full characterization of both phases (here we use a
short-hand notation):
\leftline{ --- the spin correlation}
\begin{equation}
S_i=-\frac{3}{2}g_{i,i+x}^{J}|\chi_{i,i+x}|^2,
\label{eq:s}
\end{equation}
\leftline{ --- the bond charge hopping}
\begin{equation}
T_i=2g_{i,i+x}^{t}Re\{\chi_{i,i+x}\},
\label{eq:t}
\end{equation}
\leftline{ --- the charge current}
\begin{equation}
I_i=2g_{i,i+x}^{t}Im\{\chi_{i,i+x}\},
\label{eq:i}
\end{equation}
\leftline{ --- as well as the modulated flux}
\begin{equation}
\Phi_{\pi i}=(-1)^{i_x+i_y}\Phi_{i,i+x},
\label{eq:phi}
\end{equation}
with a phase factor $(-1)^{i_x+i_y}$ compensating the modulation of the
flux within a single domain of the SF phase. Typical profiles of the
above defined observables at low doping are depicted in Fig.
\ref{fig:DFP1}.
\begin{figure}[t!]
\centerline{\includegraphics*[width=8.2cm]{4by2.eps}}
\caption {(color online)
(a,e) Hole density $n_{hi}$ (\ref{eq:ni}),
(b,f) spin correlation $S_i$ (\ref{eq:s}),
(c,g) bond charge $T_i$ (\ref{eq:t}), and
(d,h) modulated flux $\Phi_{\pi i}$ (\ref{eq:phi})
in the {\it bond-centered\/} (left) and {\it site-centered\/} (right)
FDF phases at $x=1/16$ for: $t/J=1$ (triangles), and $t/J=3$ (squares).
For comparison, circles depict the related $t/J\to 0$ solutions:
the CF phase with uniform fictitious flux $\Phi=15/32$ (left)
and a two-domain $|\Phi|=\frac{1}{2}$ SF phase (right).}
\label{fig:DFP1}
\end{figure}
The stability of the FDF phases originates from a subtle competition
between the magnetic $E_J$ and kinetic energies $E_t$. Let us first
focus on the $t/J\to 0$ limit where the {\it site-centered\/} SF phase
is stable and very competitive (among the nonmagnetic states),
in contrast to the {\it bond-centered\/} one. This extreme case
corresponds to the localization of doped holes at DWs and the
superexchange energy in the SF domains is best optimized. Indeed, by
expelling holes from the SF domains one reinforces locally the AF
correlations with a concomitant reduction of both bond charge and
current correlations. On the contrary, due to a large hole density,
both these tendencies are reversed around the DWs. However, increasing
$t/J$ leads to a much broader charge spatial distribution in the unit
cell as a larger fraction of holes enters the SF domains
(see Fig.~\ref{fig:DFP1}). Nevertheless, both FDF phases remain
competitive even in the regime of large (realistic) values
of $t/J\sim 3$ due to:
(i) enhanced short-range AF correlations deep in the SF domains
($S_i\simeq -0.33$ compared to $S\simeq -0.28$ in the uniform
phase), where the fictitious flux approaches the special value
$\Phi=\frac{1}{2}$ (local minimum of the kinetic energy in
the limit $xt/J\rightarrow 0$), and
(ii) strongly enhanced bond charge accumulated around the DWs,
typically three times larger than that in the SF phase,
due to both amplification of the $g_{ij}^t$ factors and reduced
(vanishing) fictitious flux flowing through the bond-centered
(site-centered) plaquettes at the DWs.
Of particular interest is whether one can also stabilize within the
present formalism the so-called half-filled domain flux (HDF) phases,
analogous to \emph{half-filled\/} stripes with one hole per two atoms
in a DW as observed in the cuprates around $x=1/8$. \cite{Tra95,Fuj04}
On the one hand, both self-consistent {\it bond-\/} and
{\it site-centered\/} HDF phases found at $x=1/16$ and $t/J=3$ have
a somewhat higher total energy per site ($F\simeq -1.03J$) than those
obtained for both degenerate FDF ones ($F\simeq -1.07J$), and for the
uniform SF phase ($-1.09J$). However, Table~\ref{tab:1_8} shows that
all domain flux phases become very competitive at $x=1/8$, not only
with respect to the SF phase but also with respect to a recently
proposed nonuniform $4\times 4$ superstructure. \cite{Poi05} Note also
that while the FDF phases optimize mainly $E_J$, the HDF ones are
characterized by rather low $E_t$. Therefore, we predict that large
$t/J$ rather favors the domain flux phases with partially filled DWs.
We argue that quantum fluctuations are likely to stabilize them, in
analogy to the half-filled stripe phases,\cite{stripe} or to the fully
projected $4\times 4$ checkerboard wave function which was recently
shown to be more stable than the uniform SF phase.\cite{Web06} This
suggests that other inhomogeneous solutions might be stable as well.
Unfortunately, a direct comparison of our singlet wave functions to the
original (magnetic) stripe phases\cite{Zaa89} is not possible yet since
both are described within two entirely different formalisms. Hence
further studies using more sophisticated methods (like projected wave
functions as in Ref.~\onlinecite{Web06}) are needed.
\begin{table}[t!]
\caption {
Kinetic energy per hole $E_h$ (in units of $t$), and kinetic energy
$E_t$, magnetic energy $E_J$, free energy $F$ (all per site in units of
$J$) for the locally stable phases:
{\it bond-centered\/} HDF(1)
{\it site-centered\/} HDF(2), $4\times4$ checkerboard, FDF, and SF one,
as found at hole doping $x=1/8$ and $t/J=3$.
FDF(1) and FDF(2) phases are fully degenerate.
The~lowest energy increments are given in bold characters. }
\begin{ruledtabular}
\begin{tabular}{cccccc}
phase & & $E_h$ & $E_t$ & $E_J$ & $F$ \cr
\colrule
HDF(1) & &{\bf $-$2.7856}&{ \bf$-$1.0446}& $-$0.4028 & $-$1.4474 \cr
HDF(2) & & $-$2.7843 & $-$1.0441 & $-$0.4026 & $-$1.4467 \cr
$4\times4$& & $-$2.7128 & $-$1.0173 & $-$0.4348 & $-$1.4521 \cr
FDF & & $-$2.7067 & $-$1.0150 &{ \bf $-$0.4418}& $-$1.4568 \cr
SF & & $-$2.7587 & $-$1.0345 & $-$0.4246 & $-$1.4591 \cr
\end{tabular}
\end{ruledtabular}
\label{tab:1_8}
\end{table}
\begin{figure}[b!]
\centerline{\includegraphics*[width=7.5cm]{BS.eps}}
\caption{(color online)
Electronic structure of the {\it site-centered} FDF phase (solid lines)
and SF phase (dashed lines) along the main directions of the Brillouin
zone for $x=1/16$ and $t/J=3$. Inset shows a pseudogap between the FDF
bands along the $X-Y$ direction near the Fermi energy $\mu$ (thin dashed
line).
}
\label{fig:BS}
\end{figure}
An experimental support of the FDF phases follows from angle-resolved
photoemission (ARPES) experiments on lightly doped LSCO that show
a strongly suppressed spectral weight near the pseudogapped $X=(\pi,0)$
and $Y=(0,\pi)$ points, and a quasiparticle band crossing the Fermi
energy $\mu$ along the nodal $\Gamma-M$ direction, with $M=(\pi,\pi)$.
\cite{Yos03} Both features are qualitatively reproduced in the FDF
phases -- the electronic bands are almost dispersionless along the
$X-Y$ direction, and a gap opens at $\omega=\mu$ (Fig.~\ref{fig:BS}),
indicating that transport across the DWs is suppressed. However, the
most salient feature of the electronic structure in FDF phases is a
relativistic cone-like dispersion around the $S=(\pi/2,\pi/2)$ point.
Indeed, massless Dirac excitations are at the heart of the quantum
electrodynamics in (2+1) dimensions (QED$_3$) theory of pseudogap in
the cuprates.\cite{Tes01} This feature is also found in the SF phase,
but for the uniform flux and hole distribution it occurs away from the
Fermi energy $\mu$. The shape of the electronic structure in the FDF
phase depends on the actual value of $t/J$. Firstly, a strong
localization of holes at DWs in the limit $t/J\to 0$ pushes the top of
the lower band cone well below $\mu$. Secondly, finite $t$ weakens the
stripe order so that the gap between the lower and upper band at the
$S$ point is reduced. A further increase of $t$ pushes some lower band
states above $\mu$ enabling transport along the DWs.
\section{ Discussion and Summary }
\label{sec:summa}
For possible experimental verification of the present proposal it is
important to realize that
orbital currents of the domain flux phase give rise to weak magnetic
fields (that should be experimentally distinguishable from the copper
spins). Muon spin rotation ($\mu$SR) technique is an extremely
sensitive local probe especially suited to study small modulations of
local fields. Earlier estimations \cite{Led90} give 10 to 100 Gauss
corresponding roughly to 0.03 to 0.25 $\mu_B$ in cuprates. In fact,
incommensurate order in the LSCO family seen in neutron scattering
measurements,\cite{Wak99,Wak01}
(with a large but finite correlation length) might be attributed,
at least partly, to the existence of orbital moments.
Finally, note that although the phases considered here do not break
SU(2) symmetry and do not exhibit AF long range order, on general
principle they can still sustain AF correlations on large distances
(i.e., beyond nearest neighbor sites) between copper spins.
In summary, we have introduced and investigated a new class of flux
phases that unify the remarkable properties of the SF uniform phase with
the incommensurate magnetic correlations established in the underdoped
cuprates. Bond- and site-centered FDF phases are nearly degenerate which
indicates strong fluctuations which are expected to be amplified, either
for increasing $t/J$ or for increasing doping $x$. As these phases are
only marginally unstable at the MF level, they might be stabilized by
quantum effects and explain the low temperature physics of the cuprates
in the low doping regime, where a pseudogap phase forms at higher
temperature. Therefore, the solutions presented here could be viewed as
a low-temperature instability of the nearby DDW pseudogap phase (stable
at higher temperature but below $T^*$) in the same way as the "ordinary"
stripe phases could be seen as an instability of the nearby doped AF
N\'eel state at infinitesimal $x$. Therefore, our proposal calls for
a search of experimental signatures of domain flux phases in the
underdoped cuprates, especially in the LSCO family.
\begin{acknowledgments}
We thank M. M. Ma\'ska and Z. Te\v{s}anovi\'c for insightful
discussions. We acknowledge support by the the Polish Ministry of
Science and Education under Project No. 1~P03B~068~26, by the internal
project granted by the Dean of Faculty of Physics, Astronomy and
Applied Computer Science of the Jagellonian University,
as well as by the Minist\`ere Fran\c{c}ais des Affaires Etrang\`eres
under POLONIUM contract No. 09294VH. D.P. thanks the
``Agence Nationale pour la Recherche'' (ANR) for support.
\end{acknowledgments}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,970
|
class Text::UrlCodingController < EditorController
include Uploads::Uploadable
upload_class Uploads::Text::UrlCodingFile
# GET /text/url_coding
def editor
@files = Uploads::Text::UrlCodingFile.all
respond_to do |format|
format.html { render :editor }
end
end
# POST /text/url_coding/encode_or_decode
def encode_or_decode
result = execute_for_json do |r|
input = if params[:mode].include?('file')
Uploads::Text::UrlCodingFile.find(params[:file]).read
else
params[:input]
end
encoding = params[:encoding]
if (params[:mode].include?('encode'))
r[:result] = Text::UrlCoding.new.encode(input, encoding)
else
r[:result] = Text::UrlCoding.new.decode(input, encoding)
end
end
respond_to do |format|
format.json { render :json => result }
end
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 532
|
\chapter{Architectures}
\renewcommand{\nomgroup}[1]{%
\ifthenelse{\equal{#1}{C}}{\item[\textbf{Roman Symbols}]}{%
\ifthenelse{\equal{#1}{V}}{\item[\textbf{Greek Symbols}]}{%
\ifthenelse{\equal{#1}{S}}{\item[\textbf{Abbreviations and Acronyms}]}{}
}
}
}
\pdfbookmark[1]{Nomenclature}{nomenclature}
\nomenclature[C]{$\mathcal{S}$}{State Space}
\nomenclature[C]{$\mathcal{A}$}{Action Space}
\nomenclature[C]{$\mathbb{R}$}{Real Numbers}
\nomenclature[S]{RL}{Reinforcement Learning}
\nomenclature[S]{MDP}{Markov Decision Process}
\nomenclature[S]{POMDP}{Partially Observable MDP}
\nomenclature[S]{MLP}{Multilayer Perceptron}
\nomenclature[S]{ANN}{Artificial Neural Network}
\nomenclature[S]{DL}{Deep Learning}
\nomenclature[S]{PCA}{Principal Component Analysis}
\nomenclature[S]{ICA}{Independent Component Analysis}
\nomenclature[S]{SF}{Successor Features}
\nomenclature[S]{GrICA}{Our Gradient-based ICA Algorithm (from Chapter 4)}
\nomenclature[S]{LARP}{Latent Representation Prediction (from chapter 5)}
\nomenclature[S]{RewPred}{Our Reward-predictive Representation (from Chapter 6) }
\nomenclature[S]{MINE}{Mutual Information Neural Estimation}
\nomenclature[S]{CAE}{Variational Autoencoder }
\nomenclature[S]{VAE}{Convolutional Autoencoder }
\nomenclature[S]{LEM}{Laplacian Eigenmaps }
\nomenclature[S]{Conv.}{Convolutional }
\nomenclature[S]{ReLU}{Rectified Linear Unit }
\nomenclature[S]{t-SNE}{t-distributed Stochastic Neighbor Embedding }
\nomenclature[S]{PPO}{Proximal Policy Optimization}
\nomenclature[S]{DQN}{Deep Q-Network}
\nomenclature[S]{ACKTR}{Actor Critic using Kronecker-Factored Trust Region}
\nomenclature[S]{MSE}{Mean Squared Error}
\nomenclature[S]{MBRL}{Model-based Reinforcement Learning}
\nomenclature[S]{MBRL}{Model-free Reinforcement Learning}
\nomenclature[V]{$\phi$}{Representation}
\nomenclature[V]{$\eta$}{Learning rate parameter}
\nomenclature[V]{$\pi$}{Policy function }
\nomenclature[V]{$\pi^*$}{Optimal Policy }
\nomenclature[V]{$\theta$}{The parameters of a differentiable function}
\nomenclature[C]{$\mathcal{P}$}{State Transition }
\nomenclature[C]{$P$}{Probability }
\nomenclature[C]{$\mathcal{R}$}{Reward function}
\nomenclature[C]{$ V_\pi$}{state-value function of $\pi$}
\nomenclature[C]{$ q_\pi$}{action-value function of $\pi$}
\nomenclature[C]{$\mathcal{D}$}{Data set}
\nomenclature[V]{$\Omega$}{Observation space}
\nomenclature[C]{$\mathcal{O}$}{Observation function}
\nomenclature[C]{$t$}{Time step index}
\nomenclature[C]{$a$}{Action}
\nomenclature[C]{$s$}{State}
\nomenclature[C]{$o$}{Observation}
\nomenclature[C]{$r$}{Reward}
\nomenclature[V]{$\gamma$}{Discount factor}
\nomenclature[C]{$\mathcal{L}$}{Loss function}
\printnomenclature
\newpage
\section{Reinforcement learning} \label{sec:rl}
In this section, we formalize RL for the rest of the thesis. RL is one of the main disciplines of machine learning, and it covers how agents can learn to behave optimally in an environment to maximize a cumulative reward.
\subsection{Partially observable Markov decision processes}
A partially-observable Markov decision process (POMDP) is a general framework for modeling sequential decision processes in environments that can be stochastic, complex and contain hidden information. Formally, it is a tuple
\begin{equation} \label{eq:pomdp}
(\mathcal{S}, \mathcal{A}, \mathcal{P}, \mathcal{R}, P(s_0), \Omega, \mathcal{O}, \gamma)\end{equation}
which we also refer to as the \textit{environment}. The tuple is made up of the following elements:
\begin{itemize}
\setlength{\itemindent}{0.65cm}
\item[$\mathcal{S}$:] The state space defines the possible configurations of the environment
\item[$\mathcal{A}$:] The action space describes how the agent is able to interact with the environment
\item[$\mathcal{P}$:] The transition function $\mathcal{P}: \mathcal{S} \times \mathcal{A} \rightarrow P(\mathcal{S})$ dictates the effects of different actions in different states
\item[$\mathcal{R}$:] The reward function $\mathcal{R}: \mathcal{S} \times \mathcal{A} \times \mathcal{S} \rightarrow \mathbb{R}$ determines the immediate reward given to the agent for transitioning between any two states with any action
\setlength{\itemindent}{1.3cm}
\item[$P(s_0)$:] The initial state distribution
\setlength{\itemindent}{0.65cm}
\item[$\Omega$:] The observation space defines the aspects of the environment that the agent can perceive
\item[$\mathcal{O}$:] The observation function $\mathcal{S} \times \mathcal{A} \rightarrow P(\Omega)$ defines what (potentially transformed) subset of the environment the agent receives after acting in a given state
\item[$\gamma$:] The reward discount factor
\end{itemize}
The environment starts in a state drawn from $P(s_0)$, from which the agent interacts sequentially with the environment by choosing action $a_t$ from action space $\mathcal{A}$ at time steps $t$. The agent receives an observation $o_t$ and a reward $r_t$ after each action.
The objective of an RL agent is to learn a \textit{policy} $\pi$ that determines the behavior of the agent in the environment by mapping states to a probability distribution over $\mathcal{A}$, written $\pi(a, s) = P(a_t = a | s_t = s)$. A discount factor $\gamma \in (0, 1)$ is usually included in the definition of POMDPs, and it comes into play in the optimization function of the agent. Namely, the policy should maximize the expected discounted future sum of rewards, or the expected \textit{return}, where the return is defined as
\begin{equation} \label{eq:ret}
R = \sum_{t=0}^\infty \gamma^t r_t
\end{equation}
The \textit{value function} is defined as the expectation of the return (Eq.\ref{eq:ret}), given a policy $\pi$ and an initial state $s_0 = s$
\begin{equation} \label{eq:vf}
v_\pi(s) = \mathbb{E}\left[ R | s_0 = s, \pi\right] = \mathbb{E}\left[ \sum_{t=0}^\infty \gamma^t r_t | s_0 = s, \pi\right]
\end{equation}
There is at least one \textit{optimal policy} $\pi^*$ that is better than or equal to others: $v_{\pi^*}(s) \geq v_{\pi'}(s)$ for all states $s$ and all other policies $\pi'$.
\subsection{Model-free algorithms}
Model-free reinforcement learning learns the policy or a value function directly from experience without attempting to approximate the dynamics of the environment. Two popular classes of model-free methods are \textit{value-based} methods and \textit{policy-based} methods.
Value-based methods approximate either the value function \citep{sutton1988learning} or another useful function that is similar to the value function, the \textit{action-value function} $q$. This function is defined as the expected return of following the policy $\pi$ after taking an action $a$ in a state $s$:
\begin{equation} \label{eq:saf}
q_\pi(s, a) = \mathbb{E}_\pi\left[ R_t | s_t = s, a_t=a\right] = \mathbb{E}_\pi\left[ \sum_{k=0}^\infty \gamma^k r_{t+k+1} | s_t = s, a_t=a\right]
\end{equation}
Estimating the action-value function is a pivotal step for algorithms such as Q-learning \citep{watkins1992q}. A simple one-step Q-learning updating rule is \citep{sutton2018reinforcement}:
\begin{equation} \label{eq:qlearn}
q_\pi(s_t, a_t) \leftarrow q(s_t, a_t) + \eta\left[r_{t+1}+ \gamma \max_a q(s_{t+1}, a) - q(s_t, a_t) \right]
\end{equation}
where $\eta$ is a positive learning rate parameter and the initial values of $q_\pi(s_t, a_t)$ are chosen arbitrarily. Q-learning is guaranteed to converge to the optimal policy's action-value function $q_{\pi^*}$, under certain conditions\footnote{ This depends on a good learning rate schedule and exploration techniques, which are difficult to determine in practice}, which in turn yields the optimal policy: $\pi^* = \argmaxB_a q_{\pi^*}(a, s)$. This method tabulates the values and thus works with discrete actions and state spaces. Q-learning has been combined with deep neural networks to work for actions and state spaces of higher dimensions \citep{mnih2015human}.
Policy-based methods do not learn a value function, but rather learn the policy directly by optimizing an objective function with respect to $\pi$. We describe two of those methods that we employ in this work: (1) proximal policy optimization (PPO) \citep{schulman2017proximal} and (2) actor critic using Kronecker-factored trust region (ACKTR) \citep{wu2017scalable}.
PPO optimizes the objective function
\begin{equation}
L^{CLIP}(\theta) = \hat{\mathbb{E}}_t \left[ \min(\text{ratio}_t(\theta)\hat{A}_t, \text{clip} (\text{ratio}_t(\theta), 1-\epsilon, 1+\epsilon)\hat{A}_t \right]
\end{equation}
\noindent where $\epsilon$ is a hyperparameter, $\text{ratio}_t(\theta) = \frac{\pi_\theta(a_t | s_t)}{\pi_{\theta_{\text{old}}}(a_t, s_t)}$ and $\hat{A}$ is an estimator of the advantage function $A = q_\pi(s, a) - v_\pi(s)$. The clip term returns $\text{ratio}_t(\theta)$ if $1-\epsilon < \text{ratio}_t(\theta) < 1+\epsilon$, otherwise the value is clipped to the closer boundary value. The full PPO algorithm is shown in Algorithm \ref{algo: ppo}.
\begin{algorithm}[thb]
\caption{Proximal policy optimization}\label{algo: ppo}
\begin{algorithmic}[1]
\FOR{iteration $ = 1, 2, \dots$}
\FOR{actor $= 1, 2, \dots, n$}
\STATE Run policy $\pi_{\theta_\text{old}}$ in environment for t time steps
\STATE Compute advantage estimates $\hat{A}_1 , \dots , \hat{A}_t$
\ENDFOR
\STATE Optimize $L^{CLIP}$ with respect to $\theta$, with k epochs and minibatch size $m \leq nt$
\STATE $\theta_{old} \leftarrow \theta$
\ENDFOR
\end{algorithmic}
\end{algorithm}
ACKTR applies the policy gradient updates
\begin{equation}
\theta \leftarrow \theta - \eta \hat{F}^{-1} \nabla_\theta L
\end{equation}
\noindent where $\hat{F} \approx \mathbb{E}[\nabla_\pi \log \pi (a_t | s_t) (\nabla_\theta \log \pi (a_t | s_t) )^T]$, $L$ is the log-likelihood of the output distribution of the policy and the learning rate $\eta = \min (\eta_{\max}, \sqrt{
\frac
{2\delta}
{\Delta \theta^T \hat{F} \Delta \theta }
}) $ is controlled dynamically with the trust region parameter $\delta$ to prevent the policy from converging prematurely to a poor policy.
\subsection{Model-based algorithms}
Model-based reinforcement learning (MBRL) algorithms learn the optimal policy $\pi^*$ by first estimating the transition function $\Tilde{\mathcal{P}}\approx \mathcal{P}$ and the reward function $\Tilde{\mathcal{R}}\approx \mathcal{R}$. These functions are usually called the environment \textit{dynamics} or \textit{world model} and are learned in a supervised fashion from a data set of observed transitions, $\mathcal{D} = \{(s_t, a_t, r_t, s_{t+1})_i\}$. The world models can be used in multiple different ways, depending on the algorithm, to derive the optimal policy.
For example, sampling-based planning algorithms use $\Tilde{\mathcal{P}}$ and $\Tilde{\mathcal{R}}$ to sample action sequences and calculate their expected values:
\begin{equation} \label{eq:rsmbrl}
(A_t, \dots, A_{t+\tau}) = \argmaxB_{A_{t:t+\tau}} \mathbb{E}\left[ \sum_{k=t}^{t+\tau} \gamma^k \Tilde{\mathcal{R}}(s_k, a_k) | s_t = s, s_{t+1}, \dots, s_{t+\tau} \sim \Tilde{\mathcal{P}}\right]
\end{equation}
The agent follows the action sequence associated with the highest expected reward in Equation \ref{eq:rsmbrl}. This is often combined with model-predictive control (MPC), where a new action sequence is calculated after taking the first action in the last sequence. There are different ways of choosing candidate action sequences, with the simplest being the random shooting algorithm \citep{richards2005robust}, that draws the actions from a uniform distribution.
\section{Deep learning}
\label{sec:dlrn}
For the last few years, deep learning has been on the center stage of machine learning research. We make extensive use of deep learning in this work because of its parallelizability, its efficient scaling with large data sets and its capability to approximate complex functions.
The most basic type of deep learning method is the feedforward deep network, which comprises layers of artificial neurons. The theoretical capabilities of artificial neural networks were guaranteed by \cite{cybenko1989approximation}: his Universal Approximation Theorem has the implication that any continuous function of real numbers with values in a Euclidean space can be approximated by a neural network with one hidden layer. Unfortunately, it is a pure existence theorem, leaving the task of constructing the network to the engineer.
\subsection{The artificial neuron}
An artificial neuron \citep{rosenblatt1958perceptron} is a mathematical function that multiplies each input with a constant, adds a bias to the linear combination and then applies a non-linearity to the outcome:
\begin{equation}
y = \varphi\left( \sum_{i=1}^m w_i x_i + b\right)
\label{anneq}
\end{equation}
The non-linearity $\varphi$ is known as the \textit{activation function}, the coefficients $w_i$ are known as the \textit{weights} and the term $b$ is known as the \textit{bias}.
We now briefly discuss some commonly used activation functions that are employed in this thesis. For a more comprehensive overview of recent trends in the usage of activation functions, we encourage the reader to look at a comparison by \cite{nwankpa2018activation}.
The logistic function can be used for binary classification.
\begin{equation}
\varphi_{\text{logistic}}(x) = \frac{1}{1+e^{-x}}
\label{logistic}
\end{equation}
This function "squashes" the inputs to lie between $0$ and $1$, giving the output a probabilistic interpretation.
The softmax function is an extension of the logistic function for several classes
\begin{equation}
\varphi_{\text{softmax}}(x)_i =\frac{e^{x_i}}{\sum_{i=1}^n e^{x_i}}
\label{softmax}
\end{equation}
The output of the softmax function is a vector of the same dimensionality as the input vector and sums to $1$.
The hyperbolic tangent function (tanh) squashes the input to lie between -1 and 1
\begin{equation}
\varphi_{\text{tanh}}(x) = \frac{e^x - e^{-x}}{e^x - e^{-x}}
\label{tanh}
\end{equation}
This has the computational advantage over the logistic function that biases in the gradients are avoided and 0-centered data gives rise to larger derivatives during optimization of the networks \citep{lecun2012efficient}, making them a more frequent choice as an activation function in hidden layers.
The most popular nonlinearity for deep neural networks is the rectifier function
\begin{equation}
\varphi_{\text{ReLU}}(x) = \max(0, x)
\label{relu}
\end{equation}
The rectifier function offers the same advantages as the tanh function but at a lower cost, as evaluating exponentials and performing division is avoided. The rectifier function is also called a rectified linear unit, and it is commonly abbreviated as "ReLU".
\subsection{Feedforward neural networks}
Computational units implementing the function in Eq. \ref{anneq} can be arranged hierarchically, with the input of a neuron consisting of the output of other neurons. An example feedforward neural network or \textit{multilayer perceptron} (MLP)\footnote{Feedforward neural networks are sometimes loosely referred to as multi-layer perceptrons (MLPs), named after an early artificial neuron model called the \textit{perceptron}. However, perceptrons use a hard threshold activation function while modern MLPs can use any differentiable activation, so they are often not perceptrons, in the strict meaning of the word.} is depicted in Figure \ref{feedforward_nn}.
\begin{figure*}[h]
\centering
\begin{minipage}{.96\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/feedforward_nn2.pdf}
\end{minipage}%
\caption[Illustration: A fully-connected neural network]{ \textbf{A Fully-connected neural network.} This network has three inputs and two layers: one hidden layer with four units and an output layer with two units. } \label{feedforward_nn}
\end{figure*}
The figure shows a network with one hidden layer, but it can in principle have any number of hidden layers. The same is true for the number of inputs and outputs.
\subsection{Optimizing neural networks}
Training a deep neural network involves training data and a loss function. For training an artificial neural network, an appropriate loss function has to be found to match both the task at hand along with the final layer's activation function. The loss function measures the difference between the output of the network, when the data is passed through it, and the desired outcome. The parameters $\theta$ of the network are then adjusted toward the optimal $\theta^*$ that minimize the loss function over the data
\begin{equation}
\theta^* = \argminB_\theta \sum_{i=1}^n \mathcal{L}(f_\theta(x_i), y_i)
\label{general loss}
\end{equation}
\noindent where $n$ is the number of data points and $f_\theta(x_i)$ is the prediction of a neural network with parameters $\theta$, for sample $x_i$ with the true value $y_i$. The quantity $\sum_{i=1}^n \mathcal{L}(f_\theta(x_i), y_i)$ is also known as the \textit{empirical risk}. One such example is the mean-squared error (MSE) loss
\begin{equation}
\mathcal{L}_{\text{MSE}}(f_\theta(x_i), y_i) = \left( y_i - f_\theta(x_i) \right)^2
\label{mse0}
\end{equation}
Maximizing the likelihood of Gaussian data with respect to the parameters of the assumed model that generated the data is equivalent to minimizing the MSE, making it a popular choice for regression tasks (i.e. when the output layer activation is linear or ReLU).
For classification networks with a logistic or sigmoid activation output, a suitable loss function is the cross-entropy loss function
\begin{equation}
\mathcal{L}_{\text{CE}}(f_\theta(x_i), y_i) = - \left( \sum_{j=1}^C y_{ij} \cdot \log (f_\theta(x_i) ) \right)
\label{celoss}
\end{equation}
\noindent where $C$ is the number of classes\footnote{If $C=3$, then the label vector could, for example, take the form $y_1 = (0, 1, 0)$.}. Similarly to MSE, this loss function is also motivated by the fact that minimizing the cross-entropy loss is equivalent to maximizing the likelihood of uniformly distributed i.i.d. data \citep{yao2019negative}.
So far, the loss functions we have seen require a label $y_i$ as a part of the input. This makes them \textit{supervised} learning losses. Many commonly used loss functions exist that do not require labels, those are called \textit{unsupervised} learning losses.
Once we have decided on a loss function to minimize, the next step is to choose the optimization algorithm. The most popular ones are implemented in software libraries such as Keras \citep{chollet2015keras}, MXNet \citep{chen2015mxnet}, Tensorflow \citep{abadi2016tensorflow}, Pytorch \citep{NEURIPS2019_9015} and several others.
The most common way of training deep neural networks is by employing a variation of the \textit{gradient descent} \citep{curry1944method} algorithm. Gradient descent methods take advantage of the fact that a function decreases the fastest in the negative direction of its gradient, converging at a local minimum.
An algorithm called \textit{backpropagation} \citep{linnainmaa1970representation} computes the gradient of the loss function with respect to each parameter (e.g. weights and biases) via the chain rule from calculus. These gradients are then used for an update step for each parameter:
\begin{equation}
\theta^{[i+1]} \leftarrow \theta^{[i]} - \eta \frac{\partial \mathcal{L}}{\partial \theta^{[i]}}
\label{gradientdescent}
\end{equation}
\noindent where $i$ keeps track of the index of the iteration. The parameter $\eta$ is known as the \textit{learning rate} of the optimization algorithm.
The classical gradient descent method in Equation \ref{gradientdescent} calculates the average loss over the entire data set. This can be made faster, without losing convergence guarantees, by performing a weight update using the gradient from only a subset of the training data -- or a \textit{training batch} -- in each iteration. This stochastic approximation of gradient descent is called \textit{stochastic gradient descent.}
A good learning rate is important for the practical convergence of stochastic gradient descent: if it is very small, then the time it takes to converge can be too long. However, if it is too large, then there is a risk of overshooting the local minima.
It is generally good to start off with a larger learning rate and then make it smaller with time.
Determining exactly when to decrease the size of the learning rate, and by how much, can be laborious in practice. For this reason, there have been proposed several gradient descent methods that automatically find this learning rate schedule with adaptive learning rates, for example, rmsprop \citep{tieleman2012lecture} and Adam \citep{kingma2014adam}.
\subsection{Convolutional neural networks}
The network in Fig. \ref{feedforward_nn} is a \textit{fully-connected} or \textit{dense} neural network, because every unit is connected to every unit in the preceding layer. There are other, more specialized, neural networks that are not fully-connected, one of the most important class being \textit{convolutional} neural networks. For input data with a spatial structure, for example images, convolutional neural networks are very efficient.
In contrast to dense neural networks, each unit in convolutional neural networks only receives as input a subset of the outputs from the previous layer. More specifically, each unit only receives inputs from units that are in spatial proximity of one another. Waldo Tobler's First Law of Geography captures succinctly the motivation behind convolutional networks \citep{tobler1970computer}: "everything is related to everything else, but near things are more related than distant things". Another key property of convolutional neural networks is the one of shared weights -- each computational unit in the same layer has the same set of weights, even though they receive different inputs.
These properties have the practical consequence that the number of parameters is cut down substantially: each neuron processing a $64 \times 64$ grayscale image would require $64 \cdot 64 + 1 = 4097$ weights, which is then multiplied again by the number of neurons in the layer for the total parameter count. On the other hand, a convolutional layer where each neuron processes a $7 \times 7$ window (a relatively large window size) around a pixel would require $7\cdot7+1 = 50$ parameters -- for the whole layer, due to the shared weights. Thus, processing the image input in this example with a convolutional layer instead of a dense layer with a single neuron reduces the number of parameters by a factor of $80$.
In addition to the activation function, we specify the value of four hyperparameters for convolutional layers when we describe specific network architectures in this thesis: the number of \textit{filters} to slide along the height and width of the input, the size, or the \textit{receptive field}, of the filters, the \textit{stride} and how much \textit{zero padding} to use. The receptive field dictates the sizes of the spatial dimensions (height, width) of the input that the neuron takes. In Figure \ref{fig:cnn_example}, for instance, we would say that the filter size is ($2\times2$), despite the dimension of the weights being ($2\times2\times2$) -- this is due to the size of the input depth. Note that even though these height and width values are constrained, the neuron always processes the full depth of the input.
The stride controls how many steps the filters take as the input is processed along its spatial dimensions. Zero padding amounts to adding rows and columns around the input, composed entirely of zeros, also along the depth. Padding is often done to make the output valid, for instance, if the stride or filter size would potentially cause a neuron to process inputs that are "out of bounds". This is often called \textit{valid} padding. Another purpose of padding is to pad the input with zeros to keep the original spatial dimensions unchanged, this is called \textit{same} padding. For example, zeros can be added around an image of size $12\times12$ before it is processed by a network that requires an input of $16\times16$.
The relationship between the input and output of a convolutional filter is illustrated in Figure~\ref{fig:cnn_example_lighter}. In Figure~\ref{fig:cnn_example} we add a depth dimension. In our example, the stride is 1. However, in the example, if we would want to increase the stride value then we would have to introduce zero padding.
\begin{figure}
\centering
\begin{subfigure}[b]{0.95\textwidth}
\includegraphics[width=1\linewidth]{assets/cnn_tutorial2_lighter.pdf}
\caption{Input with (height $\times$ width $\times$ depth) dimensions of ($3\times3\times1$). }
\label{fig:cnn_example_lighter}
\end{subfigure}
\begin{subfigure}[b]{0.95\textwidth}
\includegraphics[width=1\linewidth]{assets/cnn_tut1.pdf}
\caption{Input with (height $\times$ width $\times$ depth) dimensions of ($3\times3\times2$). }
\label{fig:cnn_example}
\end{subfigure}
\caption[Illustration: A convolution layer]{ \textbf{A convolutional layer.} The input is processed by a single convolutional filter with a receptive field of $2\times2$, a stride of one, no zero padding and the identity activation function $\varphi(x)=x$. The subset of the input that is included in the calculation of the upper right element of the output is highlighted by the dotted boxes.}
\end{figure}
Generally, any deep neural network is called a convolutional neural network if it has one or more convolutional layers. This holds true even if not all the layers are convolutional layers. Some popular layer types include:
\begin{itemize}
\item \textit{Subsampling} layers that keep only every $n$th row and column to reduce the computational complexity. This is usually only done as a first preprocessing step for very high dimensional inputs, where throwing away the information is not as harmful as in the intermediate layers of the network.
\item \textit{Max pooling} layers slide along the width and height of each depth slice in the input and return the largest single value in their window. They reduce the computational complexity by reducing the input dimension, and they make the representation approximately invariant to small translations.
\item \textit{Flattening} layers are technical layers that re-shape tensor or array inputs to vectors.
\item \textit{Normalization} layers for re-centering and re-scaling inputs to layers. They help speeding up and stabilizing the learning process.
\end{itemize}
Deep neural networks often have a number of parameters in the thousands or billions. This makes the interpretation of the calculations difficult, especially due to the number of layers. Visualizations of the first few convolutional layers in trained networks has been done \citep{zeiler2014visualizing}, with the result that the first layer's filters usually capture edges, corners, and color combinations. The second layer then combines these features into more complicated patterns. Higher filters then combine these features further into textures, object parts or even whole objects.
\section{Representation learning}
\label{sec:repr_learn}
In computer science in general, and machine learning in particular, the choice of the representation of the data that is being processed is crucial. This could mean choosing the right data structure for the task, such as designing a database for fast searching. This could also mean choosing the right independent variables for a statistical model.
The extraction of useful information about the data is thus an important task. This is especially true if the input is from a high-dimensional space, with the term \textit{curse of dimensionality} \citep{bellman1957dynamic} being used since the late 1950s for describing problems of this nature: the amount of data needed to make statistically significant claims grows exponentially with the dimensionality of the space that the data resides in. This makes the discovery of methods for reducing the dimensionality of the input, without discarding important information, an attractive prospect.
\subsection{Supervised representation learning}
Representations arise in artificial neural networks (ANNs) when they are trained for a regression or classification objective. One view of ANNs is that the hidden layers perform feature extraction on the input, transforming it to a more suitable form for the output layer that performs the final calculations for the task. \cite{sharif2014cnn} made use of this insight by pre-processing inputs for supervised learning models with the intermediate layer outputs of a convolutional network that was pre-trained on an object classification task. They achieved impressive results on a diverse range of tasks, such as image retrieval and scene recognition. The hierarchical structure of ANNs also has the theoretical and practical advantage that the features at each level are re-used for the different features at the higher level.
\subsection{Unsupervised representation learning}
For hierarchical methods like ANNs, representations are generated at the same time as the whole system is trained to minimize error on human tagged data. Most other representation learning methods are \textit{unsupervised} and are able to learn useful features on unlabeled data.
\subsubsection{PCA}
Principal component analysis (PCA) is an unsupervised learning method invented by \cite{pearson1901liii}. The method finds an orthogonal linear transformation $f(X) = W^TX$ for zero-mean, $d$-dimensional data $X$.
The columns $w_i$ of $W$ are the \textit{principal components} of the data $X$, which point to the direction of the greatest variance in the data. The first principal component is the solution to the equation
\begin{equation} \label{eq:pca}
w_i = \argmaxB_{||w||=1} ||Xw||^2
\end{equation}
The second component is found by applying Equation \ref{eq:pca} again to the transformed data $\hat{X}$ that is given by removing the contribution of the first component from $X$, $\hat{X} = X - ((w_1)^TX)w_1$, and so on.
All the components can also be found simultaneously by computing the eigendecomposition of the data's covariance matrix, as it has been shown that the principal components are equal to the resulting eigenvectors \citep{shlens2014tutorial}.
Dimensionality reduction can be done by creating a matrix $W_L$, consisting only of the first $L$ principal components, and applying it to the data. This yields the lower-dimensional, transformed data matrix $T_L = W_{L}^T X $. By doing this, the data is projected onto the subspace with the maximum variance. This matrix $W_L$ of principal components has the property of minimizing the reconstruction error $||X - W_L T_L ||^2$. In Figure \ref{fig:vizcomparison}, we show a visualization of the UCI ML digits data set, which consists of $8\times8$ grayscale images of hand-written digits. The figure shows the result after the data is projected on its first two principal components, showing clear clustering of the digits. We also show the clustering found by t-distributed stochastic neighbor embedding (discussed below), which separates the clusters more cleanly for this data set.
\begin{figure}[h]
\begin{adjustwidth}{0in}{0in}
\centering
\subfloat[{\bf Samples from the digits database.}]{{\includegraphics[width=.47\columnwidth]{assets/digs.png}}}
\vspace{1em}
\subfloat[{\bf PCA visualization of digits.}]{{\includegraphics[width=.45\columnwidth]{assets/pca_digs.png}}}
\qquad
\subfloat[{\bf t-SNE visualization of digits.}]{{\includegraphics[width=.45\columnwidth]{assets/tsne_digs.png}}}
\caption[Example: Dimensionality reduction by PCA and t-SNE]{\textbf{Dimensionality Reduction by PCA and t-SNE} (a) The digits database consists of $8 \times 8$ pixel images of hand-drawn digits. (b) We plot the first two principal components of the digits data set and color by digit label. (c) We visualize the two-dimensional embedding of the digit data set as learned by t-distributed stochastic neighbor embedding. }
\label{fig:vizcomparison}
\end{adjustwidth}
\end{figure}
\subsubsection{t-SNE}
Over the last few years, t-distributed stochastic neighbor embedding (t-SNE) \citep{maaten2008visualizing} has become one of the most popular dimensionality reduction techniques for visualization \citep{arora2018analysis}. The assumption behind the algorithm is that the high-dimensional input data lies on a locally connected manifold. First, an auxiliary asymmetric measure between each pair of data points is calculated according to the equation
\begin{equation} \label{eq:tsne}
p_{j|i} = \frac{\exp(-||x_i-x_j||^2 / 2 \sigma^2_i)}{\sum_{k\neq i}\exp(-x||x_i-x_k||^2/2\sigma^2_i)}
\end{equation}
\noindent where $p_{i|i} = 0$ as it is of primary interest to model pairwise similarities. The constant $\sigma_i$ is the variance of a Gaussian that is centered around $x_i$ and controls how influential nearby data points are in contrast to far away data points. Then the pairwise similarities are computed using the formula
\begin{equation} \label{eq:tsne2}
p_{ji} = \frac{p_{j|i}+p_{i|j}}{2}
\end{equation}
\noindent these similarities are defined to be symmetrized conditional probabilities to ensure that each data point makes a significant contribution to the cost function.
Next, a lower-dimensional vector of data points Y is created and initialized randomly. Each element in Y corresponds to an element in X: similarities $q_{ij}$ between data points $y_i$ an $y_j$ are calculated according to the formula
\begin{equation} \label{eq:tsne3}
q_{ij} = \frac{(1+||y_i-y_j||^2)^{-1}}{\sum_k \sum_{l \neq k} (1 + ||y_k - y_l ||^2)^{-1}}\end{equation}
The low-dimensional data points $y_i$ are then moved around to minimize the KL divergence -- a measure of the difference between two probability distributions\footnote{Note that $q$ and $p$ can be interpreted as probabilities since $\sum_{i, j} p_{ij} = \sum_{i, j} q_{ij} = 1$ and $p_{ij} > 0$ and $q_{ij} > 0$ for all $i$ and $j$. } -- between $p$ and $q$
\begin{equation} \label{eq:tsne4}
\text{KL} \left( P~\middle\|~ Q\right) = \sum_{i \neq j }\log \frac{p_{ij}}{q_{ij}}
\end{equation}
Equation \ref{eq:tsne4} is minimized using gradient descent, ensuring that points that are similar in the high-dimensional space are also similar in the new, low-dimensional space.
\subsubsection{Autoencoders}
The \textit{autoencoder} is a type of neural network\footnote{Autoencoders can consist of any types of neural network layers. For example, an autoencoder made up of convolutional layers is called a $\textit{convolutional autoencoders}$. } that consists of an \textit{encoder} part, which maps the input $x$ to an encoding (usually of a smaller size than the input), and a \textit{decoder} part, that outputs a reconstruction $y$ of the input (Figure \ref{snorri}).
\begin{figure*}[ht]
\centering
\includegraphics[width=\textwidth]{assets/encoder.pdf}
\caption[Illustration: An autoencoder]{ \textbf{An autoencoder. } This is an example of a convolutional autoencoder that is trained for reconstructing seal photographs. The encoding vector $z$ is usually much smaller than the total number of pixels in the input.} \label{snorri}
\end{figure*}
The objective function is the squared error between the input and the output
\begin{equation} \label{eq:ae}
\mathcal{L}(x, y) = || x - y ||^2
\end{equation}
Useful representations arise in this process if the correct constraints are placed on the system. Without constraints, the system could end up learning the identity function, that trivially satisfies the objective function: $||x-y|| = ||x-x|| = 0$. This problem can be overcome by including a hidden layer in the autoencoder of a lower dimensionality than the input space. In this case, the autoencoder is said to be \textit{undercomplete.}
Undercomplete, single-layer autoencoders with linear activation functions are almost equivalent to PCA. The $p$-dimensional hidden layer spans the same subspace as the first $p$ principal components, or the principal subspace, of the data \citep{baldi1989neural}. Unlike PCA, however, the weights of the hidden layer are not guaranteed to be orthonormal nor ordered. If the smallest dimensionality of a hidden layer is larger than the size of the input, the autoencoder is said to be \textit{overcomplete}. Overcomplete autoencoders can be prevented from learning the identity function if the objective function (Equation \ref{eq:ae}) is combined with a regularization term.
For example, instead of reconstructing the original input as it is, \cite{vincent2008extracting} propose that the goal could be to recover the input after it has been corrupted with noise (e.g. Gaussian noise or salt-and-pepper noise). The idea behind this is that the autoencoder has to learn representations that are stable and robust under the corruption of the input, and that the denoising task extracts a useful structure of the input distribution \citep{vincent2010stacked}.
\subsection{Self-supervised learning}
Approaches that learn representations by way of solving auxiliary tasks, in the sense that the representation that arises from the optimization is more important than achieving a good performance on the task itself, is sometimes called \textit{self-supervised} learning in the literature \citep{gogna2016semi}. For example, \cite{ha2018world} train an autoencoder to reconstruct the observations in an RL environment, but they do not take advantage of the reconstructive capabilities of the network when they train their RL policies, and they use only the encoder part of the network for visual pre-processing. Another example is the denoising autoencoder from the previous chapter.
One direction of self-supervised learning that has been followed in the literature is to invent a task that requires an understanding of the domain to solve correctly, such as the reconstructive network used by \cite{ha2018world}. Another example is the work by \cite{gidaris2018unsupervised}, who learn representations by applying random rotations to natural images and train a network to predict which rotation was applied. This encourages the network to learn high-level concepts, such as beaks, wings and talons, and their relative positions. More commonly, self-supervised learning methods consist of obscuring some part of the input and train a model to predict that part given some other subset of the input, as we do in Chapter \ref{chap:larp} and Chapter \ref{chap:rewpred}. Some variations of this idea include, for example, colorization \citep{zhang2016colorful}, where colorful images are converted to grayscale with the goal of predicting the original colors.
\section{Introduction}
\label{sec:rnintro}
Even though the dominance of humans is being tested by RL agents on numerous fronts, there are still great difficulties for the field to overcome. For instance, the data that is required for algorithms to reach human performance is on a far larger scale than that needed by humans. Furthermore, the general intelligence of humans remains unchallenged. Even though an RL agent has reached superhuman performance in one field, its performance is usually poor when it is tested in new areas.
The study of methods to overcome the problem of data-efficiency and transferability of RL agents in environments where the agent must reach a single goal is the focal point of this work. We consider a simple way of learning a state representation by predicting either a raw or a smoothed version of a sparse reward yielded by an environment. The two objectives, learning a state representation and predicting the reward, are directly connected as we train a deep neural network for the prediction, and the hidden layers of this network learn a reward-predictive state representation.
The reward signal is created by collecting data from a relatively low number of initial episodes using a controller that acts randomly. The representation is then extracted from an intermediate layer of the prediction model and re-used as general preprocessing for RL agents, to reduce the dimensionality of visual inputs. The agent processes inputs corresponding to its current state as well as the desired end state, which is analogous to mentally visualizing a goal before attempting to reach it. This general approach of relying on state representations, that are learned to predict the reward rather than maximizing it, has been motivated in the literature \citep{lehnert2020reward} and we show that our representation is well-suited for single-goal environments. Our work adds to the recently growing body of knowledge related to deep unsupervised \citep{hlynsson2019learning} or self-supervised \citep{schuler2018gradient} representation learning.
We also investigate the effectiveness of augmenting the reward for RL agents, when the reward is sparse, with a novel problem-agnostic reward shaping technique. The reward predictor, which is used to train our representation, is not only used as a part of an auxiliary loss function to learn a representation, but it is also used during training the RL system to encourage the agent to move closer to a goal location. Similar to advantage functions in the RL literature \citep{schulman2015high}, given the trained reward predictor, the agent receives an additional reward signal if it moves from states with a low predicted reward to states with a higher predicted reward. We find this reward augmentation to be beneficial for our test environment with the largest state-space.
\section{Background}
\label{sec:backrw}
\subsection{Reward shaping}
Sparse rewards in environments is a common problem for reinforcement learning agents. The agent's objective is to learn how to associate its inputs with actions that lead to high rewards, which can be a lengthy process if the agent only rarely experiences positive or negative rewards.
Reward shaping \citep{mataric1994reward, ng1999policy, brys2015policy} is a popular method of modifying the reward function of an MDP to speed up learning. It is useful for environments with sparse rewards to augment the training of the agent, but skillful applications of reward shaping can in principle aid the optimization for any environment -- although the efficacy of the reward shaping is highly dependent on the details of the implementation \citep{clark2016faulty}. In the last few years, reward shaping has been shown to be useful for complex video game environments, such as real-time strategy games \citep{efthymiadis2013using} and platformers \citep{brys2014multi} and it has also been combined with deep neural networks to improve agents in first-person shooter games \citep{lample2017playing}.
As an illustration, consider learning a policy for car racing. If the goal is to train an agent to drive optimally, then supplying it with a positive reward for reaching the finish line first is in theory sufficient. However, if it is punished for actions that are never beneficial, for instance crashing into walls, it prioritizes learning to avoid such situations, allowing it to explore more promising parts of the state space.
Furthermore, just reaching the goal is insufficient if there is competition. To make sure that we have a winning racer, a small negative reward can be introduced at every time step to urge the agent to reach the finish line quickly. Note that the details of the reward shaping in this example requires domain knowledge from a designer who is familiar with the environment. It would be more generally useful if the reward shaping would be autonomously learned, just as the policy of the agent, as we propose to do in this work.
\subsection{Reward-predictive vs. reward-maximizing representations}
\label{predvsmax}
\cite{lehnert2020reward} make the distinction between \textit{reward-maximizing} representations are \textit{reward-predictive} representations. They argue how reward-maximizing representations can transfer poorly to new environments, while reward-predictive representations generalize successfully. Take the simple grid world navigation environments in Fig. \ref{fig:transferrep}, for example. The agent starts at a random tile in the grid and gets a reward of +1 by reaching the rightmost column in Environment A or by reaching the middle column in Environment B.
The state space in Environment A can be compressed from the $3 \times 3$ grid to a vector of length 3, $[\phi_1^p, \phi_2^p, \phi_3^p]$ of reward-predictive representations. To predict the discounted reward, it suffices to describe the agent's state with $\phi_j^p$ if it is in the $j$th row.
\begin{figure}[ht!]
\begin{center}
\includegraphics[width=0.95\linewidth]{assets/transferrep.pdf}
\caption[Illustration: Reward-maximizing vs. reward-predictive representations]{\textbf{Reward-maximizing vs. reward-predictive representations}. In this grid world example, the agent starts the episode at a random location and can move up, down, left, or right. The episode ends with a reward of 1 and terminates when the agent reaches the rightmost column. Both the reward-predictive representation and reward-maximizing representation $\phi^p$ and $\phi^m$, respectively, are useful for learning the optimal policy in Environment A. The reward-predictive representation $\phi^p$ collapses each column into a single state to predict the discounted future reward. The reward-maximizing representation $\phi^m$ makes no such distinction, as moving right is the optimal action in any state. It is a different story if the representations are transferred to Environment B, where reaching the middle column is now the goal. The representation $\phi^p$ can be reused, and the optimal policy is found if the agent now takes a step left in $\phi_3^p$. However, the representation $\phi^m$ is unable to discriminate between the different states and is useless for determining the optimal policy.}
\label{fig:transferrep}
\end{center}
\end{figure}
The reward-maximizing representation for Environment A is much simpler: the whole state space can be collapsed to a single element $\phi^m$, with the optimal policy of always moving to the right.
If these representations are kept, then the reward-predictive representation $\phi^p$ is informative enough for a RL agent to learn how to solve Environment B. The reward-maximizing representation $\phi^m$ has discarded too many details of the environment to be useful for solving this new environment.
\subsection{Successor features}
The \textit{successor representation} algorithm learns two functions: the expected reward $R_\pi^{\text{SF}}$ received after transitioning into a state $s$, as well as the matrix $M_\pi^{\text{SF}}$ of discounted expected future occupancy of each state, assuming that the agent starts in a given state and follows a particular policy $\pi$. Knowing the quantities $R_\pi^{\text{SF}}$ and $M_\pi^{\text{SF}}$ allows us to rewrite the value function:
\begin{equation} \label{eq:sr0}
V_{\pi}(s) = \mathbb{E}_{s'}\left[ R_\pi^{\text{SF}}(s) M_\pi^{\text{SF}}(s, s')\right]\end{equation}
The motivation for this algorithm is that it combines the speed of model-free methods, by enabling fast computations of the value function, with the flexibility of model-based methods for environments with changing reward contingencies.
This method is made for small, discrete environments, but it has been generalized for continuous environments with so-called feature-based successor representations, or \textit{successor features} (SFs) \citep{barreto2016successor}. The SF algorithm similarly calculates the discounted expected representation of future states, given the agent takes the action $a$ in the state $s$ and follows a policy $\pi$:
\begin{equation} \label{eq:sf}
\psi_{\pi}(s, a) = \mathbb{E}_\pi \left[\sum_{t=0}^\infty \gamma^{t-1} \phi_{t+1} | s_t = s, a_t = a\right]\end{equation}
\noindent where $\phi$ is some state representation. Both the SF $\psi$ and the representation $\phi$ can be deep neural networks.
\section{Related work}
\label{sec:rnrw}
\subsection{Reward-predictive representations }
\cite{lehnert2020reward} compare successor features (SFs) to a nonparametric Bayesian predictor that is trained to learn transition and reward tables for the environment, either with a reward-maximizing or a reward-predictive loss function. \cite{lehnert2020successor} prove under what conditions successor features (SFs) are either \textit{reward-predictive} or \textit{reward-maximizing} (see distinction in Section \ref{predvsmax}). They also show that SFs work successfully for transfer learning between environments with changing reward functions and unchanged transition functions, but they generalize poorly between environments where the transition function changes.
Our work is distinct from the reward-predictive methods that they compare, as our representation does not need to calculate expected future state occupancy, as is the case for SFs. Our method scales better for more complicated state-spaces because we do not tabulate the states, as they do with their Bayesian model, but learn arbitrary continuous features of high-dimensional input data. In addition to that, learning our reward predictor is not only a "surrogate" objective function, as we use it for reward shaping as well.
\subsection{Reward shaping}
The advantages of reward shaping are well understood in the literature \citep{mataric1994reward}. A recent trend in RL research is the study of methods that can learn the reward shaping function automatically, without the need of (often faulty) human intervention.
\cite{marashi2012automatic} assume that the environment can be expressed as a graph and that this graph formulation is known. Under these strong assumptions, they perform graph analysis to extract a reward shaping function. More recently, \cite{zou2019reward} have proposed a meta-learning algorithm for potential-based automatic reward shaping. Our approach is different from previous work as we assume no knowledge about the environment and train a simple predictor to approximate (potentially smoothed) rewards, which is then used to construct a potential-based reward shaping function.
\subsection{Goal-conditioned reinforcement learning }
\cite{kaelbling1993learning} studied environments with multiple goals and small state-spaces. In their problem setting, the agent must reach a known but dynamically changing goal in the fewest number of moves. The observation space is of a low enough dimension for dynamic programming to be satisfactory in their case. \cite{schaul2015universal} introduce the Universal Value Function Approximators and tackle environments of larger dimensions by learning a value function neural network approximator that accepts both the current state and a goal state as the inputs. In a similar vein, \cite{pathak2018zero} learn a policy that is given a current state and a goal state and outputs an action that bridges the gap between them. \cite{hlynsson2020latent} learn a predictable representation that is paired with a representation predictor and combine it with graph search to find a given goal location. In contrast to these approaches, we learn a reward-predictive representation in a self-supervised manner, which is used to preprocess raw inputs for RL policies.
\section{Approach}
\label{chaptern_method}
In this section, we explain our approach mathematically. Intuitively, we train a deep neural network to predict either a raw or a smoothed reward signal from a single-goal environment. The output of an intermediate layer in the network is then extracted as the representation -- for example, by simply removing the top layers of the network. The full reward predictor network is used for reward shaping by rewarding the agent for moving from lower predicted values toward higher predicted values of the network.
\subsection{Learning the representation}
Suppose that $f_\theta: \mathbb{R}^c \rightarrow [0, 1]$ is a differentiable function parameterized by $\theta$ and $c$ is a positive integer. We use $f_\theta$ to approximate the discounted return in a POMDP with a sparse reward: the agent receives a reward of 0 for each time step except when it reaches a goal location, at which point it receives a positive reward and the episode terminates.
Given an experience buffer $\mathcal{D} = $ $\{(s_t, a_t, r_t, s_{t+1})_i\}$, we create a new data set $\mathcal{D}^* = \{ \left(s_t, a_t, r^*_t, s_{t+1} \right)_i \}$. The new rewards are calculated according to the equation
\begin{equation} \label{eq:rstar}
r^*_t = \gamma^m r_{t+m}\end{equation}
\noindent where $\gamma \in [0, 1]$ is a discount factor and $M>m>0$ is the difference between $t$ and the time step index of the final transition in that episode, for some maximum time horizon $M$. Throughout our experiments, we keep the value of the discount factor equal to $0.99$ and we train on $\mathcal{D} $ or $\mathcal{D}^*$.
Assume that our differentiable representation function $\phi: \mathbb{R}^d \rightarrow \mathbb{R}^c$ is parameterized by $\theta'$ and maps the $d$-dimensional raw observation of the POMDP to the $c$-dimensional feature vector. We train the representation for the discounted-reward prediction by minimizing the loss function
\begin{equation}
\mathcal{L}(f_\theta [ \phi_{\theta'} (s_{t+1})], r^*_t) = \left( r^*_t - f_\theta [ \phi_{\theta'} (s_{t+1})] \right)^2
\label{discounted_loss}
\end{equation}
\noindent with respect to the parameters $\theta$ of $f$ and the parameters $\theta'$ of $\phi$ over the whole data set $\mathcal{D}^*$. See Fig. \ref{fig:boat5} for a conceptual overview of our representation learning.
\begin{figure}[ht]
\begin{center}
\includegraphics[width=.92\linewidth]{assets/repl_1.pdf}
\caption[Illustration: Learning and using the representation]{\textbf{Learning and using the representation.} Our representation and reward predictor is trained with the elements highlighted in blue. The trained representation is then used for dimensionality reduction for an RL agent, that interacts with the environment, as indicated by the elements highlighted in red. }
\label{fig:boat5}
\end{center}
\end{figure}
\subsection{Reward shaping}
\cite{ng1999policy} define a reward shaping function $F$ as \textit{potential-based} if there exists a function $f: \mathcal{S} \rightarrow \mathbb{R}$ such that for all states $s, s' \in \mathcal{S}$ the following equation holds:
\begin{equation}
F(s, a, s') = \gamma f(s') - f(s)
\label{potential_based}
\end{equation}
\noindent and $\gamma$ is the MDP's discount factor. They prove for single-goal environments that every optimal policy for the MDP $M = (\mathcal{S}, \mathcal{A}, \mathcal{P}, \mathcal{R}, \mathbb{P}(s_0), \gamma)$ is also optimal for its reward shaped counterpart $M' = (\mathcal{S}, \mathcal{A}, \mathcal{P}, \mathcal{R}+F, \mathbb{P}(s_0), \gamma)$, and vice versa. They also show, for a given state space $\mathcal{S}$ and action space $\mathcal{A}$, that if $F$ is not potential-based, then there exist a transition function $\mathcal{P}$ and a reward function $\mathcal{R}$ such that no optimal policy in $M'$ is optimal in $M$.
Deciding that the reward shaping function should be potential-based is just the first step in its design. Now assume that we have an environment where an agent is tasked with reaching a goal state $g$. That is, for a given distance function $d: \mathcal{S} \times \mathcal{S} \rightarrow \mathbb{R}^+$ the agent receives a reward of 1 if it is close enough to the goal location, $d(s, g) \leq \delta$, for some reward threshold $\delta \in \mathbb{R}^+$. Otherwise, it receives a reward of 0.
The distance $d$ between the agent's location new $s'$ and the goal location $g$ can be a useful value to calculate in the design of a reward shaping function
\begin{equation}
F(s, a, s') = \begin{cases} 1 & \text{if } d(s', g) \leq \delta \\
-d(s', g) & \text{otherwise} %
\end{cases}
\label{negdist}
\end{equation}
However, this depends on the environment, as the agent could get stuck in local optima before coming close to the goal, i.e. if it would have to move through a region with a large $d(s, g)$ before it can globally minimize it. This could for example be the case in a maze environment if $d$ is the Euclidean distance between the $(x, y)$ coordinates of the agent's location and the goal location and there is a wall between the agent and the goal. \cite{trott2019keeping} propose to solve this by incorporating the potential local optima in the reward shaping function as so-called "anti-goals" $\Bar{g}$ to be avoided
\begin{equation}
F(s, a, s') = \begin{cases} 1 & \text{if } d(s', g) \leq \delta \\
\min [0, -d(s', g) + d(s, \Bar{g})] & \text{otherwise} %
\end{cases}
\label{antigoals}
\end{equation}
These states can be hand-picked by domain experts. However, adding anti-goals like this could iteratively introduce even more local optima and a solution to the original problem is not guaranteed.
It is generally not true that the distance function $d$ and all the variables needed to calculate it, such as the coordinates of the agent and the goal in a maze, are available to the agent. Even if $d$ were computable, using it naively can bring about its own problems, as was alluded to above.
We argue that instead of using $d$ in Equation~\ref{negdist}, it would be better to measure the distance between the agent and the goal in terms of how many actions the agent has to take until the goal is reached. This function is not assumed to be given, but it can be estimated as the agent is being trained on the environment, for instance by optimizing Equation~\ref{discounted_loss}.
Additionally, we would like our reward shaping function to be potential-based (Equation \ref{potential_based}) to reap the theoretical advantages. Thus, we propose a potential-based reward shaping function based on the discounted reward predictor
\begin{equation}
\begin{split}
F(s, a, s') & = \left( \gamma f_\theta ( \phi_{\theta'} [s']) - f_\theta ( \phi_{\theta'} [s]) \right) (H - I) / H \\
& = \gamma \left( f_\theta ( \phi_{\theta'} [s']) (H - I) / H \right) - f_\theta ( \phi_{\theta'} [s]) (H - I) / H \\
& = \gamma f^*(s') - f^*(s)
\end{split}
\label{ourshaped}
\end{equation}
\noindent where $f^* = f_\theta ( \phi_{\theta'} [s']) (H - I) / H $, $f_\theta$ is the reward predictor and $\phi_{\theta'}$ is our representation from the previous section. Note that both $f_\theta$ and $\phi_{\theta'}$ are assumed to be fully trained before the policy of the agent is trained, for example using data gathered by a random policy, but they can in principle also be updated as the policy is being learned. The factor $(H - I) / H$ scales down the intensity of the reward shaping where $I \in \mathbb{N}^+$ is the number of episodes that the agent has experienced and $H \in \mathbb{N}^+$ is the maximum number of episodes where the agent is trained using reward shaping. The strength of the reward shaping is the highest in the beginning to counteract potentially adverse effects of errors in the reward predictor. It is also more important to incentivize moving toward the general direction of the goal in the early stages of learning, after which the un-augmented reward signal of the environment is allowed to "speak for itself" and guide the learning of the agent toward the goal precisely.
\section{Methodology and implementation} \label{sec:exp}
\subsection{Environment} \label{subsec:env}
The method is tested on three different gridworld environments based on the Minimalistic Gridworld Environment (MiniGrid) \citep{gym_minigrid}. Tiles can be empty, occupied by a wall or occupied by lava. The structure of the environments fit naturally into our POMDP tuple template (Eq. \ref{eq:pomdp}):
\begin{itemize}
\setlength{\itemindent}{0.65cm}
\item[$\mathcal{S}$:]The constituent states of $\mathcal{S}$ are determined by the agent's location and direction (facing north, west, south or east). See Fig. \ref{fig:Nw1b} for three different world states in one of our environments.
\item[$\mathcal{A}$:]The action space $\mathcal{A}$ consists of three actions: (1) turn left, (2) turn right and (3) move forward.
\item[$\mathcal{P}$:] The transition function is deterministic. The agent relocates to the tile it faces if it moves forward and the tile is empty, and nothing happens if the tile is occupied by a wall. The episode terminates if the tile is occupied by lava or the goal. The agent rotates in place if it turns left or right.
\item[$\mathcal{R}$:] Reaching the green tile goal gives a reward of $1 - 0.9 \cdot \frac{\# \textrm{steps taken} }{\# \textrm {max steps}} $, every other action gives 0 points. The environment automatically times out after $\# \textrm {max steps}=100$ steps.
\setlength{\itemindent}{1.3cm}
\item[$\mathbb{P}(s_0)$:] Differs between the three environments (see below).
\setlength{\itemindent}{0.65cm}
\item[$\Omega$:] All $7\times7$ subset of tiles, represented by $28\times28\times3$ arrays, from the point of view of an agent who cannot see through walls, see Fig. \ref{fig:Nw2obses}.
\item[$\mathcal{O}$:] The point of view of the agent from its current viewpoint (Fig. \ref{fig:Nw2obses}) and a goal observation (Fig. \ref{fig:Nw2targets}).
\item[$\gamma$:] the discount factor is $0.99$.
\end{itemize}
\begin{figure}
\centering
\begin{subfigure}[b]{0.8\textwidth}
\includegraphics[width=1\linewidth]{assets/worldstates.png}
\caption{Full world states.}
\label{fig:Nw1b}
\end{subfigure}
\begin{subfigure}[b]{0.8 \textwidth}
\includegraphics[width=1\linewidth]{assets/obses.png}
\caption{Agent's point of view.}
\label{fig:Nw2obses}
\end{subfigure}
\begin{subfigure}[b]{0.8\textwidth}
\includegraphics[width=1\linewidth]{assets/targets.png}
\caption{Goal observations.}
\label{fig:Nw2targets}
\end{subfigure}
\caption[Example: The two-room environment]{\textbf{Two-room environment.} The red agent must reach the green goal in as few steps as possible. The agent starts each episode between the two rooms, facing a random direction (up, down, left or right). Each column corresponds to a snapshot of one episode. The light tiles correspond to what the agent sees, while the dark tiles are unseen by the agent. (a) Examples of the full state (b)~The observation from the agent's current state (c) A goal observation. This is the agent's point of view from a state that separates the agent from the goal by one action. }
\label{tworooms}
\end{figure}
We consider the following three environments:
\subsubsection{Two-room environment}
\label{tworoomimplementation}
The world is a $8 \times 17$ grid of tiles, split into two rooms, where walls are placed at different locations to facilitate discrimination between the rooms from the agent's point of view. (Fig. \ref{tworooms}). The agent is placed between the two rooms, facing a random direction. The goal is at one of three possible locations. This is a modified version of the classical four-room environment layout \citep{sutton1999between}.
\subsubsection{Lava gap environment}
In this environment, the agent is in a $4 \times 4$ room with a column of lava either one or two spaces in front of the agent (Fig. \ref{fig:Ng-1}) with a gap in a random row. The agent always starts in the upper left corner and the goal is always in the lower right corner.
\begin{figure*}[ht]
\centering
\begin{minipage}{.83\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/allgaps.png}
\end{minipage}
\caption[Example: The lava gap environment]{ \textbf{The lava gap environment.} The red agent must reach the green goal in as few steps as possible while avoiding the orange lava tiles. Each episode is randomly selected to be one of the eight pictured configurations. If the agent tries to go through the orange lava tile, it experiences an immediate episode termination with no reward. Note that the wall tiles that are lighter than the others are presently in the agent's field of vision. }
\label{fig:Ng-1}
\end{figure*}
\subsubsection{Four-room environment}
\label{fourroomimplementation}
An expansion to the two-room environment with two additional rooms (Fig. \ref{fullillus}). In this setup, both the agent and the goal location are placed at random locations within the $17\times17$ gridworld.
\begin{figure*}[ht]
\centering
\begin{minipage}{.67\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/fullillus.png}
\end{minipage}
\caption[Example: Four-room environment]{ \textbf{Four-room environment}. The agent (red triangle) must reach the goal (green square) in as few steps as possible, both are randomly placed in each episode. The $7\times7$ grid of highlighted tiles in front of the agent indicates its observation.}
\label{fullillus}
\end{figure*}
\subsection{Baselines} \label{subsec:cm}
We combine our representations with two RL algorithms as implemented in Stable Baselines \citep{stable-baselines} using the default hyperparameters:
\begin{itemize}
\item (ACKTR) Actor Critic using Kronecker-Factored Trust Region \citep{wu2017scalable}, which combines actor-critic methods, trust-region optimization, and distributed Kronecker factorization to enhance data-efficiency.
\item (PPO2) A version of the Proximal Policy Optimization algorithm \citep{schulman2017proximal}. It modifies the original algorithm by using clipped value functions and a normalized advantage.
\end{itemize}
For both algorithms, six variations are compared:
\begin{itemize}
\item (Deep RL) The RL algorithm learns the representation from scratch on raw images
\item (SF) The input is preprocessed using successor features
\item (Ours 1r) The input is preprocessed using our representation, trained on raw reward predictions
\item (Ours 1r + Shaping) The input is preprocessed using our representation and the reward is shaped, trained on raw reward predictions
\item (Ours 64r) The input is preprocessed using our representation, trained on smoothed reward predictions
\item (Ours 64r + Shaping) The input is preprocessed using our representation and the reward is shaped, trained on smoothed reward predictions
\end{itemize}
Care has been taken to ensure that each variation has the same architecture and the same number of parameters.
\subsection{Model architectures} \label{subs:ma}
Every model is realized as a neural network using Keras \citep{chollet2015keras}. Below, the representation and policy networks are used for our method and the SF comparison, the reward prediction network is used only for our method and the deep RL network is used only for the deep RL comparison, where the RL algorithm also learns the representation.
\textbf{The representation networks} are two convolutional networks (Table \ref{tab:repnet}) with a $28 \times 28 \times 3$ input, taking either the agent's current observation or the goal observation.
\begin{table}[ht]
\centering \begin{tabular}{|l @{\hskip 0.2in} r @{\hskip 0.2in} r @{\hskip 0.2in} l @{\hskip 0.2in} r @{\hskip 0.2in} c|}
\hline\rule{0pt}{2.2ex}
\textbf{Layer} & \textbf{Filters} & \textbf{Filter size} & \textbf{Stride} & \textbf{Padding} & \textbf{Output shape} \\ [0.5ex]
\hline\rule{0pt}{2.2ex}Input tensor & - & - &-&-&$28\!\times\!28\!\times\!3$ \\[1ex]
\hline \rule{0pt}{2.2ex}Convolution & 8 & $3\!\times\!3$ & 3 & None & $9\!\times\!9\!\times\!8$ \\[.5ex]
ReLU & - & - & -&- & $4\!\times\!4\!\times\!8$ \\[.5ex]
\hline\rule{0pt}{2.2ex}2D max pooling & 8 & $2\!\times\!2$ & -& None & $4\!\times\!4\!\times\!8$ \\[.5ex]
\hline \rule{0pt}{2.2ex}Convolution & 16 & $3\!\times\!3$ & 2&None & $1\!\times\!1\!\times\!16$ \\[.5ex]
ReLU & - & - & -&-& $1\!\times\!1\!\times\!16$ \\[.5ex]
\hline\rule{0pt}{2.2ex}Flatten & - & - & - &-& 16 \\[.5ex]
Dense & - & - & - &-&16 \\[.5ex
\hline
\end{tabular}
\vspace{0.1cm}
\caption[Result: Representation network]{\textbf{Representation network.}}
\label{tab:repnet}
\end{table}
The first layer subsamples the input, keeping only every other column and row. This is followed by 8 filters of size $3 \times 3$ with a stride of 3. This is followed with a ReLU activation and a $2 \times 2 $ max pooling layer with a stride value of 2. The pooling layer's output is passed to a layer with 16 convolutional filters of size $3 \times 3$ and a stride of 2 and a ReLU activation function. The output is then flattened and passed to a dense layer with 16 units and a linear activation, defining the dimension of the representation. No zero padding is applied in the convolutional layers or the pooling layer.
\textbf{The policy networks} are three-layer fully-connected networks (Table \ref{tab:polnet1}) accepting the concatenated output of the representation network for the agent's current point of view and the goal observation as an input. The first two layers have 64 units and a ReLU activation, and the last layer has 3 units and a linear activation function. The three units represent the three actions left, right, and forward in a one hot encoding. Winner takes all is used to decide on
the action.
\begin{table}[ht]
\centering \begin{tabular}{|l @{\hskip 0.3in} r @{\hskip 0.3in} c|
\hline\rule{0pt}{2.2ex}
\textbf{Layer} & \textbf{Units} & \textbf{Output shape} \\ [0.5ex]
\hline\rule{0pt}{2.2ex}Input tensor &-&32 \\[1ex]
\hline \rule{0pt}{2.2ex}Dense & 64 & 64 \\[.5ex]
\rule{0pt}{2.2ex}ReLU & - & 64 \\[.5ex]
\hline Dense & 64 &3 \\[.5ex]
ReLU & - & 3 \\[.5ex]
\hline Dense & 3 & 3 \\[.5ex]
\hline
\end{tabular}
\vspace{0.1cm}
\caption[Result: Policy network]{\textbf{Policy network.}}
\label{tab:polnet1}
\end{table}
\textbf{Our reward prediction network} is a three-layer fully-connected network (Table \ref{tab:polnet3}) with the same input as the policy network: the concatenated representation of the agent's current view and the goal observation. The first two layers have 256 units and a ReLU activation, but the last layer has 1 unit and a logistic activation function.
\begin{table}[ht]
\centering \begin{tabular}{|l @{\hskip 0.3in} r @{\hskip 0.3in} c|}
\hline\rule{0pt}{2.2ex}
\textbf{Layer} & \textbf{Units} & \textbf{Output shape} \\ [0.5ex]
\hline\rule{0pt}{2.2ex}Input tensor &-& 32 \\[1ex]
\hline \rule{0pt}{2.2ex}Dense & 256 &64 \\[.5ex]
\rule{0pt}{2.2ex}ReLU & - &64 \\[.5ex]
\hline Dense & 256 & 3 \\[.5ex]
ReLU & - & 3 \\[.5ex]
\hline Dense & 1 & 3 \\[.5ex]
Logistic & - & 3 \\[.5ex]
\hline
\end{tabular}
\vspace{0.1cm}
\caption[Result: Reward prediction network]{\textbf{Reward prediction network.}}
\label{tab:polnet3}
\end{table}
\textbf{The deep RL network} stacks the representation network and the policy network on top of each other. The representation network accepts the input and outputs the low-dimensional representation to the policy network that outputs the action scores.
\subsection{Training the representation and predictor networks} \label{subsec:policy} We collect a data set of $10$ thousand transitions by following a random policy in the two-room environment. For this data collection, each episode has a $50\%$ chance to have the goal location in the bottom room or on the left side of the top room (see the left and middle pictures in Fig. \ref{fig:Nw1b}). The reward predictor and the representation are trained in this manner for all experiments, including the lava gap and the four-room environment. Thus, we use a representation and reward predictor that have never seen lava. For the experiments with smoothed rewards, the sparse reward associated with the observations in the data set is augmented by associating a new reward to the $64$ states leading to observations with a positive reward, according to Equation \ref{eq:rstar}, with a discount factor of $0.99$. Additionally, after the reward has been (potentially) smoothed in this way, observations associated with a positive reward are oversampled $10$ times to balance the data set, regardless of whether the reward has been augmented or not.
\section{Results and discussion}
\label{sec:rwrd}
In the experiments, we compare RL agents that learn their representations from scratch (Deep RL) to agents that preprocess their inputs with different representations. We compare our representation, trained on raw reward predictions -- with (Ours 1r) or without reward shaping (Ours 1r + Shaping) -- to our method trained on smoothed reward prediction, also with (Ours 64r) or without reward shaping (Ours 64r + Shaping). We use "64r" to denote that our method was trained with reward shaping and "1r" to denote that our method was trained without augmentation. As a baseline, we compare our representation to a reward-predictive representation from the literature, Successor Features (SFs).
\subsection{Two-room environment}
We start by visualizing the outputs of our reward predictor in the rooms, depending on the goal location, in Fig. \ref{fig:rewardheatmap}. Each square indicates the average predicted reward for transitioning to the corresponding tile in the room.
The predicted reward spikes in a narrow region around the two goal locations
that were used to train the raw reward predictor (Fig. \ref{fig:1r}), but the area of states with high predicted rewards is
wider around the test goal. This difference is due to overfitting on the specific training paths that
were more frequently taken toward the respective goals, but this does not harm the generalization
capabilities of the network. The peakyness of the predictions disappears when the predictor is trained on the smoothed rewards (Fig. \ref{fig:64r}). However, higher predicted rewards in the corner of the other room appear. Both scenarios, raw and smoothed reward prediction, show promise for the application of reward shaping under our training scheme, as the agent would benefit from finding neighborhoods with higher values of predicted reward until it reaches the goal, instead of having to rely solely on a sparse reward that is only given when the agent lands exactly on the goal state.
\begin{figure}[h]
\centering
\begin{subfigure}[b]{0.75 \textwidth}
\includegraphics[width=1\linewidth]{assets/predrew_1r2.png}
\caption{Raw reward prediction.}
\label{fig:1r}
\end{subfigure}
\begin{subfigure}[b]{0.75\textwidth}
\includegraphics[width=1\linewidth]{assets/2rs.png}
\caption{Smoothed reward prediction.}
\label{fig:64r}
\end{subfigure}
\caption[Result: Predicted rewards, two-room environment]{\textbf{Predicted rewards, two-room environment.} The predictor is trained on the setups shown on the left and in the middle, and tested for the setup on the right. The color becomes warmer for states where the reward is predicted to be higher.}
\label{fig:rewardheatmap}
\end{figure}
In Figure \ref{allsingle}, we illustrate the variance of the mean reward (left side) and the variance of the optimal performance (right side) of the different methods, as a function of the time steps taken for training. We average over 10 runs and in each run we perform 10 test rollouts, so each point is the aggregate of 100 episodes in total.\footnote{Note that the standard deviation of the mean reward of all episodes, from all runs put together, is approximately $26\%$ higher than the standard deviation of the mean of the means or the mean of the mins.} The error bands indicate two standard deviations. This methodology of generating the plots also applies to Fig. \ref{fig:fromscratch}, Fig. \ref{graph:8k} and Fig. \ref{allfull2}.
The learning curves of both ACKTR and PPO2 get close to the highest achievable mean reward of $1$ the fastest using our representations. There no significant benefit from using smoothed reward shaping for ACKTR, and the raw reward shaping is in fact harmful in this case. For PPO2, the agent using our representation that is trained on raw reward predictions learns the fastest. Regular deep RL, where the representations are learned from scratch, is clearly outperformed by the variants that use reward-predictive representations. We believe that this is because RL agents can generally benefit from the input being preprocessed, as the computational overhead for learning the policy is reduced. This effect is enhanced when the preprocessing is good, which is the case for our reward-predictive representation: it abstracts away unnecessary information as it is trained to output features that indicate the distance between the agent and the goal, when the goal is in view.
The difference in aggregated mean rewards vs. aggregated minimum episode lengths can be explained due to systematically different behaviors. For example, an agent might have a weak long-term strategy of checking the different rooms, giving it poor average mean rewards, but a strong short-term tactic of taking the direct course to the goal when it sees it, giving it a good average minimum episode length.
\begin{figure*}[ht]
\centering
\begin{minipage}{.99\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/y_a.png}
\end{minipage}
\caption[Result: Two-room environment]{ \textbf{Two-room environment}. In these experiments, there are only two rooms and the agent must reach a goal that is always at the same location. The agent can traverse between the rooms and starts each episode between them, facing a random direction. The left side shows the mean of every agent's mean reward and the right side shows the mean of every agent's minimum episode length.}
\label{allsingle}
\end{figure*}
\newpage
\subsection{Lava gap environment}
\subsubsection{Learning from scratch}
The heatmaps of average predicted rewards are visualized in Fig. \ref{fig:gapheatmap}. The reward predictor was trained on the two-room environment. The tiles closest to the goal have the highest values, with a particularly smooth gradient toward the goal for the smoothed-reward predictor, which demonstrates that there is potential gain from transferring the prediction-based reward shaping between similar environments. The learning performance of the different methods can be seen in Fig. \ref{fig:fromscratch}. The decidedly fastest learning can be observed when the actor-critic method is combined with our representation, trained on raw reward predictions and without reward shaping. Regular deep RL is the second-best, but with a very large variance on the performance. Our reward shaping variations and the SFs are very close in performance, albeit significantly worse than the other two. The poor performance of reward shaping can be explained by the fact that there are very few states, which makes the reward shaping unnecessary in such a simple environment. All the methods look more similar when PPO2 optimization is applied, with respect to the mean rewards, but our variant that is trained on smooth reward prediction and uses reward shaping reaches the highest average performance in the last iterations.
\begin{figure*}[ht]
\centering
\begin{minipage}{.37\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/together.png}
\end{minipage}
\caption[Result: Predicted rewards, lava gap]{ \textbf{Predicted rewards, lava gap}. Average predicted reward per state in the lava gap environment. }
\label{fig:gapheatmap}
\end{figure*}
\begin{figure*}[ht]
\centering
\begin{minipage}{.99\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/y_b.png}
\end{minipage}
\caption[Result: Lava gap experiment]{ \textbf{Lava gap experiment.} All policies are randomly initialized and learn to solve the lava gap environment from scratch. The representations in all methods except for Deep RL are learned on the training goals in the two-room environment (see Fig. \ref{fig:rewardheatmap}). The left side shows the mean of every agent's mean reward, and the right side shows the mean of every agent's minimum episode length. }
\label{fig:fromscratch}
\end{figure*}
\subsubsection{Transfer learning}
To investigate how the methods compare for adapting to new environments, we trained the policies for 8000 steps on the two-room environment before learning to solve the lava gap environment, see Fig. \ref{graph:8k}. Our method, without reward shaping, facilitates the fastest learning for ACKTR in this case. Deep RL is the most severely affected by this change, which is probably due to the method learning a reward-maximizing representation in one environment that does not transfer well to another environment. Every PPO2 variation looks bad for this scenario, but the smooth-reward prediction representation with reward shaping has the highest mean reward and our raw-reward prediction representation has the lowest average minimum episode length.
\begin{figure*}[ht]
\centering
\begin{minipage}{.99\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/y_c.png}
\end{minipage}
\caption[Result: Re-learning experiment]{ \textbf{Re-learning experiment} The different methods are trained for eight thousand training steps on the two-room environment before being trained on the lava gap environment. The curves show the mean reward on the lava gap environment. The left side shows the mean of every agent's mean reward, and the right side shows the mean of every agent's minimum episode length.}
\label{graph:8k}
\end{figure*}
We visualize trajectories of an agent that is trained on our representation (Ours 1r) as it traverses the lava gaps environment (Fig. \ref{lavatraj}). For inspection of cases where it fails, we choose an agent that has been trained for $50$ thousand time steps only and has around $0.75$ mean reward.
\begin{figure}[ht]
\centering
\begin{subfigure}[b]{0.47\textwidth}
\includegraphics[width=1\linewidth]{assets/6lavasuccesses.png}
\caption{Six successful episodes.}
\label{fig:Ng1}
\end{subfigure}
\begin{subfigure}[b]{0.47\textwidth}
\includegraphics[width=1\linewidth]{assets/6lavafailures.png}
\caption{Six failed episodes.}
\label{fig:Ng2}
\end{subfigure}
\caption[Result: Lava gap trajectories]{\textbf{Lava gap trajectories.} A visualization of six successful and six failed trajectories by an agent that was trained up to approximately $75\%$ success rate using our representation. The color gradient goes from the first actions taken in the episode in blue to the last actions in red. Note that rotations in-place are not visualized, but only transitions between tiles. }
\label{lavatraj}
\end{figure}
\subsection{Four-room environment}
In our final comparison, we add two additional rooms to the two-room environment and randomize both the goal location and the starting position of the agent, with the results shown in Fig. \ref{allfull2}. Looking at the minimum episode lengths, for the ACKTR learner, our raw-reward prediction representation with reward shaping performs best and the one without reward shaping comes in second. There is little discernible difference between the performance of SFs and Deep RL, but they both perform significantly worse than our methods. The scale of the mean reward is a great deal lower than in the previous experiments, since the average distance between the starting tile of the agent and the goal is much larger than in the previous two environments.
For this scenario, all the methods look similarly bad for the PPO2 policy, except for our raw-reward representations, with reward shaping, which has the lowest minimum episode length. The big advantage of reward shaping in this environment compared to the two-room environment can be explained by the increased complexity, making the reward shaping more helpful in guiding the agent's search. In the previous experiments, the agent and goal locations start at fixed locations, allowing the agents to solve it by rote memorization. The reward shaping function calculated by the raw-reward predictor fares significantly better in this situation. We hypothesize that this is due to the smoothed-reward predictor distracting the agent by pushing it to corners, as the visualization in Fig. \ref{fig:64r} would suggest.
The reward shaping given by the raw-reward predictor is more discriminative, as we see in Fig. \ref{fig:1r}. The agent receives a positive reward as soon as the goal reaches its point of view, which is any location up to six tiles in front of it and no further than 3 tiles away from it to the left or to the right. This allows the reward shaping function to guide the agent directly to the goal, assuming that they are in the same room and that there is no wall obstructing the agent's field of vision.
\begin{figure*}[ht]
\centering
\begin{minipage}{.97\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/y_d.png}
\end{minipage}
\caption[Result: Full four-room environment]{ \textbf{Full four-room environment}. The agent and goal are placed at random locations at the start of each episode. The left side shows the mean of every agent's mean reward, and the right side shows the mean of every agent's minimum episode length.}
\label{allfull2}
\end{figure*}
Three successful and three failed trajectories of an ACKTR agent that has been trained, using our representation (Ours 1r) for a million time steps are visualized in Fig. \ref{viz4rooms}. We can see undesirable behavior in both the successful and the failed trajectories, that the agent wastes effort re-visiting tiles it has already been to.
\begin{figure}[h]
\centering
\begin{subfigure}[b]{0.75\textwidth}
\includegraphics[width=1\linewidth]{assets/full3succ.png}
\caption{Three successful trajectories}
\label{fig:Ng3}
\end{subfigure}
\begin{subfigure}[b]{0.75\textwidth}
\includegraphics[width=1\linewidth]{assets/full3fails.png}
\caption{Three failed trajectories}
\label{fig:Ng4}
\end{subfigure}
\caption[Result: Four-room trajectories]{\textbf{Four-room trajectories.} The agent was trained on our representations with Actor Critic using Kronecker-Factored Trust Region for a million time steps. }
\label{viz4rooms}
\end{figure}
\section{Conclusion} \label{sec:disc}
Processing high-dimensional inputs for reinforcement learning (RL) agents remains a difficult problem, especially if the agent must rely on a sparse reward signal to guide its representation learning. In this work, we put forward a method to help alleviate this problem with a method of learning representations that preprocesses visual inputs for RL methods. Our contributions are (i)~a reward-predictive representation that is trained simultaneously with a reward predictor and (ii)~a reward shaping technique using this trained predictor. The predictor learns to approximate either the raw reward signal or a smoothed version of it, and it is used for reward shaping by encouraging the agent to transition to states with higher predicted rewards.
We used a view of the goal as a second input for the methods in our experiments, but this is in principle not necessary, as moving toward the green tile as it becomes visible is sufficient. Removing the goal input might encourage the agents to learn policies that scan all the rooms faster until the goal reaches its field of vision.
We have shown the usefulness of our representation and our reward shaping scheme in a series of gridworld experiments, where the agent receives a high-dimensional observation of its goal as an input along with an observation of its immediate surroundings. Preprocessing the input using this representation speeds up the training of two out-of-the-box RL methods, Actor Critic using Kronecker-Factored Trust Region and Proximal Policy Optimization, compared to having these methods learn the representations from scratch. In our most complicated experiment, combining our representation with our reward shaping technique is shown to perform significantly better than the vanilla RL methods, which hints at its potential for success, especially in more complex RL scenarios.
\subsection{Introduction}
Our model-based LARPnet method is data-efficient and is able to speed to learning for new tasks after pre-training on a similar one. However, model-free reinforcement learning methods have a clear advantage when it comes to the length of the inference time. This is due to the fact that the graph search requires passes to a computationally heavy function to predict future latent states for each potential future step. Depending on the branching factor of the task, this can result in an explosion of computational time.
In this chapter, we propose to weave together LARPnet with a policy optimization routine to get the best of both worlds from the model-based an model-free reinforcement learning literature, a method we dub Untitled Goal-Condition Policy Learned (UGCPL).
Since we'll divert our attention to problems with reward signals for this chapter, we expand the network from the previous chapter such that it also has a module for reward prediction. This is conceptually quite simple, as only an additional scalar value needs to be predicted.
The representation will now also accept a goal vector as an input. This is
a natural augmentation of the state, as how our perception of the world is influenced by our goals \citep{meltzoff2003imitation}.
This aids in the learning of goal-conditioned policy and allows us to reap the benefit inherent in modeling the environment.
In the experiments, we show how our training regimen learns a world model which is suitable for the learning of a policy in a model-free manner. This is compared to policies trained from scratch using a model-free methodology and our method beats the baselines in a low-data regime.
\subsection{Related work} \label{sec:rw}
\textbf{Goal-Conditioned Reinforcement Learning } Kaelbling studied environments with multiple goals and small state-spaces in 1993 \citep{kaelbling1993learning}. Their problem setting has an agent with the objective of reaching a known but dynamically changing goal in the fewest number of moves. The observation space was of a low enough dimension for dynamic programming to be satisfactory in their case. Schaul et al's Universal Value Function Approximators \citep{schaul2015universal} tackle environments of larger dimensions by learning a value function neural network approximator that accepts both the current state and a goal state as the inputs. In a similar vein, Pathak et al. \citep{pathak2018zero} learn a policy that is given a current state and a goal state and outputs an action that bridges the gap between them.
\textbf{Forward Prediction Dynamics } A popular line of model-based research is learning a forward prediction model of either the full observation space \citep{watter2015embed}, a subset of it \citep{dosovitskiy2016learning} or of learned latent variables associated with the observations \citep{ke2018modeling}. Dosovitskiy et al. \citep{dosovitskiy2016learning} construct a model that predicts a low-dimensional "measurement" subset of the input, which is used for solving environments whose goals are a linear combination of these measurements. A prediction model is generally utilized for planning \citep{hlynsson2020latent, silver2017predictron} when modeling the reward is not feasible.
\textbf{World Models } Other methods incorporate a prediction model into a full replica of the environment which can be used for a simulated optimization of the agent. The seminal "world model" algorithm is Sutton's 1991 Dyna architecture \citep{sutton1991dyna} where an agent is described that models the environment dynamics and receives rewards from simulated experience in addition to real-world experience. Ha and Schmidhuber \citep{ha2018world} use a similar algorithm where the state representation is learned in an unsupervised manner. Other twists on the Dyna policy-learning scheme include SimPLE \citep{kaiser2019model}, MuZero \citep{schrittwieser2019mastering} and DreamerV2 \citep{hafner2020mastering}.
The method we propose in this chapter can be categorized as a hybrid model-based / model-free method, as it learns first a model of the environment that is then used for model-free learning
\subsection{Learning the World Model} \label{sec:wm}
In this section, the representation-learning aspect of the module is described. The novel contribution is the goal-dependency of the representations, in addition to being directly learned for the useful downstream tasks of predicting rewards and latent representations. The module as a whole is first described before each component is explained in turn.
\subsubsection{Module Outline}
The representation learning module is made up of the following components (Fig~\ref{fig:boat1}):
\begin{figure}[ht!]
\begin{center}
\includegraphics[width=0.8\linewidth]{assets/beedance_b.pdf}
\caption[Illustration: Representation Learning Module]{\textbf{Representation Learning Module } The module is comprised of representation, reward prediction and representation prediction units. Each batch contains: the observations at time steps $t$, $t+1$ and $n$, where $n$ is a random sample from the buffer, the action taken at time $t$ and the agent's internal goal at time $t$.}
\label{fig:boat1}
\end{center}
\end{figure}
\begin{enumerate}
\item Inputs
\begin{itemize}
\item The goal (fixed per rollout)
\item The observations at time steps $t$, $t+1$ and $n$ (see triplet loss section)
\item The action at time step $t$
\item The reward at time step $t+1$
\end{itemize}
\item Functions with learnable parameters
\begin{itemize}
\item The representation
\item The reward predictor
\item The latent representation predictor
\end{itemize}
\item Loss functions
\begin{itemize}
\item Triplet loss between representations
\item Mean-squared error (MSE) loss for the reward predictor
\item MSE loss for the representation predictor
\end{itemize}
\end{enumerate}
Since the module is fully differentiable, every component is optimized in an end-to-end manner during the world-model update step (see below). We don't assume a useful metric or natural ordering between the goals and action so the goal and action inputs are converted from integers to one-hot encodings.
\subsubsection{Triplet Loss}
Of the methods considered for alleviating the problem of trivial solutions in the previous chapter, we chose the triplet loss (Fig. \ref{fig:boat6}) due to being potentially more stable than whitening and requiring fewer parameters than a reconstructive loss.
\begin{figure}[ht!]
\begin{center}
\includegraphics[width=.65\linewidth]{assets/triplet_loss_worldmodel.pdf}
\caption[Illustration: Triplet Loss]{\textbf{Triplet Loss } Three copies of the representation network each receives an observation and the goal from that observation's rollout. The negative is a random observation from the buffer that is not in $\{t-1, \dots, t+2\}$ from the same rollout. }
\label{fig:boat6}
\end{center}
\end{figure}
The triplet loss function has the form
$$\mathcal{L}(A, P, N) = \max({ d_{+} - d_{-}+{m}, 0})$$
where $m$ is the margin and the positive and negative distances are defined as
$$ d_{+} = || \phi(A) - \phi(P)||^2$$
$$ d_{-} = || \phi(A) - \phi(N)||^2$$
and $\phi$ is the representation.
\subsubsection{Predicting the Next-step Reward and Latent Representation}
The representation and action at time step $t$ is simultaneously passed to two separate functions (Fig.~\ref{fig:boat7}) that predict the next-step reward and representation. Both have simple mean-squared error losses. The reward prediction network will be used to approximate the reward function in the world model and the representation prediction network approximates the transition function.
\clearpage
\begin{figure}[ht!]
\begin{center}
\includegraphics[width=.75
\linewidth]{assets/predrew_loss_worldmodel2.pdf}
\caption[Illustration: Prediction Losses]{\textbf{Prediction Losses}. Both networks receive the same inputs and are trained at once in each training step. They are drawn here with dense layers but they can in principle be any differentiable function.}
\label{fig:boat7}
\end{center}
\end{figure}
\subsection{Learning the Policy} \label{sec:policy}
\subsubsection{Train Time}
To ensure that the world model is modeling the facets of the environment that are of the most value to the agent, we do an iterative training of the world model and the policy (Alg.~\ref{alg:wm}). The (initially random) policy $\pi$ is used to gather training data in the MDP $\varepsilon_T = (\mathcal{S}, \mathcal{A}, \mathcal{P}, \mathcal{R}, \mathbb{P}(s_0), \lambda)$ for the representation $\phi$, reward predictor $\zeta$ and representation predictor $\xi$. We use the functions that make up our world model, the representation $\phi(\mathcal{S})$, the reward function is $\zeta = \hat{\mathcal{R}}$ and the transition function $\xi = \hat{\mathcal{P}}$, to create a new MDP: $\varepsilon_F = (\phi(\mathcal{S}), \mathcal{A}, \zeta, \xi, \mathbb{P}(s_0), \lambda)$. The policy is trained inside the new environment $\varepsilon_F$ and then used to gather more data again to train the world model further.
\begin{algorithm}[H]
\SetAlgoLined
Initialize environment $\varepsilon_T$\;
Initialize policy $\pi$\;
Initialize representation $\phi$, reward predictor $\zeta$ and representation predictor $\xi$\;
Initialize experience buffer $B$\;
\While{not done}{
Perform rollout using $\pi$ and append the states, actions and rewards to $B$\;
Duplicate the terminal state, action reward tuples $\kappa$ times to help balance the data set\;
\If{world model update step}{
Train $\phi$, $\zeta$, and $\xi$ on the buffer $B$\;
}
\If{policy update step}{
Assemble environment $\varepsilon_F$ with $\phi$, $\zeta$, and $\xi$\;
Train $\pi$ on $\varepsilon_F$ for $T$ time steps\;
}
Shuffle B and keep the first $N$ experiences\;
}
\caption{Training of World Model and Policy}
\label{alg:wm}
\end{algorithm}
\subsubsection{Inference Time}
When the world model and policy have been trained, the representation $\phi$ is extracted from the module. At each time step $t$, the observation $O_t$ and the goal vector $G$ are passed to $\phi$ (Fig. \ref{fig:boat5}) which yields the latent-space vector. This vector is passed to the policy $\pi$ which outputs the estimated optimal action $a_t$ which is passed to the environment, yielding $O_{t+1}$ and so on.
\begin{figure}[ht]
\begin{center}
\includegraphics[width=.7\linewidth]{assets/action_pipeline.pdf}
\caption[Illustration: Policy at Inference Time]{\textbf{Policy at Inference Time} The test time procedure is the same as for regular model-free reinforcement learning, except that the input to the policy is the latent vector given by the representation from the observation as well as the environment's goal parameter. }
\label{fig:boat5}
\end{center}
\end{figure}
\subsection{Experiments} \label{sec:exp}
In this section, we evaluate our method on a simple but dynamic navigation environment. In \ref{subsec:env} the environment we created for the experiments is introduced. In \ref{subsec:cm} we discuss the baseline methods that we compare our method to. Sec. \ref{subs:ma} contains the details of our model parameters. In Sec. \ref{subsec:policy} we describe the parameter values of Alg. \ref{alg:wm}. Finally, Sec. \ref{subsec:results} outlines the results of the experiments.
\subsubsection{Environment} \label{subsec:env}
The method is tested in a four-room gridworld environment based on the Minimalistic Gridworld Environment (MiniGrid) \citep{gym_minigrid} (Fig.~\ref{fig:boat4}). The world is a $8 \times 17$ grid of tiles, split into two rooms, with each tile containing one or zero objects.
The environment fits naturally into our MDP tuple template $(\mathcal{S}, \mathcal{A}, \mathcal{P}, \mathcal{R}, \mathbb{P}(s_0), \lambda)$:
\begin{itemize}
\item[$\mathcal{S}$:]The constituent states of $\mathcal{S}$ are determined by the agent's location (which tile it occupies) and direction (facing north, west, south or east) along with the goal's location. The steps taken since the initialization of the run and the maximum number of steps until timeout also matter for the calculation of the reward.
\item[$\mathcal{A}$:]The action space $\mathcal{A}$ consists of three action: (1) turn left, (2) turn right and (3) move forward.
\item[$\mathcal{P}$:] Each action brings about the indicated change to the state, making $\mathcal{P}$ a deterministic function.
\item[$\mathcal{R}$:] Reaching the green tile goal gives a reward of $1 - 0.9 \cdot \frac{\# \textrm{steps taken} }{\# \textrm {max step}}/ $, every other action gives 0 points. The environment automatically times out after 1000 steps.
\item[$\mathbb{P}(s_0)$:] the agent is placed between two of the rooms facing a random direction and has to go to either one of two goal locations (Fig.~\ref{fig:boat4}).
\item[$\lambda$:] the discount factor is set to $0.99$ for the purpose of all model-free policy training routines
\end{itemize}
The agent's observation is comprised of its field of vision -- a 28x28 pixel rgb array -- as well as a categorical variable describing the agent's goal.
\begin{figure}[!tbp]
\centering
\begin{minipage}[b]{0.6\textwidth}
\includegraphics[width=\textwidth]{assets/top_goal.png}
\includegraphics[width=\textwidth]{assets/bottom_goal.png}
\end{minipage}
\caption[Example: The Room Environment]{\textbf{The Room Environment } The goal locations are indicated by the green square and the run is a success when the red agent reaches it. The light gray areas are impassable walls. Each row shows a snapshot of a different state. The left side shows the full state of the environment and the right side shows the observations emitted by the environment.}
\label{fig:boat4}
\end{figure}
\subsubsection{Baselines} \label{subsec:cm}
We compare our method to canonical, state-of-the-art reinforcement learning algorithms:
\begin{itemize}
\item
For initial sanity-checks, we measure the performance of a purely \textbf{random policy} on the environment.
\item Actor Critic using Kronecker-Factored Trust Region (\textbf{ACKTR}) \citep{wu2017scalable}, which combines actor-critic methods, trust-region optimization and distributed Kronecker factorization to enhance sample-efficiency.
\item A version of Proximal Policy Optimization (\textbf{PPO2}) \citep{schulman2017proximal}. It modifies the original PPO algorithm by using clipped value functions and a normalized advantage.
\end{itemize}
The comparison algorithms are implemented by Stable Baselines \citep{stable-baselines}
and we use all the default parameters of the methods.
This includes the so-called Nature CNN architecture used for the model. This model is orders of magnitude larger than our method \ref{tab:totalparams} so we also construct a smaller version of it, see the next section for details.
\subsubsection{ Model Architectures} \label{subs:ma}
Every policy and predictor is realized as a neural network using Keras \citep{chollet2015keras}. We will describe here precisely the architecture used for each model and refer to tables in the appendix for better visualizations.
\textbf{Our representation network} is a convolutional network (Table \ref{tab:repnet}) with a $56 \times 56 \times 5$ input consisting of the raw $56 \times 56 \times 3$ visual observation stacked with the one-hot $56 \times 56 \times 2$ plane indicating the goal. The first layer subsamples the input, keeping only every other column and row. This is followed by 8 filters of size $3 \times 3$ with a stride of 3 and no padding. This is followed with a ReLU activation and a $2 \times 2 $ pooling layer with a stride value of 2. The pooling layer's output is passed to a layer with 16 convolutional filters of size $3 \times 3$ and a stride of 2 and a ReLU activation function. The output is then flattened and passed to a dense layer with 16 units and a linear activation, defining the dimension of the representation. To allow us to fix the margin of the triplet loss, we fix the scale of the features by performing an L2-normalization in the last layer:
$$ \textbf{x} \leftarrow \frac{\textbf{x}}{\sqrt{\sum_{i=1}^dx^2_i}} $$
\textbf{Our policy network} is a three-layer fully-connected network (Table \ref{tab:polnet1}) accepting the 16 dimensional representation as input. The first two layers have 64 units and a ReLU activation and the last layer has 3 units and a linear activation function.
\textbf{Our latent representation prediction network} is a four-layer fully-connected network (Table \ref{tab:polnet2}) accepting the 16 dimensional representation concatenated with the 3 dimensional one-hot representation of the action as input. The first two layers have 512 units and ReLU activations, followed by a 256 unit layer with a ReLU activation and the last layer has 16 units and a linear activation.
\textbf{Our reward prediction network} is a three-layer fully-connected network (Table \ref{tab:polnet3}) with the same input as the latent representation prediction network. The first two layers have 256 units and a ReLU activation but the last layer has 1 unit and a logistic activation function.
\textbf{The comparison policy network} is the original DQN \citep{mnih2013playing}. The input is the same as for the representation network. The first three hidden layers are convolutional layers: the first has 16 $8 \times 8$ filters with stride 4, the second has 32 filters of size $4 \times 4$ with stride 3 and the third has 32 filters of size $3 \time 3$ with stride 2. The final hidden layer is a fully-connected layer with 256 units and the output layer is a fully-connected linear layer with 3 units, one for each action. Each hidden layer has a ReLU nonlinearity. We also built a smaller version of the net to bring the parameter count closer to our method, which is the same except with a fourth of the number of convolutional filters and eight of the number of units in the hidden dense layer.
\subsubsection{Training the policy} \label{subsec:policy}
Here we fill in the details of Alg.\,\ref{alg:wm}. The policy is the fully-connected network described above, trained using PPO2.
The functions $\phi$, $\zeta$ and $\xi$ are already described above. The experience buffer has a capacity of $N = 30k$. We oversample states-action pairs that result in a positive reward $\kappa=300$ times. This number was determined by experiments to be sufficient to balance the data set, resulting in roughly a third of it containing positive rewards.
The while loop ends after 200 iterations and each rollout consists of 500 steps. The full world model is trained for the first 50 iterations, after which the representation $\phi$ stops receiving updates. The policy is likewise updated for 500 steps in the world model $\varepsilon_F$ in every iteration.
\subsubsection{Results} \label{subsec:results}
\textbf{Qualitative Analysis }
We visualize the structure in our environment as perceived by our agent in Fig.\,\ref{clusterings}. We condition the representation on the two different goal locations and find no qualitative difference. Notice how the embeddings contain a meaningful cluster of states with a wall on the right-hand side in the upper right (orange and red dots), states with a wall on the left-hand side in the bottom left (blue and purple dots) with the states surround the door in the middle (earth-colored dots).
\begin{figure*}[ht]
\centering
\begin{minipage}{.27\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/env_groundtruths.pdf}
\label{label1}
\end{minipage}%
\begin{minipage}{.36\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/0_0_env_groundtruths.pdf}
\end{minipage}
\begin{minipage}{.36\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/0_1_env_groundtruths.pdf}
\end{minipage}
\caption[Result: Representation Clustering]{ \textbf{Representation Clustering } We use t-SNE \citep{maaten2008visualizing} to visualize the topology of our 16-dimensional embeddings of the environment states as the agent faces north.}
\label{clusterings}
\end{figure*}
\textbf{Baselines } A policy that takes random actions only gets an average cumulative reward of around $0.3$, which is added to each following graph as a horizontal line. The results for ACKTR using the two different Nature CNNs are displayed in Fig.\,\ref{acktr}. There is not a noticeable difference between the larger and the smaller networks on the scale of the data that we're using. On the other hand, PPO2 performs reaches much lower reward values and is more unstable than ACKTR. (Fig.\,\ref{ppo2results}).
\begin{figure*}[ht]
\centering
\begin{minipage}{.45\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/acktr_nature.png}
\label{label1a}
\end{minipage}%
\hspace{-1em}
\begin{minipage}{.45\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/acktr_smaller.png}
\label{label2a}
\end{minipage}
\caption[Result: ACKTR Training]{ \textbf{ACKTR training results.} In each run, 10 test rollouts are performed and the mean cumulative reward is averaged.}
\label{acktr}
\end{figure*}
\begin{figure*}[ht]
\centering
\begin{minipage}{.49\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/ppo2_big.png}
\end{minipage}%
\hspace{-0.45em}
\begin{minipage}{.49\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/ppo2_small.png}
\end{minipage}
\caption[Result: PPO2 Training]{ \textbf{PPO2 training results.} The agents are considerably less stable and worse performing than ACKTR and ours. }
\label{ppo2results}
\end{figure*}
\textbf{Only Pre-trained World Models } We initially organize the training of our method in a manner akin to Ha and Schmidhuber's policy learning \citep{ha2018world}: the world model is initially trained on 75 thousand random steps, after which the policy is trained and no further updates to the world model are made.
The training curve for this setup is in Fig.\,\ref{graph:75k}.
We then vary the number of pretraining steps and present the results for 30k, 10k and 1k random initial interactions to gather data for the world models. (Fig.\,\ref{fig:varying}). The case with no world model training steps at all was also considered (Fig.\,\ref{fig:varying}, bottom right), where the agent's performance is quickly pushed to 0.
More pre-training steps are better and at least 10k steps are sufficient for training inside of the world model to significantly outperform the random baseline.
Unsurprisingly, training the policy within an untrained world model does not improve the policy's performance in the real-world environment
\begin{figure}[ht]
\begin{center}
\includegraphics[width=.65\linewidth]{assets/ownmeth2.png}
\caption[Result: Own Method after Pre-training.]{\textbf{Own Method after Pre-training.} Own method was pre-trained on 75k steps, aggregated over 3 agents with 10 test rollouts each. The error bands indicate one standard deviation from the mean.}
\label{graph:75k}
\end{center}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=.4\textwidth]{assets/ownmeth_30k.png}
\includegraphics[width=.4\textwidth]{assets/ownmeth_10k.png}
\includegraphics[width=.4\textwidth]{assets/ownmeth_1k.png}
\includegraphics[width=.4\textwidth]{assets/ownmeth_0k2.png}
\caption[Result: Our Method with Varying Initial data Collection Lengths]{\textbf{Our method with Varying Initial data Collection Lengths.}}
\label{fig:varying}
\end{figure}
\textbf{Iterative updates }
Following our full iterative world-model / policy optimization scheme from Alg.\,\ref{alg:wm} yields the results in Fig.\,\ref{ouriterative}.
This looks a little better and more stable than the versions with pre-training only. Even though our method is equipped with fewer parameters, it reaches better performance than the baselines Rl methods. Our iterative training regime is also more stable and reaches good performance quickly.
\begin{figure*}[ht]
\centering
\begin{minipage}{.65\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/rlyonthego_longer.png}
\end{minipage}
\caption[Result: Our Method with Iterative Optimization]{ \textbf{Our method with Iterative Optimization.} The policy is not tested until it has been trained 2k times.}
\label{ouriterative}
\end{figure*}
\textbf{Inverse Model Normalization }
We considered omitting the triplet loss in the hope that predicting the reward alone is sufficient for learning informative representations. However, due to the sparse-reward nature of our experiments, we found that this resulted in the system learning a representation that is constant over state-goal pairs that do not result in a reward (maximizing latent predictability) but changing only when the next step will yield a reward (maximizing reward predictability). This is not helpful for approximating the environment dynamics.
Instead of relying on the triplet loss, we also try exchanging it with an inverse model loss. By inverse model, we mean that we add a predictive network to our training module for predicting $a_t$ given $\phi_t$ and $\phi_{t+1}$. The motivation for this is that the change in the representation should be informative enough for the action to be recoverable again, which could substitude the triplet loss for preventing trivial solutions \citep{pathak2017curiosity}. The model for the inverse predictor is identical to the one for the reward prediction, except that the output layer has 3 units and a softmax activation. The results for this setup are shown in Fig.\,\ref{inversedyn}.
\begin{figure*}[ht]
\centering
\begin{minipage}{.7\columnwidth}
\centering
\includegraphics[width=\textwidth]{assets/inversedyn.png}
\end{minipage}
\caption[Result: Our Method with Inverse Model Regularization]{ \textbf{Our Method with Iterative Optimizations and Inverse Model Regularization.}}
\label{inversedyn}
\end{figure*}
\textbf{Inference Time Length } We measured the time it took for UGCPL to choose an action, compared
to LARPnets and the baseline RL models. The benchmarks were made on a machine with an Intel(R) Xeon(R) CPU E5-1650 v4 @ 3.60GHz CPU, a Tesla P40 and a GeForce GT 710 GPUs.
The LARPnets 162 states before returning the action to take, explaining the vast difference in the execution time between the LARPnets and the others.
The Intel processor has 2 threads per core and 6 cores per socket, totaling in 12 CPUs. This explains the discrepancy in the wall-clock time and CPU time for some of the algorithms, as up to twelve processors were performing computations for the process.
\begin{table}[ht]
\centering \begin{tabular}{|l c c|}
\hline\rule{0pt}{2.2ex}
\textbf{Method} & \textbf{Wall-Clock Time (ms)} & \textbf{CPU Time (ms)} \\ [0.5ex]
\hline\rule{0pt}{2.2ex}UGCPL & 921.7 $\pm$ 97.9 & 1716.0 $\pm$ 119.8 \ \ \\[.5ex]
LARPnets & 389,351.5 $\pm$ 17,807.28 & 663,413.0 $\pm$ 29,721.6 \ \ \\[.5ex]
PPO2, Larger & 22.4 $\pm$ 1.6 & 22.9 $\pm$ 1.4 \\[.5ex]
PPO2, Smaller & 24.3 $\pm$ 0.5 & 23.9 $\pm$ 0.5\\[.5ex]
ACKTR, Larger & 24.1 $\pm$ 1.2 &
23.6 $\pm$ 1.5 \\[.5ex]
ACKTR, Smaller & 25.0 $\pm$ 0.4 &
24.5 $\pm$ 0.7 \\[.5ex]
\hline
\end{tabular}
\vspace{0.1cm}
\caption[Result: A Comparison of Execution Times]{A Comparison of Execution Times.}
\label{tab:inference_times}
\end{table}
\subsection{Discussion and Future Work} \label{sec:disc}
In this chapter, we put forward Untitled Goal-Conditioned Policy Leaner (UGCPL), a hybrid model-based model-free reinforcement learning method for environments with varying goals. Initial experiments indicate that our method learns faster and is more stable than proven model-free RL methods that have similarly sized models.
Future work for this chapter includes:
\begin{itemize}
\item Add two rooms to the left and reduce the room sizes to $5 \times 5$ or $6 \times 6$
\item Add experiments where we add the goal representation rather as an input to the reward prediction and latent representation prediction functions
\item Try different forms of the goal inputs: \begin{itemize}
\item location coordinates
\item goal state (as full observation)
\end{itemize} In the case of a goal state, changing the environment to be fully observable would be preferable. Both options open up the possibility of generalizing to unseen goal locations.
\item Add more visualizations: \begin{itemize}
\item a heatmap of most visited states during test rollouts
\item most taken actions at each location
\item policy values at each state
\end{itemize}
\item Add a table or tables summarizing and aggregating the most interesting statistics in our policy training curves
\end{itemize}
Future work for the thesis as a whole includes:
\begin{itemize}
\item Add a chapter or a section where the main unsupervised learning methods (e.g. pca, sfa, t-sne, vaes, umap, lda, gda) are combined with model-based reinforcement learning. This will help bridge together the representation-focused early chapters of the thesis with the reinforcement-learning focused later chapters.
\end{itemize}
\section{Introduction}
As each method was introduced over the course of the PhD work, it was only compared to other similar methods in the literature. We now take the opportunity to compare them against each other in different environments. The cart-pole environment and the obstacle avoidance environment have the commonality that they both require only reactive short-term planning to maximize the reward, but the goal-finding environments require more long-term planning to find and reach the goal.
Every one of our representations is used for preprocessing the visual observations of each environment for RL algorithms. The RL agents are the same ones used in the previous chapter: ACKTR and PPO2, with the default parameters from the Stable Baselines package. As we were not able to solve the cart-pole environment using ACKTR, only PPO2 is used for that task. We compare the method from Chapter \ref{chap:larp}, LARP, in this manner, even though it is not trained for preprocessing inputs for model-free agents but is developed to be paired with a predictor for predictive state representation rollouts
\section{Methods}
\label{compmethods}
\subsection{Visual cart-pole}
We start by comparing our methods as visual preprocessing for a PPO2 policy on a variant of the classical cart-pole balancing task. A pole is attached to a cart that moves along a frictionless track. The goal is to keep the pole upright for as long as possible, but the agent must push the cart to the left or to the right at every time step -- choosing to remain in place is not an option. The original environment supplies four scalar variables to the agent: the cart position and velocity and the pole angle and angular velocity. The agent receives a positive reward of $+1$ for each transition.
Instead of using these scalars, we adapt this task to our paradigm by using a visualization of the environment, see Fig. \ref{fig:cart-poleillustratio21}. To begin with, we extract the rendering of the environment that is meant for debugging and visualization purposes. As we can approximate the cart position and velocity and the pole angle and angular velocity using two adjacent frames, we use the current and previous observations. To simplify the input for the agent, we take the difference of the two frames, crop the image around the cart and binarize it. The only information that is lost in this process, compared to the original environment, is the position of the cart, which is not so important for solving the task. In addition to giving the agent a positive reward of $+1$ for every time step it keeps the pole balanced, we also supply it with a negative reward of $-1$ when the pole falls down.
\begin{figure}[h]
\centering
\includegraphics[width=0.98\linewidth]{comparison/cartpole_pipeline.pdf}
\caption[Example: Visual cart-pole]{\textbf{cart-pole processing pipeline.} We replace the original 4-dimensional state space of the OpenAI gym cart-pole environment with the output of its rendering function. The previous frame is subtracted from the current frame, the non-zero pixel values are centered, cropped and the final image is converted to binary.}
\label{fig:cart-poleillustratio21}
\end{figure}
Our methods are trained on 5000 transitions that are collected from a random policy. Even though this is not a sparse-reward environment, we calculated new rewards for the RewPred network according to Equation \ref{eq:rstar} with a discount factor of $\gamma = 0.9$ and a maximum horizon of $M=6$. This has the effect that every time step is associated with a reward of $+1$, except for the six transitions leading up to the end of the episode, which have the rewards $-(0.9^5), -(0.9^4), -(0.9^3), -(0.9^2), -(0.9)$ and $-(1.0)$.
\subsection{Room environments}
We compare the performance of PPO2 and ACKTR policies as they use our methods for preprocessing on the two-room and four-room goal tasks from the previous chapter, see Section \ref{tworoomimplementation}. The data gathering for the representations used for preprocessing for the RL agents is unchanged from the previous chapter.
\subsection{Obstacle avoidance}
In this gridworld environment, the agent is placed in a room filled with circular objects that move randomly in each step (Fig. \ref{fig:obstacleavoidance_illustration}).
\begin{figure}[h]
\centering
\includegraphics[width=0.98\linewidth]{comparison/bbenv.png}
\caption[Example: Obstacle avoidance environment]{\textbf{Obstacle avoidance environment.} The agent is rewarded for maximizing the distance between itself and the closest circle. The left figure displays the full world state and the right figure displays the corresponding observation that the agent receives. }
\label{fig:obstacleavoidance_illustration}
\end{figure}
The agent receives visual inputs of dimension $56\times56\times3$ and must stay as far away from the objects as possible, as it receives a reward that is equal to the Euclidean distance between itself and the closest circle. The episode ends with a reward of $0$ after $100$ time steps or when the agent collides with a circle, which gives a reward of $-1$. The discount factor for the environment is 0.9.
\subsection{Architectures}
All representations and policies have the same architecture as the in the previous chapter, except that the output of the representation has been lowered to a 16-dimensional vector for lower computational times, see Table \ref{tab:repnet} and Table \ref{tab:polnet1}. The RL models have the same architecture except that the representation and policy modules are trained end-to-end. The prediction module of the LARP network is the same as in Chapter \ref{chap:larp}, see Table \ref{table:predictornet}. The mutual information neural estimator network used for training GrICA is the same as in Chapter \ref{chap:grica}, see Section \ref{icamethod}.
\section{Results and discussion}
\label{compresults}
\subsection{Visual cart-pole}
The results from the visual cart-pole experiment can be seen in Fig. \ref{fig:cart-poleillustration21}. The deep RL agent achieves the highest mean reward by a significant margin, probably because the environment requires the agent to take quick actions in response to the fast-changing environment.
\begin{figure}[htb]
\centering
\includegraphics[width=0.69 \linewidth]{comparison/5xcartpole.png}
\caption[Results: Visual cart-pole]{\textbf{cart-pole results.} Each point is the aggregate of 5 different policies that are trained from scratch and tested for 20 episodes, each. }
\label{fig:cart-poleillustration21}
\end{figure}
The learning curve is the worst when the agent is trained on the LARP representations, which is to be expected as it is learned to be paired with a representation predictor and graph search, which it is not used for this scenario.
The RewPred and GrICA learning curves look similarly good, with the RewPred representation achieving a slightly higher average reward. Both representations should theoretically be useful here: learning a representation that is predictive of how close the pole is from falling down (RewPred) ought to guide the agent's actions away from states where the pole is about to fall down, and recovering the three statistically independent latent variables generating the environment (GrICA), which would be a perfect compression of the environment. In this scenario, however, they do not beat the representation learning of the Deep RL algorithm.
\subsection{Room goal-finding}
The results for training on the smooth-reward prediction RewPred\footnote{Denoted "Ours 64r" in the previous chapter.} and Deep RL representations are kept in the plots from the previous chapter, and we have added the results for the GrICA and the LARP representations.
\subsubsection{Two-room environment}
The results for the goal-finding task, when the agent starts facing a random direction between two rooms and must locate a static goal, can be seen in Fig. \ref{fig:tworoomcomp}. We display here the version of the reward-predictive RewPred representation from the previous chapter that is trained on smoothed rewards.
\begin{figure}[h]
\centering
\includegraphics[width=0.98\linewidth]{comparison/onelocfix.png}
\caption[Results: Gridworld comparison, single goal location]{\textbf{Gridworld comparison: two-room goal-finding results}. The agent starts in between two rooms and get a reward from reaching a static goal location that is one of two rooms. Each point in the learning curve is aggregated from 10 initializations of policies that run 10 test episodes each. }
\label{fig:tworoomcomp}
\end{figure}
For the ACKTR policy, both the LARP and the GrICA learning curves\footnote{See the previous chapter for the RewPred results} are considerably lower than those of the other two, with the GrICA representation again looking slightly better out of the two, both when the mean reward and the minimum episode lengths are considered. This is probably also due to the fact that the advantage of the LARP representation disappears when the predictor that it is trained with is discarded and the representation is being used in a model-free setting. For the PPO2 policy, neither the policies that train on the LARP nor the GrICA representations show signs of learning to solve the environment.
\subsubsection{Four-room environment}
In this experiment, no combination of RL agent and representation shows progress toward solving the environment, except for RewPred paired with ACKTR. Both the LARP and GrICA variants barely display learning in the previous experiment, but all signs of progress disappear when the environment is sufficiently complex. The training results can be seen in Fig. \ref{fig:fourroomcomp}.
\begin{figure}[h]
\centering
\includegraphics[width=0.98\linewidth]{comparison/fourfixed.png}
\caption[Results: Gridworld comparison, four-room goal-finding]{\textbf{Four-room goal-finding results.} The agent starts at a random location get a reward from reaching a dynamic goal location that is in one of four rooms. Each point in the learning curve is aggregated from 10 initializations of policies that run 10 test episodes each.}
\label{fig:fourroomcomp}
\end{figure}
\subsection{Obstacle avoidance}
The algorithm's learning curves for the obstacle avoidance experiment can be seen in Fig. \ref{fig:obstacleavoidance}. For both PPO2 and ACKTR, we observe that preprocessing with our methods is not beneficial as the environment is solved the fastest using deep RL, and by a significant margin for ACKTR. This shows that our method is outperformed by regular deep RL for environments where short-term, reactive policies are needed -- in contrast to the goal-finding tasks, where the agent needs to execute a long-term plan.
\begin{figure}[h]
\centering
\includegraphics[width=0.98\linewidth]{comparison/bbresults.png}
\caption[Results: Obstacle avoidance]{\textbf{Obstacle avoidance results.} The agent gets a reward for keeping its distance from objects that move randomly. Each point in the learning curve is aggregated from 10 initializations of policies that run 20 test episodes each.}
\label{fig:obstacleavoidance}
\end{figure}
\section{Conclusion}
In this chapter, we investigated how the three methods, that we have developed in this PhD work, compare when they are used for preprocessing visual inputs for RL agents. The RL agents are tested in four different environments, two of which require short-term decision-making and the other two require long-term decision-making for success. Our representation that was developed in Chapter \ref{chap:grica}, GrICA, does not facilitate learning for any of the environments. The same holds true for the Chapter \ref{chap:larp} representation, LARP, although that one was not developed for preprocessing inputs to RL agents but rather to be used in conjunction with a prediction function for planning in a latent representation space. Our reward-predictive representation from Chapter \ref{chap:rewpred} is shown to speed up learning for a deep RL agent on the long-term planning tasks.
\section{ An introductory restatement of research problem, aims and/or research question}
Just as the complexity of the tasks that deep reinforcement learning (RL) is being applied to increases, so does the apparent number of problems the field has. The goal of this research was to discover useful representations that can be used to alleviate two of modern deep RL's problems, namely, those of training instability and data inefficiency. Over the course of the PhD work, we developed three representation learning methods and investigated their suitability for fulfilling this goal:
\begin{itemize}
\setlength{\itemindent}{1.55cm}
\item[GrICA:] A gradient-based ICA method for learning statistically independent features (Chapter \ref{chap:grica}). We estimate the mutual information between one output component of an encoder and all the others using a neural network. In a push-pull fashion, the mutual information estimator and the encoder are trained, resulting in a system that outputs statistically independent features of the input. The output of GrICA is compare to the output of FastICA, an established ICA problem-solving method in the literature, for noisy blind signal separation.
\setlength{\itemindent}{1.45cm}
\item[LARP:] This system, which we call "Latent Representation Predictor" (Chapter \ref{chap:larp}), learns a transition model of the environment. We evaluate our system by combining it with graph search to manipulate toy objects to match a given viewpoint. Our algorithm learns a state representation jointly with a one-step lookahead predictor. We discuss and compare three different constraints that can be placed on the system to prevent the solution from collapsing to a constant function. Our approach outperforms deep RL in a low-data regime on the viewpoint-matching task.
\setlength{\itemindent}{1.93cm}
\item[RewPred:] A reward-predictive representation, that is learned along with a jointly learned reward predictor (Chapter \ref{chap:rewpred}). The reward predictor is employed for reward shaping: The agent is rewarded for moving from states of low predicted rewards to states of higher predicted rewards. The method is tested in several grid world environments where the agent must reach a goal. The learning of deep RL agents is sped up when their inputs are preprocessed by the RewPred representation in our experiments and the reward shaping is helpful when the environment is sufficiently complex.
\end{itemize}
Not every unsupervised learning technique yields a state representation that is useful in the context of RL, as seen by the results across the board using our GrICA algorithm. However, based on our results, we have found that the training of deep RL methods can be augmented by learning appropriate representations in a self-supervised manner in environments where the agent must carry out long-term planning to reach a single goal state.
An important limitation of this work is the high cost of computational resources required for carrying out RL research. To illustrate, reproducing DeepMind's 2017 Go paper \citep{silver2017mastering} is estimated to cost 35 million dollars using Google's cloud computing service \citep{dan2018how} -- a budget currently unavailable to PhD students.
Reproducing their results only involves maximizing the performance of a single model, which does not take into account the work behind finding the final model. RL methods have many potential settings to tune, and running hyperparameter searches is costly. For this reason, we concentrated only on using the default parameters of RL model implementations as offered by the Stable Baselines package.
To make matters worse, the performance of RL techniques can be highly sensitive to the hyperparameter settings, and bad luck can cause the researcher to dismiss a method if unfortunate values are initially chosen. A larger computational budget allows researchers to try more combinations of parameters when new methods are tested, lessening the risk of promising approaches being prematurely dismissed due to bad luck.
The methods were also tested for preprocessing the visual inputs of deep RL algorithms in environments where there is a set of state that the agent must \textit{avoid}, namely, preventing a pole from falling off a cart or preventing the agent from colliding with randomly moving objects. Preprocessing the inputs using our methods is not beneficial in these cases, potentially indicating that allowing deep RL algorithms to learn the state representations is preferable for tasks that require immediate reactions to quickly changing environments, particularly where inaction leads to an undesirable outcome.
Although our gradient-based ICA was not found advantageous in our goal of augmenting deep RL training, it is successful in recovering independent, noisy sources just as well as FastICA. A promising avenue of research is to take advantage of the flexibility offered by our method. Our algorithm can be paired with any differentiable function, such as convolutional neural networks (convnets), to tackle more difficult problems, for example nonlinear ICA. Even though general nonlinear ICA problems are ill-posed, regularization can be applied to make them well-posed. This can in principle be done using our method via the design of the neural network.
One aspect of representation learning that has become popular in recent years, but was not investigated in this PhD work, is the application of memory modules in neural networks. The role of memory can easily be integrated into our methods by designing our function approximators as artificial recurrent neural networks, for example by combining long short-term memory networks with convnets.
Although the problem of learning representations in the context of RL remains unsolved, the implication of our work is that taking advantage of the rich unsupervised source of supervision that is hidden in RL environments can lead to data-efficient, stable algorithms that are resilient to changes in the environment.
A straightforward way of extending our work would be to take advantage of the full data that is given in every transition in an RL environment: the current state $s$, the action $a$ taken in the state $s$, the resulting next state $s'$ and the reward $r$ given to the agent by the environment. It would be an interesting future line of work to do this by simply combining the loss function of LARP, which trains on $(s, a, s')$ tuples, and RewPred, which trains on $(r, s')$ tuples. This new algorithm would train the representation to be simultaneously predictable for a representation predictor, but also to be useful for a reward predictor. See Fig. \ref{fig:venn} for a Venn diagram that summarizes the sources of supervision that our proposed extension would use in addition to the sources of supervision that are used by our methods.
\begin{figure}[h]
\centering
\includegraphics[width=0.5\linewidth]{comparison/venn2.pdf}
\caption[Illustration: Supervision source Venn diagram]{\textbf{Supervision source Venn diagram.} An illustration of the components of the RL transition tuples $(s, a, r, s') = (\text{state},\text{ action},\text{ reward},\text{ next state})$ that are used by our methods: GrICA (Chapter \ref{chap:grica}), LARP (Chapter \ref{chap:larp}), RewPred (Chapter \ref{chap:rewpred}). These tuples consist of all the information involved in a single transition in an RL environment. The intersection of every component corresponds to the theoretical extension of our work, combining elements of LARP and RewPred.}
\label{fig:venn}
\end{figure}
This dissertation adds to a rapidly growing body of knowledge that sits at the intersection of deep learning, reinforcement learning and representation learning. We contribute three novel methods of learning state representations to the literature and experimentally evaluate their effectiveness in the context of reinforcement learning. A long road to artificial intelligence that matches our general and efficient problem-solving capability still lies ahead of us.
\section{Introduction}
\label{icaintroduction}
The general objective of training an encoder to learn statistically independent, factorial codes of the data has been called the "holy grail" of unsupervised learning \citep{schmidhuberunsupervised}. We suggest that learning to recover few, statistically independent, latent variables of an RL environment can speed up the training of RL agents. For environments where high-dimensional observations are created from a small set of statistically independent latent variables, this technique could reduce the dimensionality of the observations without discarding unnecessary information.
Another theoretical advantage of using this kind of approach in RL settings, compared to the other methods we develop in this PhD dissertation, is that it requires only out-of-context observation data from the environment. Learning the GrICA representation does not require full transitions $(s, a, r, s')$ tuples\footnote{We use $s$ to denote the state, $a$ to denote the action, $r$ to denote the reward and $s'$ to denote the next state. } and can thus be used when the transition or reward dynamics of the environments change.
Learning representations that output statistically independent features can be done in any number of ways, for example, by trying to make each output as unpredictable as possible given the other output units \citep{schmidhuber1992learning}. We take the approach of minimizing the mutual information, as estimated by a MINE network, between the output units of a differentiable encoder network. This is done by simple alternate optimization of the two networks.
\section{Background}
\label{icabackground}
Independent component analysis (ICA) aims at estimating unknown \textit{sources} that have been mixed together into an \textit{observation}. The usual assumptions are that the sources are statistically independent and no more than one is Gaussian \citep{jutten2003advances}. The now-cemented metaphor is one of a cocktail party problem: several people (sources) are speaking simultaneously, and their speech has been mixed together in a recording (observation). The task is to unmix the recording such that all dialogues can be listened to clearly.
In linear ICA, we have a data matrix $S$ whose rows are drawn from statistically independent distributions, a mixing matrix $A$, and an observation matrix $X$:
$$X = AS$$
\noindent and we want to find an unmixing matrix $U$ of $A$ that recovers the sources up to a permutation and scaling:
$$ Y = UX $$
The general non-linear ICA problem is ill-posed \citep{hyvarinen1999nonlinear, darmois1953analyse} as there is an infinite number of solutions if the space of mixing functions is unconstrained. However, post-linear \citep{taleb1999source} (PNL) ICA is solvable. This is a particular case of non-linear ICA where the observations take the form
$$X = f(AS)$$
\noindent where $f$ operates componentwise, i.e. $X_{i, t} = f_i \left( \sum_m^n A_{i, m}S_{m, t}\right) $. The problem is solved efficiently if $f$ is at least approximately invertible \citep{ziehe2003blind} and there are approaches to optimize the problem for non-invertible $f$ as well \citep{ilin2004post}.
For signals with time-structure, however, the problem is not ill-posed even though it is for i.i.d. samples \citep{blaschke2007independent, sprekeler2014extension}.
To frame ICA as an optimization problem, we must find a way to measure the statistical independence of the output components and minimize this quantity. There are two main ways to approach this: either minimize the mutual information between the sources \citep{amari1996new, bell1995non, cardoso1997infomax}, or maximize the sources' non-Gaussianity \citep{hyvarinen2000independent, blaschke2004cubica}.
\section{Related work}
\label{icarelatedwork}
There has been an interest in combining neural networks with the principles of ICA for several decades. In Predictability Maximization \citep{schmidhuber1992learning}, a game is played where one agent tries to predict the value of one output component given the others, and the other tries to maximize the unpredictability. More recently, Deep InfoMax (DIM) \citep{hjelm2018learning}, Graph Deep InfoMax \citep{velivckovic2018deep} and Generative adversarial networks \citep{goodfellow2014generative}, utilize the work of Brakel et al. \citep{brakel2017learning} to deeply learn ICA. Our work differs from these adversarial training methods in the rules of the minimax game being played to achieve this: one agent directly minimizes the lower-bound of the mutual information, as derived from the Donsker-Varadhan characterization of the KL-Divergence, as the other tries to maximize it.
\section{Method}
\label{icamethod}
\subsection{Reinforcement learning environment}
Our representation is tested on a 2D environment where the agent is supposed to avoid a field of lava and reach a goal on the other side of the room. The full state of the environment is the whole room (Fig \ref{clusteringz}, left) and the observation is an isometric view of the agent and its point of view (Fig \ref{clusteringz}, right). The observations are $56 \times 56$ RGB images and the agent can take a step forward, turn left or turn right.
\begin{figure*}[htbp]
\centering\begin{minipage}{.525\columnwidth}\centering
\includegraphics[width=\textwidth]{ica_assets/path2.png}\label{label1icaa}
\end{minipage}%
\begin{minipage}{.3525\columnwidth}\centering
\includegraphics[width=\textwidth]{ica_assets/path1.png}\end{minipage}
\begin{minipage}{.525\columnwidth}\centering
\includegraphics[width=\textwidth]{ica_assets/path8.png}\label{label1icab}
\end{minipage}%
\begin{minipage}{.3525\columnwidth}\centering
\includegraphics[width=\textwidth]{ica_assets/path7.png} \end{minipage}\caption[Example: The lavafield environment]{ \textbf{The lavafield environment.} The world has $5\times7$ tiles and is surrounded by impassable walls. The agent (red arrow) is tasked with reaching the goal, represented by the green tile, which yields a reward and terminates the episode. The episode ends without reward if the agent touches an orange lava tile. The full world state can be seen on the right, with a slightly lighter box containing the agent. This box highlights the subset of the world that is perceived by the agent, seen on the left.}\label{clusteringz}
\end{figure*}
The episode terminates if the agent steps toward lava or the goal. The agent receives a positive reward if it reaches the goal, but the episode terminates with zero reward if it steps into the lava. There is no change if the agent is faced toward the wall and takes a step forward.
\subsection{Learning the independent components}
We train an encoder $E$ to generate an output $\left(z_1, z_2, \dots, z_k\right)$ such that any one of the output components is statistically independent of the union of the others, i.e. $P(z_i, \boldsymbol{z_{-i}}) = P(z_i)P(\boldsymbol{z_{-i}})$, where $$\boldsymbol{z_{-i}} := \left(z_1, \dots, z_{i-1}, z_{i+1}, \dots, z_k\right)$$ The statistical independence of $z_i$ and $\boldsymbol{z_{-i}}$ can be maximized by minimizing their mutual information
\begin{equation} \label{mi_definition}
I\left(Z_i; \boldsymbol{Z_{-i}} \right) =
\int_{z} \int_{\boldsymbol{z_{-i}}}
P(z_i, \boldsymbol{z_{-i}}) \log \left(
\frac{P(z_i, \boldsymbol{z_{-i}})}{P(z_i)P(\boldsymbol{z_{-i}})} \right) dz_i d\boldsymbol{z_{-i}}
\end{equation}
This quantity is hard to estimate, particularly for high-dimensional data. Note that Equation~\ref{mi_definition} can be more succinctly as the \textit{KL divergence} between $Z_i$ and $Z_{-i}$:
\begin{equation} \label{mi_definition_kld}
I\left(Z_i; \boldsymbol{Z_{-i}} \right) = D_{KL} \left( P (Z_i, \boldsymbol{Z_{-i}}) \vert| P(Z_i) P (\boldsymbol{Z_{-i}}) \right)
\end{equation}
\cite{donsker1975asymptotic} famously proved that the KL Divergence admits the representation
\begin{equation} \label{dual_kld}
D_{KL} \left( X \vert| Y \right) = \sup _{T: \Omega \rightarrow \mathcal{R}} \mathbb{E}_X[T] - \log ( \mathbb{E}_Y [e^T])
\end{equation}
\noindent where the domain $\Omega$ is a closed and bounded subset of $\mathbb{R}^d$.
\cite{belghazi2018mine} introduce a method of using the Donsker-Varadhan representation to estimate mutual information with neural networks, with an architecture they call mutual information neural estimation (MINE) networks.
To learn representations with independent components, we therefore estimate the lower bound of Eq.\ (\ref{mi_definition}) using a MINE network $M$:
\begin{equation} \label{mine_objective}
I\left(Z_i; \boldsymbol{Z_{-i}} \right) \geq L_i = \mathbb{E}_{\mathbb{J}} \left[M \left( z_i, \boldsymbol{z_{-i}} \right) \right] - \log \left( \mathbb{E}_{\mathbb{M}} \left[ e^{M \left( z_i, \boldsymbol{z_{-i}} \right) } \right] \right)
\end{equation}
\noindent where $\mathbb{J}$ indicates that the expected value is taken over the joint and similarly $\mathbb{M}$ for the product of marginals. The networks $E$ and $M$ are parameterized by $\theta_E$ and $\theta_M$. The encoder takes the observations as input and the MINE network takes the output of the encoder as an input.
The $E$ network minimizes $L := \sum_i L_i$ in order for the outputs to have low mutual information and therefore be statistically independent. In order to get a faithful estimation of the lower bound of the mutual information, the $M$ network maximizes $L$. Thus, in a push-pull fashion, the system as a whole converges to independent output components of the encoder network $E$.
In practice, rather than training the $E$ and $M$ networks simultaneously it proved useful to train $M$ from scratch for a few iterations after each iteration of training $E$, since the loss functions of $E$ and $M$ are at odds with each other. When the encoder is trained, the MINE network's parameters are frozen and \textit{vice versa.}
\begin{figure}[htbp]
\centering
\captionsetup{width=.99\linewidth}
\resizebox*{0.99 \textwidth}{!}{\includegraphics
{ica_assets/info_test.pdf}}
\caption[Illustration: Our independent feature learning system]{\textbf{Our independent feature learning system.} The system learns statistically independent outputs by alternate optimization of an encoder $E$ and a MINE network $M$ parameterized by $\theta_E$ and $\theta_M$. The MINE objective (Eq.\ \ref{mine_objective}) is minimized with respect to $\theta_E$ for weight updates of the encoder, but it is \textit{maximized} with respect to $\theta_M$ for weight updates of the MINE network.}
\label{our_method}
\end{figure}
\section{Results}
\label{icaresults}
We try our method on two scenarios: (1) we compare it to canonical implementations of ICA on a textbook example of estimating sources from noisy data and (2) we use our method with a more complex function approximator for preprocessing observations in an RL setting.
\subsection{Recovering noisy signals}
We validate the method\footnote{Full code for the noisy signal recovery experiment is available at \url{github.com/wiskott-lab/gradient-based-ica/blob/master/bss3.ipynb}} a for linear noisy ICA example \citep{sklearn}.
Three independent, noisy sources --- sine wave, square wave and saw tooth signal (Fig.\ \ref{sources}) --- are mixed linearly (Fig.\ \ref{mixed}):
$$ Y = \begin{bmatrix}
1 & 1 & 1 \\
0.5 & 2 & 1\\
1.5 & 1 & 2
\end{bmatrix} S$$
\\
The encoder is a single-layer neural network with linear activation, with a differentiable whitening layer \citep{schuler2018gradient} before the output. The whitening layer is a key component for performing successful blind source separation for our method. Statistically independent random variables are necessarily uncorrelated, so whitening the output by construction beforehand simplifies the optimization problem significantly.
The MINE network $M$ is a seven-layer neural network. Each layer but the last one has 64 units with a rectified linear activation function. Each training epoch of the encoder is followed by seven training epochs of $M$. Estimating the exact mutual information is not essential, so few iterations suffice for a good gradient direction.
Since the MINE network is applied to each component individually, to estimate mutual information (Eq.\ \ref{mine_objective}), we need to pass each sample through the MINE network $n$ times --- once for each component. Equivalently, one could conceptualize this as having $n$ copies of the MINE network and feeding the samples to it in parallel, with different components singled out. Thus, for sample $(z_1, z_2, \dots, z_n)$ we feed in $(z_i ; z_{-i})$, for each $i$. Both networks are optimized using Nesterov momentum ADAM \citep{dozat2016incorporating} with a learning rate of $0.005$.
For this simple example, our method (Fig.\ \ref{ours_bss}) is equivalently good at unmixing the signals as FastICA as implemented in the scikit-learn package \citep{scikit-learn} (Fig.\ \ref{fastica_bss}). Note that, in general, the sources can only be recovered up to permutation and scaling.
\begin{figure}[h]
\centering
\captionsetup{width=.98\linewidth}
\begin{subfigure}[b]{.49\linewidth}
\includegraphics[width=\linewidth]{ica_assets/source.png}
\caption{The original sources.}\label{sources}
\end{subfigure}
\begin{subfigure}[b]{.49\linewidth}
\includegraphics[width=\linewidth]{ica_assets/obs.png}
\caption{Linear mixture of sources.}\label{mixed}
\end{subfigure}
\begin{subfigure}[b]{.49\linewidth}
\includegraphics[width=\linewidth]{ica_assets/step2000.png}
\caption{Sources recovered by our method.}\label{ours_bss}
\end{subfigure}
\begin{subfigure}[b]{.49\linewidth}
\includegraphics[width=\linewidth]{ica_assets/ica.png}
\caption{Sources recovered by FastICA.}\label{fastica_bss}
\end{subfigure}
\caption[Result: Noisy signal recovery]{\textbf{Noisy signal recovery.} Three independent, noisy sources (a) are mixed linearly (b). Our method recovers them (c) to the same extent as FastICA (d).}
\label{fig:animals}
\end{figure}
\subsection{Lavafield environment}
For these experiments, we learn our ICA features using a convolutional neural network. We roll out 100 episodes with a fully random policy to gather data for learning the independent features: an agent is placed in the upper right corner of the environment and turns left, right or takes a step forward with equal probabilities. The result observations are then gathered until the episode terminates. This gives us 4130 observations to train the representation on for this experiment.
The representation we learn is 32-dimensional. The MINE network is the same as above, but the encoder network is a five-layer convolutional neural network. The first two layers are convolutional layers each with 32 filters, a rectified linear unit activation and no padding. The first layer has a stride of 4 and the second one a stride of 3. The output of layer 2 is then passed to a flattening layer, reshaping the tensor output to a vector input for a linear dense layer with 32 units. The output of the dense layer is then finally passed to a sphering layer, giving us the encoding. The network description is summarized in Table~\ref{tab:icarepnet}.
\begin{table}[ht]
\centering \begin{tabular}{|c c c c c c c|}
\hline\rule{0pt}{2.2ex}
\textbf{Layer} & \textbf{Filters} & \textbf{Kernel} & \textbf{Stride} & \textbf{Padding} & \textbf{Output } & \textbf{Learnable} \\
\textbf{} & \textbf{} & \textbf{} & \textbf{} & \textbf{} & \textbf{Shape} & \textbf{Parameters} \\ [0.5ex]
\hline\rule{0pt}{2.2ex}
Input & - & - &-&-&$56{\times}56{\times}5$ & 0 \\[1ex]
\hline \rule{0pt}{2.2ex}
Conv. & 32 & 3x3 & 4 & None & $14{\times}14{\times}32$ & 896 \\[.5ex]
ReLU & - & - & -&- & $4{\times}4{\times}32$ & 0 \\[.5ex]
\hline \rule{0pt}{2.2ex}
Conv. & 32 & 3x3 & 3&None & $4{\times}4{\times}32$ & 9248 \\[.5ex]
ReLU & - & - & -&-& $4{\times}4{\times}32$ & 0\\[.5ex]
\hline\rule{0pt}{2.2ex}
Flatten & - & - & - &-& 512 & 0\\[.5ex]
Dense & - & - & - &-&32 & 16416\\[.5ex]
ReLU & - & - & -&-& $32$ & 0\\[.5ex]
\hline \rule{0pt}{2.2ex}
Sphering & - & - & - &-&32 & 0\\[.5ex]
\hline
\end{tabular}
\vspace{0.1cm}
\caption[Result: Our convolutional ICA network]{\textbf{Our convolutional ICA network.} The layout is inspired by the topology of Mnih's deep Q networks \citep{mnih2013playing} except for the last layer, where we have a differentiable sphering operation instead of a dense layer.}
\label{tab:icarepnet}
\end{table}
The training of our ICA representation follows the same scheme as before: we train the estimator $M$ for seven epochs after each training epoch of the encoder. We trained the encoder for 100 epochs and the estimator for 700 epochs for this experiment.
Our trained representation is used to preprocess the visual input for a RL agent. We choose Actor Critic using Kronecker-Factored Trust Region (ACKTR) as implemented by Stable Baselines with default parameters and model. The ACKTR default model is a fully-connected neural network with two layers of 64 units each and a tanh activation function.
We trained an ACKTR model from scratch twenty times on our ICA representation, and show the results in Fig~\ref{rewzies}. This indicates that we are able to learn the environment using our method to preprocess the input for a reinforcement learning method.
\begin{figure*}[ht]
\centering
\begin{minipage}{.83\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/stonks.png}
\end{minipage}%
\caption[Result: Reward during training on the lavafield environment]{ \textbf{GrICA reward during training on the lava field environment.} The line indicates the average reward (every 1500 training steps) over 20 different agents trained from scratch. The error bands indicate one standard deviation from the mean. } \label{rewzies}
\end{figure*}
To visualize the behavior of our agent (Figure~\ref{trajectories1}), we choose three successful episodes from a fully-trained model after 100 thousand time steps of training and three unsuccessful ones from a model with 80 thousand time steps of training. It is noteworthy that the agent prefers a wide margin between itself and the lava field as it passes it, even though a more optimal strategy would have the agent walk to the right with the lava left immediately on its left-hand side. The agent also sometimes doubles back before continuing toward the goal again.
\begin{figure*}[ht]
\centering
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/path4.png}
\end{minipage}%
\hspace{-0.45em}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/path5.png}
\end{minipage}
\hspace{-0.45em}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/path11.png}
\end{minipage}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/path14.png}
\end{minipage}%
\hspace{-0.45em}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/path12.png}
\end{minipage}
\hspace{-0.45em}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/path13.png}
\end{minipage}
\begin{minipage}{.25\columnwidth}
\centering
\end{minipage}%
\hspace{-0.45em}
\begin{minipage}{.49\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/cmap.pdf}
\end{minipage}
\hspace{-0.45em}
\begin{minipage}{.25\columnwidth}
\centering
\end{minipage}
\caption[Result: Trajectories in the lavafield environment]{ \textbf{Trajectories in the lava field environment.} The first step in the trajectory is indicated by blue, then the color warms up with each step until it becomes a more saturated red color in the final step. } \label{trajectories1}
\end{figure*}
We also tried to see whether our method generalizes to a variant of the environment where the lower row of lava is moved to the bottom, punishing our strategy. There were only 3 successes in a thousand test iterations, shown in Figure~\ref{failfield}, along with three of the unsuccessful episodes.
\begin{figure*}[ht]
\centering
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/failpath4.png}
\end{minipage}%
\hspace{-0.45em}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/path6.png}
\end{minipage}
\hspace{-0.45em}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/failpath3.png}
\end{minipage}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/failpath1.png}
\end{minipage}%
\hspace{-0.45em}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/failpath5.png}
\end{minipage}
\hspace{-0.45em}
\begin{minipage}{.33\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/failpath2.png}
\end{minipage}
\begin{minipage}{.25\columnwidth}
\centering
\end{minipage}%
\hspace{-0.45em}
\begin{minipage}{.49\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/cmap.pdf}
\end{minipage}
\hspace{-0.45em}
\begin{minipage}{.25\columnwidth}
\centering
\end{minipage}
\caption[Result: Trajectories with shifted lava fields]{ \textbf{Trajectories with shifted lava fields.} This variant punishes strategies -- such as the one learned using our representation -- where the agent seeks to go all the down for safety as it goes across the room. } \label{failfield}
\end{figure*}
For comparison, we also trained a convolutional autoencoder (CAE) for reconstruction on the same data set we used to train our ICA representation. We ran the experiment again with the resulting encoding after the CAE was trained. The encoder is the same as the network used for our representation, except that it does not have the sphering layer.
The decoding portion of the network consists of a 392-unit dense layer whose output is reshaped to a $7\times7\times 8$ tensor and passed to a convolutional layer with 32 filters of size $3\times3$. The output is then up-sampled to quadruple the width and height of the tensor. This is then followed by another convolutional layer, of the same kind as the previous one, and another up-sampling layer that doubles the width and height of the tensor. The output then finally goes through a convolutional layer with 3 filters of size $3\times3$. Each layer in the decoder has a ReLU activation, except for the last which has a logistic activation to reconstruct pixel values that have been normalized lie in the range $[0, 1]$. Each convolutional layer does zero-padding to preserve the width and the height of the input tensor. See Table \ref{tab:caenet} for an overview of the architecture.
\definecolor{lightblue}{rgb}{0.8,0.85,0.9}
\definecolor{lightred}{rgb}{0.85,0.9,0.8}
\begin{table}[ht]
\centering \begin{tabular}{|c c c c c c c|}
\hline\rule{0pt}{2.2ex}
\textbf{Layer} & \textbf{Filters} & \textbf{Kernel} & \textbf{Stride} & \textbf{Padding} & \textbf{Output } & \textbf{Learnable} \\
\textbf{} & \textbf{} & \textbf{} & \textbf{} & \textbf{} & \textbf{Shape} & \textbf{Parameters} \\ [0.5ex]
\rowcolor{lightblue} \hline\rule{0pt}{2.2ex}
Input & - & - &-&-&$56{\times}56{\times}5$ & 0 \\[1ex]
\rowcolor{lightblue}\hline \rule{0pt}{2.2ex}
Conv. & 32 & 3x3 & 4 & None & $14{\times}14{\times}32$ & 896 \\[.5ex]
\rowcolor{lightblue}ReLU & - & - & -&- & $4{\times}4{\times}32$ & 0 \\[.5ex]
\rowcolor{lightblue}\hline \rule{0pt}{2.2ex}
Conv. & 32 & 3x3 & 3&None & $4{\times}4{\times}32$ & 9248 \\[.5ex]
\rowcolor{lightblue}ReLU & - & - & -&-& $4{\times}4{\times}32$ & 0\\[.5ex]
\rowcolor{lightblue}\hline\rule{0pt}{2.2ex}
Flatten & - & - & - &-& 512 & 0\\[.5ex]
\rowcolor{lightblue}Dense & - & - & - &-&32 & 16416\\[.5ex]
\rowcolor{lightblue}ReLU & - & - & -&-& 32 & 0\\[.5ex]
\rowcolor{lightred}Dense & - & - & - &-&392 & 12936\\[.5ex]
\rowcolor{lightred}ReLU & - & - & -&-& $392$ & 0\\[.5ex]
\rowcolor{lightred}Reshape & - & - & - &-&$7{\times}7{\times}8$ & 0\\[.5ex]
\rowcolor{lightred}\hline \rule{0pt}{2.2ex}
Conv. & 32 & 3x3 & 1&Same & $7{\times}7{\times}32$ & 2336 \\[.5ex]
\rowcolor{lightred}ReLU & - & - & -&-& $7{\times}7{\times}32$ & 0\\[.5ex]
\rowcolor{lightred}\hline \rule{0pt}{2.2ex}
Upsampling & - & 4x4 & - & - & $28{\times}28{\times}32$ & 0 \\[.5ex]
\rowcolor{lightred}\hline \rule{0pt}{2.2ex}
Conv. & 32 & 3x3 & 1&Same & $28{\times}28{\times}32$ & 9248 \\[.5ex]
\rowcolor{lightred}ReLU & - & - & -&-& $28{\times}28{\times}32$ & 0\\[.5ex]
\rowcolor{lightred}\hline \rule{0pt}{2.2ex}
Upsampling & - & 4x4 & - & - & $56{\times}56{\times}32$ & 0 \\[.5ex]
\rowcolor{lightred}\hline \rule{0pt}{2.2ex}
Conv. & 3 & 3x3 & 1&Same & $28{\times}28{\times}32$ & 9248 \\[.5ex]
\rowcolor{lightred}Tanh & - & - & -&-& $56{\times}56{\times}3$ & 867\\[.5ex]
\hline
\end{tabular}
\vspace{0.1cm}
\caption[Result: Convolutional autoencoder network architecture]{\textbf{Convolutional autoencoder network architecture.} The blue part highlights the encoder portion and the green part highlights the decoder portion. The encoder portion was used to preprocess the input to the RL learner for the experiment.}
\label{tab:caenet}
\end{table}
We train the CAE for 50 epochs. Even though this is a low number of epochs compared to the training for our method, its reconstructive properties are already quite good (Figure \ref{recons}).
\begin{figure*}[ht]
\centering
\begin{minipage}{.35\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/cae1.png}
\label{icacae1}
\end{minipage}%
\begin{minipage}{.305\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/cae5.png}
\end{minipage}
\begin{minipage}{.35\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/cae3.png}
\label{icacae3}
\end{minipage}%
\begin{minipage}{.305\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/cae6.png}
\end{minipage}
\caption[Result: Reconstruction by autoencoder]{ \textbf{Reconstruction by autoencoder.} The 32-dimensional latent space captures enough information to reconstruct the original observations quite accurately, even after a modest number of training epochs.}
\label{recons}
\end{figure*}
We repeat the experiment as before, but now with the CAE features instead of our ICA representation. The training curve is shown in Figure \ref{stonks2}. This straightforward baseline algorithm learns to solve the environment twice as fast as our method.
\begin{figure*}[ht]
\centering
\begin{minipage}{.93\columnwidth}
\centering
\includegraphics[width=\textwidth]{ica_assets/stonks2.png}
\end{minipage}%
\caption[Result: Reward during training on the lavafield environment (convolutional autoencoder)]{ \textbf{CAE reward during training} The line indicates the average reward (every 1500 training steps) over 20 different agents trained from scratch. The error bands indicate one standard deviation from the mean. } \label{stonks2}
\end{figure*}
\section{Conclusion}
\label{icaconclusion}
We have introduced a novel technique for training a differentiable function to perform ICA. The method consists of alternating the optimization of an encoder and a neural mutual information neural estimation (MINE) network. The mutual information estimate between each encoder output and the union of the others is minimized with respect to the encoder's parameters.
The solution learned by our approach agrees with the one learned by the canonical ICA algorithm, FastICA. An advantage of our method, however, is that it is trivially extended for overcomplete or undercomplete ICA by changing the number of output units of the neural network. We apply our algorithm on high-dimensional data to test the representation learned by our method for dimensionality reduction of visual inputs for an RL agent. The agent is able to use our representation to learn how to solve a simple navigation task, but the preprocessing offered by our approach is outperformed by a convolutional autoencoder.
Our method works in principle, as can be seen by the noisy signal recovery experiment, but its effectiveness for learning representations for RL agents remains unproven. Even though the observations of the lava field environment are fully determined by three latent variables that are statistically independent, the agent's x and y positions, along with its direction, our representation was still not useful enough to beat the relatively simple baselines.
\section{Historical context}
\section{Deep reinforcement learning}
\label{Deepreinforcementlearning}
A watershed moment for artificial intelligence happened when \cite{krizhevsky2012imagenet} combined several techniques from the literature and constructed a deep\footnote{Neural networks that process the input hierarchically using at least more than two layers of computational layers are called \textit{deep}} neural network to outperform the competition by a significant margin in an image classification contest. This was the catalyst of the so-called \textit{deep learning revolution} \citep{sejnowski2018deep} which has impacted fields such as natural language processing \citep{wolf2020transformers}, bioinformatics \citep{li2019deep}, computer vision \citep{khan2018guide}, fraud detection and many others \citep{alom2019state}.
The area of machine learning concerned with the training of deep neural networks is called deep learning. Deep learning methods have the advantage that they autonomously learn patterns in the data in a hierarchical manner. For example, edges are useful patterns for pictures of shapes such as squares, triangles and circles \citep{patrick2010ai}. The edges can be combined to corners and the number of corners can be counted for distinguishing between the different shapes.
Since deep learning encompasses a broad set of machine learning algorithms, it can be readily combined with other areas of machine learning. One such area is reinforcement learning, where general goal-directed decision-making problems are studied. Reinforcement learning (RL) methods train models that are interacting sequentially with their environments to maximize a reward signal. Deep learning is frequently combined with RL techniques, allowing the models to map the inputs, such as high-dimensional image data, directly to actions. This combination has yielded promising results in different areas, ranging from recommender systems \citep{zhang2019deep} over autonomous driving \citep{kiran2021deep} to playing games \citep{silver2017mastering}.
\section{Open problems}
\label{openproblems}
A known problem of deep neural networks is that they require a large amount of data for adequate performance. This data can be prohibitively expensive to obtain -- either in terms of time needed to create data and train the models for reinforcement learning methods or monetary cost of acquiring human-labeled training data for supervised learning methods -- which has encouraged the development of methods that learn representations from streams of more readily available, unlabeled data.
This problem increases in severity in deep reinforcement learning (DRL). In the uncompromisingly titled blog post, \textit{Deep reinforcement learning doesn't work yet}, \cite{irpan2018deep} identifies several fundamental problems of DRL. One of them is the problem of sample inefficiency, where many highly publicized state-of-the-art results on video games require hundreds of millions of frames of experience to achieve performance that humans reach in a matter of minutes.
Another problem is the one of instability. Deep neural networks are highly expressive and optimize large numbers of parameters. This makes the design of DRL models difficult, as the search of hyperparameters\footnote{A hyperparameter is broadly speaking any design choice made by the programmer before the learning of the "regular" parameters starts.} that solve the problem can be quite time-consuming. Even when a promising set of hyperparameters is found, the difference between the performance of different models learned from scratch can be significant, depending on the random seed. This increased variance comes from the new source of randomness that is introduced to RL models, compared to regular regression learning: the agents actions are stochastic, increasingly so in the beginning of learning\footnote{There is a tradeoff between exploring the environment and exploiting the expected reward signal. A common strategy for RL agents is to start the learning with a high chance of performing random actions to explore different states of the environment and then decrease this chance as the learning progresses.}.
\section{Research aim}
\label{researchaim}
In this dissertation, we propose methods for unsupervised and self-supervised learning of representations for goal-directed behavior. Self-supervised learning methods use a subset of the input to predict the rest of it, foregoing the need of annotations while taking advantage of the powerful machinery of supervised learning methods.
Tackling the open problems of data inefficiency and instability outlined above in order to further the field is our intention with this thesis. We do so by developing and investigating three different approaches: (i) unsupervised learning of a representation for RL agents, (ii) a method of jointly learning a predictor for planning a representation that is good for the transition prediction, and (iii) learning a representation for RL agents as the byproduct of reward prediction. We relate the data needed to learn the representations for our methods to the available data in the context of RL in Table \ref{tableofmethods}. Our hypothesis is that suitable state representations that reduce the complexity of high-dimensional inputs in RL settings can support a more stable and data efficient learning than having deep RL algorithms learn state representations from scratch.
\begin{table}[h]
\begin{center}
\caption[Result: Input data type per method]{ {\bf Input data type per method.} If an RL agent is in a state $s$ and performs the action $a$, it will receive a reward of $r$ and transition to the state $s'$. The methods proposed in this thesis learn state representations by processing different subsets of the data tuples $\{s,a,r,s'\}$. }
\label{tableofmethods}
\begin{tabular}{ c l r}
\textbf{Subset of $\{s,a,r,s'\}$ required for learning} & \textbf{Method} & \textbf{Chapter}
\\ [0.5ex]
\hline
$\{s\}$ & GrICA & 3\\
\hline
$\{s,a,s'\}$ & LARP & 4\\
\hline
$\{s,r,s'\}$ & RewPred & 5\\
\end{tabular}\end{center}\end{table}
\section{Thesis outline}
\label{thesisoutline}
Here we outline the structure of the thesis. Three of the chapters are adapted from the work that were published over the course of the doctoral work.
\nobibliography*
\begin{itemize}
\item \textbf{Chapter 2: Background.} In this chapter, we go in further details on the main topics in this thesis and discuss their fundamentals. We introduce the formalism of Markov decision processes and explain the difference between model-based and model-free reinforcement learning algorithms. The machinery behind deep learning is then explained and the main building blocks of deep neural networks are illustrated. The chapter concludes with a discussion of the main representation learning methods.
\item \textbf{Chapter 3: Learning gradient-based ICA by neurally estimating mutual information.} This chapter discusses an adaption of independent component analysis (ICA) for DL. We introduce a novel application of a neural method for mutual information estimation to learn a representation with statistically independent features. The chapter is an adapted version of
\begin{itemize}
\item \bibentry{hlynsson2019learning} \citep{hlynsson2019learning}
\end{itemize}
\item \textbf{Chapter 4: Latent representation prediction networks.} This chapter discusses a method for manipulable environments for jointly learning a representation of observations and a model for predicting the next representation, given an action. We learn the representation in a self-supervised manner, without the need of a reward signal. We introduce a new environment that is akin to manipulating toy objects for a viewpoint matching task. The representation is combined with a graph-search algorithm to find the goal viewpoint. The chapter is an adapted version of
\begin{itemize}
\item \bibentry{hlynsson2020latent} \citep{hlynsson2020latent}
\end{itemize}
\item \textbf{Chapter 5: Reward prediction for representation learning and reward shaping.} This chapter discusses a self-supervised learning method to map high-dimensional inputs to a lower dimensional space for RL agents. We introduce a technique where a representation learned for a reward predictor is used to shape the reward for the agents. The chapter is an adapted version of
\begin{itemize}
\item \bibentry{hlynsson2021reward} \citep{hlynsson2021reward}
\end{itemize}
\item \textbf{Chapter 6: Comparison of our methods.} In this chapter, we directly compare the three different methods to state-of-the-art deep RL methods on four different environments: a visual pole-balancing environment, two goal-finding environment and an obstacle avoidance environment
\item \textbf{Chapter 7: Summary and conclusion.} This chapter closes the dissertation with a brief summary of the thesis, concluding remarks and possible future work.
The following work was also published over the course of the doctoral studies:
\begin{itemize}
\item \bibentry{hlynsson2019measuring} \citep{hlynsson2019measuring}
\end{itemize}
The paper compares supervised learning methods, but it is too dissimilar in topic from the rest of the work and is thus chosen to be omitted from this dissertation.
\end{itemize}
\section{Introduction}
\label{sec:larpintro}
Deeply-learned planning methods are often based on learning representations that are optimized for unrelated tasks. For example, they might be trained to reconstruct observations of the environment, such as the convolutional autoencoder from the previous chapter. These representations are then combined with predictor functions for simulating rollouts to navigate the environment. We propose to rather learn representations such that they are directly optimized for the task at hand: to be maximally predictable for the predictor function. This results in representations that are well-suited, by design, for the downstream task of planning, where the learned predictor function is used as a forward model.
While modern reinforcement learning algorithms reach super-human performance on tasks such as game playing, they remain woefully sample inefficient compared to humans. An algorithm that is data-efficient~\citep{hlynsson2019measuring} requires only few samples for good performance and the study of data-efficient control is currently an active research area \citep{corneil2018efficient, buckman2018sample,du2019good,saphal2020seerl}.
Dimensionality reduction is a powerful tool for increasing the data-efficiency of machine learning methods. There has been much recent work on methods that take advantage of compact, low-dimensional representations of states for search and exploration~\citep{kurutach2018learning, corneil2018efficient, xu2019regression}. One of the advantages of this approach is that a good representation aids in faster and more accurate planning.
This holds in particular when the latent space is of much lower dimensionality than the state space \citep{hamilton2014efficient}. For high-dimensional inputs, such as image data, a representation function is frequently learned to reduce the complexity for a controller.
In deep reinforcement learning, the representation and the controller are learned simultaneously. Similarly, a representation can in principle be learned along with a forward model for classical planning in high-dimensional space. We do this with our LARP network, which is a neural network-based method for learning a state representation and a transition function for planning within the learned latent space (Fig.~\ref{Conceptual1.pdf}).
\begin{figure}[htp]
\centering
\includegraphics[width=0.9\textwidth]{assets_png/Conceptual_simpler.pdf}
\caption[Illustration: Latent representation prediction network]{{\bf Conceptual overview of our method.} The important components are the representation network along with the predictor network. Together, they comprise a LARP network, which is utilized by a planning algorithm.}
\label{Conceptual1.pdf}
\end{figure}
During training, the representation and the predictor are learned simultaneously from transitions in a self-supervised manner. We train the predictor to predict the most likely future representation, given a current representation and an action. The predictor is then used for planning by navigating the latent space defined by the representation to reach a goal state.
Optimizing control in this manner, after learning an environment model, has the advantage of allowing for learning new reward functions in a fast and data-efficient manner.
After the representation is learned, we find said goal state by conventional path planning. Disentangling the reward from the transition function in such a way is helpful when learning for multiple or changing reward functions, and aids with learning when there is no reward available at all. Thus, it is also good for a sparse or a delayed-reward setting.
A problem that can arise in representation learning is the one of trivial features. This can happen when the method is optimizing an objective function that has a straightforward, but useless, solution. For example, Slow Feature Analysis (SFA) \citep{wiskott2002slow} has the objective of extracting the features of time series data that vary the least with time. This is easily fulfilled by constant functions, so SFA requires that the representations have a variance of $1$ -- which constant functions cannot fulfill.
Constant features would similarly be maximally predictable representations for our system. Therefore, we study three different approaches to prevent this trivial representation from being learned, we either: \textbf{(i)} design the architecture such that the output is sphered, \textbf{(ii)} regularize it with a contrastive loss term, or \textbf{(iii)} include a reconstruction loss term along with an additional decoder module.
We compare these approaches and validate our method experimentally on a visual environment: a viewpoint-matching task using the NORB data set \citep{lecun2004learning}, where the agent is presented with a starting viewpoint of an object and the task is to produce a sequence of actions such that the agent ends up with the goal viewpoint. As the NORB data set is embeddable on a cylinder \citep{hadsell2006dimensionality, schuler2018gradient} or a sphere \citep{wang2018toybox}, we can visualize the actions as traversing the embedded manifold. Our approach compares favorably to state-of-the-art methods on our test bed with respect to data-efficiency, but our asymptotic performance is still outclassed by other approaches.
\section{Related work}
\label{sec:larprelatedwork}
Most of the related work falls into the categories of reinforcement learning, visual planning, or representation learning. The primary difference between ours and other model-based methods is that the representation is learned by optimizing auxiliary objectives which are not directly useful for solving the main task.
\subsection{Reinforcement learning}
There are many works in the literature that also approximate the transition function of environments, for instance by performing explicit latent-space planning computations \citep{tamar2016value, gal2016improving, henaff2017model, srinivas2018universal, chua2018deep, hafner2019learning} as part of learning and executing policies. \cite{gelada2019deepmdp} train an RL agent to simultaneously predict rewards as well as future latent states. Our work is distinct from these, as we are not assuming a reward signal during training.
\cite{ha2018world} combine vision, memory, and controller for learning a model of the world before learning a decision model. A predictive model is trained in an unsupervised manner, permitting the agent to learn policies completely within its learned latent space representation of the environment. The main difference is that they first approximate the state distribution using a variational autoencoder, producing the encoded latent space. In contrast, our representation is learned such that it is maximally predictable for the predictor network.
Similar to our training setup, \cite{oh2015action} predict future frames in ATARI environments conditioned on actions. The predicted frames are used for learning the transition function of the environment, e.g. for improving exploration by informing agents of which actions are more likely to result in unseen states. Our work differs as we are acting within a learned latent space and not the full input space, and our representations are used in a classical planning paradigm with start and goal states instead of a reinforcement learning one.
\subsection{Visual planning}
We define visual planning as the problem of synthesizing an action sequence to generate a target state from an initial state, and all the states are observed as images. Variational State Tabulations~\citep{corneil2018efficient} learn a state representation in addition to a transfer function over the latent space. However, their observation space is discretized into a table using a variational approach, as opposed to our continuous representation. A continuous representation circumvents the problem of having to determine the size of such a table in advance or during training. Similarly, \cite{cuccu2018playing} discretize visual input using unsupervised vector quantization and use that representation for learning controllers for Atari games.
Inspired by classic symbolic planning, Regression Planning Networks \citep{xu2019regression} create a plan backward from a symbolic goal. We do not have access to high-level symbolic goal information for our method, and we assume that only high-dimensional visual cues are received from the environment.
Topological memories of the environment are built in Semi-parametric Topological Memories \citep{savinov2018semi} after being provided with observation sequences from humans exploring the environment. Nodes are connected if a predictor estimates that they are close. The method has problems with generalization, which are reduced in Hallucinative Topological Memories \citep{liu2020hallucinative}, where the method also admits a description of the environment, such as a map or a layout vector, which the agent can use during planning. Our visual planning method does not receive any additional information on unseen environments and does not depend on manual exploration during training.
Causal InfoGAN \citep{kurutach2018learning} and related methods \citep{wang2019learning} are based on generative adversarial networks (GANs) \citep{goodfellow2014generative}, inspired by InfoGAN in particular \citep{chen2016infogan}, for learning a plannable representation. A GAN is trained for encoding start and goal states, and they plan a trajectory in the representation space as well as reconstructing intermediate observations in the plan. Our method is different as it does not need to reconstruct the observations and the forward model is directly optimized for prediction.
\subsection{Prediction-based representation learning}
In Predictable Feature Analysis \citep{richthofer2015predictable}, representations are learned that are predictable by autoregression processes. Our method is more flexible and scales better to higher dimensions as the predictor can be any differentiable function.
Using the output of other networks as prediction targets instead of the original pixels is not new. The case where the output of a larger model is the target for a smaller model is known as knowledge distillation \citep{bucilua2006model, hinton2015distilling}. This is used for compressing a model ensemble into a single model. \cite{vondrick2016anticipating} learn to make high-level semantic predictions of future frames in video data. Given a current frame, a neural network predicts the representation of a future frame. Our approach is not constrained only to pretrained representations, we learn our representation together with the prediction network. Moreover, we extend this general idea by also admitting an action as the input to our predictor network.
\section{Materials and methods}
\label{sec:larpmethods}
In this work, we study different representations for learning the transition function of a partially observable MDP (POMDP) and propose a network that jointly learns a representation with a prediction model and apply it for latent space planning. We summarize here the different ingredients of the LARP network -- our proposed solution. More detailed descriptions will follow in later sections.
\textbf{Training the predictor network:} We use a two-stream fully connected neural network to predict the representation of the future state given the current state's representation and the action bridging those two states. The predictor module is trained with a simple mean-squared error term.
\textbf{Handling constant solutions:} The representation could be transferred from other domains or learned from scratch on the task. If the representation is learned simultaneously with an estimate of a Markov decision process's (MDP) transition function, precautions must be taken such that the prediction loss is not trivially minimized by a representation that is constant over all states. We consider three approaches for tackling the problem: sphering the output, regularizing with a contrastive loss term, and regularizing with a reconstructive loss term.
\textbf{Searching in the latent space:} Combining the representation with the predictor network, we can search in the latent space until a node is found that has the largest similarity to the representation of the goal viewpoint using a modified best-first search algorithm.
\textbf{NORB environment:} We use the NORB data set~\citep{lecun2004learning} for our experiments. This data set consists of images of objects
from different viewpoints, and we create viewpoint-matching tasks from the data set.
\subsection{On good representations}
We rely on heuristics to provide sufficient evidence for a good --- albeit not necessarily optimal --- decision at every time step to reach the goal. Here, we use the Euclidean distance in representation space: a sequence of actions is preferred if their end location is closest to the goal. The usefulness of this heuristics depends on how well and how coherently the Euclidean distance encodes the actual distance to the goal state in terms of the number of actions.
A learned predictor network approximates the transition function of the environment for planning in the latent space defined by some representation. This raises the question: what is the ideal representation for latent space planning? Our experiments show that an openly available, general-purpose representation, such as a pretrained VGG16 \citep{simonyan2014very}, can already provide sufficient guidance to apply such heuristics effectively. Better still are representation models that are trained on the data at hand, for example, uniform manifold approximation and projection (UMAP) \citep{mcinnes2018umap} or variational auto-encoders (VAEs) \citep{kingma2013auto}.
One might, however, ask what a particularly suited representation might look like when attainability is ignored. It would need to take the topological structure of the underlying data manifold into account, so that the Euclidean distance becomes a good proxy for the geodesic distance. One class of methods that satisfy this are spectral embeddings, such as Laplacian Eigenmaps (LEMs) \citep{belkin2003laplacian}. Their representations are smooth and discriminative which is ideal for our purpose. However, they do not easily produce out-of-sample embeddings, so they will only be applied in an in-sample fashion to serve as a control experiment, yielding optimal performance.
\subsection{Predictor network}
As the representation is used by the predictor network, we want it to be predictable. Thus, we optimize the representation learner simultaneously with the predictor network, in an end-to-end manner.
Suppose we have a representation map $\phi$ and a training set of $N$ labeled data tuples
$(X_t = [o_t, a_t], Y_t = o_{t+1})$, where $o_t$ is the observation at time step $t$ and $a_t$ is an action resulting in a state with observation $o_{t+1}$. We train the predictor $f$, parameterized by $\theta$, by minimizing the mean-squared error loss over $f$'s parameters:
\begin{equation}
\underset{\theta}{\text{argmin}} \ \mathcal{L}_{\text{prediction}}(\mathcal{D}, \theta) = \underset{\theta}{\text{argmin}} \ \frac{1}{N} \sum_{t=1}^N \big \Vert \phi(o_{t+1}) - f_\theta(\phi(o_t), a_t) \big \Vert ^2
\end{equation}
\noindent where $\mathcal{D} = \{ (X_t, Y_t) \}_{t=0}^N $ is our set of training data.
We construct $f$ as a two-stream, fully connected, neural network. Using this predictor we can carry out planning in the latent space defined by $\phi$. By planning, we mean that there is a start state with observation $o_{\text{start}}$ and a goal state with $o_{\text{goal}}$ and we want to find a sequence of actions connecting them.
The network outputs the expected representation after acting. Using this, we can formulate planning as a classical pathfinding or graph traversal problem.
\subsection{Avoiding trivial solutions}
In the case where $\phi$ is trainable and parameterized by $\eta$, the loss for the whole system that only cares about maximizing predictability is
\begin{equation}
\underset{\theta, \eta}{\text{argmin}} \ \mathcal{L}_{\text{prediction}}(\mathcal{D}, \theta, \eta) = \underset{\theta, \eta}{\text{argmin}} \ \frac{1}{N} \sum_{t=1}^N \left(\phi_\eta(o_{t+1}) - f_\theta(\phi_\eta(o_t), a_t) \right)^2
\label{uselessloss}
\end{equation}
for a given data set $\mathcal{D}$. With no constraints on the family of functions that $\phi$ can belong to, we run the risk that the representation collapses to a constant. Constant functions $\phi = c$ trivially yield zero loss for any set $\mathcal{D}$ if $f_\theta$ outputs the input state again for any $a$, i.e $f(\phi(\cdot), a) = \phi(\cdot)$:
Constant representations are optimal with respect to predictability, but they are unfortunately useless for planning, as we need to discriminate different states. This objective is not present in the proposed loss function in Eq.~\eqref{uselessloss} and we must thus add a constraint or another loss term to facilitate differentiating the different states.
There are several ways to limit the function space such that constant functions are not included, for example with decoder \citep{goroshin2015learning} or adversarial \citep{denton2017unsupervised} loss terms. In this work, we do this with \textbf{(i)} a sphering layer, \textbf{(ii)} a contrastive loss, or \textbf{(iii)} a reconstructive loss.
\subsubsection{(i) Sphering the output} The problem of trivial solutions is solved in SFA \citep{wiskott2002slow} and related methods \citep{escalante2013solve, schuler2018gradient} by constraining the overall covariance of the output to be $I$. Including this constraint to our setting yields the optimization formulation:
\begin{equation}
\begin{aligned}
& \underset{\eta, \theta}{\text{minimize}}
& & \mathcal{L}_{\text{prediction}}(\mathcal{D}, \theta, \eta) \\
& \text{subject to}
& & \mathbb{E}_{\mathcal{D}}\left[ \phi_\eta \right] \hspace{7pt}= 0 \hspace{47pt}\hspace{0.1em}\text{(zero mean)} \\
&&& \mathbb{E}_{\mathcal{D}}\left[ \phi_\eta\phi_\eta^T \right]= I\, \ \ \ \ \ \ \ \ \ \text{(unit covariance)} \\
\end{aligned}
\end{equation}
\noindent We enforce this constraint in our network via architecture design. The last layer performs differentiable sphering \citep{schuler2018gradient, hlynsson2019learning} of the second-to-last layer's output using the whitening matrix $\bm{W}$. We get $\bm{W}$ using power iteration of the following iterative formula:
\begin{equation}
\bm{u}^{[i+1]} = \frac{\bm{T}\bm{u}^{[i]}}{|| \bm{T}\bm{u}^{[i]} ||}
\end{equation}
\noindent
\noindent where the superscript $i$ tracks the iteration number and $\bm{u}^{[0]}$ can be an arbitrary vector. The power iteration algorithm
converges to the largest eigenvector $\bm{u}$ of a matrix $\bm{T}$ in a few hundred, quick iterations. The eigenvalue $\lambda$ is determined, and we subtract the eigenvector from the matrix:
\begin{equation}
\bm{T} \leftarrow \bm{T} - \lambda \bm{u} \bm{u}^T
\end{equation}
\noindent the process is repeated until the sphering matrix is found
\begin{equation}\bm{W} = \sum_{j=0} \frac{1}{\sqrt{\lambda_j}}\bm{u}_j \bm{u}_j^T
\end{equation}
\noindent The whole system, including the sphering layer, can be seen in Fig~\ref{spheringdiagram}, with an abstract convolutional neural network as the representation $\phi$ and a fully-connected neural network as the prediction function $f$.
\begin{figure}[htp]
\centering
\includegraphics[width=1.0\textwidth]{assets_png/Spherin4.pdf}
\caption[Illustration: Predictive representation learning with sphering regularization]{{\bf Predictive representation learning with sphering regularization.} The observations $o_t$, and the resulting observation $o_{t+1}$ after the action $a$ has been performed in $o_t$, are passed through the representation map $\phi$, whose outputs are passed to a differentiable sphering layer before being passed to $f$. The predictive network $f$ minimizes the loss function $\mathcal{L}$, which is the mean-squared error between $ \phi(o_t) = \rho_t$ and $ \phi(o_{t+1}) = \rho_{t+1}$.}
\label{spheringdiagram}
\end{figure}
\subsubsection{(ii) Contrastive loss} Constant solutions can also be dealt with in the loss function instead of via architecture design. \cite{hadsell2006dimensionality} propose to solve this with a loss function that pulls together the representation of similar objects (in our case, states that are reachable from each other with a single action) but pushes apart the representation of dissimilar ones:
\begin{equation}
L_{\text{contrastive}}{(o, o^{'} )} = \begin{cases} || \phi (o) - \phi(o^{'}) || & \text{if } o, o^{'} \text{ are similar} \\
\max(0, m - || \phi (o) - \phi(o^{'}) || ) & \text{otherwise} \end{cases}
\end{equation}
\noindent where $m$ is a margin and $|| \cdot||$ is some --- usually the Euclidean --- norm. The representation of dissimilar objects is pushed apart only if the inequality
\begin{equation}
|| \phi (o) - \phi(o^{'}) || < m
\end{equation}
is violated. During each training step, we compare each observation to a similar and a dissimilar observation simultaneously~\citep{schroff2015facenet} by passing a triplet of (positive, anchor, negative) observations during training to three copies of $\phi$. In our experiments, the positive corresponds to the predicted embedding of $o_{t+1}$ given $o_t$ and $a_t$, the anchor, is the true resulting embedding after an action $a_t$ is performed in state $o_t$ and $\phi(o_n)$, the negative, is the representation of an arbitrarily chosen observation that is not reachable from $\phi(o_t)$ with a single action. For environments where this is determinable, such as in our experiments, this can be assessed from the environment's full state. When this information isn't available, ensuring for $\phi(o_n)$ and $\phi(o_t)$ that $|n-t|>2$ is a good proxy, even though this can result in some incorrect triplets. For example, when the agent runs in a self-intersecting path.
We define the representation of the observation at time step $t$ as $\rho_t = \phi(o_t)$ and the next-step prediction $\Tilde{\rho}_{t+1} := f\left(\phi(o_t), a_t)\right)$ for readability and our (positive, anchor, negative) triplet is thus $\left(\Tilde{\rho}_{t+1}, \phi(o_{t+1}), \phi(o_n) \right)$ and we minimize the triplet loss:
\begin{equation}
\mathcal{L}_{\text{contrastive}}(o_t, o_{t+1}, o_n, a_t) = || \rho_{t+1} - \Tilde{\rho}_{t+1} || + \max(0, m - || \rho_{t+1} - \rho_n || )
\label{ourcontrastive}
\end{equation}
\noindent It would seem that $\rho _{t+1}$ and $\Tilde{\rho}_{t+1}$ are interchangeable, since the second term is included only to prevent the representation from collapsing into a constant. However, if the loss function is
\begin{equation}
\mathcal{L}_{\text{contrastive}}(o_t, o_{t+1}, o_n, a_t) = || \rho_{t+1} - \Tilde{\rho}_{t+1} || + \max(0, m - || \Tilde{\rho}_{t+1} - \rho_n || )
\label{badcontrastive}
\end{equation}
then the network is rewarded during training for making $f$ poor at predicting the next representation instead of simply pushing the representation of $o_{t}$ and $o_n$ away from each other.
There are two main ways to set the margin $m$, one is dynamically determining it per batch \citep{sun2014deep}. The other, which we choose, is constraining the representation to be on a hypersphere using $L_2$ normalization and setting a small constant margin such as $m = 0.2$ \citep{schroff2015facenet}. The architecture for the training scheme using the contrastive loss regularization is depicted in Fig.~\ref{contrastivefigure}.
\begin{figure}[htp]
\centering
\includegraphics[scale=.99]{assets_png/triplet6_1.pdf}
\caption[Illustration: Predictive representation learning with contrastive loss regularization]{ {\bf Predictive representation learning with contrastive loss regularization.} We minimize the contrastive loss function $\mathcal{L}_{\text{contrastive}}$ (Eq. \ref{ourcontrastive}). The predicted future representation $\Tilde{\rho}_{t+1}$ is pulled toward the next step's representation $\rho_{t+1}$. However, $\rho_{t+1}$ is pushed away from the negative state's representation $\rho_{n}$ if the distance between them is less than $m$. The observation $o_n$ is randomly selected from those that are not reachable from $o_{t}$ with a single action.}
\label{contrastivefigure}
\end{figure}
\subsubsection{(iii) Reconstructive loss} Trivial solutions are avoided by Goroshin et al. \citep{goroshin2015learning} by introducing a decoder network $D$ to a system that would otherwise converge to a constant representation. We incorporate this intuition into our framework with the loss function
\begin{align}
\label{decoderloss}
\mathcal{L}_{\text{decoder}} (o_{t}, o_{t+1}, a_t) = \mathcal{L}_{\text{prediction}}(o_{t},o_{t+1}) + \mathcal{L}_{\text{reconstruction}}(o_{t},o_{t+1}) \nonumber && \\
=\left( \rho_t - \Tilde{\rho}_{t+1}\right)^2 + \alpha \left(o_{t+1} - D \left( \Tilde{\rho}_{t+1} \right) \right) ^2 \hspace{12pt} && \text{}
\end{align}
\noindent where $\alpha$ is a positive, real coefficient to control the regularization strength. Fig.~\ref{decoderlossgraphic} shows how the models and loss functions are related during the training of the representation and predictor using both a predictive and a reconstructive loss term.
\begin{figure}[htp]
\centering
\includegraphics[scale=.99]{assets_png/decoder8.pdf}
\caption[Illustration: Predictive representation learning with decoder loss regularization] {{\bf Predictive representation learning with decoder loss regularization.} At the time step $t$, the observation $o_t$ is passed to the representation $\phi$. This produces $\rho_t$ which is passed, along with the action $a_t$ at time step $t$, to the predictor network $f$. This produces the predicted $\Tilde{\rho}_{t+1}$ which is compared to $\rho_{t+1} = \phi(o_{t+1})$ in the mean-squared error term $\mathcal{L}_\text{prediction}$. The prediction $\Tilde{\rho}_{t}$ is also passed to the decoder network $D$. We then compare $\Tilde{o}_{t+1} = D(\Tilde{\rho}_{t+1})$ with $o_{t+1}$ in $\mathcal{L}_\text{decoder}$, another mean-squared loss term. The final loss is the sum of these two loss terms $\mathcal{L}_\text{total} = \mathcal{L}_\text{prediction}+\mathcal{L}_\text{decoder}$.}
\label{decoderlossgraphic}
\end{figure}
The desired effect of the regularization can also be achieved by replacing the second term in Eq.~\eqref{decoderloss} with $\alpha \left( o_{t+1} - D \left( \rho_{t+1}\right) \right) ^2$. By doing this we would maximize the reconstructive property of the latent code in and of itself, which is not inherently useful for planning. We instead add an additional level of predictive power in $f$: in addition to predicting the next representation, its prediction must also be useful in conjunction with the decoder $D$ for reconstructing the new true observation.
This approach can have the largest computational overhead of the three, depending on the size of the decoder. We construct the decoder network $D$ such that it closely mirrors the architecture of $\phi$, with convolutions replaced by transposed convolutions and max-pooling replaced by upsampling.
\subsection{Training the predictor network}
We train the representation network and predictor network jointly by minimizing Eq.~(2), Eq.~(10) or Eq.~(12). The predictor network can also be trained on its own for a fixed representation map $\phi$. In this case, $f$ is tasked as before with predicting $\phi(o_{t+1})$ after the action $a_t$ is performed in the state with observation $o_t$ by minimizing the mean-squared error between $f(\phi(o_{t}), a_t)$ and $\phi(o_{t+1})$. The networks are built with Keras \citep{chollet2015keras} and optimized with rmsprop \citep{tieleman2012lecture}.
\subsection{Planning in transition-learned domain representation space}
We use a modified best-first search algorithm with the trained representations for our experiments (Algorithm \ref{algo: gs_algo}).
\begin{algorithm}[thb]
\caption{Perform a simulated rollout to find a state that is maximally similar to a goal state. Output a sequence to reach the found state from the start state.}\label{algo: gs_algo}
\begin{algorithmic}[1]
\REQUIRE $o_{\text{start}}$, $o_{\text{goal}}$, max trials $m$, action set $\mathcal{A}$, representation map $\phi$ and predictor function $f$
\ENSURE A sequence of actions $(a_0, \dots, a_n)$ connecting the start state to the goal state
\STATE Initialize the set $Q$ of unchecked representations with the representation of the start state $\phi(o_{\text{start}})$
\STATE Initialize the dictionary $\mathbb{P}$ of representation-path pairs with the initial representation mapped to an empty sequence: $\mathbb{P}[\phi(o_{\text{start}})]\leftarrow(\varnothing$)
\STATE Initialize the empty set of checked representations $C \leftarrow \varnothing$
\FOR{$k \leftarrow 0 \text{ to } m$}
\STATE Choose $\rho'$ $\leftarrow$ $\underset{\rho \in Q}{\text{argmin}} ||\rho - \phi(o_{goal}) ||$
\STATE Remove $\rho'$ from $Q$ and add it to $C$
\FORALL{actions $a \in \mathcal{A}$}
\STATE Get a new estimated representation $\rho^* \leftarrow f(\rho', a)$ and add it to the set Q
\STATE Concatenate $a$ to the end of $\mathbb{P}[p']$ and associate the resulting sequence with $\rho^*$ in the dictionary: $\mathbb{P}[\rho^*] \leftarrow \mathbb{P}[\rho'] ^\frown (a)$
\STATE
\ENDFOR
\ENDFOR
\STATE Find the most similar representation to the goal: $\rho_{\text{result}} \leftarrow \underset{\rho \in Q \cup C}{\text{argmin}} ||\rho - \phi(o_{goal}) ||$
\RETURN{the sequence $\mathbb{P}[\rho_{\text{result}}]$}
\end{algorithmic}
\end{algorithm}
From a given state, the agent performs a simulated rollout to search for the goal state. For each action, the initial observation is passed to the predictor function along with the action. This results in a predicted next-step representation, which is added to a set. The actions taken so far and resulting in each prediction are noted also. The representation that is closest to the goal (using for example the Euclidean distance) is then taken for consideration and removed from the set. This process is repeated until the maximum number of trials is reached. The algorithm then outputs the sequence of actions resulting in the predicted representation that is the closest to the goal representation.
To make the algorithm faster, we only consider paths that do not take us to a state that has already been evaluated,
even if there might be a difference in the predictions from going this roundabout way. That is, if a permutation of the actions in the next path to be considered is already in an evaluated path, it will be skipped. This has the same effect as transposition tables used to speed up search in game trees. Paths might be produced with redundancies, which can be amended with path-simplifying routines (e.g. take one step forward instead of one step left, one forward then one right).
We do Model-Predictive Control \citep{garcia1989model}, that is, after a path is found, one action is performed and a new path is recalculated, starting from the new position. Since the planning is possibly over a long time horizon, we might have a case where a previous state is revisited. To avoid loops resulting from this, we keep track of visited state-action pairs and avoid an already chosen action for a given state.
\subsection{NORB viewpoint-matching experiments}
For our experiments, we create an OpenAI Gym environment based on the small NORB data set \citep{lecun2004learning}. The code for the environment is available at https://github.com/wiskott-lab/gym-norb and requires the pickled NORB data set hosted at https://s3.amazonaws.com/unsupervised-exercises/norb.p. The data set contains 50 toys, each belonging to one of five categories: four-legged animals, human figures, airplanes, trucks, and cars. Each object has stereoscopic images under six lighting conditions, 9 elevations, and 18 azimuths (in-scene rotation). In all of the experiments, we train the methods on nine car class toys, testing on the other toys.
Each trial in the corresponding RL environment revolves around a single object under a given lighting condition. The agent is presented with a start and a goal viewpoint of the object and transitions between images until the current viewpoint matches the goal where each action operates the camera. To be concrete, the actions correspond to turning a turntable back and forth by $20^{\circ}$, moving the camera up or down by $5^{\circ}$ and, in one experiment, changing the lighting. The trial is a success if the agent manages to change viewpoints from the start position until the goal viewpoint is matched in fewer than twice the minimum number of actions necessary.
We compare the representations learned using the three variants of our method to five representations from the literature, namely \textbf{(i)} Laplacian Eigenmaps \citep{belkin2003laplacian}, \textbf{(ii)} the second-to-last
layer of VGG16 pretrained on ImageNet \citep{deng2009imagenet}, \textbf{(iii)} UMAP embeddings \citep{mcinnes2018umap}, \textbf{(iv)} convolutional encoder \citep{masci2011stacked} and \textbf{(v)} VAE codes \citep{kingma2013auto}. As fixed representations do not change throughout the training, they can be saved to disk, speeding up the training. As a reference, we consider three reinforcement learning methods working directly on the input images: \textbf{(i)} Deep Q-Networks (DQN)~\citep{mnih2013playing}, \textbf{(ii)} Proximal Policy Optimization (PPO)~\citep{schulman2017proximal} and \textbf{(iii)} World Models~\citep{ha2018world}.
The data set is turned into a graph for search by setting each image as a node and each viewpoint-changing action as an edge. The task of the agent is to transition between neighboring viewing angles until a goal viewpoint is reached. The total number of training samples is fixed at 25600. For our method, a sample is a single ($o_t$, $o_{t+1}$, $a_t$) triplet to be predicted while for the regular RL methods it is a ($o_t$, $o_{t+1}$, $a_t$, $\rho_t$) tuple.
\subsection{Model architectures}
\subsubsection{Input} The network $\phi$ encodes the full NORB input, a $96 \times 96$ pixel grayscale image, to lower-dimensional representations. The system as a whole receives the image from the current viewpoint, the image of the goal viewpoint and a one-hot encoding of the taken action. The image inputs are converted from integers ranging from 0 to 255 to floating point numbers ranging from 0 to 1.
\subsubsection{Representation learner $\phi$ architecture} We use the same architecture for the $\phi$ network in all of our experiments except for varying the output dimension, Table~\ref{table:phiarchiteture}.
\begin{table}[htb]\begin{center}
\caption[Result: LARP representation network architecture]{{\bf Representation network architecture.}}
\label{table:phiarchiteture}
\begin{tabular}{l r r r l r}
Layer & Filters / Units & Kernel size & Strides & Output shape & Activation \\ [0.5ex]
\hline \hline
Input & & & & (96, 96, 1) & \\
\cline{1-6}
Convolutional & 64 & $5 \times 5$ & $2 \times 2$ & (45, 45, 64) & ReLU \\
\cline{1-6}
\cline{1-5} Max-pooling & & & $2 \times 2$ & (22, 22, 64) & \\
\cline{1-6} Convolutional & 128 & $5 \times 5$ & $2 \times 2$ & (9, 9, 128) & ReLU \\
\cline{1-6} Flatten & & & & (10368) & \\
\cline{1-6} Dense & 600 & && (600) & ReLU \\
\cline{1-6} Dense & \#Features& && (\# Features) & Linear \\
\end{tabular}
\end{center}\end{table}
\subsubsection{Regularizing decoder architecture $D$} The decoder network $D$ has the architecture listed in Table~\ref{table:decoder}. It is designed to approximately inverse each operation in the original $\phi$ network.
\begin{table}[htb]
\begin{center}
\caption[Result: LARP regularizing decoder architecture]{{\bf Regularizing decoder architecture.} The upsampling layer uses linear interpolation, BN stands for Batch Normalization and CT stands for Convolutional Transpose. }
\label{table:decoder}
\begin{tabular}{l r r r r l }
Layer & Filters / Units & Kernel Size & Strides & Output shape & Activation \\ [0.5ex]
\hline \hline
Input & & &&(\# Features) & \\
\cline{1-6}
Dense & 512 & &&(512) & ReLU\\
\cline{1-6}BN & & & & (512) & \\
\cline{1-6} Dense & 12800 & &&(12800) &ReLU\\
\cline{1-6} BN & & & & (12800) & \\
\cline{1-6} Reshape & & & & (10, 10, 128) & \\
\cline{1-6} CT & 128 & $5 \times 5$ & $2 \times 2$ & (23, 23, 128) & ReLU \\
\cline{1-6} Upsampling & & & $2 \times 2$ & (46, 46, 128) &\\
\cline{1-6} BN & & &&(46, 46, 128) &\\
\cline{1-6} CT & 64 & $5 \times 5$ & $2 \times 2$ & (95, 95, 64) & ReLU\\
\cline{1-6} BN & & & & (95, 95, 64) & \\
\cline{1-6} CT & 1 & $2 \times 2$ & $1 \times 1$ & (96, 96, 1) & Sigmoid \\
\end{tabular}
\end{center}
\end{table}
\subsubsection{Predictor network $f$} The predictor network $f$ is a two-stream dense neural network. Each stream consists of a dense layer with a rectified linear unit (ReLU) activation, followed by a batch normalization (BatchNorm) layer. The outputs of these streams are then concatenated and passed through 3 dense layers with ReLU activations, each one followed by a BatchNorm, and then an output dense layer, see Table \ref{table:predictornet}.
\begin{table}[htb]
\begin{center}
\caption[Result: LARP representation predictor architecture]{{\bf Represention predictor architecture.} The $\phi$ stream receives the representation as input and the $A$ stream receives the one-hot action as input. Both streams are processed in parallel and then concatenated, with each operation applied from top to bottom sequentially. The number of hidden units in the last layer depends on the chosen dimensionality of the representation.}
\label{table:predictornet}
\begin{tabular}{l r r l}
Layer & Filters / Units & Output shape & Activation \\ [0.5ex]
\hline \hline
\ \ \ \ $\phi$ Stream: Input & & (\# Features) & ReLU\\
\cline{1-4}
\ \ \ \ $\phi$ Stream: Dense & 256 & (256) & ReLU\\
\cline{1-4}\ \ \ \ $\phi$ Stream: Batch Normalization & & (256) & \\
\cline{1-4}\ \ $A$ Stream: Input & & (\# Actions) & ReLU\\
\cline{1-4}\ \ $A$ Stream: Dense & 128 &(128)& ReLU\\
\cline{1-4}\ \ $A$ Stream: Batch Normalization & & (128) & \\
\cline{1-4} Concatenate $\phi$ and $A$ streams & & (384) & \\
\cline{1-4} Dense & 256 & (256) & ReLU \\
\cline{1-4} Batch Normalization & & (256) & \\
\cline{1-4} Dense & 256 & (256) & ReLU \\
\cline{1-4} Batch Normalization & & (256) & \\
\cline{1-4} Dense & 128 & (128) & ReLU \\
\cline{1-4} Batch Normalization & & (128) & \\
\cline{1-4}Dense & \# Features & (\# Features) & Linear \\
\end{tabular}
\end{center}
\end{table}
\section{Results}
\label{larpresults}
With our empirical evaluation, we aim to answer the following research questions:
\begin{enumerate}
\item (Monotonicity) Is the Euclidean distance between a
suitable representation and the goal representation decreasing as the number of actions that separate them decreases?
\item (Trained predictability) Is training a representation for predictability, as proposed, feasible?
\item (Dimensionality) What is the best dimensionality of the latent space for our planning tasks?
\item (Solution constraints) In terms of planning performance, what are promising constraints to place on the representation to avoid trivial solutions?
\item (Benchmarking) How does planning with LARP compare to other methods from the RL literature?
\item (Generalization) How well does our method generalize to unseen environments?
\end{enumerate}
we will refer to these research questions by number below as they get addressed.
\subsection{Latent space visualization}
When the representation and predictor networks are trained, we apply Algorithm \ref{algo: gs_algo} to the viewpoint-matching task. As described above, the goal is to find a sequence of actions that connects the start state to the goal state, where the two states differ in their configurations.
To support the qualitative analysis of the latent space, we plot heatmaps of similarity between the goal representation and the predicted representation of nodes during search (Fig~\ref{fig:lem_matching}). Of the 10 car toys in the NORB data set, we randomly chose 9 for our training set and test on the remaining one.
\subsubsection{In-sample embedding: Laplacian Eigenmaps}
\label{sec:in_sample}
First, we consider research question 1 (monotonicity). In order to get the best-case representation, we embed the toy using Laplacian Eigenmaps. Embedding a single toy in three dimensions using Laplacian Eigenmaps results in a tube-like embedding that encodes both elevation and azimuth angles, see Fig \ref{fig:azimuth_cylinder}. Three dimensions are needed so that the cyclic azimuth can be embedded correctly as $\sin(\theta)$ and $\cos(\theta)$.
{
\captionsetup{aboveskip=-13pt}
\begin{figure}[htp]
\centering
\subcaptionbox*{}{\includegraphics[width=0.35\linewidth]{assets_png/merlin/current_azimuth_0202.png}}
\hspace{-1.cm}
\subcaptionbox*{}{\includegraphics[width=0.35\linewidth]{assets_png/merlin/current_azimuth_0002.png}}
\hspace{-1.cm}
\vspace{-0.45cm}
\subcaptionbox*{}{\includegraphics[width=0.35\linewidth]{assets_png/merlin/current_azimuth_-202.png}}
\vspace{5mm}
\subcaptionbox*{}{\includegraphics[width=0.35\linewidth]{assets_png/merlin/current_elevation_0202.png}}
\hspace{-1.cm}
\subcaptionbox*{}{\includegraphics[width=0.35\linewidth]{assets_png/merlin/current_elevation_0002.png}}
\hspace{-1.cm}
\subcaptionbox*{}{\includegraphics[width=0.35\linewidth]{assets_png/merlin/current_elevation_-202.png}}
\vspace{5mm}
\caption[Result: Laplacian Eigenmap representation space of a NORB toy]{{\bf Laplacian Eigenmap representation space of a NORB toy.} The three-dimensional Laplacian Eigenmaps of a toy car where elements with the same azimuth values have the same color (top) and where elements with the same elevation values have the same color (bottom). Euclidean distance is a good proxy for geodesic distance in this case.}
\label{fig:azimuth_cylinder}
\end{figure}
}
If the representation is now used to train the predictor, one would expect that the representation becomes monotonically more similar to the goal representation as the state moves toward the goal. In Fig \ref{fig:lem_matching} we see that this is the case and that this behavior can be effectively used for a greedy heuristics. While the monotonicity is not always exact due to errors in the prediction, Fig \ref{fig:lem_matching} still qualitatively illustrates a best-case scenario.
\begin{figure}[htp]
\centering
\captionsetup{width=1.0\linewidth}
\resizebox*{1. \textwidth}{!}{\includegraphics
{assets_png/merlin/lem.pdf}}
\caption[Result: Heatmap of Laplacian eigenmap latent space similarity]{
{\bf Heatmap of Laplacian Eigenmap latent space similarity.} Each pixel displays the difference between the predicted representation and the goal representation. Only the start and goal observations are given. The blue dot shows the start state, green the goal, and purple the solution state found by the algorithm.
The search algorithm can rely on an almost monotonically decreasing Euclidean distance between each state's predicted representation and the goal's representation to guide its search.
}
\label{fig:lem_matching}
\end{figure}
We conclude from this that, for a suitable representation, the Euclidean distance between a current representation and the goal representation is monotonically increasing as a function of the number of actions that separate them. This supports the use of a prediction-based latent space search for planning.
\subsubsection{Out-of-sample embedding: pretrained VGG16 representation}
Next, we consider the pretrained representation of the VGG16 network to get a representation that generalizes to new objects. We train the predictor network and plot the heat map of the predicted similarity between each state and the goal state, beginning from the start state, in Fig~\ref{fig:allinone}.
\begin{figure}[htp]
\centering
\captionsetup{width=1.0\linewidth}
\resizebox*{1. \textwidth}{!}{\includegraphics
{assets_png/lem2.pdf}}
\caption[Result: Heatmap of VGG16 latent space similarity]{
{\bf Heatmap of VGG16 latent space similarity.} The predictor network estimates the VGG16 representation of the resulting states as the object is manipulated.
\textbf{(a)} The goal lies on a hill containing a maximum of representational similarity. \textbf{(b)} The accumulated errors of iterated estimations cause the algorithm to plan a path to a wrong state with a similar shape.
}
\label{fig:allinone}
\end{figure}
The heat distribution in this case is more noisy. To get a view of the expected heat map profile, we average several figures of this type to show basins of attraction during the search. Each heat map is shifted such that the goal position is at the bottom, middle row (Fig~\ref{fig:all_seismic.png}, a).
Here, it is obvious that the goal and the $180^{\circ}$ flipped (azimuth) version of the goal are attractor states. This is due to the representation map being sensitive to the rough shape of the object, but being unable to distinguish finer details. In (Fig~\ref{fig:all_seismic.png}, b) we display an aggregate heat map when the agent can also change the lighting conditions.
Our visualizations show a gradient toward the goal state in addition to visually similar far-away-states, sometimes causing the algorithm to produce solutions that are the polar opposite of the goal concerning the azimuth. Prediction errors also prevent the planning algorithm from finding the exact goal for every task, even if it is not distracted by the polar-opposite.
\begin{figure}[htp]
\centering
\captionsetup{width=.97\linewidth}
\resizebox*{1. \textwidth}{!}{\includegraphics
{assets_png/new_map.png}}
\caption[Result: Aggregate heat maps of VGG16 representation similarities on test data]{ {\bf Aggregate heat maps of VGG16 representation similarities on test data.} The data is collected as the state space is searched for a matching viewpoint. The pixels are arranged according to their elevation and azimuth difference from the goal state at $(0^{\circ}, 0^{\circ})$ on the left and $(0^{\circ}, 0^{\circ}, 0^{\circ})$ on the right.
\textbf{(a)} We see clear gradients toward the two basins of attraction. There is less change along the elevation due to less change at each step. \textbf{(b)} The agent can also change the lighting of the scene, with qualitatively similar results. In this graphic we only measure the absolute value of the distance.
}
\label{fig:all_seismic.png}
\end{figure}
To investigate the accuracy of the search with respect to each dimension separately, we plot the histogram of distances between the goal states and the solution states in Fig~\ref{fig:allinone_histos.png}. The goal and start states are chosen randomly, with the restriction that the azimuth distance and elevation distance between them are each uniformly sampled. For the rest of the chapter, all trials follow this sampling procedure. The results look less accurate for elevation than azimuth because the elevation changes are smaller than the azimuth changes in the NORB data set. The difference between the goal and solution viewpoints in Fig~\ref{fig:allinone} left, for example, is hardly visible. If one would scale the histograms by angle and not by bins, the drop-off would be similar.
\begin{figure}[htp]
\centering
\includegraphics[width=1.\textwidth]{assets_png/allinone_histos2.png}
\caption[Result: Histograms of elevation-wise and azimuth-wise VGG16 errors]{ {\bf Histograms of elevation-wise and azimuth-wise VGG16 errors.} The histograms display the counts of the distance between goal and solution states along elevation (left) and azimuth (right) on test data. The distance between the start and goal viewpoints is equally distributed across all the trials, along both dimensions. The goal and the $180^{\circ}$ flipped (azimuth) version of the goal are attractor states.
}
\label{fig:allinone_histos.png}
\end{figure}
\subsection{Latent space dimensionality}
With the next experiment, we aim to answer research question 2 (trained predictability). While tuning the details of the design, we also tackle research questions 3 (dimensionality) and 4 (solution constraints).
We do an ablation study of the dimensionality of the representation for our method (Table~\ref{featuresablation}). The test car is an unseen car toy from the NORB data set, and the train car comes from the training set.
\begin{table}[h]
\begin{center}
\captionof{table}[Result: Ablation study of the representation dimensionality]{{\bf Ablation study of the representation dimensionality.} We change the output dimension of the representation learner subnetwork and compare it to the VGG16 representation trained on ImageNet. The performance (mean success rate) is averaged over ten separate instantiations of our systems, where each instance is evaluated on a hundred trials of the viewpoint-matching task. A trial is a success if the goal is reached by taking less than twice the minimum number of actions needed to reach it. The standard deviations range between 0.1 and 0.3 for each table entry.}
\label{featuresablation}
\begin{tabular}{l r r r r}
Representation & Dimensions & Training Car ($\%$) & Test Car ($\%$) \\ [0.2ex]
\hline\\[-2.5ex]LARP (Contrastive) & 96 &59.3& 56.8 \\
& 64 & 64.1& 60.5\\
& 32&72.3& 59.4 \\
& 16 &74.1& 59.3 \\
& 8& 82.7& 58.0 \\ [0.1ex]
\hline\\[-2.5ex]LARP (Sphering) & 96 & 41.1& 37.8 \\
& 64& \textbf{93.9}&53.7 \\
& 32& 89.8 & 51.9 \\
&16&85.2&42.6 \\
& 8 &85.1 & 40.1 \\ [0.1ex]
\hline\\[-2.5ex]LARP (Decoder) & 96& 58.0 &51.9 \\
& 64& 79.5 & \textbf{63.0} \\
& 32 & 77.8 & 61.7\\
& 16 &51.9 & 45.2 \\
& 8 &51.1 & 42.4 \\ [.1ex]
\hline\\[-2.5ex]VGG16 & 902 & 62.4 & 55.1 \\ [.1ex]
\hline\\[-2.5ex]Random Steps & & 3.5 & 3.5 \\ [1ex]
\end{tabular}
\end{center}\end{table}
There is no clear winner: the network with the sphering layer does the best on one of the cars used during training, while the reconstructive-loss network does the best on the held-out test car. The sharp difference in performance between 64 and 94 sphering-regularized representation can be explained by the numerical instability of the power iteration method for too large matrix dimensions.
The VGG16 representation is not the highest performer on any of the car toys. Many of VGG16's representation values are 0 for all images in the NORB data set, so we only use those that are nonzero for any of the images. We suggest that this high number of dead units is due to the representation being too general for the task of manipulating relatively homogenous objects. Another drawback of using pretrained networks is that information might be encoded that is unimportant for the task. This has the effect that our search method is not guaranteed to output the correct solution in the latent space, as there might be distracting pockets of local minima.
The random baseline has an average success rate of 3.5$\%$, which is very clearly outperformed by our method. As 64 is the best dimensionality for the representation on average, we continue with that number for our method in the transfer learning experiment.
We conclude that the proposed method of training a representation for predictability is feasible. So far we have evidence that 64 is the best dimensionality of the representation's latent space for our planning tasks. However, it is not yet conclusive what the best restriction is to place on the representation to avoid the trivial solution, in terms of planning performance.
\subsection{Comparison with other RL methods}
Now we divert our attention to research question 5 (benchmarking), where we compare our method to the literature.
For the comparison with standard RL methods, we use the default configurations of the model-free methods DQN and PPO as defined in OpenAI Baselines~\citep{baselines}. Our model-based comparison is chosen to be world models \citep{ha2018world} from https://github.com/zacwellmer/WorldModels. We make sure that the compared RL methods are similar to our system in terms of the number of parameters as well as architecture layout and compare them with our method on the car viewpoint-matching task.
The task setup is the same as before and is converted to an OpenAI gym environment: a start observation and a goal observation are passed to the agent. If the agent manages to reach it within 2 times the minimum number of actions required (the minimum number is calculated by the environment), the agent receives a reward and the task is considered a success. Otherwise, no reward is given.
The results of the comparison can be viewed in Fig.~\ref{fig:rlfigs}. Each point in the curve contains each method's mean success rate: the average of the cumulative reward from 100 test episodes from 5 different instantiations of the RL learner, so it is the average reward over 500 episodes in total. The test episodes are done on the same environment as is used for training, except that the policy is maximally exploiting and minimally exploring.
\begin{figure}[htp]
\centering
\subfloat[{\bf DQN performance.}]{{\includegraphics[width=.343\linewidth, angle=90]{assets_png/dqn_x_meansucc3.pdf}}}
\qquad
\hspace{-4em}
\subfloat[{\bf PPO performance.}]{{\includegraphics[width=.343\linewidth, angle=90]{assets_png/ppox_2_meansucc2.pdf}}}
\qquad
\subfloat[{\bf World models performance.}]{{\includegraphics[width=.343\linewidth, angle=90]{assets_png/wm_meansucc2.pdf}}}
\qquad
\hspace{-3em}
\qquad
\hspace{-5em}
\caption[Result: LARP reinforcement learning comparison]{{\bf Reinforcement learning comparison.} The vertical dashed lines indicate when the compared algorithm has processed the same number of transitions as our method and the horizontal dotted line indicates the test performance of our method. Each data point is the mean success rate of 100 test episodes after a varying number of training steps, averaged over 5 different seeds of each learner. The model-free methods in {\bf(a)} and {\bf(b)} train the representation and the controller simultaneously by acting in the environment and collecting new experiences. The representation in {\bf(c)} is trained on 25.6k transitions, which is the same number we use. The plot shows the optimization curve for the controller, using a Covariance-Matrix Adaptation Evolution Strategy, which hardly improves after 500 or so training steps. The horizontal line starts at 0 for world models because the representation has finished training on the observations before the controller is optimized. }
\label{fig:rlfigs}
\end{figure}
In our experiments, the DQN networks are much more sample inefficient than PPO, which in turn is more sample inefficient than our method. However, our method is more time-consuming during test time. We require a forward pass of the predictor network for each node that is searched before we take the next step, which can grow rapidly if the target is far away. In contrast, only a single pass through the traditional RL networks is required to compute the next action.
Our method reaches $93.9\%$ success rate on the train car (Table~\ref{featuresablation}) using 25.6k samples, but the best PPO run only reaches $70.5\%$ after training on the same number of samples. The best single PPO run needed 41.3k samples to get higher than $93.9\%$ success rate, and the average performance is higher than $93.9\%$ at around 55k samples. After that, some PPO learners declined again in performance. The world models policy quickly reaches the same level of performance as DQN got after 50k steps and PPO after approximately 8k steps, but it doesn't improve beyond that.
\begin{figure}[htp]
\centering
\subfloat[ {\bf} ]
{{\includegraphics[width=5.05cm]{assets_png/obstacles_checkerboard.pdf}}}
\qquad
\hspace{-1.5em}
\subfloat[{\bf} ]
{{\includegraphics[width=9.53cm]{assets_png/retrain.pdf} \vspace{-1.0em}}}
\caption[Result: LARP re-training after placing obstacles in a checkerboard pattern]{{\bf Re-training after placing obstacles in a checkerboard pattern.} {\bf (a)} The task is the same as before, but nothing happens if the agent attempts to move to a state containing a black rectangle. {\bf (b)} After training the agents, we re-tested them after we introduced the checkerboard pattern of obstacles. Our method does not allow for re-training in the new environment.}
\label{fig:checkz}
\end{figure}
We conclude that our method compares favorably to other methods from the RL literature in terms of data-efficiency.
\subsection{Modifying the environment}
We now modify the environment to answer research question 6 (generalization). To see how the methods compare when obstacles are introduced to the environment, we repeat the trial on one of the car objects except that the agent can no longer pass through states whose elevation values are divisible by 10 and azimuth values are divisible by 40 (Fig.~\ref{fig:checkz}, (a)).
As before, the goal and start locations can have any azimuth-elevation pair, but the agent cannot move into states with the properties indicated by the black rectangle. Every action is available to the agent at all locations as before, but the agent's state is unchanged if it attempts to move to a state with a black rectangle.
We trained LARP using the contrastive loss, PPO, and DQN agents until they reached $80\%$ accuracy on our planning task and then tested them with the added obstacles.
Our method loses about $10\%$ performance, but PPO loses $50\%$. Nevertheless, we can continue training PPO until it quickly reaches top performance again (Fig.~\ref{fig:checkz}, (b)). Our method is not re-trained for the new task, and DQN did not reach a good performance again in the time we allotted for re-training.
Thus, we see that our method is quite flexible and generalizes well when obstacles are introduced to the environment.
\subsection{Transfer to dissimilar objects}
We now consider research question 6 (generalization) further by investigating how well our method transfers knowledge from one domain to another.
Selecting the best dimensionality for the representation from the previous set of experiments, we investigate further their performance in harder situations using unseen, non-car objects. The models are trained on the same car objects as in the previous experiment, but they are tested on an array of different plastic soldiers: a kneeling soldier holding a bazooka, a standing soldier with a rifle, a Native American with a bow and spear and a cowboy with a rifle (Fig.~\ref{fig:merge4.png}).
\begin{figure}[htp]
\centering
\captionsetup{width=1\linewidth}
\resizebox*{1. \textwidth}{!}{\includegraphics
{assets_png/merge4.png}}
\caption[Example: Toys for transfer learning experiments]{ {\bf Toys for transfer learning experiments.} From left to right: Soldier (Kneeling), Soldier (Standing), Native American with Bow and Cowboy with Rifle.
}
\label{fig:merge4.png}
\end{figure}
\subsubsection{Qualitative results}
We offer a visualization of the learned representation of the kneeling soldier toy using our method, a convolutional encoder, and VGG16 in Fig.~\ref{fig:4apics}. Each embedding was reduced to 2 dimensions using t-SNE.
Every method structures the domain similarly. In the bottom row, we see that the largest clusters for all methods are the ones with the highest (teal dots) illumination settings, which is explained by the effect of the lighting on the pixel value intensities. Within these clusters, we see clustering based on the azimuth (middle row). Finally, within these clusters, there is a gradient structure based on elevation (top row). This is due to the elevation changing in smaller step-sizes, with 5 degree differences, than azimuth with 20 degree differences.
\begin{figure}[htp]
\captionsetup[subfigure]{justification=centering,singlelinecheck=false}
\begin{subfigure}{0.3333\textwidth}
\includegraphics[width=\linewidth]{assets_png/larp_Elevation_TSNE.pdf}
\caption{LARP elevation t-SNE} \label{fig:1picsa}
\end{subfigure}
\hspace{-2em}
\begin{subfigure}{0.3333\textwidth}
\includegraphics[width=\linewidth]{assets_png/cae_Elevation_TSNE.pdf}
\caption{CAE elevation t-SNE} \label{fig:2picsb}
\end{subfigure}
\hspace{-2em}
\begin{subfigure}{0.3333\textwidth}
\includegraphics[width=\linewidth]{assets_png/vgg_Elevation_TSNE.pdf}
\caption{VGG16 elevation t-SNE} \label{fig:3picsb}
\end{subfigure}
\smallskip
\begin{subfigure}{0.33\textwidth}
\includegraphics[width=\linewidth]{assets_png/larp_Azimuth_TSNE.pdf}
\caption{LARP azimuth t-SNE} \label{fig:4picsa}
\end{subfigure}
\hspace{-2em}
\begin{subfigure}{0.3333\textwidth}
\includegraphics[width=\linewidth]{assets_png/cae_Azimuth_TSNE.pdf}
\caption{CAE azimuth t-SNE} \label{fig:5picsb}
\end{subfigure}
\hspace{-2em}
\begin{subfigure}{0.3333\textwidth}
\includegraphics[width=\linewidth]{assets_png/vgg_Azimuth_TSNE.pdf}
\caption{VGG16 azimuth t-SNE} \label{fig:6picsb}
\end{subfigure}
\smallskip
\begin{subfigure}{0.33\textwidth}
\includegraphics[width=\linewidth]{assets_png/larp_Lighting_TSNE.pdf}
\caption{LARP lighting t-SNE} \label{fig:7picsc}
\end{subfigure}
\hspace{-0.5em}
\begin{subfigure}{0.33\textwidth}
\includegraphics[width=\linewidth]{assets_png/cae_Lighting_TSNE.pdf}
\caption{CAE lighting t-SNE} \label{fig:8picsd}
\end{subfigure}
\hspace{-0.6em}
\begin{subfigure}{0.33\textwidth}
\includegraphics[width=\linewidth]{assets_png/vgg_Lighting_TSNE.pdf}
\caption{VGG16 lighting t-SNE}
\label{fig:9picsb}
\end{subfigure}
\captionsetup{margin=0cm}
\caption[Result: LARP Latent space visualization]{ \textbf{Latent space visualization.} The clustering structure of a toy soldier embedding after dimensionality reduction with t-SNE. The top row colors the samples by elevation, the middle row by azimuth and the bottom one by lighting. The left column is the embedding given by our method using the contrastive loss term, the middle by a convolutional autoencoder (CAE), and the right by a pretrained VGG16 network.} \label{fig:4apics}
\end{figure}
\subsubsection{Quantitative results}
Our experiments include the pretrained VGG16 network because we believe that a flexible algorithm should rather be based on a generic multi-purpose-representation and not on a specific representation. To our surprise, it is outperformed by our approach on every object, even as the viewpoint-matching task is done on objects that are different from the original car toys they are trained on.
We also try transfer learning a VAE and a convolutional encoder using the same network as our representation and a UMAP embedding, with 64 features each. We display the results of the same viewpoint-matching tasks as before using these different representations on the unseen army figures in Table~\ref{moretesttoys}. Convolutional encoders have the lowest performance out of all the methods, but the VAE representation has the most similar performance to our own representations.
\begin{table}\begin{center}
\caption[Result: LARP transfer learning performance]{ {\bf Transfer learning performance.} The methods are trained on the data set of different car images, and then their performance on dissimilar toys is tested. Each number is the mean success rate of viewpoint matching out of 1000 trials.}
\label{moretesttoys}
\begin{tabular}{ l r r r r | r l}
Representation & Soldier & Soldier & Native American & Cowboy &
\\ [0.5ex]
& (Kneeling) & (Standing) & with Bow & with Rifle & Mean \\ [0.5ex]
\hline
LARP (Contrastive) & \textbf{22.7} & 11.1 & 12.1 & \textbf{20.7} & \textbf{16.7}\\
LARP (Sphering) & 18.4 & 15.3& \textbf{15.2} & 15.8& 16.2\\
LARP (Decoder) & 14.3 & \textbf{16.6} & 14.7 & 15.6 & 15.3\\
VAE & 14.4 & 13.1 & 13.6 & 13.8 & 13.7\\
VGG16 & 12.3 & 12.9 & 11.8 & 13.6 & 12.7\\
UMAP & 8.6 & 10.8 & 9.7 & 11.1 & 10.1\\
Conv. Encoder & 4.9 & 14.3 & 11.5 & 6.4 & 9.3 \\
\end{tabular}\end{center}\end{table}
Our representation is better than the others for this experiment. But we see that the performance of our method drops significantly as we attempt generalizing to different objects with changed input statistics.
Note that even though the representation clustering (Fig.~\ref{fig:4apics}) was more clear-cut using convolutional encoders and VGG, compared to ours, they did not perform as well in the trials. We attribute this to the fact that the main loss term in our representation was the one of future state predictability, which may not give as clear of a structure in two dimensions as a representation that is trained only for static image reconstruction.
\section{Conclusion}
\label{larpdiscussion}
In this chapter, we present Latent Representation Prediction (LARP) networks with applications to visual planning. We jointly learn a model to predict transitions in Markov decision processes with a representation trained to be maximally predictable. This allows us to accurately search the latent space defined by the representation using a heuristic graph traversal algorithm. We validate our method on a viewpoint-matching task derived from the NORB data set, and we find that a representation that is optimized jointly with the predictor network performs best in our experiments.
A common issue of unsupervised representation learning is one of trivial solutions: a constant representation which optimally solves the unsupervised optimization problem but brings across no information. To avoid the trivial solution, we constrain the training by introducing a sphering layer or a loss term that is either contrastive or reconstructive. Any of these approaches will do the job of preventing the representations from collapsing to constants, and none of them displays stronger performance than the others in our experiments.
Our LARP representation is competitive with pretrained representations for planning and compares favorably to other reinforcement learning (RL) methods. Our approach is a sound solution for learning a useful representation that is suitable for planning only from interactions.
Furthermore, we find that our method has better data-efficiency during training than several reinforcement learning methods from the literature.
However, a disadvantage of our approach compared to standard RL methods is that the execution time of our method scales worse with the size of the state space, as a forward pass is calculated for each node during the latent space search, potentially resulting in a combinatorial explosion.
Our approach is adaptable to changes in the tasks. For example, our search would only be slightly hindered if some obstacles were placed in the environment or some states were forbidden to traverse through. Furthermore, our method is independent of specific rewards or discount rates, while standard RL methods are usually restricted in their optimization problems. Often, there is a choice between optimizing discounted or undiscounted expected returns. Simulation/rollout-based planning methods are not restricted in that sense: If reward trajectories can be predicted, one can optimize arbitrary functions of these and regularize behavior. For example, a risk-averse portfolio manager can prioritize smooth reward trajectories over volatile ones.
Future lines of work should investigate further the effect of the different constraints on the end-to-end learning of representations suited for a predictive forward model, as well as considering novel ones. The search algorithm can be improved and made faster, especially for higher-dimensional action spaces or continuous ones. Our network could also in principle be used to train an RL system, for instance, by encouraging it to produce similar outputs as ours and thereby combining data-efficiency with fast performance during inference time.
\section*{Visual processing in context of reinforcement learning}
\vspace{1cm}
\subsection*{Dissertation for the degree of Doctor of Engineering of the Faculty of Electrical Engineering and Information Technology at the Ruhr-Universität Bochum}
\begin{tabular}[b]{ll}
& \\
& \\
& \\
& \\
Name of the author: & Hlynur Davíð Hlynsson \\
& \\
Place of birth: & Reykjavík \\
& \\
First supervisor: & Prof. Dr. Laurenz Wiskott \\
& Ruhr-Universität Bochum, Germany\\
& \\
Second supervisor: & Prof. Dr. Tobias Glasmachers \\
& Ruhr-Universität Bochum, Germany \\
& \\
Year of thesis submission: & 2021 \\
& \\
Date of the oral examination: & March 17th 2022 \\
& \\
\end{tabular}
\chapter*{Abstract}
Although deep reinforcement learning (RL) has recently enjoyed many successes, its methods are still data inefficient, which makes solving numerous problems prohibitively expensive in terms of data. We aim to remedy this by taking advantage of the rich supervisory signal in unlabeled data for learning state representations. This thesis introduces three different representation learning algorithms that have access to different subsets of the data sources that traditional RL algorithms use:
(i) GRICA is inspired by independent component analysis (ICA) and trains a deep neural network to output statistically independent features of the input. GrICA does so by minimizing the mutual information between each feature and the other features. Additionally, GrICA only requires an unsorted collection of environment states.
(ii) Latent Representation Prediction (LARP) requires more context: in addition to requiring a state as an input, it also needs the previous state and an action that connects them. This method learns state representations by predicting the representation of the environment's next state given a current state and action. The predictor is used with a graph search algorithm.
(iii) RewPred learns a state representation by training a deep neural network to learn a smoothed version of the reward function. The representation is used for preprocessing inputs to deep RL, while the reward predictor is used for reward shaping. This method needs only state-reward pairs from the environment for learning the representation.
We discover that every method has their strengths and weaknesses, and conclude from our experiments that including unsupervised representation learning in RL problem-solving pipelines can speed up learning.
\newpage
\pdfbookmark[0]{Kurzfassung der Dissertation}{kurzfassung}
\chapter*{Kurzfassung der Dissertation}
Obwohl tiefes Verstärkungslernen (VL) in den letzten Jahren große Erfolge erzielt hat, sind dessen Methoden immer noch datenineffizient, was die Lösung vieler Probleme unerschwinglich macht. Wir untersuchen die Möglichkeit, dies zu beheben, indem wir das informationsreiche Überwachungssignal in nicht gekennzeichnete Daten für die Darstellung von Lernzuständen nutzen. In dieser Arbeit werden drei verschiedene Repräsentationslernalgorithmen vorgestellt, die Zugriff auf verschiedene Teilmengen der Datenquellen haben, die herkömmliche VL-Algorithmen zum Lernen verwenden:
(i) GrICA ist von der unabhängigen Komponentenanalyse (ICA) inspiriert und trainiert ein tiefes neuronales Netzwerk, um statistisch unabhängige Komponenten der Eingabe auszugeben. GrICA minimiert die gemeinsamen Informationen von einzelnen Merkmalen mit den jeweils anderen Merkmalen. Zusätzlich erfordert GrICA lediglich eine unsortierte Sammlung von Umgebungszuständen.
(ii) Latent Representation Prediction (LARP) erfordert mehr Kontextdaten: Als Eingabe benötigt sie zusätzlich zu einem Zustand auch den entsprechenden vorherigen Zustand und eine Handlung, welche diese verbindet. Die Methode lernt Zustandsdarstellungen, indem sie die Darstellung des nächsten Zustands der Umgebung mithilfe eines aktuellen Zustands und einer aktuellen Aktion vorhersagt. Der Prädiktor wird zusammen mit einem Graphensuchalgorithmus verwendet.
(iii) RewPred lernt die Zustandsdarstellung, indem ein tiefes neuronales Netzwerk trainiert wird eine geglättete Version der Belohnungsfunktion zu lernen. Die Darstellung wird zur Vorverarbeitung von Eingaben im tiefen VL verwendet, während der Belohnungsprädiktor als Belohnungsformung dient. Diese Methode benötigt einzig Status-Belohnungs-Paare aus der Umgebung, um die Darstellung zu lernen.
Wir stellen fest, dass jede Methode ihre Stärken und Schwächen hat, und schließen aus unseren Experimenten, dass das Einbeziehen von unbeaufsichtigtem Repräsentationslernen in VL-Problemlösungspipelines das Lernen beschleunigen kann.
\pdfbookmark[0]{Dedication}{dedication}
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\pdfbookmark[0]{Acknowledgements}{acknowledgements}
\chapter*{Acknowledgements}
I want to first thank my supervisor Prof. Laurenz Wiskott for giving me the opportunity to research the niches of machine learning that I find interesting. His insightful feedback and outstanding enthusiasm and intuition for the field proved invaluable to me and others in this fast growing area of research. The advice of my second supervisor, Tobias Glasmachers, also proved extremely helpful, especially on the topic of reinforcement learning.
I'm grateful for the endless love and support from my partner Lisa Schmitz, who made the time of my PhD studies the best in my life -- so far. My special thanks go also to her parents, Rosemarie Schmitz and Georg Schmitz, for their support during this time.
I'm thankful for the helpful and pleasant environment created by the other PhD students of the Institut für Neuroinformatik (INI): Merlin Schüler, Robin Schiewer, Zahra Fayyaz, Eddie Seabrook, Mortiz Lange, Frederick Baucks, Jan Bollenbacher and Jan Tekülve. I would also like to thank two alumni of the INI, Alberto Escalante and Fabian Schönfeld, for the support they have given me. I also want to thank the INI staff outside the group for their help over the years: Arno Berg, Angelika Wille and Kathleen Schmidt.
Last but not least, I want to thank my loving family for creating the circumstances that gave me room to train the skills that I needed to pursue a PhD to begin with: Ólöf Ingibjörg Einarsdóttir, Hlynur Höskuldsson, Ólafur Hlynsson and Höskuldur Hlynsson.
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\chapter{Introduction}
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\chapter{Background}
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\chapter{Learning gradient-based ICA by neurally estimating mutual information}
\label{chap:grica}
\input{ica_chapter}
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\chapter{Latent representation prediction networks}
\label{chap:larp}
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\chapter{Reward prediction for representation learning and reward shaping}
\label{chap:rewpred}
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\chapter{Comparison of our three methods}
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\chapter{Summary and conclusion}
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\section{Introduction}
\label{sec:measuring_introduction}
\noindent In recent years, we have seen convolutional neural networks (CNN) dominate benchmark after benchmark for computer vision since the 2012 ImageNet competition breakthrough \citep{krizhevsky2012imagenet}. These methods prosper with an abundance of labeled data, and an abundance of data is often required for acceptable results \citep{oquab2014learning}. In contrast, for most people, it is only necessary to see one picture of an Atlantic Puffin to be able to identify correctly such a bird as one. \\
\indent To be fair, we have a lot of prior experience. It is easy to make a mental note: ``a puffin is a small black and white bird with orange feet and a colorful beak'' because we have learned a useful representation of the salient aspects of the image. Instead of being bogged down by the details of every exact pixel value, as an untrained AI might, we can focus our attention on the most useful features of the image. \\
\indent For this reason, investigations on the efficacy of methods to learn a concept from few samples are often done through the lens of representation learning \citep{bengio2013representation}, for example via transfer learning \citep{pan2010survey} or low-shot learning \citep{wang2018low}. \\
\indent In this work we consider a method to measure data efficiency, the performance of an algorithm as a function of the number of data points available during training time, which is an important aspect of machine learning \citep{kamthe2017data}, \citep{al2015efficient}. We quantitatively examine the performance of CNNs and hierarchical information-preserving graph-based slow feature analysis (HiGSFA) \citep{escalante2016improved} networks for varying training set sizes and for varying task types. \\
\indent HiGSFA has been chosen because it is the most recent supervised extensions of slow feature analysis (SFA) and has shown promise in visual processing with a notable distinction from CNNs: the computation layers are trained in a "greedy" layer-wise manner instead of via gradient descent \citep{escalante2016improved}. \\
\indent The methods are applied to visual tasks: a simple version of the MNIST classification task, where we vary the number of training points, and increasingly difficult tasks constructed from the Omniglot data set. Our \textbf{contribution} in this work is a novel experimental protocol for evaluation of transfer learning applied to experimentally evaluate CNNs with the slowness-based HiGSFA.
\section{Related Work}
\label{measuring_relatedwork}
\noindent Gathering data can be quite costly, so the question "how much is enough" has been considered in literature ranging from classical statistics \citep{krishnaiah1980handbook} over pattern recognition \citep{raudys1991small} to experimental design \citep{beleites2013sample}.
As data plays a central role in machine learning as well, the study of its effective use has garnered attention from all branches of the field. \\
\indent In a similar vein as our work, \citep{lawrence1998size} analyze the effect of generalization when the number of sample points are varied for supervised learning tasks. Equipped with the prior that supervised learning methods' performance obeys the inverse power law, \citep{figueroa2012predicting} trained a model to predict the classification accuracy of a model given a number of inputs.\\
\indent Transfer learning straddles the intersection between supervised learning and unsupervised learning, where the focus is uncovering representations that are both general and also useful for particular applications. The Omniglot data set we consider was introduced in \citep{lake2015human} and has been popular for developing transfer learning methods \citep{bertinetto2016learning}, \citep{edwards2016towards}, \citep{schwarz2018progress}.\\
\indent
With its sparse rewards and problems of credit assignment, reinforcement learning (RL) has a particular need for data efficiency, motivating such early works as prioritized sweeping \citep{moore1993prioritized}. More recently, \citep{riedmiller2005neural} designed the neural-fitted Q-learner for data efficiency. This method has been successfully combined with deep auto-encoder representations for visual RL \citep{lange2010deep}. Deep Q-Networks have made better still use of data for RL by combining experience replay, target networks, reward clipping and frame skipping \citep{mnih2013playing} \citep{mnih2015human}.\\
\indent
SFA was introduced in 2002 by Wiskott and Sejnowski as an unsupervised learning method of temporally invariant features \citep{wiskott2002slow}. These features can be learned hierarchically in a bottom-up manner, reminiscent of deep CNNs: slow features are learned on spatial patches of the input and then passed to another layer for slow feature learning. The method is then called hierarchical slow feature analysis (HSFA) and has attracted attention in neuroscience for plausible modeling of grid, place, spatial-view, and head-direction cells \citep{franzius2007slowness}. \\
\indent For labeled data, the method admits a supervised extension in the form of graph-based SFA (GSFA) \citep{escalante2013solve}. Information is often lost in early layers of hierarchical SFA --- that could contribute to a globally slower signal --- prompting the development of HiGSFA \citep{escalante2016improved}.\\
\indent Deep learning extensions of SFA is currently an active research area. The SFA problem is solved with stochastic optimization in Power-SFA \citep{schuler2018gradient}. A differentiable whitening layer is constructed, allowing for a non-linear expansion of the input to be learned with backpropagation. Another recent method, SPIN \citep{DBLP:journals/corr/abs-1806-02215} learns eigenfunctions of linear operators with deep learning methods and can be applied to the SFA problem as well.
\section{Methods}
\noindent Below we describe the novel experimental setup as well as the methods being evaluated using the setup. For the remainder of the article we assume CNNs to be well-known and understood but we can recommend \citep{cs231n2017convolutional} as a good pedagogical introduction to the method.
\subsection{HiGSFA}
HiGSFA belongs to a class of methods motivated by the slowness principle, which is based on the assumption that important aspects vary more slowly than unimportant ones \citep{sun2014dl}. This model takes as input data points such that data point $x_n$ is node $n$ in an undirected graph with weight $v(n)$. This can control the relative weight each data point has during the training but we set it as uniformly 1 is our experiments below.
The edge between nodes $n$ and $n'$ is $\gamma_{n, n'}$ and signifies a relationship between the data. This could be their spatial or temporal proximities or whether they belong to the same class.
For instance, during our classification tasks below, we set:
\begin{equation}
\gamma_{n, n'}=
\begin{cases}
1,& \text{if } n \text{ and } n' \text{ in same class}\\
0, & \text{otherwise}
\end{cases}
\end{equation}
Given a function space $\mathcal{F}$ with elements $g_j$, we learn slowly varying features $y_j(n) = g_j(x_n)$ of the data by solving the optimization problem \citep{escalante2013solve}:
\begin{equation}
\begin{aligned}
& \underset{g_j}{\text{minimize}}
& & \frac{1}{R} \gamma_{n, n'} \sum\limits_{n, n'} \left( y_j(n) - y_j(n') \right)^2 \\
& \text{subject to}
& & \frac{1}{Q} \sum\limits_{n} v_n y_j(n)\ \ \ \ \ \ \ \, = 0 \ \ \ \ \ \ \ \ \ \, \\
&&& \frac{1}{Q} \sum\limits_{n} v_n \left(y_j(n) \right)^2\, \ \ \ = 1 \ \ \ \ \ \ \ \ \ \ \, \\
&&& \frac{1}{Q} \sum\limits_{n} v_n y_j(n) y_{j'}(n) = 0\text{, } j' < j \ \\
& \text{where}
&&Q = \sum\limits_{n} v_n,\ R = \sum\limits_{n, n'} \gamma_{n, n'}
\end{aligned}
\end{equation}
The first constraint secures weighted zero mean, the second constraint secures weighted unit variance and the third one secures weighted decorrelation and order. \\
\indent To reduce computational complexity, we extract features of the data hierarchically. Similarly to CNNs, we extract features from $F \times F$ patches of the image data in the first layer, then extract features of $F' \times F'$ patches of the output features in the next layer and so on. The layers are trained by solving the optimization problem, one layer at a time, from the input layer to the output layer. The layer-wise parameters can be shared.
As we can experience information-loss while doing these layer-wise optimizations, an information-preserving mechanism is added. The cost function is minimized locally, so we can experience information-loss if dimensions are discarded that do not minimize the function on a local level --- but could conceivably be better for the overall problem.
For each layer (figure \ref{example}), a threshold is placed on the features with respect to their slowness. If an output feature or features would be too fast, we replace them by the most variance-preserving PCA features. Each layer thus outputs a combination of slow features and PCA features.
\begin{figure}[ht]
\fontsize{31}{05}\selectfont
\centering
{\resizebox*{0.4 \textwidth}{!}{\includegraphics
{files/graphic.PNG}}}
\caption[Illustration: HiGSFA Network Layer]{\textbf{HiGSFA Network Layer.} The feature generation is similar to that of the CNN. The layer outputs $N$ channels of slow features and $M$ channels of PCA features. The number of PCA channels features is either fixed beforehand or determined by replacing a number $M$ of the SFA features whose \textit{slowness} (cost function in eq. 2) exceeds a given threshold.}
\label{example}
\end{figure}
\subsection{General description of protocol}
The performance of two hypothesis $h_1$ and $h_2$, not necessarily from the same hypothesis set $\mathcal{H}$, is compared on a classification task. The learning curves of the two hypothesis are plotted as a function of the number of data points in the training set. This can be done simply by taking an increasing number of training points per class as we evaluate using MNIST, below. \\
\indent Alternatively, the number of training points per class are kept constant and the number of classes are varied. The relationship training and test set distributions is also altered, such that the task ranges from classical classification to transfer learning. We report a comparison of methods below using this scheme on the Omniglot data set.
\subsection{Evaluation on MNIST}
First, we compare classification accuracies on MNIST \citep{lecun1998gradient} as a function of the number of samples per class used during training. The images have a dimension of $28 \times 28$ pixels. For 100 iterations, we choose random samples from each class and use a thousand unused samples from each class for validation. Finally, the models are tested on the classic 10 thousand test images.
\subsection{Architectures}
We constructed a two-layer HiGSFA network with circa 13k parameters (the number is stochastic and changes from training set to training set), extracting 400 features from the data. The first layer has a filter size of $5\times5$ and a stride of 2, extracting 25 features for each spatial patch. The second layer has a filter size of $4\times4$ and a stride of 2, extracting 16 features for each spatial patch. \\
\indent The output of the first layer is concatenated with a copy of itself, where each element $x$ is replaced with $|x|^{0.8}$, doubling the number of channels and giving us nonlinearity. If the value of the objective function is larger than a threshold of 1.99, we select PCA features. This upper bound is motivated by the fact that non-predictive, white noise features take a value of 2 in the objective function \citep{creutzig2008predictive}. The parameters within each layer are shared. A single-layer softmax neural network was trained on the features of the second layer to handle classification, which has 4010 parameters.\\
\indent Two standard CNNs were constructed as well, one with the constraint to have a similar number of parameters as the HiGSFA network, and another with an amount closer to what is seen in practice on similar data sets. That is to say, the smaller CNN corresponds to the HiGSFA network. \\
\indent We call the smaller network CNN-1 which has 10,032 trainable parameters, excluding the number in the final layer for classification. The tasks have varying numbers of classes to be predicted, causing the classification layer to have varying numbers of parameters. CNN-1 has three convolutional layers, each one followed by ReLU and max pooling, the first two with 8 channels and the last one with 16. They are followed by a fully connected classification layer, using a softmax activation function. The first convolutional layer has a filter size of $7\times7$, and the other two have a filter size of $5\times5$. The convolutional layers have a stride of 1 and the max pooling layers have a stride of 2.\\
\indent We call the larger network CNN-2, with 116,214 parameters (not counting the classification layer). It is the same as CNN-1 except the convolutional layers have twice the number of channels, and a dense layer with 150 units is added before the classification layer. \\
\indent Note that the parameter configurations of both HiGSFA and CNNs have not been optimized for the best performance on the tasks below. They were designed to be lightweight according to general best practices \citep{hadji2018we} \citep{escalante2016improved}. This allows for more trials and tighter confidence bounds while achieving fair performance on the tasks.
\subsection{Evaluation on Omniglot}
Omniglot is a handwritten character data set consisting of 50 alphabets with 14 to 55 characters each, each character having 20 samples \citep{lake2015human}. The alphabets vary from real alphabets, such as Greek, to fictional ones, such as Alienese (from the TV show "Futurama"). Each sample was drawn by a different person for this data set. It is typically split into 30 training alphabets, and 20 testing alphabets. Note that the training-testing split separates the alphabets; all samples originating from all characters from a given alphabet appear in either the training set or the test set but not both. This makes it a transfer learning task as the training and test data set samples drawn from separate distributions.
In the original work using the data set, the methods were first trained on the 30 background alphabets, and then a 20 way one shot classification task was performed. Two samples are taken from each of 20 characters from random evaluation alphabets. One sample is placed in what we'll call a probe set, and the other in a target set. The methods then try to find the corresponding sample in the target set that is the same character as any given sample in the probe set.
\begin{figure}[ht]
\centering
{\resizebox*{0.4 \textwidth}{!}{\includegraphics
{files/omniglotnice.png}}}
\caption[Example: 16-way One Shot Classification]{\textbf{16-way One Shot Classification}. Symbols on the left are presented to the algorithm, one at a time, and the task is to find the same character from the symbols on the right.}
\label{fig-16way}
\end{figure}
In the vein of the original Omniglot task, we compare several models in three challenges. In all challenges, we do 16 way one shot classification using 1-nearest-neighbor (1-NN) under the Euclidean distance. The challenges differ in how the test set is related to the training set:
\subsubsection{Challenge 0} From 16 random characters used for training, we take two samples that the models were trained on. These samples are placed in two sets, the probe and target sets, such that each set contains one sample of each character. The model under consideration extracts features from each image. We then iterate through each feature vector from images in the probe set and find the closest feature vector from the target set. If those two vectors belong to images of the same class, then we count it as a success.
\subsubsection{Challenge 1} Same as above, but we take characters used during training for the probe set and perform classification on samples that were not used during the training.
\subsubsection{Challenge 2} Same again, but now we do the classification on characters that do not belong to alphabets used during training.
\subsection{Omniglot architectures}
All model architectures are the same for MNIST and Omniglot, but the Omniglot images are resized to $35\times35$, having the effect that HiGSFA outputs 784 features. The number of model parameters does not change as the weights are shared for the image patches. The HiGSFA features used for classification are simply the 784 output features and we do not train a neural network classifier on them.
The total number of parameters in the CNNs depend on the number of training classes, due to the classification layer. We fix the number of alphabets to 8 and vary the number of characters per class to be 4, 6, 8, 10, 12 and vice versa. The number of parameters for CNN-1 range between 18k and 35k, and for CNN-2 range between 121k and 130. If we do not count the parameters from the final classification layer, then the number of parameters for CNN-1 for these tasks is always 10,032 and the number for CNN-2 is 116,214.
After training the CNNs, we perform feature extraction by intercepting the output of the second-to-last layer. Here the assumption is that CNNs learn a representation for the classification layer \citep{DBLP:journals/corr/RazavianASC14}. We are then interested in comparing the strength of HiGSFA and CNN representations when used by a 1-NN classifier.
\begin{table*}[ht
\centering
\begin{tabular}{ r | l l | l l | l l}
\hline
Samples\,
& HiGSFA & & CNN-1 && CNN-2 &\Tstrut \\
& Acc. & Std. & Acc. & Std. & Acc. & Std. \Bstrut \\
\hline
5\, & 35.683 & $\pm$ 0.430 & $\textbf{72.361}$ &$\pm$ 0.365 & 72.320 &$\pm$ 0.094\, \,\,\ \Tstrut\\
10\, & 75.736 & $\pm$ 0.222 & $\textbf{80.392}$ &$\pm$ 0.241 & 79.551 &$\pm$ 0.175 \\
50\, & $\textbf{92.970}$ &$\pm$ 0.050 & 90.320 &$\pm$ 0.101 & 91.465 & $\pm$ 0.070 \\
200\, & $\textbf{96.246}$ &$\pm$ 0.027 & 94.672 &$\pm$ 0.062 & 95.648 & $\pm$ 0.051 \\
500\, & 97.188 &$\pm$ 0.013 & $96.579$ &$\pm$ 0.046 & \textbf{97.308} &$\pm$ 0.054 \\
2000\, & 97.887 &$\pm$ 0.009 & 98.247 &$\pm$ 0.020 & $\textbf{98.571}$ & $\pm$ 0.023 \\
6000\, & 98.134 & $\pm$ 0.008 & 98.687 &$\pm$ 0.014 & $\textbf{98.949}$ &$\pm$ 0.015 \\
\end{tabular}
\caption[Result: MNIST Accuracies]{\textbf{MNIST Accuracies.} The percentage of correctly classified samples on the test set along with the standard error of the mean (SEM). }
\label{tab:totalresults}
\end{table*}
\subsection{Training}
The models were trained on varying amounts of samples per character. The HiGSFA network was trained to solve the optimization problem on each image patch, one layer at a time. All neural networks were trained in Keras \citep{chollet2015keras} using ADAM \citep{kingma2014adam}, with default parameters, to minimize cross-entropy.\\ \indent After each epoch, the error was calculated on the validation set. Early stopping was performed after the validation error had increased four times in total during the training. The training for Omniglot is the same, except instead of early stopping, the CNNs were trained for 20 epochs in all cases.
\begin{figure*}[ht]%
\centering{{\includegraphics[width=5.7cm]{files/index3a.png} }}%
\qquad{{\includegraphics[width=5.7cm]{files/index6a.png} }}%
\qquad{{\includegraphics[width=5.7cm]{files/index2a.png} }}%
\qquad{{\includegraphics[width=5.7cm]{files/index5a.png} }}%
\qquad{{\includegraphics[width=5.7cm]{files/index1a.png} }}%
\qquad
{{\includegraphics[width=5.7cm]{files/index4a.png} }}%
\caption[Result: Classification Accuracies]{\textbf{Classification Accuracies}. There are either 8 alphabets and we vary the characters per alphabet, or vice versa. The error bars indicate the standard error of the mean. These plots are best viewed in color.}%
\label{fig:plots}%
\end{figure*}
\section{Results}
\label{measuring_results}
\subsection{MNIST Results}
We trained the models using 5, 10, 50, 200, 2000 or 4000 samples per digit. In table \ref{tab:totalresults}, we see the statistics from 100 runs, where the models were trained from random initializations, evaluated and tested. The convolutional networks have the highest accuracies when there are 2000 or more samples per class and when there are only 5 or 10 samples per class. \\ \indent However, HiGSFA has a higher accuracy than the CNN with a similar number of parameters for 500 samples per class. Furthermore, HiGSFA has higher accuracies than both CNNs for 200 and 50 samples per class. The CNN with a larger number of parameters always has higher prediction accuracies than the one with a lower number of parameters.
\subsection{Omniglot Results}
The 1-NN classifier uses the second-to-last CNN outputs or HiGSFA features. We fix either the number of alphabets, or characters-per-alphabet, to be 8 and vary the other number from 4 to 12 in increments of 2. The number of samples per character is either 4 or 16. The largest total number ($\text{alphabets} \times \text{characters per alphabet} \times \text{samples per character}$) of samples used for training is 1536 and the lowest is 128. \\
\indent In figure \ref{fig:plots}, we see the average of all the runs over the different samples per characters and number of classes. In all of the challenges, the CNNs have higher accuracies than HiGSFA. On average, CNN-2 has higher accuracies in challenges 0 and 2. Neither CNN achieves significantly better accuracy than the other in challenge 1.
\section{Discussion and conclusion}
\label{measuring_discussion}
\noindent The work of this paper is intended to facilitate understanding of algorithms from the point of view of having particularly low numbers of samples. We present simple-to-implement challenges that allow for evaluation of data efficiency in the context of representation learning. \\
\indent For the models experimented on, we see that the CNNs usually perform better, but HiGSFA outperforms the CNNs on 50 and 200 sample training sets from the MNIST data. One can speculate that the default CNN architectures ensure generalization through max-pooling whereas SFA mostly learns to generalize from a moderately sized data set. \\
\indent Another explanation for the different ranges of comparative performance optima is the choice of delta-threshold of HiGSFA. The method overestimates the slowness of the slowest features when it has too few samples. This has the effect that fewer PCA features are selected for a lower number of samples. On the other hand, with more than 200 samples, there could be too many PCA features chosen. Setting the number of slow features to be a constant for all sample sizes could be better for robustness than fixing the delta threshold. \\
\indent Notice the trend in challenge 0: the accuracy goes down as the number of samples increases. This is due to the samples used for the probe and target sets being drawn from the training set and we are training and testing on larger sets as we move from left to right. \\
\indent Overall, for the Omniglot challenges, the accuracies of the CNNs lie comfortably above the HiGSFA accuracies, but it's not always discernible whether the larger or the smaller CNN performs better. An explanation for this could be that the tasks are not difficult enough for more parameters to be necessary. The local optimality of GSFA could result in an insufficiently robust or transferable representation if there are many classes and few samples per class. \\
\indent These challenges are more complicated set of classification tasks than the MNIST ones, with a larger number of classes overall. This give CNNs an opportunity to take advantage of having been trained directly for classification when they are presented a similar task. Although HiGSFA takes advantage of class labels, it suffers in comparison for not taking into account the downstream task during training.\\
\indent For future work, a complete extension of the experiments here could include an analysis on the effect that different type of data would have on the performance. This would yield further insight than varying the number of rather homogeneous data used for training. Additionally, the performance of a wider array of popular methods can be compared. \\
\indent More types of benchmarks for comparing different models over varying training set sizes would be helpful for this kind of research. Knowledge gained from them would as well allow practitioners to choose the right model for the scale and type of the problem they wish to solve. These experiments give rise to the question: how can these methods with their different strengths and weaknesses profit from each other?
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
\label{intro}
Nuclei with extreme neutron access lying close to the neutron drip line
constantly attract interest both in theoretical and experimental research.
Experiments with radioactive nuclear beams that are conducted in Dubna, GSI,
RIKEN have opened new opportunities for obtaining exotic nuclei with impressive
neutron excess. The construction of FRIB in Michigan \cite{frib} (the
operational run is planned in 2022) would boost experimental abilities to
approach the neutron drip line.
Among major fundamental microscopic approaches in the studies of nuclei with
neutron excess one can name the Hartree-Fock-Bogoliubov approach (HFB),
Hartree-Fock plus BCS pairing (HF+BCS) with effective forces and relativistic mean field theory \cite{1,2,3,4,5,6}.
In Refs.~\refcite{7,8,9,10,11,12,13,14} we explored the possibility of existence of
islands and peninsulas of stability of nuclei with large neutron excess lying
beyond the conventional neutron drip line. The calculations in these papers were
done with the HF method using various type of effective Skyrme forces
\cite{15,16,17,18,19} and accounting for the axial deformation; the pairing was
treated in the BCS scheme. We have demonstrated that in the regions of the
nuclear chart corresponding to extreme neutrons excess around magic and ``new''
magic numbers N = 32, 58, 82, 126, 184, 258 there may exist peninsulas of
neutron stability stretching beyond the conventional neutron drip line. In this
picture a neutron rich nucleus, which is unstable against neutron separation,
may regain stability if one adds to it a certain number of neutrons thereby
shifting it to the stability peninsula. In the HF approach this stability
restoration is a result of complete filling of neutron subshells with large
angular momentum. These subshells have a large centrifugal barrier and being
partially filled they are located in the continuous spectrum, which makes the
corresponding nuclei unstable against neutron emission. However, when the
neutron number increases these subshells descend into discrete spectrum and
nuclei regain stability. The main aim of the present paper is to find stable
nuclei with the highest possible neutron to proton ratio N / Z, which we believe
sets a theoretical upper bound for this ratio. We shall consider only nuclei
with $2 \leq Z\leq 8$, since it has been shown earlier \cite{10,11,12}, the
maximal N / Z ratio can be attained only for light nuclei. The largest values of
$N$ are obtained at stability peninsulas. The most extended stability peninsulas
are obtained with the SkI2 \cite{11,12,13} set of Skyrme forces, therefore, we shall
use mostly the SkI Skyrme parameters. Let us note that various types of SkI
forces were obtained and effectively used in Ref.~\refcite{18}. The same type of forces
was used in Ref.~\refcite{20} for the description of light exotic nuclei, however,
without accounting for deformation, which is, certainly, a disadvantage
compromising the predictive power of the obtained results.
\section{Methods and Results}
The detailed exposition of the method of solving the deformed Hartree-Fock (DHF)
equations is given in Refs.~\refcite{8,21,22,23}. Here we present the results of the
calculations using SkI2 set of Skyrme forces.
One particle wave functions in DHF are expanded in the axially deformed harmonic
oscillator basis. The principle quantum number for the harmonic oscillator basis
usually does not exceed $N_0$ = 18 (amounting to 1330 basis functions). This
dimension of the basis is more than necessary for the calculations of the
isotopes with $2 \leq Z \leq 8$, which provides high accuracy and reliability of
obtained results.
In case of nuclei lying on stability peninsulas along with the DHF calculations
we do additional calculations, where HF equations are solved directly in
coordinate space under assumption of spherical symmetry (SHF method) \cite{24}.
This is reasonable because nuclei belonging to stability peninsulas indeed
possess spherical symmetry \cite{7,8,9,10,11,12,13,14}. SHF calculations make
possible the analysis of the role of continuum states in the cases when the DHF
solution is spherically symmetric.
We used the BCS constant pairing, where the pairing constant is set equal to $G=
(19.5/(N+Z))[1 \pm 0.51(N-Z)/(N+Z)]$ \cite{25}, ``+'' and ``-'' correspond to
protons and neutrons respectively. In DHF calculations pairing is restricted to
bound one-particle states. This choice of pairing as well as the role of
continuum states in the structure of nuclei lying at stability peninsulas is
discussed in Refs.~\refcite{10,11,12,13,14}. Let us note that the inclusion of continuum
states into present SHF calculations of nuclei with $2 \leq Z \leq 8$, which
form stability peninsula, did not affect the results that were obtained without
inclusion of continuum states. This is, however, typical for magic and
quasi-magic nuclei. Similar behavior has been observed for stability peninsulas
in other parts of the nuclear chart \cite{12}.
Fig. 1 shows nuclear chart, where the squares represent nuclei that are stable
against one neutron emission in DHF calculations with SkI2 forces. Exactly the
same picture is obtained with SkI1 forces. Grey squares on this chart are
experimentally known stable nuclei. We determine one neutron drip line from the
condition $S_n = 0$, where $S_n0$ denotes one neutron separation energy. Thereby, any positive value of $S_n$ means stability
against one neutron emission, even if $S_n$ is marginally small. We calculate
one neutron separation energies assuming the validity of approximation made in
Koopman's theorem. For given $Z$ the position of the neutron drip line is
determined as follows. We start with a stable isotope and increase the neutron
number until stability is lost and one neutron separation energy changes its
sign. Knowing that one-neutron drip line can exhibit nonmonotonic behavior
\cite{12} we continue increasing $N$. If at some larger value of $N$ the value
of $S_n$ changes its sign again then this means that we have located a
stability peninsula.
As we have mentioned such effect of stability restoration appears when neutron
subshells with large angular momentum getting fully filled intrude from
continuous spectrum into the bound spectrum \cite{10,11,12,13,14}. (In
\cite{nature} the formation of stability peninsulas was alternatively termed
irregular behavior of the neutron drip line). Using SkI2 set of Skyrme forces we
have found one stability peninsula situated at $^{18}$He with the fully filled
subshell 1d$_{5/2}$ and another one at $^{40}$C with the fully filled subshell
1f$_{7/2}$. These isotopes that disrupt the monotonic behavior of the drip line
are illustrated in Fig. 1, where they are highlighted with red (color online)
color and have arrows pointing at them. Both of these nuclei possess spherical
symmetry, which is typical for nuclei with fully filled shells. The neutron to
proton ratio in $^{18}$He and $^{40}$C is $N / Z = 8$ and $N / Z \simeq 5.67$
respectively, which is substantially larger than the so far known neutron to
proton ratios for stable nuclei \cite{8,9,10,11,12,13,14}.
Fig.1 also shows the stability peninsula consisting of one isotope $^{32}$C.
Later we shall discuss in detail the stability restoration for this isotope.
Fig. 2 shows one neutron separation energies as functions of $A=(Z+N)$ obtained
with SkI2 Skyrme forces. One can clearly see $S_n$ changing sign at $^{18}$He,
which results from completely filled subshell 1d$_{5/2}$ being bound. One
neutron separation energy of this isotope as estimated according to the
Koopman's theorem equals 0.45 MeV. Let us consider HF potentials corresponding to the state 1d$_{5/2}$, where this
state is weakly bound. Because the nucleus is spherical we can use SHF method,
which has the advantage of representing potentials and wave functions directly
in coordinate space \cite{10,24}. The DHF value $S_n$ = 0.450 is close to the
SHF value $S_n$ = 0.406 MeV. Fig. 3 shows the Fermi level 1d$_{5/2}$ for
$^{18}$He and the corresponding SHF potential. The dotted line depicts the wave
function of the Fermi level, which is localized under the centrifugal barrier.
The height of the centrifugal barrier in the HF potential equals 1.35 MeV, which
should additionally enhance the stability of $^{18}$He against one neutrons
emission.
When we apply the BCS scheme in case of SHF calculations we also include those localized
quasibound states with positive energy, whose wave functions are localized under
the centrifugal barrier. Other continuum states are not considered. In case of
$^{18}$He and $^{40}$C (SkI2 forces) we considered all localized quasibound
states. The states were discretized by introducing boundary conditions, which
make wave functions vanish outside the sphere with the radius 40 fm. We found
that the pairing remained zero even when we included localized quasibound states.
Fig. 4 shows one neutron separation energies for carbon calculated with SkI2
forces using the DHF method. One can see that $S_n$ increases for $A= 26$, which
signals the magicity of the number $N = 20$ near the drip line. The neutron
subshell 1f$_{7/2}$ submerses into bound spectrum becoming completely filled for
$N=34$, which provides stability against one neutron emission for $^{40}$C. At
this point $S_n = 0.597$ MeV in DHF calculations and $S_n = 0.594$ MeV in SHF
calculations. $^{40}$C is a spherically symmetric nucleus. Similar to the case
of $^{18}$He in Fig. 5 we consider the SHF potential corresponding to the Fermi
level 1f$_{7/2}$ for $^{40}$C. The SHF potential for this state has a
centrifugal barrier with the height 2.48 MeV, which additionally enhances the
stability of this isotope. In Fig. 4 one witnesses the stability restoration for
$^{32}$C (26 neutrons) , which is again connected with the state 1f$_{7/2}$.
Unlike $^{40}$C the nucleus $^{32}$C has quadrupole deformation $\beta = -
0.32$, and its last filled neutron level has quantum numbers $\Omega = 7/2^{-}$.
This level, which is the member of the multiplet 1f$_{7/2}$, intrudes into the
bound part of the spectrum when $N=26$.
Let us consider in more detail the isotope chains of He and C, which pass through
$^{18}$He and $^{40}$C. In Figs. 6, 7 one can see the neutron and proton root
mean square (rms) radii $\langle r^2_{n,p}\rangle^{1/2}$ for helium and carbon.
The arrows indicate the values for $^{18}$He and $^{40}$C, which form stability
peninsulas at $N = 16$ and $ N = 34$. Generally in neutron rich nuclei the
difference of neutron and proton rms radii $\Delta R_{n,p} = \langle
r^2_{n}\rangle^{1/2} - \langle r^2_{p}\rangle^{1/2} $ may take large values and
one can speak about neutron skin or neutron halo effects when $\Delta R_{n,p} >
0.2$ fm \cite{26}. From the figure one can see large values of $\Delta R_{n,p} $
for He and C isotopes in particular for $^{18}$He and $^{40}$C, which is a manifestation of
a large neutron halo in these nuclei. In DHF calculations for $^{18}$He we
obtained $\Delta R_{n,p} = 4.288-2.150 = 2.138$ fm and $\langle
r^2_{n}\rangle^{1/2} / \langle r^2_{p}\rangle^{1/2}\simeq 1.994 $. For $^{40}$C
we got $\Delta R_{n,p} = 4.709-2.800 = 1.909$ fm and $\langle
r^2_{n}\rangle^{1/2} / \langle r^2_{p}\rangle^{1/2}\simeq 1.682$. It is useful
to compare these values with those of extremely neutron rich $^{40}$O \cite{27},
where $\Delta R_{n,p} = 1.29$ fm and $ \langle r^2_{n}\rangle^{1/2} / \langle
r^2_{p}\rangle^{1/2}\simeq 1.436$ (SkM$^*$ forces). This suggests that there is
a very large neutron halo in $^{18}$He and $^{40}$C in the picture
corresponding to SkI2 forces.
Figs. 8, 9 show neutron and proton density distributions of $^{18}$He and
$^{40}$C calculated within SHF approximation using SkI2 forces. SHF
approximation yields the wave function in coordinate representation and is thus
more appropriate for graphical purposes. Its use in this case is justified by
the spherical form of these nuclei. Neutron halo in neutron rich nuclei is first
of all characterized by the spatially extended neutron density distribution
dominating over the ``normal'' proton density distribution. In this sense Figs.
8, 9 provide a more clear picture of neutron halo in nuclei forming stability
peninsulas. Neutron and proton density distributions in Figs. 8, 9 are typical
for neutron rich nuclei \cite{6}. Our analysis shows that the tail of neutron
distribution results from weakly bound one particle states.
\section{Conclusion}
We did HF + BCS calculations of neutron rich nuclei with charges $2 \leq Z \leq
8$. We have demonstrated that beyond conventional neutron drip line there may
exist stability peninsulas formed by $^{18}$He and $^{40}$C. These nuclei set
the record for the largest so far known neutron to proton ratio for stable
nuclei. They are spherical in shape and have a spatially extended neutron halo.
These newly found stability peninsulas complement our previous findings and
their existence agrees with the general nature of the neutron drip line forming
peninsulas at magic and quasimagic neutron numbers.
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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Bittacus parkeri är en näbbsländeart som beskrevs av George W. Byers 2004. Bittacus parkeri ingår i släktet Bittacus och familjen styltsländor. Inga underarter finns listade i Catalogue of Life.
Källor
Styltsländor
parkeri
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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ACCEPTED
#### According to
Index Fungorum
#### Published in
Hedwigia 37: 192 (1898)
#### Original name
Nectria blumenaviae Rehm
### Remarks
null
|
{
"redpajama_set_name": "RedPajamaGithub"
}
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Q: Get database paths (internal and external) I've a root app that does read the database of another app. For this I need to find the path of the database, so I do following:
String foreignAppDatabaseFolderPath = "/data/data/" + foreignPackageName + "/databases";
String foreignAppDatabasePath = foreignAppDatabaseFolderPath + "/" + foreignDbName;
But know I realised, that the user could move an app to the sd card. I anyway change the above code to following:
String myAppDatabaseFolderPath = context.getDatabasePath("db")
.getParentFile()
.getAbsolutePath();
String foreignAppDatabaseFolderPath = myAppDatabaseFolderPath
.replace(myPackageName, foreignPackageName);
String foreignAppDatabasePath = foreignAppDatabaseFolderPath + "/" + foreignAppDatabaseName;
But how do I find out the path that I should check, if the app was moved to the sd card?
String foreignAppDatabaseSdCardFolderPath = ???;
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,337
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Q: Opencv: cv2.findContours modifies image that has already been plotted? I'm encountering a odd behaviour and while I can work around it I would like to know why this is.
When I use cv2.findContours it modifies the original image, even if I haven't passed it to the function. Here is a minimal example where the picture can be found here.
import matplotlib.pyplot as plt
import cv2
img =cv2.imread('a.jpg',0)
a1=plt.subplot(121)
plt.imshow(img, cmap='Greys')
ret, thresh = cv2.threshold(img,57,255,cv2.THRESH_BINARY)
a1=plt.subplot(122)
plt.imshow(thresh, cmap='Greys')
plt.show()
temp=thresh
del thresh
contours, hierarchy = cv2.findContours(temp,cv2.RETR_TREE,cv2.CHAIN_APPROX_SIMPLE)
When I comment out the line with cv2.findContours it works fine. Why is that?
A: It happens because temp is thresh.
In python when you make an assignment like that you are not coping the object, you are just making a new reference.
Take a look at copy module to achieve your goal.
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{
"redpajama_set_name": "RedPajamaStackExchange"
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\section{Introduction}
Over recent years, we are progressively reaching a deeper understanding of the QCD phase diagram and its main properties. Combined efforts from experiment, lattice simulations and phenomenology are allowing to access regions of the $(T,\mu_B)$ plane increasingly richer in baryon density. In particular, beam energy scans \cite{Adamczyk:2017iwn} would reveal whether a critical point exists and the behaviour of QCD matter around it. This is actually one of the main objectives of the current program of hot and dense QCD matter in lattice and heavy-ion collisions \cite{Ratti:2018ksb,Bazavov:2019lgz}.
In this context, a significative advance has been to realize that the phase boundary lies close to the chemical freeze-out for physical conditions of net baryon number $B$, electric charge $Q$ and strangeness $S$, accesible to experimental heavy-ion experiments. Thus, using hadron statistical models \cite{Andronic:2017pug}, which have been very successful in the past for this purpose, one can fit hadron yields from ALICE data. The result of such fits are points on the freeze-out $(T,\mu_B)$ curve which turn out to overlap with the critical line obtained from lattice collaborations where $\mu_B$ is treated within Taylor expansions to avoid the so-called sign problem \cite{Bazavov:2018mes}. In addition, the study of fluctuations of those very same conserved changes opens up interesting possibilities. A particularly interesting analysis in this context regarding strangeness is the study of crossed susceptibilities performed in lattice works \cite{Bazavov:2014xya}. This is relevant because a combination of $BS$ and $QS$ crossed susceptibilities provides a relation between chemical potentials $\mu_{B,S,Q}$. Such relation can also be tested at freeze-out with experimental hadron yields fits or with theoretical models such as the Hadron Resonance Gas (HRG).
The $\mu_B=0$ regime is in principle much better understood. Regarding the transition, the most analyzed signals have been the inflection point of the (subtracted) light quark condensate $\mean{\bar q q}_l=\langle \bar u u + \bar d d \rangle$ and the peak of the scalar (or chiral) susceptibility $\chi_S$. Both reveal a crossover-like transition in the physical case ($N_f=2+1$ light flavors and physical quark masses) at $T_c\simeq$ 156 MeV \cite{Bazavov:2018mes,Aoki:2009sc} which in the chiral limit reduces to $T_c^0\simeq$ 132 MeV \cite{Ding:2019prx} and becomes a true phase transition, most likely of second order, for two massless flavours \cite{Pisarski:1983ms}.
An open problem in this context is to determine not only the order but the universality class (pattern) of the chiral phase transition. This depends crucially on whether the $U(1)_A$ anomalous symmetry is sufficiently restored at $T_c$ \cite{Pisarski:1983ms,Pelissetto:2013hqa,Brandt:2019ksy}, which may even affect the properties of the possible critical point at $\mu_B\neq 0$ \cite{Mitter:2013fxa}. A second-order $O(4)\equiv SU(2)\times SU(2)$ transition would be preferred in a scenario with $U(1)_A$ breaking at $T_c$, while a second-order $U(2)\times U(2)$ one would correspond to a $U(1)_A$ restored situation. The latter may even degenerate into a first order transition for strong enough $U(1)_A$ restoration \cite{Brandt:2019ksy}.
A useful perspective to explore this problem is the analysis of partners, i.e., hadronic states which should become degenerate under those symmetries. Consider for instance the pseudoscalar and scalar nonets $\pi^a=i\bar\psi_l\gamma_5\tau^a\psi_l$, $\delta^a=\bar\psi_l \tau^a \psi_l$ for isospin $I=1$, $\eta_l=i\bar\psi_l\gamma_5 \psi_l$, $\eta_s=i\bar s \gamma_5 s$, $\sigma_l=\bar\psi_l \psi_l$, $\sigma_s=\bar s s$ for $I=0$, $K^a=i\bar\psi \gamma_5 \lambda^a \psi$, $\kappa^a=i\bar\psi \lambda^a \psi$ $(a=4,5,6,7)$ for $I=1/2$. Here, $\psi_l$ is the light quark doublet and those states correspond respectively to the quantum numbers of the pion, $a_0(980)$, light and strange component of the $\eta/\eta'$, light and strange components of the $f_0(500)/f_0(980)$, kaon and $K(800)$ (or $\kappa$). For the isospin $I=0,1$ sector, chiral and $U(1)_A$ transformations connect the bilinears
\begin{eqnarray}
\pi^a\,&\xleftrightarrow{SU_A(2)}&\sigma, \quad \delta^a\xleftrightarrow{SU_A(2)}\eta_l, \\ \pi^a&\xleftrightarrow{U(1)_A}& \delta^a, \quad \sigma\xleftrightarrow{U(1)_A}\eta_l
,
\end{eqnarray}
which are the partners that have been studied in recent lattice and theoretical works on this subject. The lattice results are not fully conclusive. On the one hand, for $N_f=2+1$ flavors and physical quark masses, the analysis of~\cite{Buchoff:2013nra} shows degeneracy of $U(1)_A$ partners well above the $O(4)$ ones. On the other hand, $N_f=2$ works~\cite{Aoki:2012yj,Cossu:2013uua,Tomiya:2016jwr,Brandt:2016daq} point to $U(1)_A$ restoration at $T_c$ in the chiral limit, while for massive quarks in those works the strength of $U(1)_A$ breaking increases with the volume \cite{Brandt:2019ksy}.
\section{Ward Identities}
We have recently analyzed the chiral pattern commented above, exploiting Ward Identities derived formally from the QCD generating functional \cite{GomezNicola:2017bhm,Nicola:2018vug}. In particular, the following identity connects susceptibilities (two-point correlators at $p=0$) in the pseudoscalar $\eta_l$, $\pi$ and crossed $\eta_l\eta_s$ channels with the topological susceptibility of the anomaly operator $A(x)=\frac{3g^2}{16\pi^2}\mbox{Tr}_c G_{\mu\nu}\tilde G^{\mu\nu}$:
\begin{equation}
\chi_P^{ls}(T)=-2\frac{\hat m}{m_s} \chi_{5,disc}(T)=-\frac{2}{\hat m m_s}\chi_{top}(T),
\label{wils5}
\end{equation}
where
$\chi_{5,disc}(T)=\frac{1}{4}\left[\chi_P^\pi(T)-\chi_P^{ll}(T)\right]$ and $\hat m=m_u=m_d$. Now, one can choose a $SU(2)_A$ transformation so that
\begin{equation}
\eta_l(x)\xrightarrow{SU_A(2)} -\delta^b (x)\Rightarrow \chi_P^{ls}\xrightarrow{SU_A(2)} 0 ,
\label{chilsvanishing2}
\end{equation}
since $\eta_s$ is invariant under $SU(2)_A$ transformations and the $\delta\eta_s$ correlator vanishes by parity. Therefore, from~\eqref{wils5}, the conclusion is that for exact chiral restoration, where $\delta$ and $\eta_l$ should degenerate, $\chi_{5,disc}$ should vanish as well. Thus, $\pi^a-\eta$ degenerate and the $O(4)\times U(1)_A$ pattern is realized. This should be then the scenario in the chiral limit for two massless flavours at $T_c$, consistently with the lattice results in ~\cite{Aoki:2012yj,Cossu:2013uua,Tomiya:2016jwr,Brandt:2016daq,Brandt:2019ksy}. For $N_f=2+1$ flavours and physical masses, the strangeness contribution and the large uncertainties for $\delta-\eta_l$ degeneration~\cite{Buchoff:2013nra} might explain a stronger $U(1)_A$ breaking, consistently also with the chiral limit analysis of that collaboration \cite{Bazavov:2018mes}.
An interesting application of WI in this context is related to the temperature dependence of lattice spatial screening masses $M_i$ ~\cite{Nicola:2018vug,Nicola:2016jlj} for different $i$ channels. Assuming a scaling $M_i(T)/M_i(0)\sim \left[\chi_i (T)/\chi_i(0)\right]^{-1/2}$, the WI allow to connect $M_i(T)$ with suitably subtracted quark condensates, well under control in lattice simulations. This assumption implies that the zero momentum propagator given by the susceptibilities $\chi_i$ dominates the thermal dependence. One can actually test such scaling laws directly for lattice collaborations providing data on both screening masses and quark condensates for the same lattice setup. Such test has been performed in \cite{Nicola:2018vug} for the $\pi,K,\bar s s$ and $\kappa$ channels, which according to the WI scale as the inverse square root of $\mean{\bar q q}_l$, $\mean{\bar q q}_l+2\langle \bar s s \rangle$, $\langle \bar s s \rangle$ and $\mean{\bar q q}_l-2\langle \bar s s \rangle$ respectively. The agreement is quite good, with only two fit parameters related to the definition of subtracted condensates. It explains also the qualitative behaviour of the $M_i(T)$ around $T_c$, from the expected one of the quark condensates involved. Thus, for instance, the rapid growth of $M_\pi (T)$ would be explained by the inverse dependence $\left[\mean{\bar q q}_l (T)\right]^{-1/2}$ while $M_K$ and $M_{\bar s s}$ are softened by the $\langle \bar s s \rangle(T)$ component.
\section{Effective Theories}
Hadronic effective approaches like the HRG or ChPT (for the lightest states) are needed to provide a physically meaningful description below the transition. In connection with our previous discussion, it is worth mentioning that recent analysis within $U(3)$ ChPT (where $N_c^{-1}$ is included in the standard chiral power counting) have allowed on the one hand to verify the previously mentioned WI \cite{Nicola:2016jlj} and on the other hand to confirm the pattern of $O(4)\times U(1)_A$ restoration in the chiral limit \cite{Nicola:2018vug}. The latter is showed in Fig. \ref{fig:u3chpt} where pseudocritical temperatures associated to the degeneracy of different $O(4)$ and $O(4)\times U(1)_A$ partners, converge as the pion mass vanishes.
\begin{figure}
\centerline{\includegraphics[width=6.5cm]{chiraltc.pdf}\includegraphics[width=6.5cm]{chitopfiniteTu3.pdf}}
\caption{Left: Evolution towards the chiral limit of the different $O(4)$ and $U(1)_A$ restoration temperatures within $U(3)$ ChPT. Right: Temperature dependence of the topological susceptibility calculated within the U(3) formalism compared to lattice data from~\cite{Bonati:2015vqz} and~\cite{Borsanyi:2016ksw} with $T_c=155$ MeV.}
\label{fig:u3chpt}
\end{figure}
The $U(3)$ ChPT framework allows also to obtain a quite accurate description of the topological susceptibility $\chi_{top}$ and its thermal dependence \cite{Nicola:2019ohb}. The leading order yields
\begin{equation}
\chi_{top}^{U(3),LO}= \Sigma \frac{M_0^2 {\bar m}}{M_0^2+6B_0{\bar m}}
\label{chitoploib}
\end{equation}
with $\Sigma=B_0F^2$ the single-flavor quark condensate in the chiral limit, $B_0=M_{0\pi^\pm}^2/(m_u+m_d)$, with $M_{0\pi^\pm}$ the tree-level mass of the charged pions, $F$ the pion decay constant in the chiral limit, $M_0$ the anomalous part of the $\eta'$ mass and $\displaystyle\bar m^{-1}=\sum_{i=u,d,s} m_i^{-1}$. Expression \eqref{chitoploib} reproduces the known results for two and three light flavours in the limit $M_0\rightarrow\infty$ \cite{Leutwyler:1992yt} as well as the quenched gluodynamics limit for $m_i\rightarrow\infty$ \cite{Witten:1979vv,Veneziano:1979ec}. The NLO corrections can be found in \cite{Mao:2009sy}, while the NLO and NNLO $U(3)$ results at $T=0$ are given in \cite{Nicola:2019ohb}, including the fourth-order cumulant of the topological charge. The contribution of $\eta'$ loops and $\eta-\eta'$ mixing corrections provided by the $U(3)$ formalism are of the same order as the $K,\eta$ $SU(3)$ ones and are compatible with the lattice results in \cite{Bonati:2015vqz,Bonati:2016tvi}. In addition, the large-$N_c$ behaviour of both quantities arising naturally within this formalism agrees also with lattice analysis \cite{Bonati:2016tvi}.
The temperature evolution of the topological susceptibility within the $U(3)$ ChPT analysis, showed in Fig. \ref{fig:u3chpt}, is consistent with lattice data, even far beyond the applicability range of the theory. Although $\chi_{top}(T)$ scales perturbatively as $\mean{\bar q q}_l(T)$ (actually both quantities are proportional at LO), deviations from this behaviour are expected around the transition. Actually, from the WI in \eqref{wils5} and the WI $\chi^\pi_P=-\mean{\bar q q}_l/\hat m$, an additional contribution proportional to $\chi_P^{ll}(T)$ is present, consistently with the existence of a sizable gap between chiral and $U(1)_A$ restoration.
Finally, we remark that combining the standard ChPT expansion with unitarization arguments, one can generate thermal resonances, which show up as second-sheet Riemann poles of meson scattering amplitudes at finite temperature \cite{Dobado:2002xf}. The case of the thermal $f_0(500)$ is particularly important in the present context since it saturates the scalar susceptibility, giving rise to a peak around the crossover transition compatible with lattice data, as shown in Fig. \ref{fig:scalarsus}, even more accurately than the HRG description \cite{Nicola:2013vma,Ferreres-Sole:2018djq}.
\begin{figure}
\centerline{\includegraphics[width=8cm]{unitsuslec.pdf}}
\caption{Scalar susceptibility saturated by the unitarized thermal $f_0(500)$ pole, according to \cite{Ferreres-Sole:2018djq}. A normalization factor $A$ has been chosen to match the perturbative ChPT result at $T=0$ and the uncertainty bands given by the low-energy constants (LEC) is shown. Lattice points are taken from \cite{Aoki:2009sc}.}
\label{fig:scalarsus}
\end{figure}
\section{Conclusions}
Despite the recent advances in the understanding of the QCD phase diagram, there are still many relevant open problems such as the nature of the transition, the description of matter rich in baryon density and the critical point. We have showed that the use of theoretical tools such as Ward Identities and Effective Theories allow us to make strong claims about the pattern of the transition. It points towards $O(4)\times U(1)_A$ restoration in the limit of two massless flavours, from the analysis of partner degeneration. Related observables accurately described within this framework are screening masses, the topological charge distribution and the scalar susceptibility through thermal unitarity.
\paragraph{Acknowledgements}
Work partially supported by research contract FPA2016-75654-C2-2-P (spanish ``Ministerio de Econom\'{\i}a y Competitividad") and the Swiss National Science Foundation, project No.\ PZ00P2\_174228. This work has also received funding from the European Union Horizon 2020 research and innovation programme under grant agreement No 824093. A. V-R acknowledges support from a fellowship of the UCM predoctoral program.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,374
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HomeDune Club notes part 12 (Final)
Dune Club notes part 12 (Final)
October 6, 2017 October 12, 2017 The Anomalous Host Books19, book, club, comic, dune, frank, girl, herbert, novel
Continuing from part 11 of the Dune Book Club, run by Comic Book Girl 19. This is the last entry.
Notes Before the Twitch Stream
"How could you do such a foolish thing?" she demanded.
"He is your son," Chani said.
Jessica glared at her.
Heheh. But in all honesty, Jessica has made some questionable choices, what with drinking the blue Kool-Aid while pregnant, plus all the manipulations she causes to others, including Paul. She's not in much of a position to judge in that regard.
Paul said: "There is in each of us an ancient force that takes and an ancient force that gives. A man finds little difficulty facing that place within himself where the taking force dwells, but it's almost impossible for him to see into the giving force without changing into something other than man. For a woman, the situation is reversed."
"The greatest peril to the Giver is the force that takes. The greatest peril to the Taker is the force that gives. It's as easy to be overwhelmed by giving as it is by taking."
This sounds familiar. Oh yes, that film Mother!. In that film the "mother" is a symbol for nature, something that gives and gives and gives until there is nothing left to give, and man/god/religion represented by people who take and take and take until there is nothing left to take.
But it is stated in the novel that there is a balance to be had here. That if one cannot give without taking, or cannot take without giving, then a balance is achieved. That it is ok to take so long as something that is given, and vice-versa. Seems to imply that man and woman belong together to achieve this sort of balance in their lives, assuming they cannot gain this balance on their own.
But what does it mean that the woman is a giver and the man is a taker? Women giving love and babies? Men taking that love? Taking control, taking the lead? It's abstract, but something I'd like clarification on. Maybe Comic Book Girl 19 will provide some answers.
"'Use of atomics against humans shall be cause for planetary obliteration.'"
Something tells me that will be worth remembering in this Dune universe.
"Tell us Gurney, why were the cityfolk down there driven from their homes by the Sardaukar?"
"An old trick, my Duke. They thought to burden us with refugees."
Oh, well now. It seems as if Frank Herbert knows that an overabundance of refugees can become so much of a burden to a society that it could cause their downfall. A tactic that has been intentionally used in past wars. Surprisingly relevant today, likely more-so than when the book was written.
Jessica stopped in front of Paul, looked down at him. She saw his fatigue and how he hid it, but found no compassion for him. It was as though she had been rendered incapable of any emotion for her son.
Now this is another part that I would like more clarification on. Why does she have no compassion for her son now? Because she views him as less of a son and more of a monster, because of the actions he has been taking, because of the things he has been saying? More of a freak? Or is she becoming more like he was at an earlier point in the book, where he felt nothing for his dead father? Or is compassion something she currently can no longer give, indicating she is now less of a giver and more of a taker? Or neither?
This leads to an intense discussion between Paul and Jessica on pages 764-765. Of how ruthless he and Chani and others are, and how this disturbs Jessica who doesn't want Paul to become as ruthless and political as his father. She doesn't want him to make the same mistakes Leto and herself have made.
"Isn't it odd how we misunderstand the hidden unity of kindness and cruelty?"
"But wisdom tempers love, doesn't it? And it puts a new shape on hate. How can you tell what's ruthless unless you've plumbed the depths of both cruelty and kindness?"
Jessica is also firmly against Paul taking the Padishah Emperor's daughter Irulan as his wife for political gain and power. But then one must ask, what other possible alternative could there be to avoid all out violence and the potential destruction of Arrakis? It's too late to try any other path, just as Paul now realizes this Jihad is now an unfortunate inevitability that was destined to come as a result of him regaining power. They have won, but they have also lost. Yet Paul has rationalized the Jihad in his mind now by stating, "There are no innocents anymore." Is Paul becoming too ruthless? Or has his wisdom made him able to see the wickedness in everyone? As he said, wisdom tempers love, and how that is the case for both Paul and Jessica.
Page 766-767:
And he thought about the Guild–the force that had specialized for so long that it had become a parasite, unable to exist independently of the life upon which it fed.
[…] they'd chosen always the clear, safe course that leads ever downward into stagnation.
Living the life of a parasite is living a life that cannot possibly ever be independent, at least not once one has reached maturity. The Guild is a metaphor for oil corporations, which cannot survive without their main product, oil, and will thus do anything to keep taking and selling it. But this can also extend toward drug-addicts, people who continue to live with their parents well into their late-20s, late-30s, etc. Towards people on welfare. It can apply to many things. Hence why it was mentioned in an earlier session that one shouldn't become overly dependent on any one thing. It's bad to stay addicted to the Internet just as it is bad to only rely on your car/truck for transportation, bad to stay reliant on oil, to stay reliant on your parents, to stay reliant on the government, etc. Independence is a very valuable thing.
Anyway, so Count Fenring is someone to watch out for, as apparently he is someone who could've become the Kwizatz Haderach. And Feyd has a bastard daughter. And there's also Alia. All of these individuals, plus Paul, are those the Bene Gesserit wish to influence for their own gain. The plans within plans continue, as do the political games. It never ends, even when a victory and/or loss is had.
And the book ends with a speech from Jessica. She seems bitter about the way things have turned out, in regards to the present. But there is some solace to be had for the future, for those who will remember them. "History will call us wives," as opposed to their official position as concubine, for while they may be called concubines, they are known to be the ones the husband truly loves.
I have to admit, as the novel went on, I started to dislike Jessica even more. A part of me understands her bitterness, yet another part of me thinks that this is justified karma towards the Bene Gesserit for all their plans to control others via seduction or force or the Voice. Kinda would've liked more insight into her reasoning in the last section so that she can become more easily understood and sympathetic there.
Well, this does have me curious about the sequel.
Notes After the Twitch Stream
"Even though it is the men who sit in their positions of power, it is the scheming of women working together that truly shapes the universe."
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The Tao of Anarchy: There is no God. There is no State. They are all superstitions that are established by the power-hunger psychopaths to divide, rule, and enslave us. It's only you and me, we are all true and real existence though in one short life. That is, We all are capable to freely interact with one another without coercion from anyone. We all are capable to take self-responsibility to find ways to live with one another in liberty, equality, harmony, and happiness before leaving this world forever. We all were born free and equal among all beings on this planet. We are not imprisoned in and by a place with a political name just because we were born there by chance. We are not chained to a set of indoctrinated beliefs that have been imposed upon us by so-called traditions. This Planet is home to all of us. No one owns it. We share the benefits from and responsibility to this Earth. We pledge no oath, no allegiance to no one; submit to no authority. We are all free and equal. The only obligation we all must undertake constantly with consistency is to respect the same freedoms and rights of others.
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Busting out of Bristol, mainly movie talk
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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Sembaruthi é uma série de televisão indiana - Tamil de 2017 e produzida pela Zee Tamil. A série é estrelada por Priya Raman, Shabana Shajahan, VJ Agni nos papéis principais.
Elenco dos Personagens
Elenco
Priya Raman como 'Aadhikadavur' Akhilandeshwari
Shabana Shajahan como Parvathi Aadithya
Karthik Raj → VJ Agni como Aadhi
Elenco estendido
Oorvamubu Lakshmi como Vanaja
Sanjay Kumar Asrani como Purshothaman
Janani Ashok Kumar → Dheepthi Kapil como Aishwarya Arun
VJ Kathir como 'Aadhikadavur' Arun Purushothaman
VJ Mounika como Nandini
Narasimha Raju como Sundaram
Manobala como Mr. Perumal
Shanthi Anand como Janaki
Singapore Deepan como Vadivu
Ligações externas
Zee Tamil website
Séries de televisão da Zee Tamil
Programas de televisão em língua tâmil
Séries de televisão de romance língua tâmil
Séries de televisão da Tâmil Nadu
Dramas em língua tâmil
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,204
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require 'spec_helper'
describe CollaboratorsHelper do
let!(:cookbook) { create(:cookbook) }
let!(:collaborator1) { create(:cookbook_collaborator, resourceable: cookbook) }
let(:group) { create(:group) }
let!(:collaborator2) { create(:cookbook_collaborator, resourceable: cookbook, group: group) }
let!(:collaborator3) { create(:cookbook_collaborator, resourceable: cookbook, group: group) }
before do
expect(cookbook.collaborators).to_not be_empty
end
describe '#non_group_collaborators' do
it 'finds all collaborators not associated with a group' do
expect(helper.non_group_collaborators(cookbook.collaborators)).to include(collaborator1)
expect(helper.non_group_collaborators(cookbook.collaborators)).to_not include(collaborator2)
expect(helper.non_group_collaborators(cookbook.collaborators)).to_not include(collaborator3)
end
end
describe '#group_collaborators' do
it 'finds all collaborators associated with a group' do
expect(helper.group_collaborators(cookbook.collaborators, group)).to include(collaborator2)
expect(helper.group_collaborators(cookbook.collaborators, group)).to include(collaborator3)
expect(helper.group_collaborators(cookbook.collaborators, group)).to_not include(collaborator1)
end
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 483
|
Description: Earth view over Michigan. Lake Superior is in the bottom right corner of field of view. The Strait of Mackinac between Lake Michigan and Lake Huron is in the center field of view. Image taken during STS-121 which flew July 4 - 17, 2006.
S121E08326 - STS-121 - Earth limb view taken during STS-121.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,137
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Roberto Peretti (born 12 April 1966) is an Italian short track speed skater. He competed in the men's 5000 metre relay event at the 1992 Winter Olympics.
References
1966 births
Living people
Italian male short track speed skaters
Olympic short track speed skaters of Italy
Short track speed skaters at the 1992 Winter Olympics
Sportspeople from Turin
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,978
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O Prêmio Empire de Melhor Ator é uma das categorias dos Prêmios Empire apresentados anualmente pela revista especializada em cinema britânica Empire. O prêmio é concedido a atores por performance destacada em um papel principal, sendo uma das cinco categorias concedidas continuamente desde a primeira edição da premiação, em 1996. O ator britânico Nigel Hawthorne foi o primeiro vencedor do prêmio por sua atuação como Rei Jorge III em The Madness of King George.
Desde a sua introdução, o prêmio foi concedido a 20 atores diferentes, sendo Johnny Depp, James McAvoy e Matt Damon os maiores vencedores da categoria, com dois prêmios cada um. Depp, inclusive, foi indicado por cinco vezes, mais do que qualquer outro ator, principalmente pela franquia Pirates of the Caribbean. O mais recente vencedor é Hugh Jackman por sua performance em Logan (2017).
Vencedores e indicados
Ator
Empire de melhor ator
|
{
"redpajama_set_name": "RedPajamaWikipedia"
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| 3,520
|
#FloodRelief in Hamburg
It was a joy for me to be able to participate in #FloodRelief in #Hamburg, Iowa last week. My job was to interact with families, offer assistance, and receive their written permission to enter their homes. Many of these people are in a hopeless situation and are positively impacted when we offer to help them try to overcome the flooding they have in their lives.
We offer to pray with these families for their specific needs – I have never had anyone turn down these prayers. I also had the privilege to direct some of the volunteers who were offering to perform needed clean-up. In a flood situation, this is hard and dirty work. I believe God expects us to serve those in need as we are able. I praise God for the way He has situated GoServ Global to participate in these local disasters. Dennis Anderson and all the volunteers are such an inspiration to work around.
Perhaps you would be in a position to serve with us for a few days. Or perhaps you could help us serve by making a financial donation. There are many costs associated with this assistance – fuel, tools, meal costs, and the vehicles, trailers, and other equipment that is part of what GoServ Global brings to serve in these situations. https://goservglobal.org/give/
– Daryle Hamlin, GoServ Global Board Member
The Power of Obedience
"How did you know we were out of food?" questioned Madam Mauline, head of Bethel Orphanage.
Conwell Larson just shook his head and said, The Lord told me.
If GoServ Global hadn't brought food that day, everyone at this orphanage wouldn't have eaten for 10 days.
The orphanage had recently lost its funding and because of the impending demonstrations, the stores had shut down. It had already been a couple days since they'd eaten anything.
That day Conwell brought a volunteer to the Bethel who was serving in Haiti on a GoServ Global mission trip. This volunteer shared, "A few months ago, the Lord laid it on my heart that this trip was going to change my life."
After learning that Bethel needed $750/month to feed all the children, he said he wanted to cover this. He had been setting money aside for awhile now and so far, he had enough for 6 to 8 months, but he'd get friends to help support it too.
Many people ask Ken DeYoung – why Haiti? He shares a story about the time a mother handed him her baby in downtown Les Cayes.
So many ask, how can you do that to your child – give away your baby? But, she did it out of love – she couldn't afford to take care of her and thought that Ken could provide much more than she could.
"That tore me apart," he says. "How do you walk away from that? They're stuck in a situation where they need a little help. We can't do it all, but we all can do something."
As GoServ Global helps the physical needs, the recipients always asks, "Why are you doing this?" It's at this time that God opens their hearts for the gospel. The Lord is changing lives by helping through physical needs.
What is God calling you to be obedient in today?
The Power of a Home
LaBrise is a tiny fishing village right on the ocean in Haiti that was hit hard by Hurricane Matthew nearly 3 years ago. GoServ Global has built more than 20 Sukup Safe T Homes® in this village. One mother of 6 proudly shows us her new home.
"Even though the floor isn't yet finished, I am so happy to get this home," she said.
Her home is sparsely furnished with a table, some bowls for cooking, a tiny mat on the floor, yet she has a sparkle in her eye.
Down the road, a mother of 6/grandmother of 15 has been living in her Sukup Safe T Home® for 4 months. When asked if she likes her new home, she breaks out in a huge smile.
"This home makes me so happy," she says. "When it rains, we now stay dry."
With each home that's given, GoServ Global makes sure to share the reason why we do what we do.
"We feel the Lord has asked us to do this and we hope you see Christ's love through this," shares Ken DeYoung, GoServ Global Co-Founder and Haiti Director. "It's important to have a physical home, but it's more important to have an eternal home."
At LaBrise, GoServ Global has been helped build a church for the community in addition to the homes, and many have come to Christ.
According to Yvald, a Haitian who works with GoServ Global, more than 150 families are on the waiting list for a new home.
To give toward a Sukup Safe T Home®, click on goservglobal.org/give and choose "Safe T Home® in the dropdown.
Sukup Manufacturing Co.
#SafeTHome
Officials say that communities in eastern Nebraska and western Iowa have been hit the hardest with the recent flooding. At this time, the GoServ Global Disaster Relief Team is assessing the situation to see where we can be the most effective. When we respond, we will need volunteers and funding.
To VOLUNTEER:
Text GoServ Global Domestic Director Dennis Anderson
at (712)887-0862 with your Name, Cell, Email, Availability & Skills
To GIVE:
Click on https://goservglobal.org/give/
Choose "Domestic Disaster Relief"
Mail Your Donation to:
GoServ Global
Eagle Grove, IA 50533
Write "Domestic Disaster Relief" in the memo line
#FloodRelief #Volunteer #Donate
Iowa FFA Students Build GoServ Global's 300th Safe T Home® in Haiti in Memory of Eugene Sukup
For more than two years, Vainceur and his five boys lived in an 8'x10' tin shack with a tarp roof after Hurricane Matthew destroyed their home. Today, this Haitian family of six has a new place to call home, marking GoServ Global's 300th Sukup Safe T Home® built in Haiti. This home is extra special because it was built by the Audubon, Iowa FFA team in memory of Sukup Manufacturing Co. founder Eugene Sukup, who died this past summer at the age of 89. Sukup employees donated most of the funds for the Safe T Home®.
"The Safe T Home® really embodies two of our values as a family-owned company – making high quality products from steel and giving back," shared Steve Sukup, CFO at Sukup. "Building one of these homes in Haiti was a very fitting way to honor my father, Eugene, who founded the company and ingrained these values in it from the beginning."
Sukup Safe T Home®
After the January 2010 earthquake devastated Haiti, Brett Nelson of Sukup Manufacturing came up with the design of the Safe T Home®, measuring 18-feet in diameter and made entirely of metal, making it resistant to termites and moisture. In 2016, Hurricane Matthew devastated Haiti with winds in excess of 145 mph, putting the homes to the test. Yet, all 200 homes prevailed with just minor damage, while the vast majority of traditional homes in the area were destroyed.
Homes like Vainceur's. The father lost his home, his garden, and a year later his wife passed away, leaving him to raise all five boys alone. Vainceur shared how tough it was following the hurricane, yet today was a good day.
"Right now I feel at peace," he said. "I learned that I was getting a new home about 3 days ago."
#LivingtoServe
Not only was Vainceur touched by the Safe T Home®, so was the team that built it. Eight members of the Audubon FFA along with their advisor, Brittany Elmquist and her husband, Joe, helped build the home along with the family.
"I will not forget the look of pride on [Vainceur's] face as we handed him his keys for his new Safe T Home," shared FFA student Grace Christensen.
Eighteen-year-old Jayden Hartl added, "It was humbling to meet a family that had lost nearly everything except for each other. They were driven and doing everything they could to try and get their life back on track."
Since 2012, nearly 75 FFA students from across the U.S. have served on a GoServ Global mission trip.
"I wanted our chapter to be involved in this project to give members the opportunity to exemplify the FFA motto, 'Learning to Do, Doing to Learn, Earning to Live, Living to Serve' with emphasis on 'Living to Serve,'" shared Elmquist. "Haiti is a country in need and our members knew they could be of assistance with agricultural projects and by having great character to learn the culture and respect those involved."
After returning from Haiti, the team was so impacted by the trip that the Audubon FFA voted to sponsor Paul, one of the boys they met at the Joshua House Orphanage.
Last year, 325 volunteers served on a GoServ Global mission trip. GoServ Global shares God's love by responding to disaster, empowering sustainable community development and creating world change through hands-on involvement in Guatemala, Haiti, India, Peru, Uganda, and the United States.
Shortly after GoServ Global began in 2011, the nonprofit connected with Sukup Manufacturing to discuss how the Safe T Home® could help those in need. Not only have 300 homes been built in Haiti, 30 more are being built in Uganda to house refugee orphan children who have fled war-torn South Sudan. Ten homes have also been built in Peru and 10 in Kenya.
The need for homes is great in Haiti as there are countless more families like Vainceur's. One Safe T Home® costs $7,000 including shipping. To give toward a Safe T Home®, visit https://goservglobal.org/give/.
Vainceur and his five boys lived in this makeshift home for more than two years after Hurricane Matthew destroyed their house.
The Audubon FFA Team building the Safe T Home®.
The Audubon FFA Team inside the Safe T Home® with the kids of the family.
YOU CRUSHED IT!
We are so THANKFUL for everyone who gave to our Year-End Campaign. YOU CRUSHED our goal of $500,000!! Our grand total is $567,315!
We stand in awe of an awesome God who continues to provide for GoServ Global through our donors. Thank you so much for your continued support of our ministries around the world. May you have a blessed 2019!
YOU Crushed our Goal!!
WOW!! WOW!! WOW!!
YOU helped us crush our year-end goal of raising $500,000! Currently GoServ Global has raised $512,000!! We praise God for your gifts and continued support.
Thank you to everyone who has given to GoServ Global.
If you have not yet given, it's not too late! Your gifts will enable us to get off to a great start for 2019!
https://goservglobal.org/give/
May you have a blessed new year!
GoServ Global Reaches 84% of Goal with 3 Days Left
We are PRAISING GOD for YOUR GENEROSITY!
Just 2 days ago we reported that GoServ Global had raised $366,000 of our $500,000 year-end goal.
TODAY we are at $420,000 – reaching 84% of our year-end goal. Just $80,000 more is needed for us to reach our goal.
Thank you to everyone who has given to GoServ Global. We are blown away by your continued support!
If you have not given, it's not too late! Join us! https://goservglobal.org/give/
Nearly 75% to our Year-End Goal!!
Because of YOU – our faithful supporters – GoServ Global has reached nearly 75% of our year-end goal!! Last week we reported that we were only at 25% of our goal – ($125,000). TODAY we are $366,000 of our $500,000 year-end goal. Praise God!
Thank you to everyone who has given to GoServ Global. We appreciate your continued support! If you have not given, it's not too late! https://goservglobal.org/give/
GoServ Global needs your help as we end 2018.
GoServ Global needs your help as we end 2018. Currently, we are $379,000 short of our year-end goal.
Your year-end gift TODAY will allow us to continue serving children, widows and families in great need around the world.
If you have given to GoServ Global on Giving Tuesday or have already provided a year-end gift, we sincerely thank you for your continued support! We invite you to pray with us that others would be moved to come alongside all of us in this ministry.
If you have not yet given, there is much to be done and we need your help. Please consider a one-time gift today or sign up to be a monthly giver – goservglobal.org/give.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 9,809
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William Herbert, de Pembroke, Herbert de Cardiff (né vers 1501, mort le à Hampton Court) est un aristocrate et homme politique de la période Tudor, chevalier de l'ordre de la Jarretière. Il est le fondateur de la maison noble de Herbert.
Herbert est le fils de Richard Herbert, bâtard du de Pembroke, et de Margaret Cradock.
Homme de main
William Herbert est un jeune homme d'une ambition démesurée, doublée d'un tempérament colérique et violent. Dépeint par John Aubrey comme un bagarreur insatiable (a mad fighting fellow), le jeune Herbert fut d'abord page du comte de Worcester. Au cours d'une bagarre de la garde du comte avec des Gallois à Bristol, Herbert tua un mercier du nom de Vaughan et dut s'enfuir en France.
À son arrivée sur le continent, il s'engagea dans l'armée du roi , s'y taillant une grande réputation d'habileté et de courage au combat : : sa réputation d'homme de main était faite.
La première femme d'Herbert, Anne Parr (1515-1552), était la sœur de Catherine Parr, qui devint plus tard reine consort : il connut les faveurs de la cour par cette belle-sœur et fut anobli en 1544. Henri VIII, en reconnaissance de ses qualités d'homme de main, lui donna en apanage l'abbaye de Wilton et d'autre terres (Remesbury et le gouvernement du château de Cardiff) dès 1544. Il fit détruire l'abbaye pour édifier à la place le manoir de Wilton House dans les années 1540.
Comte en titre
Herbert fut l'un des précepteurs du prince Édouard à la mort d'Henri VIII en 1547. En tant qu'exécuteur testamentaire du défunt monarque et bénéficiaire de généreuses donations de la Couronne, Il s'imposa comme l'un des trois grands du royaume sous le règne d'Édouard, aux côtés du lord-protecteur Edward Seymour et de son rival, John Dudley, qui cherchait son appui. Il prit finalement le parti de Dudley, et à la chute de Seymour, fut récompensé par des terres dans le Wiltshire. Il fut reçu chevalier de l'ordre de la Jarretière en 1549, créé baron Herbert de Cardiff le , et 1er comte de Pembroke (dixième création) l'année suivante par ordre d'Édouard VI.
À la mort du roi Édouard VI, Herbert appuya les prétentions au trône de Jane Grey. Il arrangea le mariage de son fils aîné et héritier, Henry, avec la sœur de Jane, Catherine Grey, au manoir de Durham le , le jour même où Jane Grey épousait Guilford Dudley. Le troisième mariage de ce jour-là était celui de la fille benjamine de John Dudley, Katherine et de Henry Hastings (3e comte de Huntingdon). Lorsqu'il devint clair que Marie la catholique allait monter sur le trône, il fit mettre sa belle-sœur Catherine à la porte, et demanda le divorce. Le père de Catherine et sa sœur Jane furent tous deux exécutés pour haute trahison en sur ordre de la reine Marie. Herbert prit lui-même ses distances avec la famille Grey déchue et s'attira les faveurs de la nouvelle reine en écrasant la révolte de Thomas Wyatt.
Son corps expéditionnaire anglais arriva trop tard pour pouvoir participer à la bataille de Saint-Quentin, mais il participa au pillage de la ville. Pembroke fut le meilleur général de la reine Marie lors de la campagne de France.
Marie, quoiqu'elle eût des doutes quant à la loyauté du comte de Pembroke, le nomma pourtant gouverneur militaire de Calais, président du parlement de Galles etc. Il jouissait aussi jusqu'à un certain degré de la confiance de Philippe II d'Espagne. Il conserva son rang à la cour sous le règne d', du moins jusqu'en 1569, date où il se trouva compromis dans un projet de mariage entre Marie Stuart et le duc de Norfolk.
Selon les très vivantes Brief Lives de John Aubrey,
Herbert avait pour secrétaire Robert Streynsham, qui fut pasteur à Ospringe (près de Faversham dans le Kent).
Herbert avait une affection particulière pour son petit chien. Aubrey rapporte à ce sujet qu' On peut en effet apercevoir cet animal sur le portrait d'Herbert.
Sa mort
William meurt le , au château de Hampton Court. On l'inhume le dans la cathédrale Saint-Paul, aux côtés de sa première femme, Anne Parr-Herbert. Sa stèle funéraire a disparu dans le grand incendie de Londres (1666). Un monument dans la nouvelle crypte mentionne la disparition de ce monument historique.
Bibliographie
G. E. Cokayne, The Complete Peerage, 1910–1959
Références
Liens externes
Date de naissance incertaine (XVIe siècle)
Comte de la pairie d'Angleterre au XVIe siècle
Chevalier de la Jarretière au XVIe siècle
Gouverneur militaire
Personnalité de l'époque Tudor
Général anglais
Décès en mars 1570
Comte de Pembroke
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{
"redpajama_set_name": "RedPajamaWikipedia"
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\section{Introduction.}
The inclusive cross sections of the leading neutrons in deep inelastic scattering with protons (DIS) attracts interest since this process allows us to extract the $F_2$ deep inelastic structure function for pions ($F^\pi_2$) (see \fig{genpic} and Refs.\cite{BA} ). This process has one rapidity gap since no particles are produced in the region of rapidity between the neutron and the bunch of secondary particles with mass ($M_X$ in \fig{genpic}). For long time it has been known that the cross section of such processes has to be multiplied by factor $S^2$ which is called survival probability\cite{BJ,DOK,GLM1}. This factor stems from the possible interaction of the constituents of the projectile with the target that should be forbidden to preserve the gap.
In other words, the constituent of projectile could interact with the target in initial or final state suppressing the cross section of such process (see \fig{gensc} that illustrates such interactions).
\FIGURE[h]{
\begin{tabular}{c }
\epsfig{file=SPdisgenfig.eps,width=100mm}\\
\end{tabular}
\caption{The generic picture for leading neutron production in DIS: the Born approximation.)}
\label{genpic}
}
The two decades experience in calculation of the survival probability ( see Refs.\cite{KMRS,GLMSP,BGR,BO1,NNN,DA,MORI}) has shown that the predictions for survival probability could differ in the orders of magnitude (from $S^2$ = 0.9 to 0.01) depending on the model for strong interaction at high energy.
In this paper we develop the theoretical approach for survival probability in DIS based on high density QCD
\cite{GLR,MUQI,MV,JIMWLK,B,K}. For DIS at high energy QCD predicts that the dynamics of quarks and gluons (partons) can be described in terms of parton saturation\footnote{Parton saturation means that at high energy the density of partons (actually mostly gluons) reaches the maximum value. It is instructive to notice that in CGC the QCD coupling is small ($\bar{\alpha}_S \ll 1$). }\cite{GLR,MUQI,MV}. The new state of the matter: Color Gluon Condensate (CGC)\cite{MV,JIMWLK} will be produced in which
the amplitudes are dominated not by quantum fluctuations, but by the configurations of classical field containing large, $\sim 1/\bar{\alpha}_S$ numbers of gluons. This state is characterized by large density but small QCD coupling $\bar{\alpha}_S$. This feature results in the solid theoretical approach based on non-linear equations \cite{GLR,MUQI,JIMWLK,B,K}. It worthwhile mentioning that this theoretical approach has reached the most developed stage for DIS with which we are dealing in this paper.
\FIGURE[h]{\begin{minipage}{8cm}{
\centerline{\epsfig{file=SPdisshadpic.eps,width=75mm}}}
\end{minipage}
\begin{minipage}{6cm}{
\caption{Leading neutron production in DIS: general source of shadowing corrections }
\label{gensc} }
\end{minipage}
}
~
The main result of the paper is the equation for the inclusive production of leading neutron. The basic theoretical ideas how to approach the processes that have the rapidity gap, have been formulated in Ref.\cite{KL}. We explore these ideas to obtain the equation. We found the solution to the new equation and show that the interaction in initial and final sate will lead to the cross section that falls down at high energy. In other words, the survival probability turns out to be small at high energy.
The paper is organized as follows. In the next section we will derive the equation and discuss the high energy asymptotic behaviour of the solution. Section 3 is devoted to the initial condition to the equation, while in section 4 we obtain the numerical solution to the equation. In conclusion we summarize the main results.
\section{The equation}
\subsection{Derivation of the equation in the dipole approach}
In inclusive leading neutron production (ILNP) the produced partons could interact between themselves as well as with the target in the final state, unlike in the case of total cross section for which we have the non-linear Balitsky-Kovchegov equation \cite{B,K} . In principle, the interaction in the final state means that the cross section of the process does not depend only on the structure of the wave function of the colliding particle as it is for the total cross section. However, in Ref.\cite{KL}(see also Ref. \cite{KOVD}) it is shown on the example of diffraction production, that in the processes which are inclusive, the different type of interactions in the final state cancel each other. In this section we argue that ILNP is also belongs to the class of such inclusive processes as diffraction production.
In ILNP we can see three typical moments of time\footnote{We will consider all processes in the light-cone frame and will use the light-cone perturbative theory (see Ref.\cite{BRODLE})} : at $x^- = - \infty$ we have fast virtual photon
(or, better to say, a system of partons in the coherent state of the virtual photon) and the target, at $x^- \,=\,0$ these
partons interact with the target and the produce partons that propagate to $x^-= + \infty$ where the detectors are placed which measure this system of partons. Actually in our case we do not measure these partons which means that we sum over all possible final states with only one restriction that their total mass is equal to $M_X$(see \fig{genpic}). The same time structure we have in complex conjugated amplitude in which we denote times as $\bar{x}^-$ (see \fig{timestr}).
\FIGURE[h]{
\begin{tabular}{c}
\epsfig{file=SPdistime.eps,width=100mm,height=50mm}\\
\end{tabular}
\caption{The time structure of the inclusive production of leading neutrons.The low panel shows our notation for the process shown in the upper panel. The straight solid lines denote the initial dipole in the low panel. }
\label{timestr}
}
\fig{timestr} shows the particular contribution to the cross section of interest. From $x^- = - \infty$ to $x^- =0$ the wave function of the fast dipole consists of system of two quark-antiquark pairs and two gluons, at $x^- = 0$ this system interacts with the pion which destroys its coherence. As a result the components of the system (two gluons and two quark-antiquark pairs ) are produced. The components interact in the time interval $0 < x^- < + \infty $. The gluons can be emitted and absorbed in the final state. Because of this we cannot use optical theorem that reduces the cross section to the imaginary part of the elastic amplitude. The key observation is that absorption and emission in the final state ( for times $x^- >0$ and $\bar{x}^- > 0$) cancel each other. This cancellation was first proven in Ref.\cite{CHMU}. It is found that we have two types of cancellations
shown in \fig{2cancel}. The first type is cancellation of the gluon emitted in the final sate and which can be caught by the detector (see the first diagram in \fig{2cancel}-A) with gluons emitted and absorbed in the final state in the amplitude and the conjugated amplitude (see the second and third diagrams in \fig{2cancel}-A). The second type of cancellation is shown in \fig{2cancel}-B. The produced gluon from the initial wave function, that exists from $x^- = -\infty$ to $x^- =+ \infty$, cancels by the gluon from the wave function that has been absorbed in the final state and, therefore cannot be measured by the detector. Notice that the gluon in the first diagram of \fig{2cancel}-B has been emitted in the final state in the conjugated amplitude. In \fig{2cancel} we denote the gluon by quark and antiquark lines since we consider our process at large $N_c$ where $N_c$ is the number of colours.
\FIGURE[h]{
\begin{tabular}{c}
\epsfig{file=SPdiscancel.eps,width=100mm,height=50mm}\\
\end{tabular}
\caption{Two types of cancellations in the final state}
\label{2cancel}
}
Armed with these cancellations we can show that in our process the emission and absorption in the final state does not contribute to the cross section. To illustrate this point we consider the example of \fig{timestr}. One can see from \fig{cantime} that emission of the upper gluon in \fig{cantime}-1 is canceled by diagram of \fig{cantime}-2 which describes the emission and absorption of the upper gluon in the final state (actually for cancellation we need to add the diagram of \fig{cantime}-2 type for the conjugated amplitude). The absorption of the low gluon in \fig{cantime}-1 is canceled by the diagram of \fig{cantime}-3. This diagram describes the emission of the gluon from the initial state in the amplitude but the emission of gluon from the final state in the complex conjugated amplitude. The cancellation of emission and absorption in the final state means that we can used the optical theorem for interaction of the dipole with virtual pion (see \fig{genpic}). It is worthwhile mentioning that this cancellation works in any complex diagrams which differs only by the gluon shown in \fig{2cancel} \cite{CHMU}.
The formal proof of the discussed cancellation can be done using the method of mathematical induction. Let us assume
that for emission of $n$-gluons we have the cancellation and they can be characterized by the initial wave function of colorless dipole. The emission of $n + 1$ gluon by one dipole can be described by the sum of the diagrams of \fig{1gl}. One can see that diagrams of the set A in \fig{1gl} cancels as well as the diagrams of set B , due to the cancellation give by \fig{2cancel}.
The only diagram that remains and gives the contribution is the diagram of \fig{1gl}-C.
Since the initial condition for $N^\pi$ contains only one dipole we conclude that we can describe this processes by the initial wave function of dipoles.
Now we can derive the equation based on the same ideas as have been used in the derivation of Balitsky-Kovchegov (BK) equation, since the ILNP stems from the structure on the initial wave functions of colliding particles. Let us denote by $N^\pi\left( x, b,Y,Y_g\right) $ the imaginary part of the
amplitude shown in \fig{genpic}. $Y_g$ denotes the rapidity gap between the neutron and the slowest hadron among the produced particles (see
\fig{genpic}).
\FIGURE[h]{
\begin{tabular}{c}
\epsfig{file=SPdiscantime.eps,width=100mm}\\
\end{tabular}
\caption{The example of cancellation of emission and absorption in the final state for the contribution of the diagram of \fig{timestr} to the cross section.}
\label{cantime}
}
A long before the interaction the incoming dipole decays into two dipole each of them could scatter separately and produced the leading neutron. These two dipoles can interact simultaneously producing leading neutrons. However, we have another process which does not produced any particles that fill the rapidity gap. One dipole scatters elastically while the second produces the leading neutron. \fig{eq} shows these three ways of interaction. All these terms we can see in \fig{eq}. The first term shows the separate interaction of each dipole while the second term describe the
simultaneous interaction of two dipoles. The third and the forth terms describe the ILNP by one dipole while the second dipole undergoes the elastic scattering. The analytical form of this equation looks as follows:
\FIGURE[h]{
\begin{tabular}{c}
\epsfig{file=SPdisglem.eps,width=120mm}\\
\end{tabular}
\caption{The emission of one gluon by the dipole. The diagrams with the gluon emitted and absorbed by the same quark (antiquark) are not shown but they have the same pattern.}
\label{1gl}
}
\FIGURE[h]{
\begin{tabular}{c}
\epsfig{file=SPdisceq.eps,width=100mm}\\
\end{tabular}
\caption{The graphic form of the equation. The vertical dotted lines denote the time of interaction in the amplitude or in complex conjugated amplitude.
If such line crosses the blob it means that the interaction occurs. The wave lines denote the infinite time and if such line goes through the blob it means that the blob describe the production of particles.}
\label{eq}
}
\begin{eqnarray} \label{EQ}
&&\frac{\partial N^\pi\left( x_{10}, b;Y,Y_g\right)}{\partial Y}\,\,=\\
&=&\,\,\frac{\bar{\alpha}_S}{2 \pi}\,\int d^2 x_2 \frac{x^2_{10}}{x^2_{02}\,x^2_{12}}\,\left\{N^\pi\left( x_{02}, \vec{b} - \frac{1}{2}\vec{x}_{12};Y,Y_g\right)\,+\,N^\pi\left( x_{12}, \vec{b} - \frac{1}{2}\vec{x}_{02};Y,Y_g\right)\right.\nonumber\\
&-& \,\,\left.N^\pi\left( x_{12}, \vec{b} ;Y,Y_g\right)\,\,+\,\, N^\pi\left( x_{02}, \vec{b} - \frac{1}{2}\vec{x}_{12};Y,Y_g\right)\,N^\pi\left( x_{12}, \vec{b} - \frac{1}{2}\vec{x}_{02};Y,Y_g\right)\right.\nonumber\\
&-&\,\,\left.2 N^\pi\left( x_{02}, \vec{b} - \frac{1}{2}\vec{x}_{12};Y,Y_g\right)\,N\left( x_{12}, \vec{b} - \frac{1}{2}\vec{x}_{02};Y \right)\,\,-\,\,2 N\left( x_{02}, \vec{b} - \frac{1}{2}\vec{x}_{12};Y \right)\,N^\pi\left( x_{12}, \vec{b} - \frac{1}{2}\vec{x}_{02};Y,Y_g\right) \right\}\nonumber
\end{eqnarray}
where $N\left( x_{10},b,Y\right)$ is the solution of Balitsky-Kovchegov equation.
\subsection{ BFKL Pomeron calculus and inclusive production of leading neutron}
As it is well known the non-linear BK equation for the elastic amplitude corresponds to summation of `fan' diagram in the framework of the BFKL Pomeron calculus \cite{GLR,BRA}. The equation for the ILNP stems from the AGK cutting rules\cite{AGK}. These rules has been proven in QCD for all processes in which we do not have emission of the gluon from the triple BFKL Pomeron vertex (see Refs.\cite{LEPR,JAKO,KOTU,GEVE,BARY,TRE}). Our process belongs to this class and we can safely apply the AGK cutting rules. The contribution to the imaginary part of the elastic scattering amplitude can be viewed as sum to three different processes which are shown in \fig{agkproc}. If the rapidity $Y'$ is the position of the triple Pomeron vertex the simplest `fan' diagram generates three different processes: in the first one (double cut in \fig{agkproc}) the state with double density of particle(gluons) is produced while in the second process (single cut in \fig{agkproc}) the density of the particle is the same as in the single Pomeron exchange; the third process is the diffraction production in which we do not produce a particle in this rapidity gap. The AGK cutting rules establish the relations between these processes and they are shown in \fig{agk}-A.
\FIGURE[h]{
\begin{tabular}{c c}
\epsfig{file=cutpom.eps,width=40mm}& \epsfig{file=agk-incl.eps,width=90mm}\\
\fig{agkproc}-a & \fig{agkproc}-b\\
\end{tabular}
\caption{The processes that corresponds to triple BFKL Pomeron contribution to the total cross section..}
\label{agkproc}
}
\FIGURE[h,b]{
\begin{tabular}{c }
\epsfig{file=SPdisAGK.eps,width=90mm}\\
\end{tabular}
\caption{The relation between the AGK cutting rules and contribution to the inclusive production of leading neutrons. The helix lines denote gluons, pions are shown by the dashed lines. It should be noticed that in \fig{agk}-B between two exchanges of pions the thick line denotes the neutron.}
\label{agk}
}
The difference between coefficients that are shown in \fig{agk}-A and the standard ones is related to the fact that we use for the contribution of the cut Pomeron the contribution to the total cross section (see \fig{agkproc}-a). instead of the contribution to the imaginary part of the amplitude. As we know from the unitarity constraint: $ 2\, \mbox{Im}\,A \,=\, \sigma_{tot}$.
Having \fig{agk}-A in mind we can see that the leading neutrons can be produced from the first and second contributions while the third one corresponds to the diffraction production and it contributes only to the spectrum of leading protons (see \fig{agk}-B). Replacing Pomerons by the the sum of `fan' diagrams we obtain the equation given by \eq{EQ}. The direct relation between dipole language in QCD and the BFKL Pomeron calculus for the inclusive processes have been noticed in Ref.\cite{KL}. The powerful theorem on cancellation of the interaction in the final state in the Pomeroin language are hidden in the assumption that only Pomerons and their interaction contribute to the inclusive processes. Therefore, the dipole consideration can be considered as the theoretical argument for the Pomeron calculus.
\subsection{Solution at ultra high energy}
We need to find an initial condition to \eq{EQ} before searching for the solution. However, the experience with BK equation shows that the asymptotical behaviour at high energies does not depend on the initial solution \cite{LT}. Using the approach of Ref. \cite{LT} we can find the solution noticing that the solution to BK equation approaches unity at ultra high energies. Substituting $N =1$ in \eq{EQ} we obtain the following equation for $N^\pi$
~
~
\begin{eqnarray} \label{EQHE}
&&\frac{\partial N^\pi\left( x_{10}, b;Y,Y_g\right)}{\partial Y}\,\,=\\
&=&\,\,\frac{\bar{\alpha}_S}{2 \pi}\,\int d^2 x_2 \frac{x^2_{10}}{x^2_{02}\,x^2_{12}}\,\left\{-\,N^\pi\left( x_{02}, \vec{b} - \frac{1}{2}\vec{x}_{12};Y,Y_g\right)\,-\,N^\pi\left( x_{12}, \vec{b} - \frac{1}{2}\vec{x}_{02};Y,Y_g\right)\right.\nonumber\\
&-& \,\,\left.N^\pi\left( x_{12}, \vec{b} ;Y,Y_g\right)\,\,+\,\, N^\pi\left( x_{02}, \vec{b} - \frac{1}{2}\vec{x}_{12};Y,Y_g\right)\,N^\pi\left( x_{12}, \vec{b} - \frac{1}{2}\vec{x}_{02};Y,Y_g\right)\right\}\nonumber
\end{eqnarray}
Assuming that $N^\pi $ falls down at high energy we can neglect the $(N\pi)^2$ - term and one can see that \eq{EQHE} can be re-written in the form:
\begin{eqnarray} \label{EQHE1}
&&\frac{\partial N^\pi\left( x_{10}, b;Y,Y_g\right)}{\partial Y}\,\,=\\
&=&\,\,\frac{\bar{\alpha}_S}{2 \pi}\,\int d^2 x_2 \frac{x^2_{10}}{x^2_{02}\,x^2_{12}}\,\left\{ -\left( \,N^\pi\left( x_{02}, \vec{b} + \frac{1}{2}\vec{x}_{12};Y,Y_g\right)\,+\,N^\pi\left( x_{12}, \vec{b} - \frac{1}{2}\vec{x}_{02};Y,Y_g\right)\right. \right.\nonumber\\
&-& \,\,\left.\left. N^\pi\left( x_{12}, \vec{b} ;Y,Y_g\right)\,\right) \,-\,2\,N^\pi\left( x_{01};Y,Y_g\right)\,\right\}\nonumber
\end{eqnarray}
This equation can be solved
using the double Mellin transform for $\tilde{N}$, namely,
\begin{equation} \label{MT}
N^\pi\left( \xi, b;Y,Y_g\right)\,\,=\,\,\int^{\epsilon + i \infty}_{ \epsilon - i \infty} \frac{d \omega}{2 \pi i} \int^{\epsilon + i \infty}_{ \epsilon - i \infty} \frac{d f}{2 \pi i} \, e^{ \omega Y \,+\,f \xi}\, n^\pi\left( f, b;\omega,Y_g\right)
\end{equation}
where $\xi\,=\,\ln\left( x^2_{01}\,\right)$. It should be stressed that we need to consider $x^2_{10}\,Q^2_s\left( Y,b\right) \,\gg\,1$ since only in this region we can replace $N$ by unity ($Q_s$ is the saturation momentum for $N^\pi$).
Indeed, for $n^\pi$ we obtain the following equation
\begin{equation} \label{EQHE4}
\omega \,n^\pi\left( f, b;\omega,Y_g\right)\,\,=\,\,-\bar{\alpha}_S \Big\{\chi(f) \,n^\pi\left( f, b;\omega,Y_g\right)\,\,+\,4 \frac{\partial n^\pi\left( f, b;\omega,Y_g\right)}{\partial f}\Big\}
\end{equation}
where $\chi\left( f \right) \,=\,2 \psi(1) - \psi(f) - \psi(1 -f)$ is the BFKL kernel \cite{BFKL} in $f$-representation ($\psi$ is di- gamma function , see formulae {\bf 8.360 - 8.369} in Ref.\cite{RY}).
The solution to \eq{EQHE4} is
\begin{equation} \label{NTIL}
\tilde{n}^\pi\left( f, b;\omega,Y_g\right)\,\,=\,\,C(Y_g,b)\,\,e^{ + \frac{\omega \,f}{4 \bar{\alpha}_S} \, + \,\frac{1}{4} \int^f_0 d f' \chi\left( f'\right)}
\end{equation}
Taking Mellin integral of \eq{MT} by the steepest decent method we obtain the following equations for the saddle points:
\begin{equation} \label{SP}
\frac{ f_{SP}}{4 \bar{\alpha}_S}\,\,+\,Y\,=\,0;\,\,\,\,\,
\,\,\,\frac{\omega_{SP} }{4 \bar{\alpha}_S}\,\,+ \frac{1}{4} \chi\left( f_{SP}\right) \,\,+\,\,\xi\, = \,0;
\end{equation}
Taking into account that $\chi\left( f \right)\,\,\xrightarrow{f \,\gg\,1}\,\,- 2 \ln f $ we obtain the solution:
\begin{equation} \label{HESOL}
N^\pi\left( \xi, b;Y,Y_g\right) \,\,=\,\,\,C(Y_g,b)\,\,e^{ - 4 \bar{\alpha}_S Y \, \left( \xi \, -\,\ln \xi\right)}
\end{equation}
This solution demonstrates that the influence of the interaction in initial and final states are so essential that they lead to decrease of the cross section of the inclusive production of the leading neutrons. This makes the extraction of pion deep inelastic structure from this experiment problematic if not impossible. However, for more practical conclusions it is necessary to solve \eq{EQ} in more realistic kinematic region. For this goal we need to know the initial condition that we are going to discuss in the next section.
\section{Initial conditions}
The problem of the initial conditions actually includes two different issues. The first is to find the expression for the Born Approximation (see \fig{genpic}) for the leading neutron production in DIS for the initial energy. The second one relates to the explicit form of shadowing correction at the same low energy.
Restricting ourselves by calculation the survival probability we do not need to know the details of Born Approximation which can be found in Ref.\cite{BA}, since they cancels in the expression for the survival probability, namely,
\begin{equation} \label{S2}
S^2\,\,=\,\,\frac{d \sigma_{incl}\left( \mbox{exact with shadowing corrections}\right)}{d Y_n \,d^2 p_{n,T}}\Big{/}\frac{d \sigma_{incl}\left( \mbox{Born Approximation of \fig{genpic}}\right)}{d Y_n \,d^2 p_{n,T}}
\end{equation}
where $Y_n $ and $p_{n,T}$ are rapidity and transverse momentum of produced neutron.
The Born approximation at low energies looks as it is shown in \fig{baga}.
The expression for this diagram takes the following form (see Ref. \cite{BA} ):
\begin{equation} \label{BAPH}
z \frac{d \sigma^{BA}_{p \to n}}{d z d^2 q_T}\,\,=\,\,\frac{1}{16 \pi^2}\,q^2_T\frac{ G^2_{p\pi^+n}\left( q^2_T\right)}{\left( m^2_\pi + q^2_T\right)^2} \left( 1 - z\right)^{ 1 - 2 \alpha_\pi\left( q^2_T\right)}\,\frac{4 \pi^2\,\alpha_{em}}{Q^2}\,F^\pi\left( x_\pi; Q^2\right)
\end{equation}
where $\alpha_{em}$ is the fine structure constant. In the rest frame of proton the longitudinal momentum, carried by pion , is equal to $q_L\,=\,(1 - z)m_N/\sqrt{z}$ and
\begin{eqnarray} \label{BANOT}
&& x_\pi \,=\,\frac{x}{1 - z}\,=\,\frac{Q^2}{Q^2\,+ \,M^2_X};\,
\,Y_g\,\,=\,\,-\ln(1 - z);\,\,\,\,\alpha_\pi =
\alpha' \left( m^2_\pi - q^2_T\right) \,\,\to\,\,\mbox{pion Regge trajectory}
\end{eqnarray}
\FIGURE[h]{
\begin{tabular}{c }
\epsfig{file=SPdisBAga.eps,width=70mm}\\
\end{tabular}
\caption{Born Approximation for $\gamma^* p$ scattering art low energies. The dashed line describes pion, the solid arrowed line corresponds to quark(antiquark)}
\label{baga}
}
For initial condition we need to take $F^\pi\left( x_\pi \to 1, Q^2\right)$ at $x_\pi \to 1$. For calculation of survival probability (see \eq{S2}) we do not need to know the value of $F^\pi$ and even its $x_\pi$ dependence. The only ingredient that we need, has not appeared in \eq{BAPH}. The total cross section corresponds the $\gamma^* \pi$ amplitude that is taken at momentum transferred from virtual photon to virtual photon ($\Delta$ in \fig{baga}) to be equal to zero. For calculation of the survival probability we need to know the $\Delta$ dependence of this amplitude. We explain this fact a little bit below. The expression for such an amplitude takes the following form
\begin{eqnarray} \label{BAPH1}
&&N^\pi\left( \Delta; Q;Y= Y_g,Y_g\right)\,\,=\\
&&\,\,\frac{1}{16 \pi^2}\vec{q}_T \cdot (\vec{\Delta} - \vec{q})_T \frac{G_{p\pi^+n}\left( q^2_T\right)}{m^2_\pi + q^2_T}\frac{ G_{p\pi^+n}\left(( \vec{\Delta} - \vec{q})^2_T\right) }{m^2_\pi +( \vec{\Delta} - \vec{q})^2_T}\left( 1 - z\right)^{ 1 - \alpha_\pi\left( q^2_T\right)\,-\,\alpha'_\pi \left( (\vec{\Delta} - \vec{q})^2_T\right)}\,\frac{1}{Q^2}\,F^\pi\left( x_\pi; Q^2;\Delta\right)\nonumber
\end{eqnarray}
We do not know the dependence of $F^\pi$ on $\Delta$. In the additive quark model (see \fig{baga}) it is natural to assume that $ F^\pi\left( x_\pi; Q^2;\Delta\right)\,\,=\,\, F^\pi\left( x_\pi; Q^2\right) \times G_\pi\left( \Delta^2\right)$ where $G_\pi$ is the electro-magnetic form factor of pion. On the other hand
the main contribution for scattering at low energy gives the $\rho$-resonance which contribution has no $\Delta$-dependence.
Integrating \eq{BAPH1} over $q_T$ and going to impact parameter representation
\begin{equation} \label{IPR}
N^\pi\left( b; Y=Y_g,Y_g \right) \,\,=\,\,\int \frac{d^2 \Delta_T}{(2 \pi)^2}\,e^{i \vec{\Delta}_T \cdot \vec{b} }N^\pi\left( \Delta\right)
\end{equation}
we obtain that
\begin{equation} \label{AB}
N^\pi\left( b \right)\,\,=\,\,N_g\left( Y_g\right)\,\int d^2 b' \,G_\pi \left( \vec{b} - \vec{b}'\right)\,T^2\left( b' \right)
\end{equation}
~
where factor $N\left( Y_g\right) $ includes the dependence of $Y_g$($z$) and does not contribute to the calculation of the survival probability (see \eq{S2}). In \eq{AB} $G_\pi\left( b \right)$ is the impact parameter image of $G_\pi \left( \Delta \right)$ while
\begin{equation} \label{AB1}
T\left( b \right)\,\,=\,\,\frac{\partial }
{\partial b}\int \frac{d^2 q_T}{(2 \pi)^2}\,e^{i \vec{q}_T \cdot \vec{b} } \left( 1 - z\right)^{\alpha'_\pi q^2_T} \frac{G_{p \pi^+ n}\left( q^2_T\right)}{m^2_\pi + q^2_T}\,\,=\,\,\frac{1}{2 \pi} \int q^2_T d q_T J_1\left( q_T\, b\right)\,\frac{G_{p \pi^+ n}\left( q^2_T\right)}{m^2_\pi + q^2_T}\left( 1 - z\right)^{\alpha'_\pi q^2_T}
\end{equation}
We use $G_\pi\left( \Delta\right)$ in the standard form
\begin{equation} \label{GPI}
G_\pi\left( \Delta\right) \,\,=\,\,\frac{1}{1 + \Delta^2/\mu_\pi^2}
\end{equation}
where $\mu^2_\pi = 0.6 GeV^2$ is taken from the measured value of the electro-magnetic radius of pion:$ R_\pi = 0.66 \pm 0.01 fm $\cite{RPI}. For $G_{p \pi^+ n}$ form factor there exists a variety
of different experimental (phenomenological ) information (see Ref. \cite{BA} for details). We take this form factor to be proportional to electro-magnetic form factor of proton in the spirit of the additive quark model that we pictured in \fig{baga}. It takes a form
\begin{equation} \label{GPPIN}
G_{p \pi^+ n}\left( q_T\right)\,\,=\,\,g_{p \pi^+ n}\,\,G_p\left( q_T\right)\,\,=\,\,\frac{g_{p \pi^+ n}}{\left( 1 + q^2_t/\mu^2_p\right)^2}
\end{equation}
with $\mu^2_p \,=\,0.72 GeV^2$ which corresponds to $R_p = 0.862 \pm 0.012 fm$. In Ref.\cite{BA}
is suggested to replace
\begin{equation} \label{REPL}
G_{p \pi^+ n}\left( q_T\right) e^{\alpha'_\pi q^2_T Y)_g} \,\longrightarrow\,\,\frac{1}{1 + q^2_T/\mu^2_{eff}}
\,\,\,\mbox{with}\,\,\,\,\frac{1}{\mu^2_{eff}}\,\,=\,\,\frac{2}{\mu^2_p}\,\,+\,\,\alpha'_\pi Y_g
\end{equation}
This expression describes correctly the small $q_T$ behaviour which is the most essential feature of the pion exchange.
Using \eq{REPL} we obtain
\begin{equation} \label{SIMLT}
T\left( b \right)\,\,=\,\,\frac{\mu^2_{eff}}{\mu^2_{eff} - m^2_\pi}\,\Big( m_\pi K_1\left( m_\pi b \right)\,-\,\mu_{eff}\,K_1\left( \mu_{eff} b\right)\Big)
\end{equation}
We will use \eq{REPL} in our estimates.
Now we need to specify the initial condition for BK equation. As it will be seen below we cannot calculate the survival probability without introducing the impact parameter dependence of the scattering amplitude. It is known, that BK equation has a problem with taking into account the large $b$-dependence of the scattering amplitude \cite{KOWI} and should be
modified at large values of $b$. We suggest a different approach in the spirit of the additive quark model, assuming that we have two different scales inside the proton: the size of the proton and the size of the constituent quark which is much smaller that the size of proton.
Since the saturation scaler is larger that $1/R_{\mbox{constituent quark}}$ we can integrate all amplitude in the BK-equations over impact parameter, In this picture the entire $b$-dependence will be concentrated in initial conditions and will be determined by the form factor of proton.
In this model we view a proton in the same way as tritium in the Glauber approach (see Ref.\cite{LETA}).
Such an approach could be relevant only if we know that the radius of interaction between dipole and constituent quark does not increase with energy. In high energy phenomenology based on soft Pomeron approach, the increase of the radius of interaction $R$ with energy looks as follows
\begin{equation} \label{CQM}
R^2\,= R^2_Q + \alpha'_{P} \ln(s)\,\,<\,\,R^2_p
\end{equation}
where $R_p $ is the size of the proton and $R_Q$ is the size of the constituent quark, $\alpha'_P$ is the slope of the Pomeron trajectory. Fortunately, some models have recently been discussed with very small value of $\alpha'_{{I\!\!P}}\, \approx\, 0.01 GeV^{-2}$ \cite{SOFT} and \eq{CQM} could be valid at high energies.
We will fix the initial condition using results from Ref.\cite{AAMQS} in which a perfect fit to HERA DIS data was made in framework of BK equation. We use the same initial conditions as in this paper, namely,\footnote{Golec-Biernat and Wusthoff (GBW) model being very simple, describe DIS data\cite{GBW} while McLerran-Venugopalan formula is the correct initial condition in Colour Gluon Condensate approach\cite{MV}}
\begin{eqnarray}
&&\mbox{GBW model:}\,\,\,\,\, N\left( x_{10},Y=Y_g\right) = \sigma_0\,
\Big( 1 \,-\, \exp\left( - \left( x^2_{01}\, Q^2_{0 s}\right)^\gamma/4\right)\Big)\,; \label{IC01} \\
&&\mbox{MV formula:}\,\,\,\,\, N\left( x_{10},Y=Y_g\right) = \sigma_0\,
\left( 1 \,-\, \exp\left( - \left( x^2_{01}\, Q^2_{0 s}\right)^\gamma\,\ln\left( \frac{1}{ x_{10}\,\Lambda_{QCD}}\,+\,e\right)/4\right)\Rb\,;\label{IC02}
\end{eqnarray}
but we introduce the $b$ dependence considering that initial saturation momentum $Q^2_{0s}$ depends on
$b$ in the following way:
\begin{equation} \label{IC1}
Q^2_{0s} \,\,\longrightarrow \,\, Q^2_{0s}\left( b\right)\,\,=\,\,Q^2_{0s}\,G_p\left( b\right) \,\,=\,\,Q^2_{0s}\, m b\,K_1\left( m b \right)
\end{equation}
where $G_p\left( b\right)$ is the $b$ image of \eq{GPPIN}. Therefore, \eq{IC01} and \eq{IC02} transform into the following expressions
\begin{eqnarray} \label{IC2}
N\left( x_{10},Y=Y_g\right) = \int \,d^2 b \,N\left( x_{10},Y=Y_g; b \right)\,\,=\,\,\left\{\begin{array}{l}
\int d^2 b \Big( 1 \,-\, \exp\left( - \left( x^2_{01}\, Q^2_{0 s}\left( b \right)\Rb^\gamma/4\right)\Big) \\ \\ \\
\int d^2 b \Big( 1 \,-\, \exp\left( - \left( x^2_{01}\, Q^2_{0 s}\left( b \right)\Rb^\gamma\ln\left( \frac{1}{ x_{10}\,\Lambda_{QCD}}\,+\,e\right)/4\right)\Big) \end{array}
\right.
\end{eqnarray}
Considering \eq{IC01} and \eq{IC2} at small $x_{01}$ ($x^2_{01}\, Q^2_{0 s} \ll\,1$)
we see that
\begin{equation} \label{IC3}
\sigma_0 \left( Q^2_{0 s}\right)^\gamma\,\,=\,\,\int d^2 b \left( Q^2_{0 s}\left( b\right)\Rb^\gamma
\end{equation}
This equation gives us the value of
$Q^2_{0s}$ as function of $\sigma_0$ and $m$.
In our solution we took two values for $Q^2_{0s}$ in \eq{IC1}: first one, considering $m$ being the same as in the electromagnetic form factor of proton $ m^2 = 0.72\,GeV^2$; and the second one, taking $Q^2_{0s}$ in \eq{IC01} and \eq{IC02} being equal to $Q^2_{0s}$ in \eq{IC01}(\eq{IC02}) but changing $m$ to satisfy \eq{IC3}.
Since it turns out that $\gamma$ is close to
1, we take as a first try \eq{IC1} with $\gamma=1$.
In this case we have simple initial condition for BK equation in momentum representation for \eq{IC01}
\begin{equation} \label{IC4}
N\left( k,Y=Y_g, b\right)\,\,=\,\,\int x_{01} d x_{01}\, J_0\left( b x_{01}\right) \,\frac{ N\left( x_{01},Y=Y_g,b\right) }{x^2_{01}}\,\,=\,\,\frac{1}{2} \Gamma_0\left( k^2/Q^2_{0s}\left( b \right)\Rb
\end{equation}
where $\Gamma_0$ is incomplete Euler gamma function (see formulae {\bf 8.25} in Ref.\cite{RY}). In the case of the initial condition of \eq{IC02} we did not find a simple analytical form and perform the integral of \eq{IC4} numerically.
The easiest way to get the initial condition for $N^\pi$ is to write them in coordinate representation. Assuming that at large $Q^2$ $ F^\pi_2 = (2/3)F^p_2$ due to the quark counting rules \cite{LF} we can obtain the initial condition for $N^\pi$ in the form
of \eq{IC01} and \eq{IC02} in which we replace $Q^2_{0s}(b) $ by $(2/3) Q^2_{0s}(b) $. In other words the initial conditions for $N^\pi$ have the form
\begin{eqnarray} \label{IC21}
&& N^\pi_{BA}\left( x_{10},Y=Y_g; b \right)\,\,=\\
&&\,\,N_g(Y_g)\,G_p\left( b \right) \int d^2 b' \,G_\pi \left( \vec{b} - \vec{b}'\right)\,T^2\left( b' \right)\left\{\begin{array}{l}
\Big( 1 \,-\, \exp\left( - \frac{2}{3}\left( x^2_{01}\, Q^2_{0 s}\left( b \right)\Rb^\gamma/4\right)\Big) \\ \\ \\
\Big( 1 \,-\, \exp\left( - \frac{2}{3} \left( x^2_{01}\, Q^2_{0 s}\left( b \right)\Rb^\gamma\ln\left( \frac{1}{ x_{10}\,\Lambda_{QCD}}\,+\,e\right)/4\right)\Big) \end{array}\nonumber
\right.
\end{eqnarray}
However, we need to multiply these initial values of $N^\pi_{BA} $ by the survival probability since the interaction in the initial state can fill the rapidity gap for the leading neutron production.
In the case of \eq{IC1} the survival probability is equal to
\begin{eqnarray} \label{SP}
\mbox{For GBW model:} &~& S^2 \,\,=\,\,\exp\left( - \frac{1}{2} x^2_{01}\,Q_{0 s}^2\,G_p\left( b \right)\Rb;\nonumber\\
\mbox{For MV formula:} &~& S^2 \,\,=\,\,\exp\left( - \frac{1}{2} x^2_{01}\,Q_{0 s}^2\,G_p\left( b \right)\ln\left( \frac{1}{ x_{10}\,\Lambda_{QCD}}\,+\,e\right)\Rb;
\end{eqnarray}
since due to unitarity constraint such $S^2$ corresponds to probability not to have any inelastic interaction which can spoil the rapidity gap\cite{BJ,GLM1}.
Therefore the initial condition for $ N^\pi$ in the coordinate representation has a form
\begin{eqnarray}
&&N^\pi\left( x_{01}, b, Y=Y_g, Y_g\right)\,\,\,=\,\,\, S^2 N^\pi_{BA} \left( x_{01}; b;Y=Y_g,Y_g\right)\,\,\nonumber\\
&& \mbox{For GBW model:}\,\,=\,\,N_g \left( Y_g\right)\,\Big( 1 \,-\, \exp\left( - \frac{2}{3}\left( x^2_{01}\, Q^2_{0 s}\left( b \right)\Rb^\gamma/4\right)\Big)\nonumber\\
&&~~~~~~~~~~~~~~~~~~~~~\times\,\, \exp\left( - \frac{1}{2} x^2_{01}\,Q_{0 s}^2\,G_p\left( b \right)\Rb \int d^2 b' \,G_\pi \left( \vec{b} - \vec{b}'\right)\,T^2\left( b' \right)\label{ICCOR1}\\
&& \mbox{For MV formula:}= \,N_g \left( Y_g\right)\,\left( 1 \,-\, \exp\left( - \frac{2}{3} \left( x^2_{01}\, Q^2_{0 s}\left( b \right)\Rb^\gamma\ln\left( \frac{1}{ x_{10}\,
\Lambda_{QCD}}\,+\,e\right)/4\right)\Rb\nonumber\\
&&~~~~~~~~~~~~~~~~~~~~~\times \exp\left( - \frac{1}{2} x^2_{01}\,Q_{0 s}^2\,G_p\left( b \right)\ln\left( \frac{1}{ x_{10}\,\Lambda_{QCD}}\,+\,e\right)\Rb
\int d^2 b' \,G_\pi \left( \vec{b} - \vec{b}'\right)\,T^2\left( b' \right) \label{ICCOR2}
\end{eqnarray}
Going to momentum representation we have the initial condition in the form:
\begin{equation} \label{INMR}
N^\pi\left( k, b, Y=Y_g, Y_g\right)\,\,\,= \,\,\,2 \pi \int x_{01} d x_{01} \,J_0\left( x_{01}\,k\right)\, \frac{N^\pi\left( x_{01}, b, Y=Y_g, Y_g\right)}
{x^2_{01}}\,\,\nonumber\\
\end{equation}
Factor$N\left( Y_g\right) $ is not important for the calculation of the survival probability if we neglect $\left( N^\pi\right)^2$-term in
\eq{EQ} (see below). However, we need it for the estimates of the accuracy with which we can neglect this term. It is equal to \cite{BA}
\begin{equation} \label{NG}
N_g\left( Y_g\right) \,\,=\,\,\frac{g^2_{p \pi^+ n}}{16 \pi^2}\,e^{- Y_g}\,
\,\approx \,\,2.2 \,e^{-\,Y_g}
\end{equation}
\section{Numerical solution}
In this section we will discuss numerical solutions of two equation: BK equation and \eq{EQ}, in momentum representation
\begin{eqnarray}\label{MRP}
N\left( x_{01}, b, Y\right)\,\,& = &\,\,x^2_{01}\,\int k dk J_0\left( k x_{01}\right) \,N\left( k, b, Y\right);\nonumber\\\,\,
N^\pi\left( x_{01}, b, Y, Y_g\right) &= &x^2_{01}\,\int k dk
J_0\left( k x_{01}\right)\, N^\pi\left( k, b, Y, Y_g\right);
\end{eqnarray}
In this representation BK equation looks as follows
\begin{eqnarray} \label{BKMRP}
\frac{\partial N\left( k, b, Y\right) }{ \partial Y}\,&=&\,\\
& & \bar{\alpha}_S\left\{\int \frac{d^2 k'_\perp }{\left( \vec{k} - \vec{k}^{\,\prime} \right)^2_\perp}\,\Big(N\left( k^{\,\prime}, b, Y\right)
\,-\,\frac{k^2_\perp}{ k'^2_\perp \,+\,\left( \vec{k} - \vec{k}^{\,\prime} \right)^2_\perp} \, N\left( k, b, Y\right) \Big)\,-\, N^2\left( k, b, Y\right)\right\} ;\nonumber
\end{eqnarray}
This equation we solve with the initial condition given by \eq{IC2}.
After finding the solution to \eq{BKMRP} we solve the following equation:
\begin{eqnarray} \label{EQMPR}
\hspace{-0.2cm}&& \frac{\partial N^\pi\left( k, b, Y,Y_g\right) }{ \partial Y}\,=\,\\
&& \bar{\alpha}_S\left\{\int \frac{d^2 k'_\perp }{\left( \vec{k} - \vec{k}^{\,\prime} \right)^2_\perp}\,\Big(N^\pi\left( k^{\,\prime}, b, Y,Y_g\right)
\,-\,\frac{k^2_\perp}{ k'^2_\perp \,+\,\left( \vec{k} - \vec{k}^{\,\prime} \right)^2_\perp} \, N^\pi\left( k, b, Y,Y_g\right)\Big) - 4\,N\left( k, b, Y\right)\,N^\pi\left( k, b, Y,Y_g\right)\right\} ;\nonumber
\end{eqnarray}
with the initial condition given by \eq{INMR}
\eq{EQMPR} differs from \eq{EQ} in the momentum representation by the $\left( N^\pi\right)^2$-term which we neglected in this equation. Indeed, $N^\pi$ in Born approximation is much smaller than $N$ both experimentally and theoretically, since it describes a specific configuration that contribute to the inclusive cross section given by $N$. This configuration is suppressed by factor $e^{-Y_g}$. The second argument stems from the solution at high energies (see section 2.2) which shows that $\left( N^\pi\right)^2$ turns out to be much smaller than $ 4\,N\, N^\pi $.
We proceed with solution of \eq{EQMPR} but after finding the solution to this equation we will check that the $\left( N^\pi\right)^2$-term
is small.
Using the solution to \eq{EQMPR} we can find $S^2$ for dipole scattering which is equal to
\begin{eqnarray} \label{S2F}
& \mbox{$S^2$}\,\,\,=\,\,\,\int d^2 b\, N^\pi\left( k,b,Y,Y_g\right)\Big{/}\int d^2 b \,N^\pi_{BA}\left( k,b,Y,Y_g
\right)&
\end{eqnarray}
where $N^\pi$ is the solution to \eq{EQMPR} while $N^\pi_{BA}$ is given by \eq{BAPH}.
One can see that for self-consistent calculations we need to estimate the contribution of the Born Approximation using \eq{AB} as the initial condition,
solving the linear BFKL equation.
\begin{eqnarray} \label{EQLIN}
\hspace{-0.2cm}&& \frac{\partial N^\pi\left( k, b, Y,Y_g\right) }{ \partial Y}\,=\,\\
&& \bar{\alpha}_S\left\{\int \frac{d^2 k'_\perp }{\left( \vec{k} - \vec{k}^{\,\prime} \right)^2_\perp}\,\Big(N^\pi\left( k^{\,\prime}, b, Y,Y_g\right)
\,-\,\frac{k^2_\perp}{ k'^2_\perp \,+\,\left( \vec{k} - \vec{k}^{\,\prime} \right)^2_\perp} \, N^\pi\left( k, b, Y,Y_g\right)\Big) \right\}\nonumber
\end{eqnarray}
Therefore, we need to solve numerically three equations: \eq{BKMRP}, \eq{EQMPR} and \eq{EQLIN}.
We notice that using a new variable for GBW initial condition (see \eq{IC01})
\begin{equation} \label{KAPPA}
\kappa\left( b \right)\,\,=\,\,k{\Big/} Q_{0s}\left( b \right)
\end{equation}
the initial conditions for these three equations can be written in the following form
\begin{eqnarray}
\mbox{\eq{BKMRP}}\,\,&\longrightarrow&\,\, N\left( k,Y=Y_g, b\right)\,\,=\,\,\frac{1}{2} \Gamma_0\left( \kappa^2\left( b \right)\Rb \,;\label{FIC1}\\
\mbox{\eq{EQMPR}}\,\,&\longrightarrow&\,\, N\left( k,Y=Y_g, b\right)\,\,=
N_g\left( Y_g\right)\, \int d^2 b' \,G_\pi \left( \vec{b} - \vec{b}'\right)\,T^2\left( b' \right) \,\nonumber\\
& & ~~~~~~~~~~~~~~~~~~~~~~~\times \int \frac{d r}{r}\Big(1 - e^{-\frac{1}{6}\,r^2}\Big)\,e^{ - \frac{1}{2} r^2}\,J_0( \kappa r);\label{FIC2}\\
\mbox{\eq{EQLIN}}\,\,&\longrightarrow&\,\, N^\pi\left( k,Y=Y_g, b\right)\,\,=
\,\,\frac{N_g\left( Y_g\right)}{Q^2_{0s}\left( Y_g, b\right)}\, \int d^2 b' \,G_\pi \left( \vec{b} - \vec{b}'\right)\,T^2\left( b' \right) \,\,\frac{1}{2} \Gamma_0\left(\frac{2}{3} \kappa^2\left( b \right)\Rb ;\label{FIC3}
\end{eqnarray}
Since \eq{EQMPR} and \eq{EQLIN} are linear equations with respect to $N^\pi$ we can find the solution to them with the simplified initial conditions
\begin{eqnarray}
\mbox{\eq{EQMPR}}\,\,&\longrightarrow&\,\, N^\pi\left( k,Y=Y_g, b\right)\,\,= \,\, \int \frac{d r}{r}\Big(1 - e^{-\frac{1}{6}\,r^2}\Big)\,e^{ - \frac{1}{2} r^2}\,J_0( \kappa r) \,\,\;\label{FIC21}\\
\mbox{\eq{EQLIN}}\,\,&\longrightarrow&\,\, N^\pi\left( k,Y=Y_g, b\right)\,\,=
\,\frac{1}{2}\,\Gamma_0\left(\frac{2}{3} \kappa^2\left( b \right)\Rb;\label{FIC22}
\end{eqnarray}
and the solutions with the initial conditions of \eq{FIC2} and \eq{FIC3} can be obtained as
\begin{equation} \label{SOL1}
N^\pi\left( k,Y; b\right)\,\,=\,\, \,\,\frac{N_g\left( Y_g\right)}{Q^2_{0s}\left( Y_g, b\right)}\, \int d^2 b' \,G_\pi \left( \vec{b} - \vec{b}'\right)\,T^2\left( b' \right) \,\,N^\pi\left( \kappa\left( b \right), Y\right)\,
\end{equation}
where $N\left( \kappa\left( b \right), Y\right)$ is the solution to \eq{EQMPR} or to \eq{EQLIN} with the initial conditions given by \eq{FIC21} or \eq{FIC22}.
All equations that we are discussing here are conformal invariant and can be re-written in variables $\vec{\kappa}$ and $\vec{\kappa}'$ in stead of $\vec{k}$ and $\vec{k}' $. Hence actually we need to solve the system of three equations (\eq{BKMRP}, \eq{EQMPR} and \eq{EQLIN}) with the initial conditions of \eq{FIC1}, \eq{FIC21} and \eq{FIC22} to find $N\left( \kappa, Y\right)$ and $N^\pi\left( \kappa,Y\right)$. In spite of simplicity of \eq{FIC1}.\eq{FIC21} and \eq{FIC22} they have clear shortcoming since cannot reproduce a correct behaviour accordingly to operator product expansion at large values of $k^2$. Indeed, they fall down exponentially instead of $1/k^2$. Therefore, we can trust these equations only at $k^2 \leq Q^2_s$. Trying to find a compromise between simplicity and rigorousness we chose the initial condition for $N^\pi$ in the form
\begin{equation} \label{ICNUM1}
N^\pi_{BA} \left( x_{01}, b; Y=Y_g,Y_g\right)\,\,=\,\, \frac{2}{3} \,x^2_{01}\,\ln\left(\frac{1}{x_{01} \Lambda_{QCD}}\right)
\end{equation}
which is the expansion of \eq{IC21} for McLerran-Venugopalan formula at small values of $x_{01}$.
We can only treat $x_{01} < 1/Q_s$ with this initial condition but since $Q_s$ for low energy in DIS with a pion is small we believe that we can use \eq{ICNUM1} as the first approximation. In our equation for $N^\pi$ the solution of BK equation is essential only for $x_{01} \leq Q_s$ and, therefore, we can use the GBW model for the initial condition. The same situation in the initial condition for $N^\pi_{BA}$.
Finally, we use
\begin{eqnarray}
\mbox{BFKL equation:}& ~~~~~& \frac{2}{3}x^2_{01}\,Q^2_{0s}\ln\left( \frac{1}{x_{01}\,\Lambda_{QCD}}\right) ; \label{NUM22}\\
\mbox{our equation:}& ~~~~~&\frac{2}{3}x^2_{01}\,Q^2_{0s}\ln\left( \frac{1}{x_{01}\,\Lambda_{QCD}}\right) \exp\Big( - x^2_{01}\,Q^2_{0s}/4\Big) ; \label{NUM23}
\end{eqnarray}
These equations take the following form in the momentum representation:
\begin{eqnarray}
\mbox{BK equation:}& ~~~~~& \frac{1}{2} \Gamma_0\left( k^2/Q^2_{0s}\right) ; \label{NUM31}\\
\mbox{BFKL equation:}& ~~~~~& \frac{1}{3}\,Q^2_{0s}/k^2; \label{NUM32}\\
\mbox{our equation:}& ~~~~~&\frac{1}{3}\,1/Q^2_{0s}\left( -\Gamma_0\left( - \frac{k^2}{Q^2_{0s}}\right)
\, \exp\Big( - k^2/Q^2_{0s}\Big)\right);\label{NUM33}
\end{eqnarray}
The expression in \eq{NUM33} follows from the following simple calculations:
\begin{eqnarray}\label{CAL}
\ln\Lb1/ x^2_{01}\right) & \xrightarrow{\mbox{Fourrier transform}} & \frac{1}{k^2};\nonumber\\
(x^2)^n \ln \Lb1/ x^2_{01}\right) & \xrightarrow{\mbox{Fourrier transform}} & \left(- \frac{1}{k^2} \frac{d^2}{(d \ln k^2)^2}\right)^n \frac{1}{k^2} \,\,=\,\,(-4)^n (n!)^2 \frac{1}{(k^2)^{n+1} }
\end{eqnarray}
and from formula {\bf 8.357} of Ref.\cite{RY}.
We need to find the pion deep inelastic structure function, using $N^\pi$ and $N^\pi_{BA}$,
for calculating the value of the survival probability. In the dipole approach the cross section for the virtual photon with the pion can be expressed through the amplitude of the dipole-pion interaction in the following way for massless quarks:
\begin{equation} \label{DIXS}
\sigma_{\gamma^* \pi}\left( Q, Y\right) \,\,=\,\,\int d^2 x_{01}\,|\Psi\left( Q;x_{01}\right) |^2\,\sigma_{\mbox{dipole-$\pi$}}\left( x_{01},Y\right)\,\,=\,\,\int d^2 x_{01}\,|\Psi\left( Q;x_{01}\right)|^2\,\int d^2 b N^\pi\left( x_{01},Y; b\right)\
\end{equation}
where \cite{WAFU}
\begin{equation} \label{WF}
|\Psi\left( Q;x_{01}\right)|^2\,\,=\,\,\frac{2 N_c \alpha_{em}}{\pi}\sum_f Z^2_f \,\int d z [ z^2 + (1-z)^2]\,\bar{Q}^2 K_1^2\left( \bar{Q} x_{01}\right)
\end{equation}
where $Z_f$ is the fraction of the electrical charge $\alpha_{em}$ carried by quark of flavour $f$; $Q$ is the photon virtuality and $\bar{Q}^2 = Q^2 z (1 - z)$ ; $z$ is the fraction of photon energy carried by the quark an $N_c$ is the number of colours. Using \eq{MRP} \eq{DIXS} can be re-written in the form
\begin{equation} \label{DIMR}
\sigma_{\gamma^* \pi}\left( Q, Y\right) \,\,= \,\, \frac{2 N_c \alpha_{em}}{\pi\,Q^2}\sum_f Z^2_f\,\,\int k\, d k\, \Phi^2_{\gamma^*}\left( Q,k\right) \int d^2 b \,N^\pi\left( k ,Y; b \right)
\end{equation}
where
\begin{eqnarray} \label{PHI}
\Phi^2_{\gamma^*}\left( \tau=\frac{Q}{k}\right) \,&=&\,Q^4\,\int d^2 x_{01}\int d z\,z (1-z)\, [ z^2 + (1-z)^2] \,x^3_{01} \,J_0\left( k x_{01}\right)\ K_1^2\left( \bar{Q}\, x_{01}\right) \\
&= &8\,\tau^4\int d z\, z (1 - z)\, [ z^2 + (1-z)^2] \frac{(1 - \tilde{\kappa}^2)
\sqrt{1 + 4 \tilde{\kappa}^2}\,+\,8 \tilde{\kappa}^2 ( 1 + \tilde{\kappa}^2)\mbox{ ArcCsch}\left( 2 \tilde{\kappa}\right)}{ (1 + 4 \tilde{\kappa}^2)^2 \sqrt{1 + 4 \tilde{\kappa}^2}}\nonumber
\end{eqnarray}
where $\tilde{\kappa} = \bar{Q}/k = \tau \sqrt{z(1-z)}$.
Using $N^\pi\left( \kappa,Y\right)$ , \eq{DIMR} and \eq{PHI} the final expression for the survival probability (see \eq{S2F}) has the following form
{\Large
\begin{eqnarray} \label{S2FF}
& \mbox{$S^2$}\,\,\,=\,\,\,\frac{\int d^2 b \, \int d^2 b' \,G_\pi \left( \vec{b} - \vec{b}'\right)\,T^2\left( b' \right)\,\int^{\infty}_{\Lambda_{QCD} /Q_{0s}(b)}\kappa d \kappa\, \Phi^2_{\gamma^*}\left( Q/\left( Q_{0s}(b)\, \kappa\right)\Rb\,N^\pi\left( \mbox{\normalsize\eq{EQMPR}};\, \kappa , Y\right)}{\int d^2 b \, \int d^2 b' \,G_\pi \left( \vec{b} - \vec{b}'\right)\,T^2\left( b' \right)\,\int^{\infty}_{\Lambda_{QCD} /Q_{0s}(b)}\kappa d \kappa\, \Phi^2_{\gamma^*}\left( Q/\left( Q_{0s}(b)\, \kappa\right)\Rb\,N^\pi\left( \mbox{\normalsize\eq{EQLIN}};\,\kappa, Y\right)}&
\end{eqnarray}
}
In \eq{S2FF} we use the infrared cuttoff $k = \Lambda_{QCD}$ since for smaller $k$ we cannot use \eq{ICNUM1} for the dipole amplitude.
\begin{figure}
\begin{tabular}{c c}
\epsfig{file=Nbk.eps,width=80mm} & \epsfig{file=Npi.eps,width=80mm} \\
\fig{sol}-a & \fig{sol}-b\\
\epsfig{file=Nba.eps,width=80mm} &{\begin{minipage}{80mm}{\vspace{-30mm} Solutions to equations at different rapidities:
\fig{sol}-a shows the solution to the Balitsky-Kovchegov equation with the initial solution of \protect \eq{FIC1};
the solution to new equation (see \protect\eq{EQMPR} ) with the initial condition of \protect\eq{FIC2} is plotted in \fig{sol}-b, while the solution of the BFKL equation with the initial condition of \protect\eq{FIC3} is shown in \fig{sol}-c. The value of $Y_g$ is taken to be equal to 3. }
\end{minipage}}
\\
\fig{sol}-c & \\
\end{tabular}
\caption{Solutions to equations as function of $\kappa$ at different energies}
\label{sol}
\end{figure}
The solutions to \eq{BKMRP},\eq{EQMPR} and \eq{EQLIN} with the initial conditions given by \eq{FIC1},\eq{FIC2} and \eq{FIC3} are shown in \fig{sol}. One can see that the solution of the linear BFKL equation (see
\fig{sol}-c ) steeply increases with energy while the solution to the Balitsky-Kovchegov equation shows only a mild increase with rapidity ( see
\fig{sol}-a). The solution to the new equation increases with energy but starts to fall down at very high energies (see \fig{sol}-c). From \fig{sol} one can see that the term $\left( N^\pi\right)^2$ turns out to be much smaller than the term $4 \,N\, N^\pi$ in \eq{EQ} for small $\kappa$ ( $ \kappa \leq 2$). For large $\kappa$ this term is much smaller than the linear term in the equation ( $N^\pi \,\ll\,\left( N^\pi\right)^2$). Therefore, we can conclude {\it a posteriori} that we can neglect $\left( N^\pi \right)^2$-term in \eq{EQ} and reduce this equation to \eq{EQMPR} which has been solved.
The main result of the paper: the estimates for the survival probability ( see \eq{S2FF}) , is shown in \fig{sp} for two different choice of the dependence of the saturation momentum on $b$ given by \eq{IC1}. The first one shown in solid lines, corresponds to \eq{IC1} where $m$ is chosen the same as in the electromagnetic
form factor of the proton and value of $Q^2_{0s}$ is found from \eq{IC3}. The second choice was to fix the value of $Q^2_{0s}$ to be the same as in Ref.\cite{AAMQS} but the value of $m$ is determined by \eq{IC3}. The survival probability is shown by dotted lines in \fig{sp}. The qualitative features are seen in \fig{sp}: the value of the survival probability is small and its decreases with the growth of energy (rapidity). The smallness stems mostly from the steep increase of the solution to the linear BFKL equation while to the considerable decrease contribute two factors: the increase of the solution to linear equation and decrease of the solution to the new equation (see \eq{EQMPR}). The third interesting feature is that the value of the survival probability at high energies (large values of rapidity) does not depend on the initial conditions for $\kappa \geq 2$. It is worthwhile mentioning that the errors that stem from the different initial condition turns out to be smaller than $\delta S^2/S^2 \leq 0.1$ for any value of $\kappa$.
\FIGURE[h]{
\centerline{\epsfig{file=smodelo1vs2logwhite2.eps,width=110mm}}
\vspace{-1.5cm}
\caption{The values of the survival probabilities for leading neutron production in DIS as a function of the photon virtuality ($q$) at different energies (rapidities).The solid and dotted line corresponds to different choice of the value for the typical mass in \eq{IC1}. The solid lines describe the initial condition with $m$ chosen to be the same as in the electromagnetic for factor of proton and the value of $Q^2_{0s}$ is determined by \eq{IC3}, while dotted lines present the different choice: $Q^2_{0s}$ is taken to be the same as in Ref.\protect\cite{AAMQS} while $m$ is the solution of \eq{IC3}.}
\label{sp}
}
\section{Conclusions}
The main result of this paper is \eq{EQ} (see \fig{eq}) for the cross section of the inclusive production of leading neutrons in DIS. This equation stems from the direct generalization of the approach developed in Ref.\cite{KL} for the diffractive production in DIS. The asymptotic solution to this equation as well as the numerical solution to \eq{EQ} shows that the survival probability defined in \eq{S2}, is small and steeply falls down with energy. We believe that these features of the survival probability are general and does not depend on a particular process that we consider. Being the first theoretical attempt to calculate the survival probability this paper shows that the survival probability could be as small as $10^{-3}$ at high energies.
However, the numbers we need to take with considerable cautions, since these estimates depend crucially on the assumed impact parameter dependence of both the DIS structure function and the Born approximation for the leading neutron inclusive cross section. Unfortunately, the phenomenological analysis of DIS data based on Balitsky-Kovchegov equation (see Ref. \cite{AAMQS}) was performed neglecting the impact parameter dependence. Therefore, to obtain the reliable estimates we need to re-visit the DIS data and re-do the analysis using Baitsky-Kovchegov equation the impact parameter depending initial conditions.
Therefore, we consider this paper as only the first step to the reliable estimates for the experimentally measured cross section. The small value of the survival probability as well as its energy dependence make difficult the task of extraction of the deep inelastic structure function for pion, measuring the spectrum of the leading neutron.
\section*{Acknowledgements}
We thank Boris Kopeliovich for the instructive discussion on Born Approximation for leading neutron production in DIS and for providing us a possibility to read Ref.\cite{BA} before publication.
This work was supported in part by the Fondecyt (Chile) grant 1100648.
\input{SPdis-ref.tex}
\end{document}
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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Hassab may refer to:
Hassab operation, an elective surgical procedure in portal hypertension.
Dr. Mohammed Aboul-Fotouh Hassab, an Egyptian surgeon.
Hassab hospital, a hospital in Alexandria.
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
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Деребчи́н (, ) — село в Шаргородском районе Винницкой области Украины.
История
Первое письменное упоминание о Деребчине относится к 1648 году в циркулярах Богдана Хмельницкого. На карте Боплана он также был обозначен как поселение на берегу речки Деребчинка.
В энциклопедии Брокгауза и Ефрона находим, что Деребчин относился к Подольской губернии, Ямпольского уезда. Тогда здесь проживало 2033 человека, были 2 православные церкви и школа. У помещика, барона А. А. Маса — опытное поле на 22 десятины и сельскохозяйственная опытная станция; тут же дождемерная и грозовая станция. Дальнейшее развитие села было тесно связано с построением А. А. Массом сахарного завода.
Про название речки, которая протекает через село, много ходит легенд. Но в разных источниках её называют по-разному. В справочнике малых рек Украины она называется Деребчинка. На сайте Верховной рады Украины она называется Волчанка. В речку Деребчинка в районе села Деребчин впадает ручей Волчок. Для местных жителей он известен как технический пруд сахарного завода. Такая путаница связана с тем, что на местах, в советах, находятся люди, далеки от знаний географии о земле, на которой живут. Речка Волчанка протекает через соседнее село Зведёновку.
В июле 1995 года Кабинет министров Украины утвердил решение о приватизации находившихся здесь сахарного завода и обеспечивавшего его сырьём свеклосовхоза.
В июне 2000 года было возбуждено дело о банкротстве сахарного завода.
По переписи 2001 года население составляло 2201 человек.
Религия
В селе действует Чудо-Михайловский храм Шаргородского благочиния Могилёв-Подольской епархии Украинской православной церкви. В селе Деребчин действует костел. Построен во времена перестройки на деньги мирян.
Адрес местного совета
23532, Винницкая область, Шаргородский р-н, с. Деребчин, ул. Ленина, 93
Примечания
Ссылки
Учётная карточка на сайте Верховной рады
«Мій Деребчин… Моє село…»
Погода в с. Деребчин
Населённые пункты Шаргородского района
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"redpajama_set_name": "RedPajamaWikipedia"
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Q: How to hide BottomNavigationView when navigation bar appears by swipe from bottom? I want to hide BottomNavigationView when swipe from bottom edge of screen and system navigation bar appears. Now system navigation bar is translucent and hovered above BottomNavigationView.
Activity XML:
<?xml version="1.0" encoding="utf-8"?>
<android.support.v4.widget.DrawerLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:id="@+id/drawer_layout"
android:layout_width="match_parent"
android:layout_height="match_parent"
tools:openDrawer="start"
android:fitsSystemWindows="false">
<android.support.design.widget.CoordinatorLayout
android:layout_width="match_parent"
android:layout_height="match_parent">
<include
layout="@layout/include_toolbar"/>
<FrameLayout
android:id="@+id/content_frame"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:layout_below="@+id/appbar"/>
<android.support.design.widget.BottomNavigationView
android:id="@+id/bottom_navigation"
android:layout_width="match_parent"
android:layout_height="56dp"
android:layout_alignParentBottom="true"
android:background="@color/app_background"
app:itemIconTint="@color/main_text_color"
app:labelVisibilityMode="unlabeled"
android:paddingHorizontal="@dimen/normal_margin"
app:elevation="2dp"
app:menu="@menu/bottom_navigation_main"
android:layout_gravity="bottom"/>
</android.support.design.widget.CoordinatorLayout>
<android.support.design.widget.NavigationView
android:id="@+id/nav_view"
android:layout_width="wrap_content"
android:layout_height="match_parent"
android:layout_gravity="start"
app:headerLayout="@layout/nav_header_main"
app:menu="@menu/activity_main_drawer" />
</android.support.v4.widget.DrawerLayout>
Fragment OnResume():
public override void OnResume()
{
base.OnResume();
if (ParentActivity.BottomNavigation != null)
ParentActivity.BottomNavigation.Visibility = ViewStates.Visible;
View decorview = ParentActivity.Window.DecorView;
var uiOptions =
SystemUiFlags.HideNavigation |
SystemUiFlags.ImmersiveSticky;
decorview.SystemUiVisibility = (StatusBarVisibility)uiOptions;
}
Fragment implements View.IOnSystemUiVisibilityChangeListener
public void OnSystemUiVisibilityChange([GeneratedEnum] StatusBarVisibility visibility)
{
if (((int)visibility & (int)SystemUiFlags.Fullscreen) == 0)
{
if (ParentActivity.BottomNavigation != null)
ParentActivity.BottomNavigation.Visibility = ViewStates.Gone;
}
else
{
if (ParentActivity.BottomNavigation != null)
ParentActivity.BottomNavigation.Visibility = ViewStates.Visible;
}
}
Listener doesn't react to the appearance of the navigation bar.
OnSystemUiVisibilityChange() doesn't called when navigation bar apperas after swipe
A: You need OnSystemUiVisibilityChangeListener- https://developer.android.com/reference/android/view/View.OnSystemUiVisibilityChangeListener
For example, in your activity onCreate():
window.decorView.setOnSystemUiVisibilityChangeListener { visibility ->
// Note that system bars will only be "visible" if none of the
// LOW_PROFILE, HIDE_NAVIGATION, or FULLSCREEN flags are set.
if (visibility and View.SYSTEM_UI_FLAG_FULLSCREEN == 0) {
// TODO: The system bars are visible. Make any desired
// adjustments to your UI, such as showing the action bar or
// other navigational controls.
} else {
// TODO: The system bars are NOT visible. Make any desired
// adjustments to your UI, such as hiding the action bar or
// other navigational controls.
}
}
You can then keep your bottom navigation view visibility in sync with the system UI.
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{
"redpajama_set_name": "RedPajamaStackExchange"
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Research Trends -
Issue 24 – September 2011
Research assessment
September 2011/ Judith Kamalski, M'hamed el Aisati and Henk F. Moed
On the assessment of institutional research performance
This article distinguishes between top-down and bottom-up approaches to assess institutional performance, as well as 'article downloads' versus citation data.
A standard way of bibliometrically analyzing the performance of an institution is to select all of its publications and then calculate publication- and citation-based indicators for the institution as a whole. But there are other ways of assessing performance, and these come in top-down and bottom-up varieties. In general, bottom-up approaches tend to produce more reliable results than top-down, and also make it possible to look at performance at the level of groups of departments within an institution. Next, we illustrate a new set of indicators bases on "usage".
Top-down and bottom-up approaches
One of the most challenging tasks in bibliometric studies is to correctly identify and assign scientific publications to the institutions and research departments in which the authors of the paper work. Over the years, two principal approaches have been developed to tackle this task.
The first is the top-down approach, which is used in many, if not all, ranking studies of universities. In a top-down assessment, one typically notes the institutional affiliations of authors on scientific publications, and then selects all publications with a specific institutional affiliation. Even though this process is very simple, difficulties can arise. These can be conceptual issues (e.g., are academic hospitals always a part of a university?) or problems of a more technical nature (e.g., an institution's name may appear in numerous variations). A bibliometric analyst must therefore be aware of these potential problems, and address them properly.
The second, bottom-up approach begins with a list of researchers who are active in a particular institution. The next step is to create a preliminary list of all articles published by each researcher, which are sent to these individuals for verification to produce a verified database. This approach allows for the grouping of authors into research groups, departments, research fields, networks, or for an analysis of the entire institution.
While top-down approaches can be conducted more easily than bottom-up studies, mainly because they do not directly involve the researchers themselves, they are often less informative than bottom-up ones. For example, top-down approaches cannot inform managers about which particular researchers or groups are responsible for a certain outcome, nor can they identify collaborations between departments. So despite the ease of use of top-down approaches, there is a need to supplement them with bottom-up analyses to create a comprehensive view of an institution's performance.
The analysis of usage data
A different method of assessing of an institute's performance is by analyzing the 'usage' of articles, as opposed to citations of articles. Usage, in our analysis, is measured and quantified in terms of the number of clicks on links to the full-text of articles in Scopus.com, which demonstrates the intention of a Scopus.com user to view a full-text article. Here we use a case-study of an anonymous "Institute X" in the United Kingdom as an example of what usage data analysis has to offer.
In this case study, we analyze papers from 2003–2009, and usage data from 2009. We first identified countries that click through the full text of articles with at least one author based in Institute X. Next, we determined the total number of full-text UK articles accessed by each country, and calculated the proportion of these that were linked to Institute X (that is, articles with at least one author based at the Institute). Finally, we identified the 30 countries with the highest proportion of downloads of articles affiliated with Institute X. The results are shown in Figure 1.
Figure 1 – For the Top 30 countries viewing UK articles, the percentage of downloads of articles with at least one author from Institute X compared to downloads of all articles with at least one author from the UK. Source: Scopus.
Figure 1 also shows that of the 30 countries clicking through to the greatest number of full-text UK articles, the English-speaking countries of Australia, Canada and the US cite the greatest proportion of articles originating from Institute X. This is shown geographically in the map in Figure 2.
Figure 2 – Who is viewing articles from Institute X? Source: Scopus.
Similarly, one can look at downloads per discipline to assess the relative strengths of an institute.
Figure 3 – Relative usage of Institute X's papers per academic discipline compared with UK papers in the discipline. The relative usage in Figure 3 is calculated as follows: (Downloads of Institute X/Papers from Institute X)/(Downloads UK/Papers UK).For Mathematics, Neuroscience, Nursing, Psychology and Health Professionals Institute X's publications have a higher relative usage than for the entire UK.
We can also look at downloads over time. Figure 4 shows the increasing contribution of Institute X's downloads to all UK downloads, suggesting that Institute X is playing a more and more important role in research in the UK.
Figure 4 — Institute X's papers downloads as a percentage of UK's papers downloads per year.
As these examples demonstrate, usage data can be used for a number of different types of analyses. One major advantage they have over citation analyses is that citations of papers only accrue in the months and years following their publication, as new papers cite the article under analysis. Usage statistics, by contrast, begin to emerge as soon as an article is available for download, and so can give a more immediate view of how researchers, and the groups and institutes to which they belong, are performing. And while the full meaning and value of usage data remains up for debate, usage analysis is nonetheless represents a useful addition to the more conventional bibliometric analysis based on citations.
Country Trends
September 2011/ Gali Halevi and Henk F. Moed
Emerging scientific networks
In countries with an emerging science base, how much do key institutions participate in "outward" versus "inward" collaboration networks? This article shows different patterns in these networks for different countries.
Examining the scientific output of countries around the world is an effective way to identify emerging scientific competencies on national, institutional and topical levels. Various studies in this area have identified up-and-coming countries in South America, Africa, Asia and Europe1–5. These studies not only describe how particular countries actually invest in their science by mapping publications by research topics and disciplines, but can also help identify the factors that stimulate or harm scientific development by pointing to over- or under-investment in particular fields and/or research groups.
Inward or outward?
In this piece we focus not only on the scientific output as seen in publications, but also on the formation of emerging scientific networks in a number of countries from different geographical regions. These networks were defined in terms of "Inward" and "Outward" connections. "Inward" connections denote scientific collaborations mostly conducted between institutions in the same country; "Outward" connections are those between institutions in different countries. Looking at the Inward/Outward characteristics of these emerging scientific networks reveals the differences between institutions and countries at the level of international versus domestic scientific participation, and also helps identify the specific disciplines and topics that foster such scientific network exchanges.
Countries of interest
This study focuses on the analysis and identification of institutions in selected countries in Africa, Central America, Eastern Europe, Arab nations and South Asia, all of which have shown a surge in scientific output in the past 5 years. The analysis was conducted in four steps. In the first step, a selected list of countries per region was compiled (see Table 1). In the second step, these countries were searched using Scopus database for 2005–2010 publications. The country with the higher number of publications was then searched individually in the third step in order to identify the institution with the highest scientific output. Finally, using Scopus Affiliation Profile, further analysis into each institution's topics and collaborations was completed. The results are presented in Table 2.
Africa South Africa, Nigeria, Egypt, Kenya, Tunisia, Algeria, Morocco, Tunisia, Uganda, Namibia, Ghana, Cameroon
Eastern Europe Estonia, Latvia, Lithuania, Poland, Czech Republic, Slovakia, Hungary, Romania, Bulgaria, Slovenia, Croatia, Bosnia-Herzegovina, Serbia, Kosovo, Albania, Montenegro, Macedonia
Arab Countries Iran, Iraq, Jordan, Lebanon, Qatar, Saudi Arabia, Syria, Turkey, United Arab Emirates, Yemen
Central & South America Panama, Costa Rica, El Salvador, Nicaragua, Honduras, Guatemala, Belize, Argentina, Brazil, Bolivia, Chile, Colombia, Ecuador, Paraguay, Peru, Uruguay, Venezuela
South Asia Indonesia, Laos, Malaysia, Philippines, Singapore, Thailand, Vietnam
Table 1 – List of selected regions and countries.
Table 2 shows the five countries displaying the highest number of publications in the different regions, and the institutions that display the largest number of publications, for 2005–2010. These results suggest that the nature of scientific collaborations — Outward or Inward — are not determined by the scientific field under study. For example, both Singapore and Saudi Arabia published significantly in Engineering, yet these countries show different collaborative characteristics: the former tend to be Inward, while the latter are Outward. Similarly, while both South Africa and the Czech Republic are strong in Medicine, they typically engage in Inward and Outward collaborations, respectively.
Close to sight, close to heart
In fact, the distinction between Outward and Inward collaborations obscures the fact that both kinds of collaboration tend to occur between geographically close countries. For example, Saudi Arabia's Outward collaborations are largely carried out with groups based in India and Pakistan, countries that are relatively close to Saudi Arabia compared with, say, the US or Western Europe. Likewise, while the Czech Republic collaborates with institutions outside its borders, they are typically geographically close (that is, other European countries).
This examination of disciplinary foci and collaborative formations shows that despite the differences in research activities and collaborative trends, collaborations are typically formed between institutions that show relative geographical proximity. This trend could be a result of many factors. For example, researchers may be more likely to form personal connections with colleagues from nearby countries, perhaps because they encounter each other at regional talks and conferences more often than colleagues from countries further afield. In addition, researchers may find it easier to work with colleagues who share the same language, or other cultural characteristics.
Region Country Most productive institution Dominant disciplines in most productive institution Collaborative orientation Most productive institution's major collaborators
Africa South Africa University of Cape Town Medicine and Agricultural & Biological sciences Inward Univ Stellenbosch; Univ Witwatersrand; Groote Schuur Hospital; South African Medical Research Council
Central America Costa Rica Universidad de Costa Rica Agricultural and Biological Sciences Outward Texas A and M Univ; Smithsonian Tropical Research Institute; Univ Nacional Autónoma de México; Univ Sao Paulo
Eastern Europe Czech Republic Univerzita Karlova v Praze (Charles Univ, Prague Medicine and Biochemistry Outward Institutions in Russia, France and the UK
Arab Saudi Arabia King Fahd Univ Petroleum and Minerals Engineering Outward Institutions in IEEE, India and Pakistan
South Asia Singapore National University of Singapore Engineering, Physics and Astronomy Inward Inst. Materials Research and Engineering, A-Star, Inst. Infocomm Research, A-Star, Yong Loo Lin School of Medicine
Table 2 – Most productive institutions and their collaborators in five countries.
Toivanen, H., Ponomariov, B. (2011) African regional innovation systems: Bibliometric analysis of research collaboration patterns 2005-2009. Scientometrics, Vol. 88, No. 2, pp. 471–493.
Zhou, P., Glänzel, W. (2010) In-depth analysis on China's international cooperation in science. Scientometrics, Vol. 82, No. 3, pp. 597-612.
De Castro, L. A. B. (2005) Strategies to assure adequate scientific outputs by developing countries - A Scientometrics evaluation of Brazilian PADCT as a case study. Cybermetrics, Vol. 9, No. 1.
García-Carpintero, E., Granadino, B., & Plaza, L. M. (2010) The representation of nationalities on the editorial boards of international journals and the promotion of the scientific output of the same countries. Scientometrics, Vol. 84, No. 3, 799–811.
Nguyen, T. V., & Pham, L. T. (2011) Scientific output and its relationship to knowledge economy: An analysis of ASEAN countries. Scientometrics, (1 July 2011), 1–11.
The value of bibliometrics
September 2011/ Sarah Huggett
Heading for success: or how not to title your paper
Does the choice of a certain title influence citation impact? Research Trends investigates the relevant properties of a scientific title, from length to punctuation marks.
The title of a paper acts as a gateway to its content. It's the first thing potential readers of the paper see, before deciding to move on to the abstract or full text. As academic authors want to maximize the readership of their papers it is unsurprising that they usually take a lot of care in choosing an appropriate title. But what makes a title draw in citations?
Is longer better?
Bibliometric analyses can be used to illuminate the influence of titles on citations. Jamali and Nikzad, for example, found differences between the citation rates of articles with different types of titles. In particular, they found that articles with a question mark or colon in their title tend to be cited less1. The authors noted that "no significant correlation was found between title length and citations", a result conflicting with another study by Habibzadeh and Yadollahie finding that "longer titles seem to be associated with higher citation rates"2.
Research Trends investigates
Faced with inconsistent evidence, Research Trends decided to conduct its own case study of scholarly papers published in Cell between 2006 and 2010, and their citations within the same window. Overall, there was no direct correlation between title length (measured in number of characters) and total citations. However, comparing the citation rates of articles of different lengths revealed that papers with titles between 31 and 40 characters were cited the most (see Figure 1). There were also differences in average number of citations per paper depending on the punctuation used in the titles: for instance, the few papers with questions marks in their titles were clearly cited less, but titles containing a comma or colon were cited more (see Figure 2). There were no papers with a semicolon in their title, and only one (uncited) paper with an exclamation mark in its title. It is interesting to note that the ten most cited papers in Research Trends' case study did not contain any punctuation at all in their titles.
The authors explain
Research Trends contacted authors from highly cited papers in its corpus for their take on the influence of titles on citations. For some authors, such as Professor Deepak Srivastava — who published a paper in Cell with a title that included three commas3 — the main emphasis when choosing a title is semantics: "We chose a title that would reflect the major findings of the paper and the conclusion we would like the field to derive from the contribution. I don't pay too much attention to the title's effect on citations." Interestingly, different criteria are used for title assignment depending on the type of paper, as explained by Professor Ben Blencowe: "For research articles, I try to use titles that are concise while conveying the most interesting and surprising new results from the study. For review titles, I generally start with the main overall subject followed by a colon and then one or more subtopics that best describe the contents of the review. My 2006 Cell review on alternative splicing4 followed this format. It is not clear to me that this format increases citation impact — I would hope that the overall information content, timeliness and quality of writing in a review are directly related to citation impact! — but using punctuation in this way helps to convey at a glance what the review is about."
Are you having a laugh?
Given that straightforwardly descriptive paper titles run the risk of being dull, some authors are tempted to spice them up with a touch of humour, which may be a pun, a play on words, or an amusing metaphor. This, however, is a risky strategy. An analysis5 of papers published in two psychology journals, carried out by Sagi and Yechiam, found that "articles with highly amusing titles […] received fewer citations", suggesting that academic authors should leave being funny to comedians.
In sum, the citation analysis of papers according to title characteristics is better at telling authors what to avoid than what to include. Our results, combined with others, suggest that a high-impact paper should be neither too short nor too long (somewhere between 30 and 40 characters appears to be the sweet spot for papers published in Cell). It may also be advisable to avoid question marks and exclamation marks (though colons and commas do not seem to have a negative impact on subsequent citation). And even when you think you have a clever joke to work in to a title, it probably won't help you gain citations. Finally, while a catchy title can help get readers to look at your paper, it's not going to turn a bad paper into a good one.
Figure 1 – Average number of citations per paper by title length for papers published in Cell 2006–2010, and their citations within the same window. Data labels show number of papers. Source: Scopus.
Figure 2 – Average number of citations per paper by punctuation mark for papers published in Cell 2006-2010, and their citations within the same window. Data labels show number of papers. Source: Scopus.
Jamali, H.R. & Nikzad M. (2011) Article title type and its relation with the number of downloads and citations. Scientometrics, online first. DOI: 10.1007/s11192-011-0412-z
Habibzadeh, F. & Yadollahie, M. (2010) Are Shorter Article Titles More Attractive for Citations? Cross-sectional study of 22 scientific journals. Croatian Medical Journal, Vol. 51, No. 2, pp. 165–170.
Zhao Y., Srivastava D., Ransom J.F., Li A., Vedantham V., von Drehle M., Muth A.N., Tsuchihashi T., McManus M.T. & Schwartz R.J. (2007) Dysregulation of cardiogenesis, cardiac conduction, and cell cycle in mice lacking miRNA-1–2. Cell, Vol. 129, No. 2, pp. 303–317.
Blencowe, B. J. (2006) Alternative splicing: new insights from global analyses", Cell, Vol. 126, No. 1, pp. 848–858.
Sagi, I. & Yechiam, E. (2008) Amusing titles in scientific journals and article citation. Journal of Information Science, Vol. 34, No. 5, pp. 680–687.
September 2011/ Matthew Richardson
A "democratization" of university rankings: U-Multirank
Research Trends reports on a new multi-dimensional approach of ranking universities. Its unique property is that it does not collapse different scores into one overall score, thereby increasing transparency.
The rise of university ranking systems has engendered status anxiety among many institutions, and created a "reputation race" in which they strive to place higher up the university charts year on year. Concerns have been aired that this is leading to an homogenization of the university sector, as aspiring institutions imitate the model of more successful research-intensive institutions. And while the ranking scores do capture an important aspect of each university's overall quality, they don't speak to a diverse range of other issues, such as student satisfaction within these institutions.
U-Multirank is a new initiative to change this. The system — designed and tested by the Consortium for Higher Education and Research Performance Assessment, and supported by the European Commission — aims to increase transparency in the information available to stakeholders about universities, and encourage functional diversity of the institutions1. Unlike traditional university rankings such as the ARWU2, QS3 and THE4 rankings, U-Multirank features separate indicators that are not collapsed into an overall score. In this article Frans van Vught, project leader of U-Multirank, discusses development of the system and his hopes for it.
Traditional university ranking systems encourage institutions to focus on areas that carry the greatest ranking weight, such as scientific research performance. One benefit of these rankings is that they publicize the achievements of universities that perform well, albeit in this specific range of activities. Will U-Multirank move away from a culture of looking for success stories?
U-Multirank is a multi-dimensional, user-driven ranking tool, addressing the functions of higher education and research institutions across five dimensions: research, education, knowledge exchange, regional engagement and international orientation. In each dimension it offers indicators to compare institutions. In this sense it certainly focuses on the goals institutions set themselves. But unlike most current rankings, U-Multirank does not limit itself to one dimension only (research). It allows institutions to show whether they are winners or improvers over a range of dimensions.
As it is impossible to directly measure the quality of an institute, proxy measures, such as graduation rates and publication output, have to be used instead. Yet as Geoffrey Boulton argues, "[i]f ranking proxies are poor measures of the underlying value to society of universities, rankings will at best be irrelevant to the achievement of those values, at worst, they will undermine it."5 What criteria have you considered when selecting indicators, and are there indicators you would like to include but cannot at present?
When ranking in higher education and research we need to work with proxy indicators, since a comprehensive and generally acceptable set of indicators for 'quality' does not exist. Quality and excellence are relative concepts and can only be judged in the context of the purposes stakeholders relate to these concepts. Quality in this sense is 'fitness for purpose', and purposes are different for different stakeholders.
For the selection of U-Multirank's indicators we made use of a long and intensive process of stakeholder consultation, which included a broad variety of stakeholders, including the higher education and research institutions themselves. This stakeholder consultation reflected the criterion of 'relevance' in the process of indicator selection. In addition we used the criteria of validity, reliability, comparability and feasibility. For 'feasibility' we focused on the availability of data and the effort required to collect extra data. We tried to ensure that data availability would not become the most important factor in the selection process. However, the empirical pilot test of the feasibility of U-Multirank indicators showed that particularly in the dimensions of 'knowledge exchange' and 'regional engagement' data availability is limited.
A recent report drew attention to U-Multirank's 'traffic light' rating system, commenting that "institutions should not be ranked on aspects that they explicitly choose not to pursue within their mission."6 Is this a valid criticism? Could it lead — as the authors suggest — to a decrease in functional diversity as "institutions compet[e] to avoid being awarded a poor ranking against any of the criteria"?
I think this argument is invalid. U-Multirank is user-driven. This is based on the fundamental epistemological position that any description of reality is conceptually driven; rankings imply a selection of reality aspects that are assumed to be relevant. Any ranking reflects the conceptual framework of its creator, who should therefore be a user of the ranking. U-Multirank is a 'democratization' of rankings.
We designed a tool that allows users to select the institutions or programs they are interested in. This is U-Map7, a mapping instrument that allows the selection of institutional activity profiles. In U-Multirank only comparable institutions are compared: apples are compared with apples, not oranges. Institutions that do not pursue certain mission aspects should not be compared on these aspects. U-Multirank is designed to avoid this, so as not to encourage imitation or discourage functional diversity. On the contrary, U-Multirank shows and supports the rich diversity in higher education systems.
However harmful to the goal of encouraging diversity, traditional ranking systems have the advantage that people know how to read them: the simplest comparison between universities is seeing which has the higher rank. Will U-Multirank's users need guidance to compare institutions?
We hope to address both the wish to have a general picture of institutional performances and the wish to go into detail. U-Multirank offers a set of presentation modes that allow both a quick and general overview of multidimensional performance on the one hand, and a more detailed comparison per dimension on the other. Testing these presentation modes with different groups of stakeholders showed that our approach was highly appreciated and additional guidance was not needed. The general overview is presented in the so-called 'sunburst charts' that show a multidimensional performance profile per institution (see Figure 1). The detailed presentations are offered as tables in which performance categories are shown per indicator.
Figure 1 – U-Multirank's 'sunburst' charts "[give] an impression 'at a glance' of the performance of an institution".8 The charts show the performance of each institution across a number of indicators, with one 'ray' per indicator: where an institution ranks highly in an indicator, the 'ray' is larger. These indicators are grouped into categories around the chart. These two charts show the performance of two institutions: a large Scandinavian university (top) and a large southern European university (bottom).
Curriculum Vitae: Frans van Vught
Frans van Vught (1950) is a high-level expert and advisor at the European Commission. In addition he is president of the European Center for Strategic Management of Universities (ESMU), president of the Netherlands House for Education and Research (NETHER), and member of the board of the European Institute of Technology Foundation (EITF), all based in Brussels. He was president and Rector of the University of Twente, the Netherlands (1997–2005). He has been a higher education researcher for most of his life and published widely in this field. His many international functions include membership of the University Grants Committee of Hong Kong, the board of the European University Association (EUA) (2005–2009), the German 'Akkreditierungsrat' (2005–2009), and the L.H. Martin Institute for higher education leadership and management in Australia. Van Vught is a sought-after international speaker and has been a consultant to many international organizations, national governments and higher education institutions all over the world. He is honorary professor at the University of Twente and at the University of Melbourne, and holds several honorary doctorates.
http://www.u-multirank.eu/
http://www.arwu.org/index.jsp#
http://www.topuniversities.com/university-rankings/world-university-rankings
http://www.timeshighereducation.co.uk/world-university-rankings
Boulton, G. (2010). University rankings: Diversity, excellence and the European initiative. League of European Research Universities Advice Paper. No. 3, June.
Beer, J. et al. (2011). Let variety flourish. Times Higher Education, 2 June.
http://www.u-map.eu/
U-Multirank (2011). The design and testing the feasibility of a multi-dimensional global university ranking. Draft version for distribution at the U-Multirank conference, Brussels, Thursday 9 June 2011.
Reporting Back
September 2011/ Gali Halevi
Mapping & Measuring Scientific Output
This event focused on scientific output measurements, methodologies and mapping techniques. Research Trends summarizes and reports back.
Hundreds of delegates participated in a day-long symposium on scientific evaluation metrics, held in Santa Fe New Mexico on May 10th 2011, the result of a collaboration between Elsevier and Miriam Blake, Director of the Los Alamos National Laboratory (LANL) Research Library. This symposium focused on scientific output measurements, methodologies and mapping techniques, and was globally broadcasted from the conference ballroom, where world-renowned speakers presented and discussed existing and emerging metrics used to evaluate the value and impact of research publications.
Measuring the impact and value of scientific publications is critical as governments are increasingly seeking to distribute research funds in ways that support high-quality research in strategically important fields.. Through the years, several methodologies and metrics have been developed in order to address some of the many factors that can be taken into consideration when assessing scientific output. New evaluative metrics have emerged to capitalise on the wealth of bibliometric data in analyzing citation counts, article usage, and the emergence and significance of collaborative scientific networks. In addition, ever-increasing computational power enables rigorous relative and comparative analysis of journal citations and publication relationships to be calculated and used in unique ways, including a variety of visualization solutions.
Symposium themes generated from registrants feedback and comments
The symposium offered insight into the topic of research evaluation metrics as a whole. The discussion was headed by Dr. Eugene Garfield and Dr. Henk Moed, who addressed established and emerging trends in bibliometrics research, with both stressing the necessity of using more than one method to accurately capture the impact of research publications and authors. Emerging and innovative approaches using journal and scientific networks, weighted reference analysis and article usage data were also presented. Dr. Jevin West discussed the latest developments in the EigenFactor (http://www.eigenfactor.org); Dr. Henry Small unveiled a new method for citations text mining in emerging scientific communities; Dr. Johan Bollen presented the MESUR (http://www.mesur.org/MESUR.html) project; and Dr. Kevin Boyack (http://mapofscience.com) demonstrated how co-citation analysis can be used to identify emerging and established scientific competencies within institutions as well as countries. The methodological discussion was accompanied by a demonstration of visualization solutions that capture these relationships and enable a broad view of scientific trends, networks and research foci.
More than a thousand words
The power of visualizing such networks was demonstrated by Dr. Katy Börner, who headed the discussion on the variety and diversity of scientific mapping tools. Dr. Börner brought a wealth of examples through the "Places & Spaces" (http://scimaps.org/) exhibition, which was displayed in the conference room and via her presentation. Maps for scientific policy and economic decision makers, along with maps for forecasting and research references, were among the examples displayed and discussed by Dr. Börner. This was followed by Mr. Bradford Paley, who discussed visual and cognitive engineering techniques that support the analysis of scientometric networks (http://wbpaley.com/brad/Elsevier.html).
Multidimensionality
With the evident paradigm shift from print and paper to official and nonofficial online networks, as well as usage data and the wealth of data that they offer, the main discussion point during the symposium was the need for multidimensionality of measurements that capture and represent the complex arena we call "Scientific Impact". Today, using one method, value or score to determine whether a researcher, research group or institution is indeed impactful seems invalid. If there is a lesson to be learned from this research event, it is that the scientific community has to find the correct and fair balance between a variety of computational metrics and qualitative peer-review processes.
Presentations & Audio recordings of this event are available:
http://www.elsevier.com/wps/find/librarianshome.librarians/LCPresentations
OECD (2010), Performance-based Funding for Public Research in Tertiary Education Institutions: Workshop Proceedings, OECD Publishing. http://dx.doi.org/10.1787/9789264094611-en
…That there are now more than 37 h-index variants?
Since its proposition by physicist Jorge Hirsch in 20051, the h-index has become a popular bibliometrics measure to evaluate scientists, and has featured regularly in Research Trends2–4. The simplicity and intuitiveness of the h-index have contributed to its popularity, but also to its criticism by a community wishing for more precise and unbiased measures, as the h-index tends to favor late-career scientists. As a consequence, several corrections to the metrics have been put forward: a recent paper has identified no less than 37 h-index variants that have emerged in the past 6 years. Interestingly the study found high levels of correlation between the h-index and most variants, suggesting that many of these tend to measure the same aspect.
1. Hirsch, J.E. (2005) An index to quantify an individual's scientific research output. Proceedings of the National Academy of Sciences of the United States of America, Vol. 102, No. 46, pp. 16569–16572.
2. Egghe, L. (2007) From h to g: the evolution of citation indices. Research Trends, September.
3. Bornmann, L. (2008). The h-index and its variants: which works best? Research Trends, May
4. Plume, A. (2009). Measuring up: how does the h-index correlate with peer assessments? Research Trends, May.
5. Bornmann, L., Mutz, R., Hug, S.E. & Daniel, H.D. A multilevel meta-analysis of studies reporting correlations between the h index and 37 different h index variants. Journal of Informetrics, Vol. 5, No. 3, pp. 346–359.
https://www.researchtrends.com/wp-content/uploads/2011/11/Research_Trends_Issue24.pdf
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Marele Premiu al Japoniei din 2022 (cunoscut oficial ca Formula 1 Honda Japanese Grand Prix 2022) a fost o cursă auto de Formula 1 ce s-a desfășurat între 7-9 octombrie 2022 pe Circuitul Suzuka din Suzuka, Japonia. Aceasta a fost cea de-a optsprezecea rundă a Campionatului Mondial de Formula 1 din 2022.
Max Verstappen și-a asigurat al doilea titlu mondial după ce a terminat cursa pe primul loc, în fața lui Sergio Pérez și Charles Leclerc. În ciuda faptului că doar 28 dintre cele 53 de tururi programate au fost parcurse, au fost acordate puncte complete din cauza unei lacune în regulament privind modul în care ar trebui alocate punctele, regulile precizând că punctele reduse ar trebui acordate numai în cursele scurte care se termină în condiții de steag roșu. Întrucât această cursă s-a încheiat în condiții de steag verde, acest sistem nu a fost aplicat. Textul regulamentului sportiv a fost modificat ulterior pentru , astfel încât cursele care ajung la mai puțin de 75% din distanță să aplice criteriile de puncte de cursă scurtată, indiferent dacă o cursă se termină în condiții de steag roșu sau verde în viitor.
Calificări
După calificări, Max Verstappen a primit o mustrare de către comisari pentru un incident din Q3, care a implicat pierderea controlului mașinii, ce l-a forțat pe Lando Norris să manevreze în jurul lui Verstappen în virajul 130R. Nu a fost emisă nicio penalizare pe grilă.
Note
– Pierre Gasly s-a calificat pe locul 17, dar a fost nevoit să înceapă cursa de pe linia boxelor din cauza modificărilor aduse ansamblului aripei spate, balastului aripei față și configurației suspensiei.
– Nicholas Latifi a primit o penalizare de cinci locuri pe grilă pentru că a provocat o coliziune cu Zhou Guanyu în runda anterioară. A câștigat o poziție, deoarece Gasly trebuia să înceapă cursa de pe linia boxelor.
Cursă
Cursa a început la ora locală 14:00, pe 9 octombrie 2022, sub o ploaie torențială și a fost suspendată cu steag roșu în turul 2 după ce pilotul Carlos Sainz Jr. a pierdut controlul mașinii și a acvaplanat în bariere. Cursa a fost reluată la ora locală 16:15 în spatele mașinii de siguranță.
Note
– Distanța cursei a fost programată inițial să fie parcursă pentru 53 de tururi, înainte de a fi scurtată din cauza unui steag roșu.
– Charles Leclerc a terminat pe locul doi, dar a primit o penalizare de cinci secunde pentru că a părăsit pista și a câștigat un avantaj.
– Pierre Gasly a terminat pe locul 17, dar a primit o penalizare de drive-through (convertită într-o penalizare de timp de 20 de secunde după cursă) pentru viteză excesivă în condiții de steag roșu.
Clasamentele campionatelor după cursă
Clasament piloți
Clasament constructori
Notă: Doar primele cinci locuri sunt prezentate în ambele clasamente.
Textul îngroșat indică concurenții care mai aveau șansa teoretică de a deveni Campion Mondial.
Referințe
Japonia
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Now that the US Photo Marketing Association trade show has decamped from the winter calendars, we look to shows like photokina and the professional trade shows in the US as our main source of information for what's happening in photography, at least from the tools of the trade perspective. We attend them to see what the photo industry is up to and how the products they present, and how they present them, will affect how we make, share, and process images. You never know what creative work the latest software or cameras or lenses might engender, and you increasingly have to look out for distractions and false starts.
With that in mind the following are observations, opinions, product reveals, and some info we thought would be of interest to you. We'll start with what might be a major shift in camera and, subsequently, lens design, the "mirrorless" interchangeable lens camera systems.
The Nikon D7000 is part of the new breed of D-SLR with amped up sensors (in this case Nikon's EXPEED 2) with intense processing power that will certainly change how we work with our images, here with 16.2 megapixels, 6 fps, and 1080p HD video capability..
While there were camera announcements from Canon and Nikon prior to the show, mainly updates on previous models with more video features and improved processors, all of which we will cover in coming test reports, many of the newest cameras, aside from the usual raft of point-and-shoots, were less than traditionally designed APS-C or Micro Four Thirds models. An exception was the Olympus E-5, an E-3 inspired 12-megapixel brick house of a camerawith HD video, a faster image processor,and 10 "art filters" available. I characterizeit as such because an Olympus booth staffer insisted on demonstrating its toughness by repeatedly standing on it, and he was no lightweight himself. Also in this classic mold is the prototype Sigma SD1, with a Foveon sensor that they say will deliver their equivalent of 48 megapixels and much enhanced monochrome performance. Prototype means it was shown under glass and that we may see it in more operational status later this year.
The "mirrorless" Panasonic GH2 offers HD movies, touchscreen shooting, and a very fast AF system in a 16-megapixel Micro Four Thirds chip. The Live View finder is one of the most viewable, being composed of 1.53 million "dots." Shown here, the camera with a Panasonic 3D lens, which when mounted sets the camera to produce an MPO (3D viewable) file and a JPEG.
A number of the new cameras, however, were in the somewhat new class of "mirrorless" camera systems, many with APS-C sensors. The appellation makes them sound like they are missing something, and it defines what they are not, which is a D-SLR. The "R" in D-SLR of course stands for "reflex," or the way light is reflected from the lens up to the prism finder. In "R" cameras when a picture is made the mirror is jerked up and out of the way so the light can travel straight back from lens to sensor or film. The newest interchangeable lens cameras from the likes of Sony, Samsung, and Panasonic (note the common consumer electronics community) all dispense with this way of directing light and use a variety of methods to get the light where it needs to go, all with enhanced AF speed and accuracy vs. former Live View-type systems. They use less moving parts so cameras like the modestly priced Sony Alpha 55 can give you 10 frames per second (fps) shooting with an AF setup that follows the action in as impressive fashion as a quite high-priced, high-speed D-SLR of recent years past.
Photokina is known for previews of cameras not ready for sale but anticipated, as Joe Farace says, "real soon now." The Sigma SD1 is a culmination of coordinated efforts by Sigma and Foveon, which they acquired, and will have an (in their math) equivalent of 48-megapixel output. It was shown "under glass" only.
Hold on—the Sony Alpha 55 and Panasonic GH2 are still in the classic 35mm form factor, so do they count as "mirrorless"? Yes, because in the Sony, for example, the mirror system is what they call "translucent," which in the end means the mirror does not move during capture but in somewhat quantum fashion both reflects the image up to the finder (an EVF or electronic viewfinder), the monitor back if you choose, and through to the sensor for exposure, all without lifting a finger, if you will. The light, in essence, is both transmitted and reflected with no mirror motion during capture.
Yet, more cameras are eschewing the classic 35mm form factor for the "microprocessor with lens" design, typified by the Sony NEX-3 and 5 (see our review earlier this year in the October, 2010, issue) and the new Samsung NX100. Samsung has been making stabs at the D-SLR market in fits and starts, and there were even rumors about their assuming the Pentax brand years back, but now they have, I think wisely, taken another course. Their first in this class was the NX10 and now they have introduced the NX100, albeit with a fairly radical design that has you making common settings with a button on the lens that evokes menus for white balance, ISO, Exposure modes, etc. that you change by turning the focusing ring on the lens, which reverts to its normal function once you switch to Manual Focusing mode. The benefit, once you get the hang of it? You don't have to make settings using buttons and the camera back menu display so you can stay plugged into the image as you work. Note that these cameras are in the 14+ megapixel range and offer every function of a full-featured D-SLR, and then some, plus of course video.
Samsung's NX100 is part of the design change found in the latest "mirrorless" cameras with a slim body, a 14.6-megapixel APS-C sensor, and a coming line of lenses. The twist here? You touch the i-Function button on the lens and make changes to settings by turning the focusing collar on the lens! Note top hot shoe—you can add an optional EVF finder when the better "organic" LED monitor doesn't do the job.
The question is—will this new approach sound the death knell of the "classic" D-SLR design? There are certain benefits, such as enhanced Live View options, with much faster AF than previously available, the use of APS-C-sized sensors in much smaller main bodies, and, thankfully, enhanced viewing thanks to much higher resolution screens. On the other hand, these cameras by force of their design offer EVF viewing, as plug-in viewfinder options (hot shoe and slot) or in a sort of non-penta-prism, penta-prism style finder.
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Q: Django: Contribute to third party app django-lazysignup I want to contribute to django-lazysignup a django third party app. I tried so far the following steps
*
*I set up a regular django app named custom-user
*I used virtualenv and install required library on virtualenv
*I fork and clone the github repository of django-lazysignup
*I run the sudo pip install -e /path/to/folder/django-lazysignup command
I am trying to run command python manage.py makemigrations on custom-user project but it showing ImportError: No module named 'lazysignup'.
Any help will be appreciated
A: As, per the official documentation, try to install the django-lazysignup using pip
pip install django-lazysignup
Once that's done, you need to add lazysignup to your INSTALLED_APPS. You will also need to add lazysignup's authentication backend to your site's AUTHENTICATION_BACKENDS setting:
AUTHENTICATION_BACKENDS = (
'django.contrib.auth.backends.ModelBackend',
'lazysignup.backends.LazySignupBackend',
)
Finally, you need to add lazysignup to your URLConf, using something like this:
urlpatterns += (
url(r'^convert/', include('lazysignup.urls')),
)
Here, is an official documentation to follow Official doc
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Q: Is it possible to cause segmentfault even when the accessed address is accessable? I meet a amazing segmentation fault when I am debugging a crash.
It shows segmentation fault in a line which is dereferenced a char* pointer. But when I use gdb to dereference the pointer, no error is reported from gdb.
My platfrom is linux. Any ideas?
A:
But when I use gdb to dereference the pointer, no error is reported from gdb.
This answer explains why this happens. There is nothing "amazing" about it.
A: the answer is no, it is not possible.
but to find out why, install valgrind, and run
valgrind ./yourexe
usually it tells you most of the errors you overlooked. remember to compile your binary using gcc -g without -O options, so you can see the source code line numbers.
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{"url":"http:\/\/openstudy.com\/updates\/557a49fde4b0e4e582aa0bab","text":"## anonymous one year ago help please ! to two decimal places, find the value of k that will make the function f(x) continuous everywhere.\n\n1. anonymous\n\n|dw:1434088494322:dw|\n\n2. freckles\n\nevaluate both the left and right limit of x=4\n\n3. freckles\n\n$\\lim_{x \\rightarrow 4^-}f(x)=? \\\\ \\lim_{x \\rightarrow 4^+}f(x)=?$\n\n4. freckles\n\noops -4\n\n5. anonymous\n\nmy choices are: 11.00 -2.47 -0.47 none of these\n\n6. freckles\n\nok can you evaluate both: $\\lim_{x \\rightarrow -4^-}f(x)=? \\\\ \\lim_{x \\rightarrow -4^+}f(x)=?$\n\n7. freckles\n\nhint ^- means look to the left (which is the left function of x=-4 and use it to plug in -4 into) hint ^+ means look to the right (which is the right function of x=-4 and use it to plug in -4 into) both the left and right limit need to be equal so that you can have the actual limit at x=-4 exist\n\n8. anonymous\n\no.o im lost lol\n\n9. freckles\n\n|dw:1434077995749:dw|\n\n10. freckles\n\n|dw:1434078038396:dw|\n\n11. anonymous\n\nis it A?\n\n12. freckles\n\nI don't know. Haven't done the problem.\n\n13. freckles\n\nwould you know how to evaluate: $\\lim_{x \\rightarrow -4}(3x+k) \\text{ or } \\lim_{x \\rightarrow -4}(kx^2-5)$\n\n14. anonymous\n\nno. o.o\n\n15. freckles\n\nBoth functions are continuous at x=-4 why don't you evaluate the limits by replacing x with -4?\n\n16. freckles\n\nand you want both (left and right limits of x=-4) sides to be equal so you have $3(-4)+k=k(-4)^2-5$\n\n17. freckles\n\ncan you solve linear equations?\n\n18. anonymous\n\nDo you have to take a limit here? Can you just substitute -4 for x and set the two parts equal to each other?\n\n19. freckles\n\none of the things we need for continuity at x=-4 is: $\\lim_{x \\rightarrow -4}f(x)=L$ we get to have this if : $\\lim_{x \\rightarrow -4^{-} }f(x)=\\lim_{x \\rightarrow -4^{+}}f(x)=L$ so formally the answer is yes to that question\n\n20. freckles\n\nto the limit one\n\n21. freckles\n\nand informally ( I would say) yes to the second question","date":"2016-10-22 23:58:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.903049647808075, \"perplexity\": 1848.8808609630246}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-44\/segments\/1476988719079.39\/warc\/CC-MAIN-20161020183839-00009-ip-10-171-6-4.ec2.internal.warc.gz\"}"}
| null | null |
A suspected car bomb exploded at the entrance to a hotel in the center of the Somali capital early on Sunday morning, damaging parts of the hotel and killing at least two people, a police officer and a witness said, according to Reuters.
There was no immediate claim of responsibility after the blast, which was followed by gunfire.
The Islamist militant group al Shabaab has frequently launched attacks in Mogadishu, often detonating a bomb to break through security and then sending fighters into buildings.
"A car bomb rammed into the gate of Sahafi hotel. So far I have seen two civilians dead," Major Ahmed Nur, a police officer, told Reuters.
The hotel, which lies in a place in the capital known as K-4, is often used by lawmakers and government officials.
"K-4 is the busiest street and the death toll may rise. We believe al Shabaab was behind it," Nur said, after the blast sent a plume of smoke above the capital on the Indian Ocean coast.
A Reuters witness saw wrecked cars and destroyed motorbikes in the area, as well as two dead civilians lying outside. At least three others were injured. Some parts of the hotel were damaged, while the witness reported shooting inside.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,183
|
Q: Can i run nightly and stable compliers? I am on rust stable, but i am trying to use rocket. I don't think it works on the stable complier. Can i run both the nightly and stable complier on my system?
A: If you use rustup, you can have both toolchains on your system. You can use rustup install nightly to install nightly, then you can use rustup default nightly/stable to change which version of rustc is used. You can also use rustup run nightly/stable rustc to run rustc as one version without changing the default.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,168
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\section{The leading model}
\label{sec:model}
Here we review some of the disordered systems where a relevant non
linear interaction may arise and our model applies. The basic
Hamiltonian of $N$ adimensional angular variables $\phi\in [0:2\pi]$
is given by
\begin{equation}
{\cal H}_J[\phi]=
-\hspace*{-.5cm}\sum_{\footnotesize{\begin{array}{c} i_1<\!i_2, i_3<\!i_4
\\
i_1<\!i_3 \end{array}}}^{1,N}\hspace*{-.5cm}J_{\bf{i}}
\cos(\phi_{i_1}+\phi_{i_2}-\phi_{i_3}-\phi_{i_4})
\label{mainHam}
\end{equation}
where ${\bf i}=\{i_1,i_2,i_3i_4\}$ and $J_{\bf i}$ are random
independent identically distributed interaction variables. Formally,
the couplings can vary from short- to long-range, depending on the
structure of the four-index interaction tensor $J_{\bf i}$. If we
choose $J_{\bf i}\neq 0$ for any distinct quadruple $i_1, \ldots,
i_4$, independently of the geometric position, we can build a
mean-field theory in which the system is fully connected. In this case
the average $J_{\bm i}$ and the variance of its distribution must
scale as $1/N^3$ to guarantee thermodynamic convergence of (free)
energy density. The interaction can, otherwise, be bond-diluted with
arbitrary degree of diluteness, adopting a sparse tensor whose
non-zero elements do not scale with the number of modes,
\\
\indent
As we show in the following, the Hamiltonian, Eq. (\ref{mainHam}) is
derived in different contexts, and the various parameters may have
different interpretation. In this manuscript we want to derive general
properties that are expected assuming a simple, yet reasonable,
Gaussian distribution for the random coupling coefficients, with a
non-vanishing mean value. Varying the ratio between the standard
deviation and the mean value we control a different degree of
disorder. Hence, these results applies to the various cases in which
random wave propagation, localization and not-negligible nonlinear
effects are important; a few of them are detailed in the following.
\\ \indent As a thermodynamic approach is adopted, one can argue if
the statistical mechanic techniques also apply in those systems where
the definition of a temperature is not straightforward, as,
specifically, nonlinear optical wave propagation in disordered media.
This particular problem can, then, be treated as for constraint
satisfaction problems in computer science,
\cite{Kirkpatrick94,Monasson99,Mezard02,Mezard09} where - at the end
of the calculation - the limit of zero-temperature is taken and it is
shown that a transition is expected as the number of constraints grows.
\subsection{Random active and passive electromagnetic cavities}
\label{ss:rl}
We start from the electromagnetic energy inside a dielectric cavity
(due to the generality of the considered model similar examples can be
found in a variety of systems):
\begin{equation}
\mathcal{E}_{EM}=\int {\bf E}(\bm r)\cdot {\bf D}(\bm r)~ dV
\end{equation}
The displacement vector is written in terms of a position dependent
relative dielectric constant $\epsilon_r({\bf r})$:
\begin{equation}
{\bf D}({\bf r})=\epsilon_0 \epsilon_r({\bf r}) {\bf E}({\bf
r})+\epsilon_0 {\bf P}_{NL}({\bf r})
\end{equation}
with ${\bf P}_{NL}$ the nonlinear polarization. In absence of the
latter, for a closed cavity, the field can be expanded in terms of the
modes of the system. In the presence of disorder these modes may
display a different degree of localization as, e.g., in a
disordered photonic crystal (PhC). \cite{Conti08PhC} For a closed cavity
these modes form a complete set and the field can be expanded in terms
of the modes
\begin{equation}
{\bf E}=\Re \left[\sum_{n=1}^N
a_n(t) \exp{\left(-\imath\omega_n t\right)} {\bf E}_n({\bf r})\right]
\label{modeexpansion}
\end{equation}
with ${\bf E}=\{E^x,E^y,E^z\}$. As far as a nonlinear polarization is
not present, the coefficients $a_n$ are time-independent. Conversely,
in the general case, taking for ${\bf P}_{NL}$ a standard third order
expansion, one has for the non-linear interaction Hamiltonian
\begin{eqnarray}
{\cal H}&=&-\langle{\int \epsilon_0 {\bf E}\cdot {\bf P}_{NL} dV
}\rangle
\nonumber
\\
&=&- \hspace*{-.5cm}\sum_{\omega_j+\omega_k
=\omega_l+\omega_m} \hspace*{-0.5cm}\Re\left[G_{jklm}~
a_j a_k a_l^* a_m^*\right]
\label{Ha1}
\end{eqnarray}
where $\langle \ldots \rangle$ is the time average over an optical cycle and
the sum ranges over all distinct $4$-ples for which the condition
\begin{equation}
\omega_j+\omega_k
=\omega_l+\omega_m
\label{f:MLresonance}
\end{equation}
holds, with $j,k,l,m=1,\ldots,N$.
The effective interaction occurring among mode-amplitudes reads:
\begin{eqnarray}
G_{jklm}&=&\frac{\imath}{2}\sqrt{\omega_j\omega_k\omega_l\omega_m}
\\
\nonumber
&&\times
\int_V d^3r~
\chi^{(3)}_{\alpha\beta\gamma\delta}(\omega_j,\omega_k,\omega_l,\omega_m;
\mathbf r)
\\
\nonumber
&& \hspace*{1cm}
\times ~ E^\alpha_j(\mathbf r) E_k^\beta(\mathbf r) E_l^\gamma(\mathbf r)
E_m^\delta(\mathbf r)
\label{f:G4}
\end{eqnarray}
with $\alpha, \beta, \gamma, \delta = x,y,z$. This coefficient
represents the spatial overlap of the electromagnetic fields of the
modes modulated by the non-linear susceptibility $\chi^{(3)}$. The
disorder is induced, e.g., by the random spatial distribution of the
scatterers (as in random lasers) that leads to randomly distributed
modes and, hence, to random susceptibilities and
couplings among quadruple of modes.
\\ \indent If the cavity is open, the mode set is no more complete,
the modes whose profile decays exponentially out
of the cavity are taken for the
expansion (\ref{modeexpansion}), all the others form the radiation
modes. Under standard approach \cite{HausBook, SakodaBook,
Hackenbroich:01, Hackenbroich03, Angelani06} the coefficients in the
expansion that weight the radiation modes can be expressed in terms of
the disordered cavity one, and this results into linear terms in the
Hamiltonian (open cavity regime). Thus, for an open cavity, Eq. (\ref{Ha1})
becomes
\begin{equation}
{\cal H}=-\Re\Biggl[~
\sum_{j<k} G^{(2)}_{jk} ~ a_j a_k^* +\hspace*{-.5cm}
\sum_{\omega_j+\omega_k=\omega_l+\omega_m}\hspace*{-.5cm}
G^{(4)}_{jklm} ~ a_j a_k a_l^* a_m^*\Biggr]
\label{Ha2}
\end{equation}
The Hamiltonian expressions, Eqs. (\ref{Ha1}), (\ref{Ha2}), can be also
obtained starting from the corresponding Langevin dynamical equations,
as detailed, e.g., in Ref. [\onlinecite{Angelani06long}]:
\begin{eqnarray}
\dot a_n(t)&=&\sum_j G^{(2)}_{jn} a_j
+\hspace*{-.5cm}\sum_{\omega_j+\omega_n=\omega_k+\omega_l} \hspace*{-.5cm}
G^{(4)}_{jkln} a_j^* a_k a_l + \eta_n(t)
\nonumber
\\
&=&-\frac{\partial \cal H}{\partial a_n^*}+ \eta_n(t)
\label{f:Langevin}
\end{eqnarray}
where $\eta_n(t)$ is a white noise, for which
\begin{equation}
\langle
\eta_j(t)\eta_k(t')\rangle = 2T\delta_{jk}\delta(t-t')
\label{f:noise}
\end{equation}
\\ \indent Here $T$ is a ``heat-bath'' temperature, whose physical
interpretation depends on the specific system. In the case of a
random laser it represents the spontaneous emission and $k_B T\cong
\hbar/\tau$, with $\tau$ the amplifying level
lifetime. \cite{Angelani06long,YarivBook}
\\
\indent
Comparing Eq. (\ref{f:Langevin}) with the master equation for
mode-locking lasers in ordered cavities \cite{Haus00, HausBook}
\begin{eqnarray}
&& \dot a_n(t)\displaystyle= \left(g_n-\ell_n+i D_n\right)a_n
\nonumber
\\
&&\hspace*{1cm}+(\gamma-i\delta)
\hspace*{-.5cm}\sum_{\omega_j+\omega_n=\omega_k+\omega_l}\hspace*{-.5cm}
a_j^* a_k a_l + \eta_n(t)
\label{f:haus_master}
\end{eqnarray}
we can understand the physical role played by the parameters of the
probability distribution of the $G$'s. Indeed, $g_n$ is the gain
coefficient of the $n$-th mode in a round-trip through the cavity,
$\ell_n$ the loss term, $D_n$ the group velocity of the wave packet,
$\gamma$ the coefficient of the saturable absorber (responsible for
passive mode-locking) and $\delta$ the coefficient of the Kerr lens
effect. Neglecting the latter we can see that a system with positive
average of the $G_{jklm}$ corresponds to the presence of a saturable
absorber. In the case of peaked probability distribution for the
couplings $P(G)$, i.e., weak disorder, the system will tend to display
the same spectrum of many equally spaced modes typical of mode-locking
lasers. In the present formalism this will be a ferromagnetic
phase. One might, then, wonder what happens when the disorder is
so strong to prevent the occurrence of this phase and, even, when the
random coefficient corresponding of $\gamma$ is negative (i.e., when
passive mode-locking is absent). We will discuss this issue in
Sec. \ref{ss:satabs}.
\\
\indent
In the ``strong cavity limit'', the linear coupling between modes is
negligible and $G_{mn}^{(2)}$ is diagonal (i.e., one accounts only for the
finite-life time of the modes) and
\begin{equation}
{\cal H}=-\Re\Biggl[
\sum_{i=1}^N G^{(2)}_{ii} |a_i|^2 +\hspace*{-.5cm}
\sum_{\omega_{i_1}\!+\omega_{i_3}\!=\omega_{i_2}\!+\omega_{i_4}}\hspace*{-.5cm}
G^{(4)}_{i_1i_2i_3i_4}~ a_{i_1} a_{i_3} a_{i_2}^* a_{i_4}^*\Biggr]\text{.}
\label{Ha3}
\end{equation}
Note that the modes in the disordered cavity may display a different
degree of localizations, as in the case of disordered PhC.
Correspondingly, the distribution of the overlaps $G$ spreads.
Moreover, the constituents of the overlap integral are also very
difficult to calculate from first principles. Indeed, to our
knowledge, the only specific form of the non-linear susceptibility has
been computed by Lamb \cite{Lamb64} for a two-level system (without
disorder). Eventually, to estimate the coupling distribution from the
experimental data is a very complicated inverse statistical
problem, cf., e.g., Refs. [\onlinecite{Weigt09,Mora10}] and references
therein, and, so far, the reconstruction of the $G$'s, for example, from
measurements of random laser spectra has never been achieved.
The interplay between susceptibility and spatial
distribution of modes leading to $G$'s is, then, a very challenging problem
that deserves a systematic and sophisticated treatment that goes
beyond the aim of the present work.
\\ \indent In the following we will consider a mean-field approach in
which all modes are connected among each other.
We will, thus, approach the study of our model by means of Gaussian
distributed $G$'s with non-vanishing average, as detailed below.
\\
\indent
The leading regime considered in this work is, actually, driven by a {\it
quenched amplitude approximation}, which is obtained by retaining the
amplitudes $A_n=|a_n|$ (and correspondingly the energies of the modes)
as slowly varying w.r.t. the phase $\phi_n=\arg(a_n)$, such that the
resulting interaction Hamiltonian (retaining only those terms
depending on the phases, and considering the strong or closed cavity
regime, cf. Eq. (\ref{Ha3})), turns out to be \cite{Angelani06long, Leuzzi09}
\begin{eqnarray}
{\cal H}&=&-\hspace*{-.6cm }
\sum^{1,N}_{\omega_{i_1}\!+\omega_{i_3}\!=\omega_{i_2}\!+\omega_{i_4}}\hspace*{-0.9cm}'
\hspace*{.2cm} G_{i_1i_2i_3i_4} ~A_{i_1} A_{i_2}
A_{i_3} A_{i_4} \times
\label{f:Haphi2}
\\
\nonumber
&&\qquad\qquad\cos(\phi_{i_1}+\phi_{i_3}-\phi_{i_2}-\phi_{i_4})
\end{eqnarray}
where the sum $\sum '$ is limited to those terms that depend on the
phases (i.e., we neglect terms whose indices are such that the argument of
the cosine vanishes, e.g., $i_1=i_2$ and $i_3=i_4$)
and $G$ is assumed real-valued.
\\
\indent
Actually, in the physical systems of our interest,
it is not necessary that the resonant condition Eq. (\ref{f:MLresonance})
for having four modes interact in the mode-locking regime is satisfied
exactly. Indeed, it is enough that the mode combination tone
$\omega_{i_1}$ lies inside an interval around
$\omega_{i_2}+\omega_{i_4}-\omega_{i_3}$ corresponding to its
linewidth. \cite{MeystreBook} In the case, e.g., of the random laser,
in which many modes oscillate in a relative small bandwidth and are
densely packed in frequency space so that the their linewidth overlap,
this observation supports the further mean-field-like approximation
$\omega_i\simeq\omega_0$, $\forall ~ i$. In our model, therefore, the
spectral distribution of the angular frequencies will be considered as
strongly peaked around $\omega_0$ and $\omega_{i_1}+\omega_{i_3}\simeq
\omega_{i_2}+\omega_{i_4} \simeq 2\omega_0$ so that the ``selection
rule'' Eq. (\ref{f:MLresonance}) is always satisfied.
\\ \indent A suitable normalization and the introduction of an inverse
temperature-like parameter $\beta$ leads, eventually, from
Eq. (\ref{f:Haphi2}) to
\begin{equation}
\beta{\cal H}_J[\phi]=
-\beta\hspace*{-.5cm}\sum_{\footnotesize{\begin{array}{c} i_1<\!i_2, i_3<\!i_4
\\
i_1<\!i_3 \end{array}}}^{N}\hspace*{-.5cm}J_{\bf{i}}
\cos(\phi_{i_1}+\phi_{i_2}-\phi_{i_3}-\phi_{i_4})
\label{phase:Ham}
\end{equation}
with
\begin{eqnarray}
&&\beta \equiv \frac{\langle A^2\rangle^2 }{k_B T_{\rm bath}}
\label{def:beta}
\\
&&J_{\bf{i}}=J_{i_1 i_2 i_3 i_4}\equiv\frac{G_{i_1 i_2 i_3 i_4}}{V^2}
\frac{A_{i_1}A_{i_2}A_{i_3}A_{i_4}}{\langle A^2\rangle^2}
\label{def:Ji}
\end{eqnarray}
where $T_{\rm bath}$ is the heat-bath temperature, variance of the
white noise $\eta$, cf. Eq. (\ref{f:noise}) induced by spontaneous
emission, and the squared volume factor guarantees thermodynamic
convergence ($\beta {\cal H} \propto V\sim N$). The average energy
per mode is ${\cal E}_0 = \omega_0 \langle A^2\rangle$. This is
proportional to the so-called {\em pumping rate} ${\cal P}$ induced on the
random laser by the pumping laser source. We will define it as:
\begin{equation}
{\cal P}^2\equiv J_0\frac{\langle
A^2\rangle^2}{k_B T_{\rm bath}}
\label{def:Pump}
\end{equation}
encoding the experimental evidence that decreasing the heat bath
temperature \cite{Wiersma01} or increasing the energy of the pumping
light source \cite{Leonetti10} has the same qualitative
effect. The proportionality factor $J_0$ in Eq. (\ref{def:Pump}) is
a material dependent parameter function of the angular frequency
$\omega_0$ of the peak of the average spectrum, cf. Eq. (\ref{f:G4}),
\begin{equation}
J_0=V\omega_0^2 \int_V ~d^3r~\chi^{(3)}(\omega_0; \bm r)
~|E(\bm r)|^2
\label{def:J0}
\end{equation} in which $|E(\bm r)|= \langle E_n^2\rangle \sim 1/V$. Assuming
that the non-linear susceptibility does not scale with the number of modes,
the above integral
scales as $1/V$ and $J_0$ does not scale with the size of the system.
The average of $J_{\bm i}$, instead, scales as $1/V^3$, according to
the definitions Eqs. (\ref{f:G4}) and (\ref{def:Ji}).
\\ \indent To the sake of qualitative comparison with the outcome of
experiments the statistical mechanic inverse temperature $\beta$ can
be expressed in terms of the squared pumping rate as:
\begin{equation}
\beta = \frac{{\cal P}^2}{{J}_0}
\label{f:beta_pump}
\end{equation}
\subsection{Finite temperature Bose-Einstein condensates}
A similar situation is found in the finite temperature Bose Einstein
condensation with random potential. The zero temperature
Gross-Pitaevskii equations \cite{Dalfovo99} reads as
\begin{equation}
\imath\hbar \frac{\partial \Phi}
{\partial t}=-\frac{\hbar^2}{2m}\nabla^2
\Phi+ V_{\text{ext}}(\bm r) \Phi+g |\Phi|^2 \Phi
\label{GP1}
\end{equation}
where $V_{\text{ext}}(\bm r)$ is an externally set disordered
potential and $g=4\pi \ell \hbar^2/m$, with $\ell$ being the $s$-wave
scattering length. An analogous model holds for
reduced-dimensionality cases.
\\
\indent
The modes satisfy the time-independent linear Schroedinger
equation
\begin{equation}
-\frac{\hbar^2}{2m}\nabla^2 \Phi_n+ V_{\text{ext}}(\bm r) \Phi_n=E_n \Phi_n
\end{equation}
Their interaction can be treated variationally by letting
\begin{equation}
\Phi(\bm r,t)=\sum_n a_n(t) \Phi_n({\bf r}) \exp{\left(-\imath
\frac{E_n}{\hbar}t\right)} \text{.} \end{equation}
\\
\indent
A finite temperature model for BEC is the Stoof equation,
\cite{Stoof99,Stoof01} which is here written as
\begin{eqnarray}
\label{Stoof}
\imath\hbar \frac{\partial \Phi}{\partial t}&=&
\left[1+\hbar\frac{\beta_K}{4}\Sigma^{K}(\bm r,t)\right]
\\
&&\times
\left[-\frac{\hbar^2}{2m}\nabla^2 \Phi+ V_{\text{ext}}(\bm r) \Phi+g
|\Phi|^2 \Phi\right]+\eta(\bm r,t)
\nonumber
\end{eqnarray}
with $\beta_K = 1/k_B T$ ($k_B$ is the Boltzmann constant) and where
the finite temperature noise is such that
\begin{equation}
\langle \eta^*(\bm r',t') \eta(\bm r,t) \rangle=\frac{\imath\hbar}{2}
\Sigma^{K}(\bm r,t)\delta
(t-t')\delta^{(3)}(\bm r-\bm r')\text{.}
\end{equation}
$\Sigma^{K}(\bm r,t)$ being the Keldish self-energy, which
is imaginary valued (for its expression see
Ref. [\onlinecite{Stoof01}]) and $\hbar \Sigma^K\propto -\imath
\beta_K^{-2}$ (see Ref. [\onlinecite{Stoof04}]). Expanding over
the complete set of the zero temperature equations, one obtains
\begin{eqnarray}
&&\imath \hbar \dot a_n(t)=
-\imath \sum_j \alpha_{jn} a_j E_j
e^{-\frac{\imath t}{\hbar}(E_j-E_n)}\\
\nonumber
&&\quad+\sum_{jkl} \left( G_{jkln}-\imath K_{jkln} \right) a_l^* a_j a_k
e^{-\frac{\imath t}{\hbar}(E_j+E_k-E_l-E_n)}\\
\nonumber
&&\quad +\eta_n(t)
\end{eqnarray}
where $\eta_n(t) = \int d^3 {\bf r}~ \eta({\bf r},t) \phi_n({\bf r},t)$,
and the mode-overlap coefficients are defined as:
\begin{equation}
G_{jklm}=g \int \Phi_j \Phi_k \Phi_l \Phi_m d^3{\bf r}
\end{equation}
and
\begin{equation}
K_{jklm}=\frac{\imath \beta_K \hbar g}{4} \int \Sigma^K(\bm r) \Phi_j
\Phi_k \Phi_l \Phi_m d^3{\bf r}\text{.}
\end{equation}
Finally, the linear
coupling coefficients come out to be
\begin{equation}
\alpha_{jk}=\frac{\imath \beta_K \hbar }{4} \int \Sigma^K(\bm r)
\Phi_j \Phi_k d^3{\bf r}
\end{equation}
While retaining the synchronous terms (such that $E_j+E_k-E_l-E_n=0$),
the resulting equations are, hence, of the same form of those reported
in Sec. \ref{ss:rl} for the disordered electromagnetic cavity, being
the energy of the eigenstates in place of the angular frequency.
Indeed, a strong coupling regime is attained when there is an enhanced
region for the density of states. Conversely, in other spectral regions,
both the linear and the nonlinear coupling terms are averaged out by the
rapidly oscillating exponential tails.
\\ \indent Let us consider, for example, a periodic external potential
with some degree of disorder. In this case, a Lifshitz tail
\cite{lifshitz64} is present, that is, a region with energies inside
the forbidden gap corresponding to localized modes. This modes will
all have approximately the same energy $E\cong E_B$ where $E_B$ is the
band-edge energy, and will couple both among each other and with the
delocalized Bloch modes at the band-edge. Correspondingly, the
relevant equations for the strongly coupled modes are
\begin{eqnarray}
\imath \hbar \dot a_n(t)&=&-\imath \sum_j \alpha_{jn}
a_j E_B
\label{dynamicBEC}
\\
&&
\nonumber
+\sum_{jkl} \left( G_{jkln}-\imath
K_{jkln} \right) a_l^* a_j a_k+\eta_n(t)
\end{eqnarray}
The other modes (those far from the spectral gap) will be those mediating the
thermal bath. The quenched amplitude approximation eventually leads to the
phase-dependent Hamiltonian, Eq. (\ref{phase:Ham}).
\\ \indent As discussed in the following section of the manuscript,
even in the zero temperature limit a transition is expected. This
corresponds to the existence of a replica symmetry breaking transition
in Bose Einstein condensates for finite and vanishing temperature,
mediated by the degree of disorder and heuristically following the
phase diagram reported in Fig. \ref{fig:PhDi_P_R} below.
\subsection{Nonlinear optical propagation
in disordered media and the zero temperature limit}
The nonlinear optical propagation of a light beam is described by the
paraxial equation
\begin{equation} \imath\frac{\partial A}{\partial z}+\frac{1}{2
k}\nabla_{x,y}^2 A+\frac{\Delta n}{2 k n}A=0 \end{equation}
where $A$ is the optical amplitude, $k$ the wavenumber, $n$ is the
bulk refractive index and $\Delta n$ is its perturbation due to
disorder and optical nonlinearity (Kerr effect):
\begin{equation}
\frac{\Delta n}{2 k n}=U(x,y)+n_2 |A|^2. \end{equation}
The nonlinear coefficient $n_2$ can be either
positive (focusing) or negative (defocusing), while $U(x,y)$ can be a
perturbed (by disorder) periodical potential or a completely
disordered (speckle pattern) external potential. The resulting
equation reads as
\begin{equation} \imath\frac{\partial A}{\partial z}+\frac{1}{2
k}\nabla^2 A+ U(x,y) A+\frac{n_2}{2 k n}|A|^2 A=0\text{.} \end{equation}
This formally corresponds (with different meanings for the variable) to the zero-temperature two-dimensional limit of the
Gross-Pitaevskii equations detailed above, cf. Eq. (\ref{GP1}).
\\ \indent In this case, as well, the field can be expanded in terms of
transversely localized (in two dimensions they are always localized)
electromagnetic modes, the energies being replaced by their
propagation wave-vectors. When there are bunch of modes such that
their wave-vectors are similar, these will be strongly coupled and
result into dynamical equations like Eqs. (\ref{f:Langevin}),
(\ref{dynamicBEC}). This approach can be extended to
three-dimensional propagation, encompassing the dynamics of
ultra-short pulses in random media as will be reported elsewhere.
\\ \indent The replica symmetry breaking transitions investigated in
the following will in general correspond to varying coherence
properties of the beam, eventually resulting in unstable speckle
patterns. The $\beta\to\infty $ limit of the statistical mechanical
formulation of the problem has to be taken in this case (see, e.g.,
Ref. [\onlinecite{Leuzzi01}] for a simple case example in the
framework of constraint satisfaction problems).
\section{Randomness in mode-coupling coefficients}
\label{sec:random}
Let us consider our model Hamiltonian, Eq. (\ref{f:Haphi2}), in the
mean-field fully connected approximation in which the
non-vanishing components of the
four index
tensor $J_{i_1,i_2,i_3,i_4}=J_{\bf i}$ are distributed as
\begin{eqnarray} {\overline{J_{\bf
i}}}&=&J_0/N^3
\label{f:Jave}
\\
{\overline
{(J_{\bf i}-{\overline{J_{\bf i}}})^2}}&=&\sigma^2_J/N^3
\label{f:Jvar}
\end{eqnarray}
The coefficient $J_0$ was already introduced in the case of random lasers,
cf. Eq. (\ref{def:J0}), and $N$ is the number of dynamic variables (mode
phases) of the system, proportional to the volume $V$. The overbar
denotes the average over the disorder.
\\ \indent To quantify the amount of disorder, we introduce the
``degree of disorder'' parameter, i.e., a size independent ratio
between the standard deviation of the distribution of the coupling
coefficients $J_{\bf i}$ and their mean:
\begin{equation} R_J\equiv \frac{\sigma_J}{J_0}
\end{equation}
The limits $R_J\rightarrow 0$ and $R_J\rightarrow\infty$ correspond,
respectively, to the completely ordered and disordered case.
The other relevant parameter for our investigation is the inverse
temperature $\beta$. For random lasers it is
related to the normalized pumping threshold for ML, defined in our
model as, cf. Eq. (\ref{f:beta_pump}),
\footnote{If $J_0=0$ we are in the completely disordered case
$R_J=\infty$ (also realizable by means of a finite $J_0$ and
$\sigma_J^2=\infty$). In Ref. [\onlinecite{Angelani06long}] ${\cal P}$
has been defined as $\sqrt{\beta k_B T_{\rm bath}}$, simply amounting
to an adimensional rescaling ${\cal P}\to {\cal P}\sqrt{J_0\beta_{\rm
bath}}$ w.r.t. our model case.}
\begin{equation}
{\cal P}=\sqrt{\beta J_0}=\sqrt{\frac{\bar \beta}{R_J}}
\end{equation}
where $\bar\beta\equiv\beta\sigma_J$. \cite{Leuzzi09} In general,
$\beta$ increases as the strength of nonlinearity increases or the
amount of noise is reduced.
\subsection{The ordered limit, saturable absorbers
in random lasers, defocusing versus focusing}
\label{ss:satabs}
With specific reference to the laser systems, as $J_0$ grows the
effect of disorder is moderated and for small enough $R_J$ the model
corresponds to the ordered case, previously detailed in Ref.
[\onlinecite{Angelani07}]. As also previously reported in
Ref. [\onlinecite{Gordon03}], a passive mode-locking (PML) transition
is predicted as a paramagnetic/ferromagnetic transition
occurs in $\beta$.
\\ \indent Indeed, in our units, when $R_J\rightarrow0$, ${\cal
P}={\cal P}_{\rm PML}\cong 3.819$ (see Fig. \ref{fig:PhDi_P_R}), in
agreement with the ordered case. \cite{Angelani06} ${\phantom
.}$\footnote{A factor of $8$ has to be considered because of the
over-counting of terms in the Hamiltonian of the model studied in
Ref. [\onlinecite{Angelani06}] with respect to
Eq. (\ref{f:Haphi2}). This factor can be absorbed into the temperature
yielding the pumping threshold ${\cal P}_{\rm PML}=\sqrt{8/T_0}$. If
we insert $T_0\cong 0.717$, i.e., the temperature at which the FM
phase first appears in complete absence of disorder we obtain ${\cal
P}_{\rm PML}\cong 3.34$. This also exactly corresponds to the spinodal
value of ${\cal P}=3.3412$ for $J_0/\sigma_J\to\infty$ in the present
model.} As explained below, the deviation from this value quantifies
an increase of the standard ML threshold ${\cal P}_{\rm PML}$ due to
disorder. The specific value for ${\cal P}_{\rm PML}$ will depend on
the class of lasers under consideration (e.g., a fiber loop laser or a
random laser with paint pigments), but the trend of the passive ML
threshold with the strength of disorder $R_J$ in
Fig. \ref{fig:PhDi_P_R} has a universal character. The pumping rate
$\mathcal{P}$ contains $J_0$: for a fixed disorder the threshold will
depend on the nonlinear mode-coupling.
\\ \indent A key point here is that the transition from continuous
wave to passive mode-locking (PM $\to$ FM) only occurs for a specific
sign of the mean value of the coupling coefficient $J_0$, as shown in
Fig. (\ref{fig:PhDi_T_J0}). Comparing Eqs. (\ref{f:Langevin}) and
(\ref{f:haus_master}) one observes that this formally corresponds to
the presence of a saturable absorber in the cavity (see also
Ref. [\onlinecite{Haus00}] and Sec. \ref{ss:rl}).
In typical random lasers such a device is not present, and, hence,
this ferromagnetic transition is not expected.
\\
\indent
On the other hand, the
reported phase diagram, Fig. (\ref{fig:PhDi_T_J0}) predicts that
starting from a standard laser supporting passive/mode-locking and
increasing the disorder the second order transition acquires the
character of a glass transition.
A notable issue is that this phase-locking transition (normally ruled
out for ordered lasers without a saturable transition), spontaneously
occurs increasing $\beta$, as an effect of the disorder and the
resulting frustration.
\\ \indent With reference to nonlinear waves, the spontaneous
phase-locking process is expected for a specific sign of the nonlinear
susceptibility (corresponding to repulsive interactions for BEC and
defocusing nonlinearities for optical spatial beams), for $T=0$,
amounting to $J_0/\sigma_J>0$ in Fig. (\ref{fig:PhDi_T_J0}) (the
threshold is at $J_0/\sigma_J\cong 4$). For example, for a
nonlinear optical beam propagating in a disordered medium, it is
expected that above a certain degree of disorder, there is a transition
from a coherent regime to a ``glassy coherent phase'', characterized
by a strong variation from shot to shot of the speckle pattern and,
more in general, of the degree of spatial coherence.
\section{Fundamentals of Statistical Mechanics of Disordered Systems}
\label{sec:statmech}
Hereby we report an extremely concise summary of ideas and techniques
developed to deal with disordered systems. The aim is to let the
non-expert reader find his/her way through the computation of the
properties of our model that we present in Sec. \ref{sec:computation}
and App. \ref{app}.
\subsubsection{Disorder and frustration:
\\ quenched disorder as technical tool.}
\label{sec:frustration}
The main issue determining complex features, not present in ordered
systems and involving collective processes that cannot be understood
just looking at local properties, is {\em frustration}. This is
usually a the consequence of disorder, not necessarily {\em quenched }
disorder, though. Indeed, also in materials whose effective
statistical mechanic representation is carried out through
deterministic potentials (as, e.g., for colloidal particles), a
geometry-induced disorder can set up, determining frustration and a
consequent multitude of degenerate stable and metastable states
typical of glasses
\cite{Barrat90,Hansen95,Kob94,Kob95a,Kob95b,Sciortino99,Mezard99,Coluzzi00}
and spin-glasses. \cite{Marinari94a,Marinari94b,Cugliandolo95}
Quenched disorder, i.e., the explicit appearance of random
coefficients in the Hamiltonian, allows an analytic computation, but
the results are general and do not depend on the specific source of
frustration.
\subsubsection{Statistical mechanics of a disordered system:
\\ the replica trick.} In the presence of quenched disorder, one can
compute the statistical mechanics of the system, averaging
over the probability distribution of the disorder. In order to do
this the so-called replica trick
\cite{Sherrington75,Parisi79,Parisi80,MPVBook} can be adopted, or,
else, the equivalent cavity method. \cite{Mezard86,MPVBook}
\\
\indent
The free energy of a single
disordered system sample, denoted by $J$, is
$\Phi_J=-1/\beta \log Z_J$.
Correspondingly, the physically relevant average free energy
can be written as
\begin{equation} \Phi=-\frac{1}{\beta} {\overline {\log Z_J}}
\label{f:Fen_ave}
\end{equation}
where the overbar denotes the
average over the distribution of the $J$'s. The latter coincides with
the thermodynamic limit of any $\Phi_J$ according to the
self-averaging property required in order to have macroscopic
reproducibility of experiments (the thermodynamics of a huge system
does not depend on the local distribution of interaction
couplings).
\\ \indent To perform the average in Eq. (\ref{f:Fen_ave}) is highly
non trivial and one can proceed by considering $n$ copies of the
system, Eq. (\ref{f:Haphi2}),
\begin{equation}
{\cal H}[\{\phi\}] \to \sum_{a=1}^n {\cal H}[\{\phi^{(a)}\}]
\label{f:Hphirep}
\end{equation}
The average free energy per spin can, then, be
computed in the replicated system, as
\begin{eqnarray}
&&\beta \Phi=-\lim_{N\to \infty}
\frac{1}{N}~{\overline {\log Z_J}}=-\lim_{N\to \infty}
\lim_{n\to
0}\frac{{\overline {Z^n_J}}-1}{N~n}
\nonumber
\\
\label{f:Phi_rep}
\end{eqnarray}
where the average of the generic power of the partition function
${\overline {Z^n_J}}$ is somehow computed for a finite integer $n$
and, eventually, the analytic continuation to real $n$ and the limit
$n\to 0$ are performed.
\subsubsection{Oddities of the replica formulation.}
Actually, to evaluate ${\overline {Z^n_J}}$, one makes use of the
saddle point approximation holding for large $N$ (see Appendix
\ref{app} for the specific case considered in this work). That is, one
practically inverts the limits $N\to \infty$ and $n\to 0$ as expressed
in Eq. (\ref{f:Phi_rep}). Yet, the method works. It took many years
to rigorously overcome this oddity and a mathematical proof of the
existence of the free energy can be found in
Refs. [\onlinecite{Guerra03,Talagrand06}].
\subsubsection{A probability distribution as an order parameter.}
The main novelty of the characterization of the spin-glass phase,
historically first obtained by the replica method and subsequently
confirmed by other methods, is that the order parameter is a whole
probability distribution function describing how different
thermodynamic states are correlated. The degree of the correlation
between two states is called {\em overlap}. In mean-field theory
different states exist that can be more or less correlated according
to their distance on a tree-like hierarchical space called {\em
ultrametric}. \cite{Mezard84}
\subsubsection{ Complexity as a well-defined thermodynamic potential.}
Besides numerous and hierarchically organized globally stable states,
glasses also display a large number of metastable states, that is,
excited states of relatively long lifetime. In the mean-field theory
such lifetime is, actually, infinite in the thermodynamic limit
because of the divergence of the free energy barriers with the size of
the system, see, e.g., Ref. [\onlinecite{CC05}]. This means that,
contrarily to what happens in real glasses, \cite{Leuzzi07} the number
of metastable states at a given observation timescale does not change
with time (after a given transient period). Below a certain
temperature (called {\em dynamic} or {\em mode coupling} temperature),
the number ${\cal N}$ of metastable states grows exponentially with
the size $N$ of the system ($N$ being the number of modes in our
cases). One can then define an entropy-like function counting the
metastable states as
\begin{equation}
\Sigma \equiv \frac{1}{N}\log {\cal N} \ .
\label{def:complexity}
\end{equation}
This is called {\em configurational entropy} in the framework of
structural glasses, else {\em complexity} in spin-glass theory and its
applications to constraint satisfaction and optimization problems.
One can further look at the metastable states of equal free energy
density $f$: ${\cal N}(f)=\exp N\Sigma(f)$ and at the free energy
interval, above the equilibrium free energy $f_{\rm eq}$,
in which the complexity
is non zero: $f\in [f_{\rm eq}:f_{\star}]$.
\section{Statistical mechanical properties }
\label{sec:computation}
Starting from the Hamiltonian, Eq. (\ref{f:Haphi2}), replicated
according to the prescription Eq. (\ref{f:Hphirep}), and averaging
over the disorder with the Gaussian probability expressed by Eqs.
(\ref{f:Jave})-(\ref{f:Jvar}), one obtains the
following expression for the average of the $n$-th power of the partition
function, cf. Appendix \ref{app}:
\begin{eqnarray}
&&{\overline {Z_J^n}}=\int{\cal
D}\mathbf{Q}~{\cal D}\mathbf{\Lambda}~ e^{-N~n~G\left[
\mathbf{Q},\mathbf{\Lambda}\right]}
\label{f:Zintegral}
\\ \nonumber &&n~G\left[
\mathbf{Q},\mathbf{\Lambda}\right]=n~A\left[
\mathbf{Q},\mathbf{\Lambda}\right] +\log Z_\phi\left[\mathbf{\Lambda}
\right]
\\ && n~A \left[\mathbf{Q},\mathbf{\Lambda}\right] \equiv
-\frac{\beta^2\sigma_J^2}{32} \sum_{a=1}^n\Bigl(1+\left| \tilde
r_a\right|^4\Bigr) -\frac{\beta J_0}{8}\sum_{a=1}^n\left| \tilde
m_a\right|^4 \nonumber
\\ \nonumber
&&\hspace*{.5cm}-\frac{\beta^2\sigma_J^2}{16}\sum_{a<b}^{1,n}\Bigl(q_{ab}^4+\left| r_{ab}\right|^4\Bigr)
-\sum_{a<b}^{1,n}\bigl[
q_{ab}\lambda_{ab}+\Re\left(r_{ab}\bar\mu_{ab}\right)\bigr] \\ &&\hspace*{1cm}-
\sum_{a=1}^n\Re\bigl[\tilde r_a{\bar{\tilde \mu}}_a+\tilde m_a\nu_a
\bigr]
\end{eqnarray}
\begin{eqnarray}
&&Z_\phi\left[\mathbf{\Lambda} \right]\equiv
\int\prod_{a=1}^n d\phi_a e^{-\beta{\cal H}_{\rm
eff}[\{\phi\};\mathbf{\Lambda}]}
\label{f:Zphi_main}
\\
&&-\beta{\cal H}_{\rm eff}[\{\phi\};\mathbf{\Lambda}]\equiv
\sum_{a<b}^{1,n}\Re\bigl[e^{\imath(\phi_a-\phi_b)}\lambda_{ab}
+e^{\imath(\phi_a+\phi_b)}\bar\mu_{ab}\bigr]
\nonumber
\\
\label{f:Hphi_main}
&&\hspace*{2cm} +\sum_{a=1}^n\Re\bigl[ e^{2\imath \phi_a}{\bar{\tilde
\mu}}_a+e^{\imath \phi_a}\bar\nu_a \bigr]
\end{eqnarray}
\begin{eqnarray}
\nonumber &&{\cal
D}\mathbf{Q}\equiv \prod_{a<b}^{1,n}N^2 dq_{ab} dr_{ab}\times
\prod_{a=1}^n N^2 d\tilde r_a d\tilde m_a \\ \nonumber &&{\cal
D}\mathbf{\Lambda}\equiv \prod_{a<b}^{1,n} \frac{d\lambda_{ab}}{2\pi}
\frac{d\mu_{ab}}{2\pi}\times \prod_{a=1}^n \frac{d\tilde
\mu_a}{2\pi}\frac{d\nu_a}{2\pi} \end{eqnarray}
where $\mathbf{Q}=\{q,r,\tilde
r,\tilde m\}$ and $\mathbf{\Lambda}=\{\lambda,\mu,\tilde\mu,\nu\}$.
The overlap matrices $q_{ab}$, $\lambda_{ab}$ are real-valued,
whereas the others have complex elements.
\\
\indent
The
integral Eq. (\ref{f:Zintegral})
is evaluated by means of the saddle point approximation
(valid for large $N$).
The above expressions need a form of the matrices $q_{ab}$, $r_{ab}$,
$\lambda_{ab}$ and $\mu_{ab}$ to be completed. Contrarily to what
might seem reasonable, the form providing the thermodynamically stable
solution is not the one in which all replicas are equivalent, i.e.,
all elements in the matrices $q_{ab}$, $r_{ab}$, $ \lambda_{ab}$,
$\mu_{ab}$ are equal. One must, thus, resort to a spontaneous {\em
Replica Symmetry Breaking}. In Appendix \ref{app} we report the
computation of thermodynamics both in the Replica Symmetric (RS)
approximation and in the ``one step'' Replica Symmetry Breaking Ansatz
(1RSB), i.e., the exact solution for the system under probe. In the
following we, thus, analyze the properties of the latter
solution.
\\
\indent
Spin-glass systems described by more-than-two-body interactions,
cf. Eq. (\ref{f:Haphi2}), are known to have low temperature phases that
are stable under the 1RSB Ansatz. \cite{Gardner85,Crisanti92}
\footnote{Since in our model the dynamic variables are continuous
phases, the whole low $T$ phase is consistently described by the 1RSB
solution, unlike models with discrete variables such as the Ising
$p$-spin model \cite{Gardner85} where a further transition occurs at
the so-called Gardner temperature.} Under this Ansatz,
taking the $n\to 0$ limit, the free energy functional $\beta \Phi$
reads, cf. Appendix \ref{app},
\begin{eqnarray}
\label{f:repPhi_1rsb}
&&\beta \Phi(m;{\bf Q}_{\rm sp}^{(1)},{\bf \Lambda}_{\rm sp}^{(1)})=
G(m;{\bf Q}_{\rm sp}^{(1)},{\bf \Lambda}_{\rm sp}^{(1)})=
\\
\nonumber
&&\quad=-\frac{\bar\beta R_J}{8}|{\tilde m}|^4
-\frac{{\bar\beta}^2}{32}\Bigl[
1
-(1-m)\left(q_1^4+|r_1|^4\right)
\\
\nonumber
&&\qquad -m\left(q_0^4+|r_0|^4\right)+|{r_d}|^2
\Bigr]
-\Re\Big[\frac{1-m}{2}\left(\lambda_1q_1+\bar\mu_1r_1\right)
\\
\nonumber
&&\qquad+\frac{m}{2}\left(\lambda_0q_0+\bar\mu_0r_0\right)
-{\bar \mu_d} {r_d} - {\bar \nu}{\tilde m}\Bigr]+ \frac{\lambda_1}{2}
\\
\nonumber
&&\qquad -\frac{1}{m}\int {\cal D}[\bm{0}]\log\int{\cal D}[\bm{1}]
\left[\int_0^{2\pi}\!d\phi~\exp{\cal L}(\phi; \bm{0},\bm{1})
\right]^m
\end{eqnarray}
where $\bm{0}=\{x_0,\zeta_0^R,\zeta_0^I\}$,
$\bm{1}=\{x_1,\zeta_1^R,\zeta_1^I\}$,
${\cal D}[\bm{a}]$ is the product of three Normal distributions
and
\begin{eqnarray}
\nonumber
&&{\cal L}(\phi;\bm{0},\bm{1})\equiv\Re\Bigl\{e^{\imath\phi}\Bigl[
\bar\zeta_1\sqrt{\Delta \lambda-|\Delta \mu|}+
\bar\zeta_0\sqrt{\lambda_0-|\mu_0|}+
\\
\label{f:calL}
&&\quad x_1\sqrt{2\Delta \bar\mu}
+x_0\sqrt{2\bar\mu_0}
+\bar\nu\Bigr]
+e^{2\imath\phi}\left(\bar \mu_d-\frac{\bar\mu_1}{2}\right)
\Bigr\}
\end{eqnarray}
with $\Delta\lambda=\lambda_1-\lambda_0$, $\Delta \mu=\mu_1-\mu_0$.
For later convenience
we define the following averages over the action
$e^{\cal L}$, cf. Eq. (\ref{f:calL}):
\begin{eqnarray}
c_{\cal L}\equiv \langle
\cos\phi\rangle_{\cal L} \equiv \frac{\int_0^{2\pi} d\phi~\cos\phi~e^{\cal L}}
{\int_0^{2\pi} d\phi~e^{\cal L}}
\\
s_{\cal L}\equiv \langle
\sin\phi\rangle_{\cal L}\equiv \frac{\int_0^{2\pi} d\phi~\sin\phi~e^{\cal L}}
{\int_0^{2\pi} d\phi~e^{\cal L}}
\end{eqnarray}
The values of
the order parameters
$\lambda_{0,1}, \mu_{0,1}, \mu_d$ and $\nu$
are
yielded by
\begin{eqnarray}
&&\lambda_{0,1}=\frac{{\bar\beta}^2}{4} \left(q_{0,1}\right)^3~
;\quad
\mu_{0,1}=\frac{{\bar\beta}^2}{4}|r_{0,1}|^2~ r_{0,1}
\label{f:la_q_1rsb}
\\
&&\tilde\mu= \frac{{\bar\beta}^2}{8}|\tilde r|^2{\tilde r}~~
;\qquad \nu=\frac{\bar\beta R_J}{2}|\tilde m|^2{\tilde m}
\label{f:mu_r_1rsb}
\end{eqnarray}
The parameter $m$ (without tilde!), whose meaning will be discussed
below, takes values in the interval $[0,1]$. The remaining
parameters are obtained by solving the self-consistency equations:
\begin{eqnarray}
\label{f:speq_q1_R}
&&\hspace*{-4mm}
q_1=\langle \langle c_{\cal L}^2 \rangle_{m}\rangle_{\bf 0}+
\langle \langle s_{\cal L}^2\rangle_{m}\rangle_{\bf 0}
\\
\label{f:speq_q0_R}
&&\hspace*{-4mm}
q_0=\langle \langle c_{\cal L} \rangle_{m}^2\rangle_{\bf 0}+
\langle \langle s_{\cal L}\rangle_{m}^2\rangle_{\bf 0}
\\
\label{f:speq_r1R}
&&\hspace*{-4mm}
r_1= \langle \langle c_{\cal L}^2 \rangle_{m}\rangle_{\bf 0}
-\langle \langle s_{\cal L}^2 \rangle_{m}\rangle_{\bf 0}
+2 \imath \langle \langle c_{\cal L} s_{\cal L} \rangle_{m}\rangle_{\bf 0}
\\
\label{f:speq_r0R}
&&\hspace*{-4mm}
r_0=\langle \langle c_{\cal L} \rangle_{m}^2\rangle_{\bf 0}
-\langle \langle s_{\cal L} \rangle_{m}^2\rangle_{\bf 0}
+2 \imath \langle \langle c_{\cal L} \rangle_{m}\rangle_{\bf 0}
\langle \langle s_{\cal L} \rangle_{m}\rangle_{\bf 0}~~
\\
\label{f:speq_rd}
&&\hspace*{-4mm}
\tilde r=\langle \langle \langle
e^{2\imath \phi}
\rangle_{\cal L}\rangle_{m}\rangle_{\bf 0};
\qquad\tilde m=\langle \langle
\langle e^{\imath \phi}
\rangle_{\cal L}\rangle_{m}\rangle_{\bf 0}
\end{eqnarray}
where the averages are defined as
\begin{eqnarray}
\langle(\ldots )\rangle_m&\equiv&
\frac{\int{\cal D}[\bm{1}](\ldots )\left[\int_0^{2\pi}\!
d\phi~e^{{\cal L}(\phi;\bm{0},\bm{1})}
\right]^m}
{\int{\cal D}[\bm{1}]\left[\int_0^{2\pi}\!d\phi~e^{{\cal L}
(\phi;\bm{0},\bm{1})}\right]^m}
\\
\langle(\ldots )\rangle_{\bf 0}
&\equiv&
\int{\cal D}[\bm{0}](\ldots )
\end{eqnarray}
These equation are solved numerically by an iterative method.
The overlap parameters $q_{0,1}$ are real-valued,
whereas $r_{0,1}, {\tilde r}$ and ${\tilde m}$
are complex. ``One step'' parameters $X_{0,1}$ ($X=q,r$) enter with a
probability distribution that can be parametrized by the
so-called
{\em replica symmetry breaking parameter} $m$, such that
\begin{equation}
P(X)=m~\delta(X-X_0)+(1-m)\delta(X-X_1).
\label{f:1RSB_prob}
\end{equation}
The resulting independent parameters (there are ten of them) that can
be evaluated by solving Eqs. (\ref{f:speq_q1_R})-(\ref{f:speq_rd})
must be combined with a further equation for the parameter $m$. This
is strictly linked to the expression for the {\em complexity} function
of the system.
\section{Complexity}
\label{sec:complexity}
In the order parameter Eqs. (\ref{f:la_q_1rsb})-(\ref{f:speq_rd}) $m$
is left undetermined. An additional condition is needed to fix the
value for this parameter. The first possibility is treating $m$ as a
standard order parameter: in this case the thermodynamic state
corresponds to extremizing the replicated free energy (thus, {\em
maximizing} it
\footnote{Technically speaking, this is due to the fact that all the
terms of the free energy functional depending on two replicas
observables have $n-1$ or $n-m$ factors in front, cf. App. \ref{app},
and in the $n\to 0$ limit this factors change.}), i.e., implementing
the self-consistency equation
\begin{equation} \frac{\partial \Phi(m;{\bf Q}_{\rm sp},{\bf \Lambda}_{\rm
sp})}{\partial m}=0
\label{f:dphi_dm}\end{equation}
The highest temperature at which
a solution exists with $m\leq 1$ furnishes a transition temperature between
paramagnet and glassy phase: the Kauzmann or {\em static} temperature
($T_s$). This is an {\em equilibrium thermodynamic} phase transition.
\\ \indent This approach, however, does not reflect the known physical
circumstance that a glassy system exhibits excited metastable states
also at temperature $T$ above $T_s$, \footnote{The very existence of a
Kauzmann temperature, also called the {\em ideal glass transition
temperature}, in structural glasses is, actually, a matter of debate.}
where the equilibrium phase is paramagnetic. Vitrification, indeed,
is due to the presence of a not vanishing complexity at a temperature
above $T_s$ (and below some $T_d>T_s$), i.e., to the presence of a
number of energetically equivalent states with free energy $f>f_{\rm
eq}(T)$. Since, however, energy barriers tend to infinity in the
thermodynamic limit in the mean-field approximation, the system
dynamics is forever trapped in one of these states for $T<T_d$.
The temperature $T_d$ is, thus, called {\em dynamic} transition temperature.
\\ \indent Across this transition the complexity $\Sigma$, defined in
Eq. (\ref{def:complexity}), starts being different from zero. Exactly
at $T=T_d$ the complexity as a function of free energy, $\Sigma(f)$,
has a delta-shaped non-zero peak
at the free energy $f_1$ which corresponds to a maximum
of $\Sigma(m)$ for a value of $m=m(f_1)=1$. In our 1RSB formalism:
\begin{equation}
\frac{\partial \Sigma(m;{\bf Q}_{\rm sp},{\bf \Lambda}_{\rm sp})}{\partial m}=0
\end{equation}
As $T$ decreases ($T_s<T<T_d$), the complexity is not vanishing for an
increasing range of free energies $f^*>f>f_1$ that corresponds to a
range for $m$: $m^*< m <1$. The complexity shows a maximum for $m\leq
1$ at $m_*$ ($f=f_*$) solution of $d\Sigma/dm=0$, while it is at its
minimum value for $m=1$ and $f=f_1$. We stress that this is not a
solution to Eq. (\ref{f:dphi_dm}).
\\ \indent Lowering the temperature, at $T=T_s$ the minimum value of
complexity - corresponding to $m=1$ - vanishes, i.e., it is a solution
to Eq. (\ref{f:dphi_dm}), and $f_1=f_{\rm eq}$ corresponds to the free
energy density of the global glassy minima of the free energy
landscape: as mentioned above, we are in presence of a thermodynamic
phase transition and the thermodynamic stable phase is a glass.
\\ \indent The physically significant value for $m$ is $m^*$,
corresponding to the maximum of $\Sigma$. It denotes the value of
free energy $f^*$ where the number of states is maximum and
exponentially higher than the number of states at any $f<f^*$, and,
hence, the most probable (among those of the metastable states). At
the thermodynamic transition point from the paramagnetic state to the glassy
($T=T_s$) it holds $f_{PM}=f_1=f_{\rm eq}=\Phi$. \footnote{
The paramagnetic phase exists as metastable also at $T<T_s$ but the
phase space is disconnected and the ergodicity is broken because of
infinite barriers.}
Below $T_s$ $f_1<f_{\rm eq}$ (hence, $\Sigma(f_*)<\Sigma(f_{\rm eq})=0$)
and the physically relevant $\Sigma(f)$ has a support $[f_{\rm eq},f_*]$.
\\ \indent In the following we will analyze the whole complexity
vs. free energy curve $\Sigma(f)$ at given $\beta,J_0$ and the
behavior of the minimal positive complexity $\Sigma(T)$ (and $\Sigma({\cal
P})$) between $T_s$ and $T_d$.
\subsection{Computing the complexity functional}
In Eq. (\ref{def:complexity}) one needs to know the number of
metastable states, that are the local minima of the free energy
landscape. Would we know the landscape, though, we would have solved
the problem already. If self-consistency equations for local order
parameters are known, a possible analytic approach to get information
on the complex landscape is to guess a trial free energy functional
whose stationary equations lead back to the self-consistency
equations. This is what Thouless, Anderson and Palmer (TAP) proposed
in the framework of spin-glasses starting from the self-consistency
equations for local magnetizations. \cite{TAP77} Starting from TAP
functional and TAP equations and considering solutions to the TAP
eqs. as {\em states} (with some assumptions to be {\em a posteriori}
satisfied) one can build the functional $\Sigma$ from
Eq. (\ref{def:complexity}), cf., e.g.,
Refs. [\onlinecite{Bray80,Crisanti03,Crisanti03b,Annibale03,
Crisanti04,Crisanti04b,Aspelmeier04,Crisanti05}].
\\
\indent
A comparative study
to the TAP-derived complexity functional and the replicated free
energy, computed in a general scheme that includes the Parisi Ansatz,
\cite{Mueller06} allows to show that the Legendre Transform of
$\Phi$ with respect to the single state free energy coincides with
Eq. (\ref{def:complexity}).
According to this approach,
in our model the complexity can, thus, be explicitly
computed as the Legendre transform of Eq. (\ref{f:repPhi_1rsb}):
\begin{eqnarray}
&&\Sigma(m;{\bf Q}_{\rm sp},{\bf \Lambda}_{\rm sp})
\label{f:Sigma}
\\
\nonumber
&&\hspace*{1cm}= \min_m \left[-\beta m \Phi(m)+\beta m f\right]
\\
\nonumber
&&\hspace*{1cm}= \beta m^2\frac{\partial\Phi}{\partial m}
\\
&&\hspace*{1cm}=\frac{3}{4}\beta^2m^2
\left(|q_1|^4+|r_1|^4-|q_0|^4-|r_0|^4\right)
\nonumber
\\
\nonumber
& &\hspace*{1.1cm}+\int {\cal D}[\bm{0}]\log\int{\cal D}[\bm{1}]
\left[\int_0^{2\pi}\!\!\!\!d\phi~\exp{\cal L}(\phi; \bm{0},\bm{1})
\right]^m
\\
&&\hspace*{1.1cm} -m\int {\cal D}[\bm{0}]\langle\log
\int_0^{2\pi}\!\!\!\!d\phi~\exp{\cal L}(\phi; \bm{0},\bm{1})
\rangle_m
\nonumber
\end{eqnarray}
where the single state free energy
\begin{equation}
f=\frac{\partial (m\Phi)}{\partial m}
\end{equation}
is
conjugated to $m$. Since the above expression is proportional to
$\partial \Phi/\partial m$, equating $\Sigma=0$
provides the missing equation to determine the order parameters
values.
\section{Phase Diagram and Complexity}
\label{sec:phdi}
By varying the normalized pumping rate ${\cal P}$ and the degree of
disorder $R_J$, we find three different phases, as shown in Fig.
\ref{fig:PhDi_P_R} in the $({\cal P}, R_J)$ plane and in Figs.
\ref{fig:PhDi_T_J0}, \ref{fig:PhDi_T_J0_det} in the $(T,J_0)$ plane.
\begin{figure}
\includegraphics[height=.99\columnwidth, angle=270]{PhDi_P_RJ.eps}
\caption{Phase diagram in the ${\cal P}, R_J$ plane. Three
phases are present: PM (low ${\cal P}$), FM (high ${\cal P}$/weak
disorder) and SG (high ${\cal P}$/strong disorder). The full lines
are thermodynamic transitions, the dashed line represents the dynamic
PM/SG transition. }
\label{fig:PhDi_P_R}
\end{figure}
\begin{figure}
\includegraphics[height=.99\columnwidth, angle=270]{PhDi_T_J0.eps}
\caption{Phase diagram in the plane $J_0,T$ in $\sigma_J$ units. Also
negative $J_0$ are considered. Three phases are found: PM (high $T$,
low $J_0$), FM (low $T$/large $J_0$) and SG (low $T$/low or negative
$J_0$). The full lines are thermodynamic transitions: {\em random}
first order between PM and SG and {\em standard} first order between
PM and FM and between SG and FM. The dashed line represents the
dynamic PM/SG transition. }
\label{fig:PhDi_T_J0}
\end{figure}
\begin{figure}
\includegraphics[height=.99\columnwidth, angle=270]{PhDi_T_J0_det.eps}
\caption{(Color online) Detail of the $J_0,T$ phase diagram around the
tricritical point. Full lines are thermodynamic transitions. Also the
transition between the SG (1RSB) and the approximated RS solution for
the FM phase is displayed (double-dotted line) showing no appreciable
difference with the exact one. The dashed line represents the dynamic
PM/SG transition. The dotted bold line represents the FM spinodal
lines both inside the PM and the SG phases. The spinodal of the RS FM
phase is shown as well (smaller dots). }
\label{fig:PhDi_T_J0_det}
\end{figure}
{\em Paramagnetic phase ---} For low ${\cal P}$ the only phase present
is completely disordered: all order parameters are zero and we have a
``paramagnet'' (PM); for the random laser case this phase
is expected to correspond to a
noisy continuous wave emission, and all the mode-phases are
uncorrelated. Actually, this phase exists for any degree of disorder
and pumping, yet it becomes thermodynamically sub-dominant as ${\cal
P}$ (or $\beta$) increases and, depending on the degree of
disorder, the spin-glass or the ferromagnetic phases take over.
\\ \indent {\em Glassy phase ---} For large disorder, as ${\cal
P}$/$\beta$ grows, a discontinuous transition occurs from the PM to a
spin-glass (SG) phase in which the phases $\phi$ are frozen but do not
display any ordered pattern in space. First, along the line ${\cal
P}_d=\sqrt{\bar\beta_d/R_J}$, in Fig. \ref{fig:PhDi_P_R}, or at
$T/\sigma_J=1/\bar\beta_d=0.15447$ in Figs. \ref{fig:PhDi_T_J0},
\ref{fig:PhDi_T_J0_det} (dashed lines) a dynamic transition occurs.
Indeed, the lifetime of metastable states is infinite in the
mean-field model and the dynamics gets stuck in the highest lying
excited states. The thermodynamic state is, however, still PM.
Fig. \ref{fig:PhDi_T_J0_det} displays a detail of the tricritical
region where. There, besides thermodynamic transition lines, we also
plot as dotted curves the lines at which the ferromagnetic phase first
appears as metastable, i.e., the spinodal lines.
\begin{figure}[t!]
\includegraphics[height=.99\columnwidth,angle=270]{Sigma_Temp_Pump.eps}
\caption{Complexity $\Sigma({\cal P})$ of the lowest lying glassy
states in free energy between the values of the pumping rate
corresponding to the dynamic and static transition from the PM to the
SG phase at $R_J=0.5$. }
\label{fig:Sigma_P_SG}
\end{figure}
\begin{figure}[t!]
\includegraphics[height=.99\columnwidth,angle=270]{Sigma_Temp_Pump3.eps}
\caption{Left: Complexity of the lowest lying glassy states in free
energy $\Sigma({\cal P})$ between dynamic and static transition from
the PM to the SG phase along $R_J=0.3,0.4$ and $0.5$ lines. The
qualitative behavior is identical for any $R_J\gtrsim 0.3$. Right:
$\Sigma$ vs. the effective temperature $T$ in $\sigma_J$ units.}
\label{fig:Sigma_T_SG}
\end{figure}
\begin{figure}[t!]
\includegraphics[width=.99\columnwidth]{Sigma_SG_f_Ts.eps}
\caption{$\Sigma(f)$ (left) and $\Sigma(m)$ (right) in the glassy
phase at the static transition effective temperature,
$T=0.14099$. This is the picture holding for any $R_J\gtrsim 0.3$. }
\label{fig:Sigma_SG_f_Ts}
\end{figure}
\begin{figure}[t!]
\includegraphics[width=.99\columnwidth]{Sigma_SG_f_Ti.eps}
\caption{$\Sigma(f)$ (left) and $\Sigma(m)$ (right) in the glassy
phase at the static transition effective temperature, $T=0.15<T_d$. The
lowest state free energy of metastable glassy states is denoted by
$f_1$ (i.e., corresponding to $m=1$ in the right panel, see text). The
free energy of maximum complexity is denoted by $f^*$, correspondingly
$m^*$ in the right hand side plot. }
\label{fig:Sigma_SG_f_Ti}
\end{figure}
In Fig. \ref{fig:Sigma_P_SG} we plot the complexity of the metastable
glassy states of lowest free energy between the dynamic and the static
transition. In the left panel of Fig. \ref{fig:Sigma_T_SG}
$\Sigma({\cal P})$ is displayed for three different values of $R_J$;
the threshold pumping for non-zero minimal complexity grows as the
degree of disorder $R_J$ decreases, as well as the corresponding
${\cal P}$ range. In the right panel $\Sigma(T)$ is plotted and it is
independent of $R_J$. In Figs. \ref{fig:Sigma_SG_f_Ts} and
\ref{fig:Sigma_SG_f_Ti} we display two instances of the whole
complexity curve both vs. $f$ and $m$ at $T=T_s$ and at a higher
temperature $T<T_d$.
\\ \indent Across the full line ${\cal P}_s(R_J)=\sqrt{\bar
\beta_s/R_J}$, in Fig. \ref{fig:PhDi_P_R} or, alternatively, across
$T/\sigma_J=1/\bar\beta_s =0.14099$ in Fig. \ref{fig:PhDi_T_J0}, a
true thermodynamic phase transition from the continuous wave
(paramagnetic) phase to the ``glassy coherent light'' (spin-glass)
phase occurs. The order parameter $q_1$ (the Edwards-Anderson
parameter $q_{\rm EA}$ \cite{Edwards75}), discontinuously jumps at the
transition from zero $q_{1}>q_0=0$, while $\tilde m=r_0=r_1=r_d=0$
(see Fig. \ref{fig:op}, bottom panel). The SG phase exists for any value
of $R_J$ and $\bar \beta> \bar \beta_s$.
\\ \indent In the stable SG phase, metastable states (with infinite
lifetime) continue to exist so that the thermodynamic state is
actually unreachable along a standard dynamics starting from random
initial condition. In Fig. \ref{fig:Sigma_f} we plot the typical
behavior of the complexity versus the single state free energy at
$T/\sigma_J=0.1$, qualitatively identical to the left panel of
Fig. \ref{fig:Sigma_SG_f_Ts} displaying $\Sigma(f)$ at $T=T_s$.
{\em Ferromagnetic phase ---} For weak disorder a random ferromagnetic
(FM) phase turns out to dominate over both the SG and the PM phases.
The transition PM/FM line is the standard passive ML threshold (see
e.g. [\onlinecite{Gordon02,Gordon03}]) and it turns out to be first
order in the Ehrenfest (i.e., thermodynamic) sense \cite{Leuzzi07,
Ehrenfest33}. From Fig. \ref{fig:PhDi_P_R} we see that it takes place
at growing pumping rates ${\cal P}$ for increasing $R_J$ until it
reaches the tricritical point with the SG phase. In the $(T,J_0)$
plane it occurs at large - positive - $J_0$, cf.
Fig.\ref{fig:PhDi_T_J0}
\\ \indent To precisely describe the FM phase in the 1RSB Ansatz we
have to solve eleven coupled integral equations
[Eqs. (\ref{f:speq_q1_R})-(\ref{f:speq_rd}) and Eq. (\ref{f:dphi_dm})
($\Sigma(m;\bm Q_{\rm sp}), \bm\Lambda_{\rm sp})=0$),
cf. Eq. (\ref{f:Sigma})].
In evaluating their solutions we have to consider that, in the region
where the FM phase is thermodynamically dominant, both the PM and the
SG solutions also satisfy the same set of equations. Besides,
unfortunately, the basin of attraction of the latter two phases - in
terms of initial conditions - is much broader than the FM one.
Starting the iterative resolution from random initial conditions,
determining the FM transition and spinodal
lines becomes, thus, numerically demanding.
\\ \indent An approximation can be obtained by considering the Replica
Symmetric (RS) solution for the FM phase (FM$_{\rm rs}$). This reduces
the number of independent parameters to seven ($q_1=q_0$,
$r_1^{R,I}=r_0^{R,I}$, $r_d^{R,I}$ and $\tilde m^{R,I}$). The
corresponding transition line is shown as a
\begin{widetext}
\begin{minipage}{0.99\textwidth}
\centering
\includegraphics[width=\textwidth]{disc_P_RJ_6.eps}
\figcaption{Discontinuity of the order parameters at the transition
points for three values of $R_J$. Top Left panel: jump in $q_{0,1}$,
at the PM/FM transition in
${\cal P}$ for small disorder, $R_J\simeq 0.1$; top right: discontinuities in $r_{0,1}$, ${\tilde r}$ and ${\tilde m}$ at the same transition. For such small $R_J$
the replica symmetry breaking is practically invisible: $q_1\simeq
q_0$, $r_1\simeq r_0$ [to the precision of our computation, ${\cal
O}(10^{-5})$]. Mid left panel (across tricritical region in
Fig. \ref{fig:PhDi_P_R}: $q_{0,1}$ vs. ${\cal P}$ at $R_J\simeq 0.26$ where, increasing the pumping
rate, first a PM/FM transition occurs followed by a FM/SG one.
Mid right panel: $r_{0,1}$, $\tilde r$ and $\tilde
m$ vs. ${\cal P}$ for the same interval. First
order transition point are signaled by vertical lines. Left bottom panel:
$q_{0,1}$ vs. ${\cal P}$ for large disorder, $R_J=0.4$ across the
PM/SG random first order transition. Right bottom: $r_{0,1}$, $\tilde r$ and $\tilde
m$ are always zero in the SG and in the PM phase.}
\label{fig:op}
\end{minipage}
\end{widetext}
\noindent dashed-dotted line in
Fig. \ref{fig:PhDi_T_J0_det}, where, {\em around the transition}, we
observe no practical difference with the exact SG/FM, even though the
replica symmetry is clearly broken.
In Fig. \ref{fig:op} we show the discontinuous behavior of
the order parameters across various transitions. As disorder is small
(top panel) one can observe that the RSB of the solution representing
the passive mode-locking phase vanishes, at least for what concerns
the limit of precision of our computation. As the degree of disorder
takes values around the tricritical point the RSB is clearly visible
(mid panel), both in the FM and in the SG phases. For increasing
disorder the FM is absent ($R_J\gtrsim 0.263$) and at high pumping/low
temperature only the glassy random laser phase remains.
\begin{figure}
\includegraphics[width=.49\columnwidth]{Sig_SG.eps}
\includegraphics[width=.49\columnwidth]{Sig_FM.eps}
\protect\caption{Complexity vs. free energy curve is plotted in the
SG phase (left) at $T/\sigma_J=0.1$ and in the FM phase (right).}
\label{fig:Sigma_f}
\end{figure}
We must necessarily implement the 1RSB Ansatz, though, to determine
the not-vanishing extensive complexity which signals the presence of a
large quantity of excited states with respect to ground states and
study its behavior in $T$ and $R_J$. This, as anticipated, also
implies the occurrence of a dynamic transition besides the
thermodynamic one. In the phase diagrams, Figs. \ref{fig:PhDi_P_R},
\ref{fig:PhDi_T_J0}, \ref{fig:PhDi_T_J0_det}, this takes place between
PM and SG, where the state structure always displays a non-trivial
$\Sigma$, for any $\bar \beta>\bar \beta_d$. Whether an exclusively
dynamic transition can occur as a precursor to the FM phase, as well,
could not be directly established in the present work. Indeed, the
region of expected dynamic transition lies beyond the spinodal FM
line, already very difficult to obtain numerically because of the
competition with the SG and PM solutions. However, the existence of a
metastable FM phase (cf. spinodal line in
Fig. \ref{fig:PhDi_T_J0_det}) with an extensive complexity, cf. e.g.,
Figs. \ref{fig:Sigma_f} and \ref{fig:Sigma_FM_f}, might well
correspond to an arrest of the dynamic relaxation towards equilibrium
of the system.
\begin{figure}
\includegraphics[width=.99\columnwidth]{Sigma_f_J010.eps}
\caption{Complexity curves of the FM phase at $R_J=3.54$ at
temperatures between $T=0.082\sigma_J$ (right most) and
$T=0.139\sigma_J$ (left most). Both the magnitude of the maximal
complexity and the free energy interval in which $\Sigma(f)>0$
decrease. Notice that the equilibrium free energy decreases as
temperature increases.}
\label{fig:Sigma_FM_f}
\end{figure}
\begin{figure}[t!]
\includegraphics[width=.99\columnwidth]{Phi_SG_FM.eps}
\caption{Top panel: free energy of the FM and SG phases vs. $R_J$ at
$T=0.0785$. As the degree of disorder increases the system undergoes
a first order phase transition from a ferromagnetic phase to a
spin-glass. Mid panel: order parameters $r_1,r_0$, $\tilde r$ and the
magnetization $\tilde m$ are shown vs. $R_J$. Beyond the transition
point their values drop to zero in the SG phase. Bottom panel: $q$
order parameters for the FM and the SG phase.}
\label{fig:opSGFM}
\end{figure}
\\
\indent
In the right
inset of Fig. \ref{fig:Sigma_f} we show, e.g., $\Sigma(f)$ in the
FM phase at $(R_J,{\cal P})=(0.28,5.92)$. This has to be
compared with the SG complexity at the same temperature (left inset
of Fig. \ref{fig:Sigma_f}) that is sensitively larger and does not depend
on the $R_J$: the maximum complexity drops of about
two orders of magnitude at the SG/FM transition, thus
unveiling a corresponding {\em high to low complexity transition}.
\\ \indent In Fig. \ref{fig:opSGFM}, at a relatively low temperature
$T=0.0785$ we show the behavior of the 1RSB (equilibrium) free energy
and order parameters across this SG (high complexity)/FM (low
complexity) transition. The transition is first order in $R_J$.
\section{Conclusion}
\label{sec:conclusion}
We have reported on an extensive theoretical treatment of the
thermodynamic and dynamic phases of nonlinear waves in a random
systems. The approach allows to treat nonlinearity and an arbitrary
degree of disorder on the same ground, and predict the existence of
complex coherent phases detailed in a specific phase-diagram. The
whole theoretical treatment is limited to the quenched-amplitude
approximation, which allows to catch the basic phenomenology and to
demonstrate the existence of phases with a not-vanishing complexity in
a variety of physical systems, and specifically random lasers, finite
temperature BEC and nonlinear optics. This approximation will be
removed in future works, and novel exotic phases of light in
nonlinear random system will be detailed.
Our theoretical work shows that the interplay of nonlinearity and
disorder leads to the prediction of substantially innovative physical
effects, which bridge the gap between fundamental mathematical models
of statistical mechanics and nonlinear waves. This allows to identify
frustration and complexity as the leading mechanisms for a coherent
wave regime in nonlinear disordered systems. Natural extension of
this work will be considering the quantum counterpart of the predicted
transitions, and the analysis of out of equilibrium nonlinear waves
dynamics.
\acknowledgments The research leading to these results has received
funding from the European Research Council under the European
Community's Seventh Framework Program (FP7/2007-2013)/ERC grant
agreement n. 201766 and from the Italian Ministry of Education,
University and Research under the Basic Research
Investigation Fund (FIRB/2008) program/CINECA grant code RBFR08M3P4.
|
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after many years working together we now know our strengths and our weaknesses - and we work as a great team when it's soooooo busy at Christmas time.
whether you love your heels or prefer the muddy fields, we have the bag for you!
this was our 1st home and we were attracted by the green door, and the low price due to there being much diy work to complete!
I was contacted by Jim to see if I could help out with illustrations for his campaign called 'Save 9 lives'. Jim is 22 and he's currently awaiting a heart transplant whilst campaigning for organ donation.
i finally got some new business cards printed for myself - i've had years without them and decided I needed them in my life!
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{
"redpajama_set_name": "RedPajamaC4"
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{"url":"https:\/\/tex.stackexchange.com\/questions\/617229\/pst-pdf-and-beamer-conflict\/617267#617267","text":"pst-pdf and beamer conflict\n\nFollow up to this question reporting conflict between [auto-]pst-pdf and hyperref. This is apparently due to the fact that pst-pdf uses preview internally, and preview is currently incompatible with some hyperref mechanisms, as discussed along this page and then this page.\n\nThe workaround proposed by Ulrike Fischer currently works for simple cases, but not when including PostScript code within frame environment of the beamer class.\n\n\\documentclass{beamer}\n\n\\usepackage{pstricks}\n\\usepackage[pspdf={-dALLOWPSTRANSPARENCY}]{auto-pst-pdf}\n\n\\makeatletter\n\\AtBeginDocument{\n\\ifpdf\\else\n\\ifPreview\n\\let\\Hy@FirstPageHook\\relax\n\\let\\Hy@EveryPageAnchor\\relax\n\\fi\n}{}\n\\fi\n}\n\\makeatother\n\n\\begin{document}\n\n\\begin{frame}\nSome text\n\\begin{pspicture}(0,0)(5,5)\n\\psline(0,0)(5,5)\n\\end{pspicture}\nOther text\n\\end{frame}\n\n\\end{document}\n\n\nNote that only loading the beamer class does not trigger the bug, it's the frame environment that triggers it.\n\nI am looking for a workaround that would allow me to use PStricks in beamer presentations with pdflatex from an up-to-date (2021) texlive.\n\n\u2022 it is not a direct incompability with hyperref. preview is not compatible with the new latex shipout code and hyperref is one the cases where you get problems. I have some doubts that the preview maintainer will address this in the near future. I would suggest to either use pstools + pdfcrop or to switch to lualatex. It now supports pstricks through the luapstricks package, and if you run into problems there is an active maintainer. Sep 29 '21 at 20:49\n\u2022 Many thanks for the tips. I'll first look into pstools before switching engines, which would require much more work. If pdfcrop can replace preview in pstools, do you think it could also do so in pst-pdf? Sep 29 '21 at 21:19\n\u2022 Looks like pstool does not deal with pspicture environment; it is only designed to work with psfrag, not pstricks. Or did I miss something? Sep 29 '21 at 22:06\n\u2022 Run the document with lualatex then you do not need pst-pdf Oct 1 '21 at 10:17\n\nYou can try the following.\n\n\\documentclass{beamer}\n\\usepackage{pstricks}\n\\usepackage[pspdf={-dALLOWPSTRANSPARENCY}]{auto-pst-pdf}\n\n\\makeatletter\n\n\\AtBeginDocument{\n\\ifpdf\\else\n\\ifPreview\n\\RemoveFromHook{shipout\/firstpage}[hyperref]\n\\RemoveFromHook{shipout\/before}[hyperref]\n\\fi\n}{}\n\\fi\n}\n\\makeatother\n\\begin{document}\n\n\\begin{frame}\nSome text\n\\begin{pspicture}(0,0)(5,5)\n\\psline(0,0)(5,5)\n\\end{pspicture}\nOther text\n\\end{frame}\n\n\\end{document}","date":"2022-01-25 23:37:30","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7945117950439453, \"perplexity\": 2563.42374304234}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-05\/segments\/1642320304876.16\/warc\/CC-MAIN-20220125220353-20220126010353-00562.warc.gz\"}"}
| null | null |
# DJing For Dummies®, 2nd Edition
**Table of Contents**
Introduction
About This Book
Conventions Used in This Book
Foolish Assumptions
How This Book Is Organised
Part I: Stepping Up to the Decks
Part II: Stocking Up Your DJ Toolbox
Part III: The Mix
Part IV: Getting Noticed and Playing Live
Part V: The Part of Tens
Icons Used in This Book
Where to Go from Here
Part I: Stepping Up to the Decks
Chapter 1: Catching DJ Fever
Discovering DJing Foundations
Equipping yourself
Making friends with your wallet
Knowing your music
Researching and discovering
Connecting your equipment
DJing Takes Patience and Practice
Working as a DJ
Chapter 2: Starting Up with the Bare Bones
Making a List, Checking It Twice
Considering Input Devices
Thinking about turntables
Deciding on CD decks
Musing on MP3s and PCs
Mixing It Up with Mixers
Monitoring Your Music with Headphones
Powering Things Up with Amplifiers
Figuring Out the Furniture
Considering ergonomics and stability
Selecting store-bought stands
Killing vibration with bricks and air
Locating Your DJ Setup
Chapter 3: Shopping for Equipment
Taking Stock Before You Shop
Trying before you buy
Budgeting your money
Crossing over with digital DJing
Buying Brand New
Cruising the high street
Opting for online shopping
Buying Second-hand
Bidding on auction websites
Scanning newspapers
Dipping into second-hand and pawn shops
Making Sure That Your Kit Works
Checking cables
Testing turntables
Vetting CD decks
Monitoring mixers
Assessing headphones
Sounding out amplifiers and speakers
Chapter 4: Retro Chic or PC Geek? Buying Records, CDs and MP3s
Sizing Up Records, CDs and MP3s
Circling around vinyl formats
Polishing up on CD options
Byting into MP3s
Researching and Buying Your Tunes
Buying MP3s
Purchasing CDs and records
Choosing what to buy
Weighing up Classic and Current
Protecting Your Records and CDs
Storing records
Cleaning CDs, records and needles
Repairing vinyl
Fixing warped records and CDs
Repairing scratched/cracked CDs
Backing up digital libraries
Part II: Stocking Up Your DJ Toolbox
Chapter 5: Keeping Up with the Tech-Revolution: Format Choices
Clashing CDs against Vinyl
Finding your format
Reflecting on vinyl
Keeping up with CDs
Choosing Analogue or Digital
Functionality: My Way Is Best!
Turntables and records are heavy and cumbersome
Turntables don't have built-in effects
You can't see the music on CD
Using CDs lacks aesthetic performance
Bars don't have turntables for DJs any more
Turntables are more expensive than CD decks
Can't We All Just Get Along?
Hybrid turntables let you have it all
The new kid: Digital DJing
Chapter 6: Getting Decked Out with Turntables
Avoiding Cheap Turntables
Motoring in the right direction
Watching out for pitch control design
Identifying Key Turntable Features
Start/Stop
On/Off
33/45/78 RPM
Strobe light
Deckplatters
Target light
Pitch control
Counterweight/height adjust
Antiskate
Removable headshell/cartridge
45 RPM adaptor
Customising Your Sound with Advanced Turntable Features
Pitch range options
Pitch bend and joystick control
Tempo Reset/Quartz Lock
Master Tempo/Key Lock
Digital display of pitch
Adjustable brake for Start/Stop
Reverse play
Different shaped tonearms
Removable cabling
Digital outputs
Battle or club design
Built-in mixer
Setting Up Turntables
Deckplatter
Tonearm
Peripherals
Servicing Your Turntables
Chapter 7: Perfecting Your Decks: Slipmats and Needles
Sliding with Slipmats
Choosing an appropriate slipmat
Winning the friction war
Getting Groovy with Needles and Cartridges
Feeling the Force with Counterweight Settings
Nurturing Your Needles
Chapter 8: Spinning with CDs
Knowing the Requirements of the DJ's CD Deck
Laying out the design
Navigating the CD
Adjusting the Pitch
Smoothing Out Vibrations
Working with the Cue
Locating the cue
Storing the cue
Checking the cue
Starting the tune
Taking Advantage of Special Features
MP3 playback
Master Tempo
Hot Cues
Loop
Sample banks
Reverse play
BPM counters
Digital DJ software control
Having Fun Experimenting
Chapter 9: Bits and PCs: Digital DJing
Designing Your Digital DJ Setup
Processing computer hardware
Memory and processor considerations
Stability
Controlling the Digits
Laptop/computer only
Enhancing the basics by adding hardware
DVS using records and CDs
Connections and requirements
Adding Hardware Controllers
All-in-one hardware controllers
Control and effect
Putting CD decks and mixers in control
Your way is the best way . . . for you
Picking Out the Software
Software designed for DJs
Taking Control
Livening up software choice
Bridging the gap
Exploring Alternatives
DJing with iPods and USB drives
Mixing on the move
Chapter 10: Stirring It Up with Mixers
Getting Familiar with Mixer Controls
Inputs
Outputs
Multiple channels
Cross-faders
Channel-faders
Headphone monitoring
EQs and kills
Input VU monitoring
Gain controls
Balance and pan controls
Hamster switch
Punch and transform controls
Built-in effects
Effects Send and Return
Built-in samplers
Built-in beat counters
Beat light indicators
MIDI controls
Choosing the Right Mixer
The seamless mix DJ
The scratch DJ
The effects DJ
The rock/party/wedding DJ
Servicing Your Mixer
Chapter 11: Ear-Splitting Advice about Not Splitting Your Ears: Headphones
Choosing a Good Set of Headphones
Single-sided, coiled cords
Swivelling earpieces
User-replaceable parts
Sticking it to your ears
Remembering that the Volume Doesn't Have to Go Up to 11
Using Earplugs
Chapter 12: Letting Your Neighbours Know That You're a DJ: Amplifiers
Choosing Suitable Amplification
Settling on your home stereo
Purchasing powered speakers
Opting for separates
Allowing a power margin for error
Working with Monitors
Working with the speed of sound
Positioning your monitor
Noise Pollution: Keeping an Ear on Volume Levels
Protecting your ears
Neighbourhood watch
Realising that you only need one speaker
Chapter 13: Plugging In, Turning On: Set-up and Connections
Getting Familiar with Connectors
RCA/Phono connections
XLRs
Quarter-inch jack
Plugging Into the Mixer
Connecting turntables to a mixer
Connecting CD decks to a mixer
Connecting iPods and personal MP3s players to a mixer
Connecting a computer as an input device
Choosing your mixer inputs
Plugging in your headphones
Connecting effects units to a mixer
Connecting mixer outputs
Connecting a mixer to your home hi-fi
Connecting a mixer to powered speakers
Connecting a mixer to your PC/Mac
Troubleshooting Set-up and Connections
Everything's connected, a record (or CD) is playing, but I can't hear any music through the amplifier
I can hear the music from the amp now, but I can't hear anything through the headphones
One of the turntables sounds really bad: it's distorting and the high frequencies sound fuzzy
Why do my needles keep jumping when cueing?
I hear a really strange humming noise coming from my turntables
Why is everything distorting badly when I play a CD?
Why is everything really quiet when using my turntables, even when everything is turned up to maximum?
Everything sounds nice through the mixer, but distorts through the amp
Music is playing through the mixer, but I can't get any music into the PC
The meters are flashing like mad in the software, I'm able to record what's going in, but nothing is coming back out of the PC
Why doesn't my recording device seem to record anything when connected directly to the mixer?
Part III: The Mix
Chapter 14: Grasping the Basics of Mixing
Knowing What Beatmatching's All About
Discovering How to Beatmatch
Choosing skills over thrills
Setting up your equipment
Locating the first bass beat
Starting your tunes in time
Adjusting for errors
Knowing which record to adjust
Using the Pitch Control
Understanding BPMs
Calculating BPMs
Matching the pitch setting
All hands (back) on decks
Playing too slow or too fast
Taking your eyes off the pitch control
Introducing Your Headphones
Switching over to headphone control
Cueing in your headphones
Centring your head with stereo image
Practising with your headphones
Using new tunes
Quick Beatmatching
Chapter 15: Picking Up on the Beat: Song Structure
Why DJs Need Structure
Multiplying beats, bars and phrases
Hearing the cymbal as a symbol
Everything changes
Counting on where you are
Actively listening to your tunes
Studying Song Structure
Repeating the formula
Accepting that every tune's different
Developing your basic instincts
Listening to a Sample Structure
Chapter 16: Mixing Like the Pros
Perfecting Placement
Intros over outros
Melodic outro
Melodic intro
Mixing Breakdowns
Controlling the Sound of the Mix
Bringing the cross-fader into play
Unleashing channel-faders
Letting you in on a big, curvy secret
Balancing it out with EQs
Using Mixing Tricks and Gimmicks
Spinbacks and dead-stops
Power off
A cappella
Cutting in
Effecting the transition
Mixing Different Styles of Music
The wedding/party/rock/pop mix
The R and B mix
Drum and bass, and breakbeat
Beatmatching tunes with vastly different tempos
Chapter 17: Scratching Lyrical
Setting Up Equipment the Right Way
Weighing up needles
Wearing out your records
Giving slipmats the slip
Touching up mixers
Making the mixer a hamster
Preparing for the Big Push
Marking samples
Following a line-up
Fixing the hole in the middle
Scratching on CD, MP3 and Computer
Marking CDs
Scratching on PC
Mastering the Technique
Getting hands on
Changing sample sounds
Starting from Scratch and Back Again
Scratching without the cross-fader
Introducing cross-fader fever
Combining scratches
Juggling the Beats
Offsetting
Practice, dedication and patience
Part IV: Getting Noticed and Playing Live
Chapter 18: Building a Foolproof Set
Choosing Tunes to Mix Together
Beatmatching – the next generation
Mixing with care
Changing gear
Getting in tune with harmonic mixing
Keying tunes
Knowing how much to pitch
Developing a Style
Easing up on the energy
Changing the key
Increasing the tempo
Avoiding stagnation
Respecting the crowd
Demonstrating your style
Chapter 19: Creating a Great Demo
Preparing to Record the Demo
Programming your set
Picking and arranging the tunes
Bridging the gaps
Practising your set
Practise makes more than perfect
Setting up to record
Correcting recording levels
Looking After Sound Processing
Keeping an even volume
Setting your EQs
Testing, testing
Adjusting the amplifier
Performing the Demo
Staying focused
Becoming a perfectionist
Listening with an open mind
Making a Demo CD on Computer
Editing your mix
Burning a CD
Creating a track-split CD
Sending Off the Mix
Chapter 20: Getting Busy With It: Working as a DJ
Marketing Yourself
Flooding the world with your demo
Playing for free
Joining an Agency
Researching an agency
Meeting the criteria to join
Keeping agencies in your musical loop
Cutting your losses
Networking Your Way to Success
Selling yourself
Making friends
Going undercover
Marketing Yourself on the Internet
Chapter 21: Facing the Music: Playing Live
Investigating the Venue
Scoping out a club
Gearing up to party
Preparing to Perform
Selecting the set
Organising your box
Knowing What to Expect at the Club
Dealing with nerves
Getting used to your tools
Working in a loud environment
Playing Your Music
Reading a crowd
Handling requests
Taking over from someone else
Finishing the night
Part V: The Part of Tens
Chapter 22: Ten Resources for Expanding Your Skills and Fan Base
Staying Current with Media
Visiting DJ Advice Websites
Getting Answers through DJ Forums
Reading Other Books
Getting Hands-On Advice
Listening to Other People's Mixes
Participating in Competitions
Hosting Your Own Night
Uploading Podcasts or Hosted Mixes
Immerse Yourself in What You Love
Chapter 23: Ten Answers to DJ Questions You're Too Afraid to Ask
Do I Need to Talk?
What Should I Wear?
How Do I Go to the Toilet?
Can I Invite My Friends into the DJ Booth?
How Do I Remove the Beat, or Vocals?
How Do I Choose My DJ Name?
Do I Get Free Drinks? (And How Do I Get Drinks from the Bar?)
Who Does the Lighting for the Night?
Should I Reset the Pitch to Zero After Beatmatching?
What Do I Do If the Record or CD Skips or the Software Crashes?
Chapter 24: Ten Great Influences on Me
Renaissance: Disc 1
Tonsillitis
La Luna: 'To the Beat of the Drum'
Ibiza 1996, Radio 1 Weekend
The Tunnel Club, Glasgow
Jamiroquai: 'Space Cowboy'
Digital DJing
Alice Deejay: 'Better Off Alone'
Delirium: 'Silence'
Sasha and Digweed, Miami 2002
Chapter 25: Ten DJing Mistakes to Avoid
Forgetting Slipmats/Headphones
Taking the Needle off the Wrong Record
Banishing Mixer Setting Problems
Getting Drunk when Playing
Surfing while Mixing
Leaning Over the Decks
Avoiding Wardrobe Malfunctions
Spending Too Long Talking to Someone
Leaving Your Last Tune Behind
Not Getting Paid Before You Leave
Chapter 26: Ten Items to Take with You When DJing
All the Right Tunes
Making It Personal with Headphones and Slipmats
You're a Star! Taking a Digital Recorder/Blank CD
Packing Your Tools and Saving the Day
Always Being Prepared: Pen and Paper
Keeping Fuelled with Food and Drink
Spreading the Music with Demos
Keeping Moving with Car Keys
Have Wallet, Will Travel
Just Chilling: Chill Mix for the Ride Home
DJing For Dummies®, 2nd Edition
by John Steventon
DJing For Dummies®, 2nd Edition
Published byJohn Wiley & Sons, LtdThe Atrium, Southern Gate, Chichester, West SussexPO19 8SQEngland
Email (for orders and customer service enquires): cs-books@wiley.co.uk
Visit our Home Page on www.wiley.com
Copyright © 2010 by John Wiley & Sons, Ltd, Chichester, West Sussex, England.
Published by John Wiley & Sons, Ltd, Chichester, West Sussex.
All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher for permission should be addressed to the Legal Department, Wiley Publishing, Inc, 10475 Crosspoint Blvd, Indianapolis, Indiana 46256, United States, 317-572-3447, fax 317-572-4355, or online at www.wiley.com/go/permissions
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Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.
British Library Cataloguing in Publication Data: A catalogue record for this book is available from the British Library.
ISBN: 978-0-470-66372-1
ISBN: 978-0-470-97074-4 (ebk), ISBN 978-0-470-66404-9 (ebk), ISBN 978-0-470-66405-6 (ebk)
Printed and bound in Great Britain by Bell and Bain Ltd, Glasgow.
10 9 8 7 6 5 4 3 2 1
About the Author
John Steventon, also known as Recess, was transformed from clubber to wannabe DJ by BBC Radio 1's 1996 'Ibiza Essential Mix'. Fascinated by what he heard, he bought a second-hand pair of turntables, his best friend's record collection, and started to follow the dream of becoming his newest hero, Sasha.
With no other resource available when he first started DJing, John would take notes, writing articles to refer to if ever he felt like he needed help. Joining the Internet revolution meant 15 megabytes of free Web space, and as he'd already written these notes about learning how to DJ, John thought it would be good to share that information with the rest of the world wide web. He created the 'Recess' persona, and expanded the site as his knowledge grew. Originally a small, basic Web site, www.recess.co.uk has grown over the years both in size and reputation, to become one of the foremost online resources for learning how to DJ – the place where newbie DJs turn to.
Having developed a career as a TV editor at the same time, now heading up post-production at a TV production company, he has scaled down the time spent DJing in clubs, but Recess is always online to help the new DJ overcome those first few hurdles, and offer advice to those who need that extra bit of reassurance.
John is 31, plays way too much squash and poker, is married to Julie, and they both live together with their daughter, cats and a smile on the outskirts of Glasgow, Scotland.
Dedication
This book is dedicated to my Dad, Richard Steventon, who I'm sure would have got a kick out of seeing his son write a book.
To Julie: my best friend, my wife, my smile; without whom I'd be half a person. You are my lobster. And for this second edition, a new addition; to Jaime Steventon, I still can't believe we made a person. I can't wait to know you.
Author's Acknowledgements
My list of acknowledgments is surprisingly long, but these are the people without whom this book would not have been inspired, created, or nearly as long as it ended up!
Thanks to Graham Joyce, who sold me his record collection and started me on this journey, who got me my first break in a roundabout way, and took me to the place that I eventually met my wonderful wife. My sister, Pamela Tucker, who claims if it wasn't for her, I wouldn't have made friends with Graham and is therefore responsible for everything good in my life! My mum, Mary Steventon for being my Mum and for helping with the text accuracy in this book (even if she had NO idea what it all meant). My uncle, David Steventon, for sowing the seed that maybe people would find my writing interesting; my lovely in-laws, Jim (sorry, 'Sir'), Margaret (the lasagne queen), and Vicki Fleming for entertaining Julie while I spent months writing this book; Carol Wilson for making sure I wasn't signing away the rest of my life; and Lucky, Ziggy, and Ozzy for being my writing companions.
Ian, Jason, Nichol, Al, Gus, Jonny, Dave, Gary, Tony, Iain, and the other poker people for letting me blow off steam until 7 in the morning trying to take their money. All the staff and DJs at what used to be Café Cini in Glasgow where I got my break as a DJ. Paul Crabb for inspiration and distraction (I know, I still can't believe I wrote a book before you!) and Flora Munro for work deflection and a hell of a cup of coffee.
This book wouldn't have had half the info in it if it wasn't for the following people helping me out and kindly granting me permission to reuse images of their gear: David Cross at Ableton, Adam Peck at Gemini, Stephanie Lambley for Vestax images, Sarah Lombard at Stanton, Tara Callahan at Roland, Mike Lohman at Shure, Sarah O'Brien at PPLUK, Carole Love at Pioneer, Grover Knight at Numark, David Haughton at Allen & Heath, Wilfrid at Ortofon, Justin Nelson at NGWave, Ryan Sherr at PCDJ, Laura Johnston at Panasonic, Jeroen Backx at Freefloat, all at Etymotic, NoiseBrakers, Sony, and Denon, Mark Davis from Harmonic-mixing.com, Yakov V at Mixedinkey.com for his help with the Harmonic Mixing info, everybody on all DJing Internet forums for letting me bug them for the past eight months, all the visitors to my Recess Web site, and everyone else who has touched this book in any way – I can't mention everyone, but thank you all.
And finally, from Wiley, Rachael Chilvers, whose support, understanding, and encouragement made it a pleasure to write this book, so that it never felt like work and never became something I didn't want to do (and also for laughing at my poor jokes and stories).
Phew . . . let's hope I never win an Oscar!!
Thanks for reading this book. Good luck, keep the beats tight.
Publisher's Acknowledgements
We're proud of this book; please send us your comments through our Dummies online registration form located at www.dummies.com/register/.
Some of the people who helped bring this book to market include the following:
Commissioning, Editorial and Media Development
Publisher: David Palmer
Production Manager: Daniel Mersey
Project Editor: Rachael Chilvers
Content Editor: Jo Theedom
Proofreader: Charlie Wilson
Cover Photo: © Sergei Bachlakov
Cartoons: Rich Tennant (www.the5thwave.com)
Composition Services
Project Coordinator: Lynsey Stanford
Layout and Graphics: Ashley Chamberlain, Melanee Habig, Joyce Haughey
Proofreader: Laura Albert
Indexer: Ty Koontz
Publishing and Editorial for Consumer Dummies
Diane Graves Steele, Vice President and Publisher, Consumer Dummies
Kristin Ferguson-Wagstaffe, Product Development Director, Consumer Dummies
Ensley Eikenburg, Associate Publisher, Travel
Kelly Regan, Editorial Director, Travel
Publishing for Technology Dummies
Andy Cummings, Vice President and Publisher, Dummies Technology/General User
Composition Services
Debbie Stailey, Director of Composition Services
Introduction
People come to DJing from different places and for different reasons, but you can split them up into those who love the music, those who want to make money and those who think that DJing is cool and want to be famous. You may fall into one or all three of these categories, but the most important one is loving the music.
If you're a good DJ and get lucky you could become rich and famous, but when starting off if you don't love the music you may become bored and impatient with the time and practise you need to invest in your skills, and quit. Even if you do manage to get good at DJing, if you don't love playing and listening to the music night after night, working in clubs will start to feel too much like work. DJing isn't work; it's getting paid to do something you love.
When I started DJing I already loved the music, but the first time I experienced the true skill of a DJ working a crowd (Sasha, Ibiza 1996) I fell in love with DJing, and knew I wanted to be one. The mechanics of it didn't occur to me until I first stood in front of two turntables and a mixer; all I wanted to do was play other people's music and have control over a crowd.
About This Book
This book is based on my website www.recess.co.uk that, since 1996, has given new DJs all over the world the start they needed to become great DJs.
Because beatmatching is a complicated and important skill for DJs who want to play electronic dance music (house, trance, progressive, drum and bass, breakbeat and so on) it has its own chapter (14), and I mention it frequently. However, the book also contains the mixing skills and musical structure knowledge that enable you to mix rock, indie and pop music, or to DJ at weddings or other parties, so no one's left out. I use a very simple technique for starting off as a DJ, which begins with the basics of starting tunes and matching beats and then covers the skill of creating transitions between tunes, important for any kind of DJ to master, whether you're a rock, wedding, pop or dance DJ. You can find many other ways to develop your skills, but because these other approaches skip the basics, and involve a lot of trial and error and confusion, I've had much more success coaching DJs with this method than with any other.
You can find the equipment sections and how to use the variety of function options available to you in Parts I and II, and these are relevant to all DJs. Part III covers mixing skills like beatmatching, scratching, musical structure and mix transitions. Please don't assume that because different skills are associated with certain genres that party DJs should rip out the beatmatching and scratching information or that club DJs should skip anything that mentions party DJing. Knowledge is skill, and the more skilful you are as a DJ, the better you'll become, and the more work you'll get.
Conventions Used in This Book
DJs often describe musical terms like beat structure using phrases that, to the uninitiated, can sound like gibberish. So if a boffin uses ten words to describe something, I try to put it across in a reader-friendly way.
I call the music you DJ with tunes or tracks. I've steered away from calling each track a song, because songs can imply vocals, and not all music you play as a DJ will have vocals.
A friend of mine read Michael Crichton's Jurassic Park and decided that instead of reading the various different dinosaur names, she'd read each one as dinosaur. I've done the same thing with CD/turntables/MP3 players and software in this book, describing them as decks unless I'm writing in specifics. I figured you'd get bored of lines such as 'Go to your turntable/CD player/PC/iPod and start the tune. Then go to the other turntable/CD player/PC/iPod and put on a different tune'. Repetition isn't a good thing. I repeat, repetition isn't a good thing.
On a practical note:
Italic emphasises and highlights new words or terms that I define.
Boldfaced text indicates the action part of numbered steps.
Monofont text displays web addresses.
I alternate between male and female pronouns to be fair to both genders!
Foolish Assumptions
I assume that you find lines like the last one in the previous section amusing. Don't worry; I know I'm not funny, so I don't try too often. I won't distract you from the subject at hand, but every now and then something takes over and I try to be funny and entertaining. I apologise for that now, but after all, an entertaining, humorous approach is what the For Dummies series of books is famous for.
Apart from that, this book assumes that you want to be a DJ, that you want to put in the time it takes to get good at it, you love the music and you won't get fed up when it takes longer than ten minutes to become the next Tiësto, Zane Lowe, DJ Qbert or award-winning wedding DJ. I also assume that you don't have vast experience of music theory.
How This Book Is Organised
All For Dummies books are put together in a reader-friendly, modular way. You can look at the table of contents, pick a subject, flick to that page and find the information you need.
The book still has a structure as a whole, like any other book. It starts at the beginning, with choices on what equipment to use, moves onto the process of developing DJ skills and ends playing live to a crowd of a thousand people. This structure means that you can read it from cover to cover like any book, with you as the good-looking hero or heroine!
Part I: Stepping Up to the Decks
Part I describes the core pieces of equipment that you need in order to be a DJ and the best ways to build your collection of tunes. I also dedicate a chapter to the art of shopping, with advice on shopping in the high street and going online to research and buy your tunes and equipment.
Part II: Stocking Up Your DJ Toolbox
From a format choice of CD or vinyl or digital DJing, to how the controls on the mixer work, Part II is all about using, choosing, connecting and setting up your equipment for DJ use. I wouldn't dare to presume to tell you exactly what to buy, but I do offer advice on what may be most suitable for you and your budget.
Part III: The Mix
The nitty-gritty of DJing. From creating transitions between tunes, starting them at the correct points, beatmatching and the complicated moves demanded by the scratch artist, Part III deals with all the information you need to develop your skills as a DJ. This information is important, so spend lots of time with this part, because these chapters describe key techniques that mould and shape you as a DJ.
Part IV: Getting Noticed and Playing Live
After developing your DJ skills, the next step is to get work and show people just how good you are. Part IV gives lots of information on how to sell yourself, how to create a great sounding (and looking) demo and what to do when you get work. DJing isn't simply a case of standing in the DJ booth expecting everyone to love everything you play!
Part V: The Part of Tens
These chapters squeeze in the last tips, tricks and common sense reminders that ease the way toward you becoming a successful, professional DJ.
Icons Used in This Book
Every now and then, a little For Dummies symbol pops up in the margin of the book. It's there to let you know when something's extra useful, essential for you to remember, may be dangerous to your equipment or technique, or if what follows is technical gobbledegook.
This one's easy: it highlights something you should burn into your memory to help your progress and keep you on the right path on your journey to becoming a great DJ.
Tips are little bits of info that you may not need, but they can help speed up your development, make you sound better and generally make your life easier as a DJ.
When you're starting out as a DJ, you may need to navigate your way through a number of tricky situations. A few of them end with broken records/needles and CDs, a crashed computer or a damaged reputation as a DJ. Heed the advice when you see this icon, and proceed with caution.
They're unavoidable; words put together by someone else in a small room that mean absolutely nothing. Where possible, I try to translate technical DJing terms into plain English for you.
Where to Go from Here
Go to the kitchen, make yourself a sandwich, pour a nice cold glass of water or hot pot of coffee, put on some music you love and jump into Chapter 1 – or whichever chapter takes your fancy! If you want to know about beatmatching, go to Chapter 14; if you want to know how to connect your equipment, go to Chapter 13.
When you feel inspired, put down the book and try out some of the techniques you've read about. If you want to spend 20 minutes mixing between tunes so you can hear the music, but don't want to concentrate on your skills, do it! Your love of the music and DJing is just as important as the mechanics of how you do it, if not more.
You can also jump online and check out the video and audio clips that support this book at www.recess.co.uk. The site that I've used to develop DJs from all over the world is now a resource for this book, just for you. You can drop me a line there, and ask me anything you want to know.
Part I
Stepping Up to the Decks
In this part . . .
Knowing what equipment you need, and where to get the music you want to play when you start your DJing journey can be a bit of a mystifying minefield. These opening chapters take you through the essentials you need to start DJing, and explore the shopping options open to you.
Chapter 1
Catching DJ Fever
In This Chapter
Having what it takes to be a DJ
Mixing mechanics and creativity
Reaching the journey's end – the dance floor
The journey you take as a DJ – from the very first tune you play when you enter the DJ world to the last tune of your first set in front of a club filled with people – is an exciting, creative and fulfilling one, but you need a lot of patience and practice to get there.
DJ gadgets, iPod apps and console games like DJ Hero are introducing and inspiring new waves of people to become DJs daily. Hundreds of DJs over the world are on a quest to entertain and play great music. Everyone needs an advantage when they compete with hundreds of like-minded people. Your advantage is knowledge. I can help you with that.
Discovering DJing Foundations
DJing is first and foremost about music. The clothes, the cars, the money and the fame are all very nice, and nothing to complain about, but playing the right music and how a crowd reacts is what makes and moulds a DJ. As the DJ, you're in control of everybody's night. As such, you need to be professional, skilful and knowledgeable about what the crowd wants to hear, and ready to take charge of how much of a good time they're having.
What kind of DJ you become lies in how you choose, use and respect your DJ tools and skills. Become a student of DJing as well as someone who loves music and performing to a crowd, and your foundations will be rock solid.
Equipping yourself
When you first begin your DJing journey, you can equip yourself with two things: knowledge and hardware.
You can split knowledge into two: what you're about to learn, and what you already know. In time, you can pick up and develop mixing skills like beatmatching, scratching, creating beautiful transitions and choosing music that plays well together.
A sense of rhythm, a musical ear for what tunes play well over each other and the ability to spot what makes a tune great are all things that you'll have developed from the day you were born. Out of those three things, a sense of rhythm can be the best secret weapon you bring when first finding out how to DJ. I've played the drums since I was ten, which gave me a very strong sense of rhythm and a sixth sense for beat and song structure.
Don't worry if you don't know your beats from your bars, or your bass drums from your snare drums; I explain all in Chapters 14 and 15. You need to dedicate some considerable time to developing a feel for the music and training your brain to get into the groove, but with time and concentration, you won't get left behind. The same goes for developing a musical ear, and recognising what tunes have the potential to be great. With experience, dedication, determination and yes, more time, you can develop all the musical knowledge you need to become a great DJ.
The hardware you use as a DJ can define you just as much as the music you play. The basic equipment components you need are:
Input devices to play the music: You can choose from CD players, MP3 players, a computer with DJing software or DJ turntables that play records.
A mixer: This box of tricks lets you change the music from one tune to the other. Different mixers have better control over how you can treat the sound as you mix from tune to tune.
A pair of headphones: Headphones are essential for listening to the next record while one is already playing.
Amplification: You have to be heard, and depending on the music you play, you have to be LOUD!
Records/CDs/MP3s: What's a DJ without something to play?
Providing that your wallet is big enough, making the choice between CD and vinyl is no longer a quandary. The functions on a turntable are equally matched by those on a CD player, and digital DJing (see Chapter 9) means you can use your turntables to play MP3s on computer software, so you're not even limited by the availability of music that's released (or not released) on vinyl. So the decision comes down to aesthetics, money and what kind of person you are. You may love the retro feel of vinyl and enjoy hunting for records in shops, or you may like the modern look of CD players or the versatility of computer DJing and prefer the availability of MP3s and CDs – it's your choice.
Making friends with your wallet
DJing costs money. Whether you shop online or go to the high street, the first thing to do is look at your finances. If you've been saving up money for long enough, you may have a healthy budget to spend on your equipment. Just remember, the expense doesn't stop there. New tunes are released every day and you'll be bursting to play the newest, greatest tunes. You may start to think of buying other items in terms of how many tunes you could get instead. I remember saying once, 'Fifty pounds for a shirt? That's ten records!'
You don't get the personal touch, but shopping online can be cheaper for equipment and music. And if you can't afford new DJ equipment right now use demo software on a computer to develop your skills, and then spend money on DJ equipment or controllers for the software when you can. Flip through to Chapters 3 and 9 for more information.
Knowing your music
Throughout the years I've been helping people to become DJs, one of the most surprising questions I've been asked is, 'I want to be a DJ. Can you tell me what music I should spin?' This question seems ridiculous to me. Picking the genre (or genres) of your music is really important, because you need to love and feel passionate about playing this music for the rest of your DJ career. (Head to Chapters 4 and 5 for more on genre and music formats.)
After you've found your musical elixir, start to listen to as much of it as you can. Buy records and CDs, listen to the radio, search the Internet for information on this genre and discover as much as you can. This groundwork is of help when choosing tunes you want to play and when looking for artists' remixes, and is an aid to developing your mixing style. Doing a tiny bit of research before you leap into DJing goes a long way towards helping you understand the facets and building blocks of the music you love. Become a student of trance, a scholar of jungle, a raconteur of rock and a professor of pop – just make sure that you start treating your music as a tool, and be sure to use that tool like a real craftsman.
Researching and discovering
You know the music you want to play, you've decided on the format that's right for you, you've been saving up for a while; now you need to wade through the vast range of equipment that's available and be sure that you're buying the best DJ setup for the job at hand.
With technology advancing faster than I can write this book, you can easily get lost in the features that are available to you on CD decks, turntables, mixers and software releases. Take as much time as you can to decide on what you want to buy. Go online and do some research and ask others in DJ forums for their thoughts on the equipment you're thinking about buying. Make sure that you're buying something that does what you want it to do, and that any extra features aren't bumping up the price for something you'll never use.
Here's a brief guide to what to look for when buying equipment:
Turntables designed for DJ use need a strong motor, a pitch control to adjust the speed the record plays at and a good needle. They also need to have sturdy enough construction to handle the vibrations and abuse that DJing dishes out. A home hi-fi turntable won't do, I'm afraid. Check out Chapter 6 for more.
Mixers ideally have 3-band EQs (equalisers) for each input channel, a cross-fader, headphone cue controls and a good display to show you the level (volume) at which the music is sent out of the mixer so you don't blow any speakers accidentally. Chapter 10 goes into more detail on this and other functions on the mixer.
CD decks need to be sturdy enough that they won't skip every time the bass drum booms over the speakers. Jog wheels, easy-to-navigate time and track displays, and a pitch bend along with the pitch control are all important core features of a CD turntable. Chapter 8 is dedicated to everything CD-related.
You can use computers that use DJ software in various ways. From mouse clicks and keyboard strokes and dedicated hardware to simply using your existing turntables/CD decks and a mixer to control music on the computer, I explain all the choices in Chapter 9.
Headphones need to be comfortable, sound clear when played at high volume and cut out a lot of external noise from the dance floor so that you don't have to play them too loud. Your ears are very important, so try not to have your headphones at maximum all the time. Chapter 11 is the place to go for guidance on headphones and protecting your ears.
Volume and sound control are the watchwords for amplification. You don't need a huge amplifier and bass-bins for your bedroom, but similarly, a home hi-fi isn't going to be much use in a town hall. Chapter 12 helps you find the right balance.
Connecting your equipment
After you have all the pieces of your DJ setup, your final task is to put together the jigsaw. Knowing how to connect your equipment isn't just important, it's totally vital. If you don't know what connects to what, and what the ins and outs of your setup are, you can't troubleshoot when things go wrong. And things do go wrong, at the worst of times.
Eventually, you'll be showing off your DJ skills and someone may ask you to play at a party with your equipment; equipment that you connected up a year ago, with the help of your 4-year-old brother. Think of the soldier who has to assemble a gun from parts to functional in minutes; that's how comfortable you need to be when connecting together the parts of your DJ setup – except you only need to kill 'em on the dance floor. (Chapter 13 tells you all you need to know about connections.)
DJing Takes Patience and Practice
No matter what kind of DJ you are – rock, dance, party, indie, drum and bass or any of the hundreds of other genres out there – it's all about picking the right tunes to play for the people in front of you, and the transition as you mix between them.
Picking the right tunes comes with knowledge, experience and the ability to read how the people are reacting on the dance floor (check out Chapters 20 and 21 for more on this), but you can discover, develop and refine the mechanics of how to get from tune to tune through practise and dedication.
Beatmatching (adjusting the speed that two tunes play at so that their bass drum beats constantly play at the same time) is the mechanical aspect that's regarded as the core foundation of the house/trance DJ. Given enough time, patience and practice, anyone can learn the basics I describe in Chapter 14.
Many genres of music aren't so tied into the skill of beatmatching because the speeds of the various tunes mixed together vary so much it's almost impossible to do. But this doesn't mean there's no skill in rock, pop or party DJing – the music you play is a lot more important than the transition, but you still need to avoid a cacophony of noise as you mix between tunes.
After the core skills of creating the right kinds of transitions, what sets a good DJ apart from an okay DJ is his or her creativity. You need another set of building blocks to help develop this creativity. How you stack up these blocks plays a big part in determining how skilled a DJ you become:
Good sound control is the first building block of your skill and creativity. You need a good ear to gauge whether one tune is too loud during a mix, or if you have too much bass playing to the dance floor. This skill is something that develops, and you can hone it through experience, but a DJ with a good ear for sound quality is already halfway there. Chapter 16 covers sound control to create a great-sounding mix, and Chapters 19 and 21 have information about controlling the overall sound of your mix when playing live or when making demo mixes.
A knowledge of the structure of a tune is the second essential building block in your quest to becoming a creative DJ. Knowing how many bars and phrases make up larger sections of tunes is important for creating exciting mixes. In time, DJs develop a sixth sense about how a tune has been made, and what happens in it, so they don't have to rely on pieces of paper and notes to aid them with their mixes. Chapter 15 takes you through this structure step by step.
Although scratching is considered more of a stand-alone skill, you can harness this technique to add a burst of excitement and unpredictability to the mix. This is the third building block to creative DJing. Instead of letting a CD or record play at normal speed, you stop it with your hand and play a short section (called a sample) backwards and forwards to create a unique sound.
This also helps with the mechanics of using your equipment when DJing. People are taught to be scared of touching their records, or don't have the gentle touch needed to work with vinyl or a CD controller properly. Scratching soon sorts all that out, leaving no room for excuses. Your dexterity working with your tunes increases tenfold by the time you've developed even the most basic of scratch moves as described in Chapter 17.
It's all about style
Style is the true creative avenue, because it's all down to the music. The order you play your tunes in, changing keys, mixing harmonically, switching genre, increasing the tempo and creating a roller-coaster ride of power and energy are the reasons why one DJ is better than the other.
Working as a DJ
The hardest bit about performance is actually getting the chance to perform. Hundreds of people fight over every job in the entertainment industry and you need to come out on top if you want to succeed.
You need to set yourself apart from the competition and make sure that you have the skills to sell yourself. Convince club owners and promoters that you're going to be an asset to their club, and then perform on the night. Here's what you need to do:
Demo mixes are your window to the world. They're the first way to let people know what you're like as a DJ. Whether it's your friends, your boss or someone in the industry, a demo is an exhibition of your DJ skills. Only release your best work, and don't make excuses if it's not good enough. Chapter 19 has the information you need about demos.
Market yourself well. Use all the avenues I describe in Chapter 20 to get even the most basic start in a club or pub or party night.
After you've secured any kind of work, your development from beginner to DJ is only halfway through. You've spent time creating a good mix in the bedroom, but now, no matter whether you're playing Cream in Liverpool or the Jones's wedding in a town hall, you need to pull off a successful night.
Your technique may be a little weak, but if you're playing the right tunes, that can be forgiven. (That's not an excuse to skip the basics, though!) The idea is to create a set that tries to elicit emotional and physical reactions from the crowd; in other words, they dance all night and smile all night.
Consider the following (all of which I cover in more detail in Chapters 20 and 21):
Like anything new, preparation is the key to a successful night. Leave yourself with no surprises, do as much investigation as possible, research the unknown, settle any money matters and make sure that you and the management (or wedding party) are on the same musical playing field, so that all you have to worry about on the night is entertaining the crowd.
Reading the crowd is the most important skill you can develop and you may take weeks, months, even years to master the technique properly. The tells you pick up from the body language on the dance floor rival any poker player's. You look at the dance floor and instantly react to how people dance, and what their expressions are, and then compensate for a down-turn in their enjoyment or build upon it to make it a night to remember.
Because you're the main focal point of the night, you also have to be a people person. You're the representative of the club, and so need to act accordingly. One wrong word to the wrong person, one wrong tune played at the wrong time or even something as simple as appearing as if you're not enjoying yourself can rub off on the dance floor, and your job as an entertainer is on thin ice.
Above all, always remember – from the bedroom to a bar, from a town hall wedding to the main set at a huge night club in Ibiza, or playing a warm-up DJ set before a huge rock band takes the stage – you're here because you want to be a DJ. You love the music, you want to put in the time, you want to entertain people and you want to be recognised for it.
Chapter 2
Starting Up with the Bare Bones
In This Chapter
Discovering a DJ's basic equipment
Choosing your format
Getting to know the vital controls and functions
Putting an end to feedback and vibrations
Using the right furniture
You have lots of options when it comes to choosing and buying your first set of DJ equipment. The amount of money you have to spend is one factor. Any decision about using vinyl, CDs or MP3s to mix with obviously has a huge impact on what you buy, and the music and mixing style you want to adopt also plays a big part in your first DJ setup.
Consider this chapter as a shopping list of equipment you need to be a DJ. Later chapters help guide you towards the best equipment to use, and the most suitable equipment for your budget.
Making a List, Checking It Twice
As with any craft, you need to ensure that you get the right set of tools for the job. Any DJ setup consists of the following basic elements, each of which I describe later in this chapter:
Input devices: Turntables, CD decks, MP3 players and computers are the common DJ input devices. In the case of turntables and CDs, you usually need two of them.
A mixer: You use this to change the music that plays through the speakers from one input device to the other.
Headphones: These plug into the mixer so you can hear the next tune you want to play without anyone else hearing it through the speakers.
Amplifier: Without an amplifier (and speakers), the people on the dance floor won't hear any of the great music you've chosen to play.
Something to put it all on: You could sit on the floor cross-legged, with everything laid out on the carpet, but it's probably easier to build, buy or borrow some furniture.
Add to that a few metres of cabling, some understanding neighbours and a bunch of CDs, MP3s or records, and your DJ journey can begin.
Considering Input Devices
As a DJ you can choose from a wide range of input devices. Because even the most basic of DJ skills involves mixing from one tune to another without a pause in the music, this often means you need two of them:
Turntables: These play records, usually vinyl. If you're only using turntables to DJ with, you'll need two.
CD decks: These come either as individual players, or two CD players built into one box. Some only play CDs, others also play MP3 files burnt to CD (see the later section 'Musing on MP3s and PCs', and Chapters 4 and 8 for more).
DJ software on a computer: This usually has at least two windows with a player in each for controlling music stored on a hard drive.
MP3 players and MP3 gadgets: iPods and the Tonium Pacemaker spring to mind, for example. Sometimes you only need one of these, depending on the mixer you use and what the DJ gadget is.
Whatever else comes along in the future: Who knows, you may soon be able to think of music and it'll play out of your fingers . . .
Although what to use is technically your choice, depending on the genre of music you want to play, your decision may already have been made for you. Check out Chapter 5 for more on format decisions.
If you have loads of CDs and loads of records and want to mix between formats, it may seem like a good idea to just have one CD deck and one turntable and mix between them. However, this may lead to a lot of confusion, and force your hand in many mix situations. You'll have to mix from vinyl to CD, to vinyl to CD, and so on. You'll never be able to mix one CD to another, or one record to another. If you think you'll primarily be a vinyl DJ, you could gamble and buy one CD deck to go with your two turntables in the hope that you'll never want to mix from CD to CD, but that's still a risk. If you're planning on just using CDs, you may want to have a turntable that you can incorporate into your DJ setup, or use to transfer your vinyl tunes onto CD.
Thinking about turntables
Turntables are the workhorse of the DJ industry. They've been around in one form or another since the dawn of recorded music, and have played records in clubs and been a vital part of dance music since its conception. A record is a circular piece of hard but flexible vinyl with a single spiral groove cut into each side that starts on the outer edge and eventually ends up near the centre of the record. This groove contains millions of tiny bumps and variations that contain the music information.
To turn these bumps back into music, the needle (also called a stylus, with a diamond tip) sits inside this groove. You place the record on a rotating disc (called a deckplatter) so that the needle travels from any particular starting point in the groove and gradually works its way towards the centre. The bumps and variations in the groove cause the needle to vibrate and these vibrations are converted to an electrical signal, which (in a DJ setup) is sent to a mixer that converts this signal into music.
You must use the correct kind of turntable. The one that comes with your parents' hi-fi is unlikely to be suitable for DJing (unless of course your dad is Fatboy Slim). Record players on home hi-fis are meant for playing records in one direction, at a normal speed, and aren't built to deal with knocks and vibrations like a DJ turntable must.
The bare minimum requirements for a DJ's turntable are:
A variable pitch control to adjust the speed of the record (typically through a range of 8 to 12 per cent faster or slower than normal). Advanced turntables give the option of up to 100 per cent pitch change, but if this is your first turntable, that isn't a vital option right now.
A removable headshell to use different kinds of DJ-suitable needles and cartridges (see Chapter 7 for more information).
A smooth surface to the deckplatter so it will turn under the slipmat (a circular piece of felt that sits between the record and the deckplatter; see Chapter 7 for more).
Enough motor power to keep the turntable spinning under the slipmat if you hold the record stopped with your hand.
Because of their build quality and strength, the Technics 1200 and 1210 series of turntables have become the industry standard in the DJ booth, although the top-range Vestax turntables have made a considerable dent in Technics' former monopoly. However, even second-hand Technics and Vestax decks are expensive pieces of kit, so fortunately for the DJ on a budget, DJ turntables by other manufacturers emulate this classic design, such as the Gemini TT02 shown in Figure 2-1.
The advantages of this familiar design are the layout of controls and the position and size of the pitch control. The long pitch control running down the right-hand side of the turntable enables the DJ to be a lot more precise when setting the playing speed for the record. Some of the really cheap turntables on the market have very small pitch sliders or knobs, making it harder to change the pitch by the minute amounts sometimes necessary.
Although the manufacturers have added features, rounded corners and improved upon designs, this basic design in Figure 2-1 is one you come across most often when choosing a DJ turntable – all around the world. (Chapter 6 has a lot more detail about turntables and their various features including different styles of turntable motor, and how the torque (power) of the motor can help or hinder your mixing capabilities.)
**Figure 2-1:** The Gemini TT02 turntable.
Deciding on CD decks
Once upon a time you could only play a CD at normal speed, and you had to place your CD players on cotton wool to prevent vibrations making the CD skip. As for starting a CD at the right time, from the right place? Hit and hope was a common mantra when CDs first came out.
Fortunately for everyone, the design and technology of CD decks for DJ use has improved immensely over the years.
As with turntables (see the preceding section), when choosing your CD decks try to avoid standard domestic CD players that you use with a hi-fi or portable, personal CD players. Even if you're a rock, indie or party DJ who isn't planning to beatmatch, where you need to change the speed of the music using a pitch control (see Chapter 14 for more on beatmatching), DJ CD decks are a lot easier to control and can take a lot more abuse and vibration than a typical home CD player.
CD decks designed for DJs should include the following vital functions:
Pitch control (the same as with turntables, having a range of at least 8 per cent faster or slower than normal).
A set of controls that lets you easily find the song or part of the song you want to play. These controls are either buttons that skip through the CD, or a jog wheel, which turns clockwise and anti-clockwise to skip through the CD with more precision.
A time display that you don't have to squint at to read (especially in the dark!).
Optional basic controls that I strongly suggest include:
Pitch bend (to temporarily speed up or slow down the CD without using the pitch control).
An anti-skip function built into the CD player (which prevents the CD from skipping from all the bass vibrations in a loud environment).
Ability to play CD-RW discs (rewritable CDs that you can write to and erase a number of times) and MP3 discs (see the next section).
The pitch bend feature isn't necessarily vital on beginners' CD decks, but without it, you'll face a lot of difficulty if you're beatmatching. And without anti-skip, you have to be careful not to bump your decks or set the bass in the music too high because the CD will most likely skip. There's sometimes a familiar, 'retro cool' sound when a record jumps, but when a CD skips, you want to hit the decks with a hammer!
Even though most home CD players can play CD-R (recordable on once only) and CD-RW discs, basic DJ CD decks may not have that feature. With the Internet giving access to a lot of rare music, you'll want your CD decks to play burnt CDs without skipping.
Chapter 8 has detailed descriptions of CD deck functions, and how to use them.
Musing on MP3s and PCs
MP3s are computer music files that have been compressed (reduced in size) but still retain most of the original sound quality. This makes them easy to download and send over the Internet, and they take up very little storage space on computer hard discs and personal MP3 players, like iPods (a popular MP3 player).
To give you an idea of how this compression helps, my iPod is only 60 gigabytes in size, but it contains enough music that I wouldn't hear the same tune play for six weeks! I'd need over 800 CDs to hold the same amount of music.
As MP3s start off as computer files, you have a few different ways to utilise them:
Create traditional CDs. You can burn MP3s to a CD and play in the same way as a traditional CD that plays on any CD player. You can only fit 74 minutes of music on one CD using this method. Most CD-burning software has a setting that can automatically convert MP3s so that you can burn them as traditional CDs.
Make MP3 CDs. By keeping the music compressed in MP3 format, you can fit a lot more tunes on one CD. Depending on the length and bit rate of each of the tunes, you should be able to fit over 100 tunes on one CD. MP3 CDs have the added bonus of letting you sort the music into folders, which can help when trying to find 1 tune out of 100.
These MP3 CDs won't play on every CD player or DJ CD deck, though. Be sure to check when buying your equipment if you're planning on using MP3 CDs. DJ CD decks that play MP3 CDs are normally identical in design and layout to CD decks that won't play MP3s; you just have to pay a little more for them.
Use hard-drives. Lots of CD decks such as the Denon DNHS5500 or the Pioneer CDJ400 and CDJ2000 let you bypass the need to burn CDs, and enable you to connect external hard-drives via USB (Universal Serial Bus) containing all your music files. Some have internal hard-drives too, but connecting external drives is a more versatile way to manage and work with your tunes. These decks normally have comprehensive menu systems to help you find the right track quickly.
Use software. Digital DJing has swept through the DJ community, allowing DJs to store thousands of music files on computers and use a variety of methods to control DJing software to play back and mix the music together.
The advantage of using a computer to mix is that the software normally contains the entire DJ mixing package. In a series of windows, or one well-designed window, the software gives the user at least two input players on screen and a mixer. So all you need is a lot of music files and your PC's soundcard connected to an amplifier, and you're a DJ! Digital DJing can get a lot more complicated though; Chapter 9 covers the various options.
Try out DJ toys and gadgets. Many DJ toys and gadgets are available that move DJing away from the DJ booth and into the palm of your hand. Products like the Tonium Pacemaker, the Nextbeat and even an app for your iPhone let you mix music wherever you are. These gadgets tend to use MP3s because of file sizes, but the products with bigger, internal hard-drives let you mix uncompressed, CD-quality tunes if that's your desire. Chapter 9 describes these toys and gadgets in more detail.
Mixing It Up with Mixers
The mixer is the glue that keeps the night running smoothly, and the dancers dancing without falling over. The purpose of the mixer is to change the music that you hear through the speakers from one input to another without any gaps. Chapter 10 contains more information on everything to do with mixers.
The most basic features a mixer must have for DJ use are:
A cross-fader: On most DJ mixers the important control that helps to change the sound from one input to another is the cross-fader. As you move the cross-fader from left to right (or reverse), the sound you hear through the speakers gradually changes from one deck to the other. If you leave the cross-fader in the middle, you hear both songs playing at the same time. How you change the music from one song to the other is a massive part of how you're regarded as a DJ.
At least two input channels: Each should have a switch to select a phono input (for turntables) or a line input (for everything else).
Headphone monitoring with Pre Fade Listen (PFL): PFL (or cue) lets you hear the music through the headphones without it playing through the speakers. This is important when you want to find the right start point for the next tune, and is vital when you're beatmatching.
LED indicators: These display the sound level coming into and going out of the mixer.
Gain controls: You use these in conjunction with the input LED indicators. They're extremely important for keeping the overall volume of the mix smooth, creating a professional sound to the mix.
EQs (equalisers) for the bass, mid and high sound frequencies: These three simple controls help you add creativity, and improve the sound quality of the mix, transforming lacklustre transitions from one tune to another into great-sounding, seamless ones.
Budget mixers (around £50) aren't likely to have EQ controls. These aren't 100 per cent necessary if you're a party DJ who doesn't create long, overlapping mixes, but for the sake of around £30 more, you can find a mixer that has everything I recommend at an affordable price range from manufactures like Numark, Stanton and Behringer.
With these functions you have a lot of control over your mixes and can go a long way towards sounding like a pro. A whole range of features and functions can help you adjust and improve your mixes, but they aren't as vital as the six I describe in the preceding list.
Monitoring Your Music with Headphones
Don't underestimate the importance of a really good set of headphones. When you're in the middle of a noisy DJ booth, your headphones are the only way to ensure that the mix is as smooth as your hairstyle.
Though not a major factor when practising DJing in your bedroom, in the live arena using clear headphones that don't distort when you turn them up really loud is extremely important. If you can't easily and clearly hear the records you're playing now and want to play next, your mix has the potential to go really wrong, really quickly!
When choosing a good starter set of DJ headphones, concentrate on comfort and sound. Make sure they're soft and nice to wear, and that when you use them you can hear a good bass thump and the high frequencies are clear. If you get a chance to test them at quite a loud volume, carefully do so (you don't want to damage them, or your ears), just to make sure that they don't distort or that the mid-range frequencies don't drown out the bass beats.
If you choose to buy budget headphones so you can afford better turntables, I strongly recommend that you spend your first DJ pay cheque on a good pair of DJ-specific headphones – you'll only encounter problems with poor headphones and may not get any more pay cheques! Check out Chapter 11 for loads more about headphones.
Powering Things Up with Amplifiers
The sound signal that comes out of the mixer is barely strong enough to power your headphones, so you need something to increase (amplify) this signal so that it drives some speakers (makes 'em work). You can amplify your music in four different ways (Chapter 12 has more on these options):
Buy a separate amplifier and speakers. This choice can be a bit costly, but it's a great way of doing it.
Plug the mixer's output cable into the CD or AUX port in the back of your home stereo (if you have one). I prefer this method at home when starting off, because it cuts down on the amount of equipment you need – and money you have to spend – and it means that you may already have a built-in tape or MiniDisc recorder to record your mixes.
Use powered speakers – speakers that contain a built-in amplifier. Provided that they're sufficiently powerful to let you hear the music loud enough, they'll suffice.
For professional use, my preference is a great monitor by JBL (which DJs use in booths a lot).
Use the speakers on your Mac or PC, which are often powered speakers, like the previous option. Instead of connecting the speakers directly to the mixer, you can connect your mixer to a computer's soundcard first. This method has the added bonus of being able to record to your computer anytime, for easy uploading of your mixes to the Internet.
Figuring Out the Furniture
Furniture is probably the most overlooked and least thought about aspect of your DJ setup. Some people spend weeks researching the best decks and mixer to buy and completely forget that in the end they need something to put them on.
Two items of furniture for you to consider are:
Something to put your decks and mixer on
Somewhere to keep your records and discs
Considering ergonomics and stability
When looking for a DJ desk, you need something that's solid enough so the needle doesn't jump or the CD doesn't skip when your cat breathes on it. Even more important is the height level of your decks and mixer.
If you need to bend down to use your equipment, you'll end up like the Hunchback of Notre Dame after all the hours of practice you'll be putting in. So make sure that your equipment is at a height that enables you to practise with your body erect and your shoulders back, in line with your spine. I have a great friendship with Dr Dan, my chiropractor, due to years of not following my own advice!
Correct ergonomics for any desk (and that includes a DJ 'desk') are that you don't need to reach, stretch or bend to use the equipment. Ideally, you want to stand tall, with your shoulders back and your elbows at 90 degrees when DJing. Protect your neck, too, by looking down at the controls rather than craning your neck downwards like a goose!
Although everybody's height is different, these ergonomic principles mean that if you're using something like a computer desk, you probably need to find some bricks or a couple of breezeblocks to raise your decks up to a comfortable height.
Selecting store-bought stands
A few desk units are specifically designed for DJ use, with an adjustable height, a flat top for your decks and mixer, and some big cabinets underneath to keep your records in. My concern with keeping everything in the same unit is that if you're flopping all your records around in the cabinet when trying to find a tune, moving 50 records from left to right creates a hell of a wallop, and is likely to skip the needle.
Check out any online DJ store (and eBay), and you find a great range of DJ desks and stands. Nearly all of them are flat-pack so you need to assemble them yourself – make sure you pack some patience with your screwdriver!
I've found that the king of the flat-pack, IKEA, do a great unit (in the 'Billy' range; see www.ikea.co.uk) that your decks can fit on/in – the only problem is that the shelves would never take the weight of 2,000 tunes. Hard plastic shelving from DIY stores can step in to hold your CDs and records, but make sure the unit is level, and store your records so that the opening is against a wall. I had a terrible accident with Timo Maas's Ubik when it dropped out of its sleeve because of a wonky shelving unit – let's just say it's half the record it used to be . . .
I've gone through a few different setups. My first was to have everything on an ironing table, which was very precarious! Then I used a big unit that my dad had built in the 1970s, but I now use a bespoke desk I built myself. My decks and mixer are 'Recessed' inside the top section, and my CD decks and laptop are held up with dedicated stands bought on eBay. (My website, www.recess.co.uk, has photos and guidance on how to build such a desk.)
Killing vibration with bricks and air
Another point to consider with your furniture is how to minimise vibrations. CD decks that don't have good anti-skip can stop playing properly if something bumps into them, or if way too much bass vibration travels from the speakers, through the desk and onto the CD deck. As a vinyl DJ, although there's a good chance your needles will skip if you bump into your desk, the main concern with speaker vibrations is feedback, or howl round.
The purpose of the needle is to translate vibrations from the record groove into sound. Feedback happens when the sound from your speakers reaches the turntable (through sound vibrations), and is re-amplified – which reaches the turntable, and is re-amplified. This re-amplification creates a snowball effect (a re-re-re-re-re-amplification), creating a ringing noise that rapidly gets louder and louder, which is known as feedback. It hurts your ears and your speakers, so try to avoid it.
Whether you're a CD or vinyl DJ, avoid putting speakers on the same unit that your decks are on. If you can't avoid that arrangement, try to minimise the vibrations by sitting decks on something that absorbs the vibration. As in many bedrooms of budding DJs across the world, I used to sit my decks on top of bricks for this purpose.
If you're looking for a classier way of doing the same thing, you can use specially designed 'feet' for your turntables. Made out of metal, they replace the normal rubber feet that are on each corner of the turntable to absorb vibrations more effectively than a brick can. These Isolator feet can be quite expensive (around £90 for four). A fantastic alternative if you can afford £30 is the Freefloat 'cushion' that you sit the decks on top of (Figure 2-2 shows the Freefloat deck stabiliser). This cushion not only stabilises the decks, but has the added advantage of looking a lot better than some bricks 'borrowed' from a building site!
**Figure 2-2:** The Freefloat deck stabiliser.
Locating Your DJ Setup
Where you set up your decks in the bedroom has probably already been decided by the current position of your bed and television, but if you have loads of space to tinker with and can consider positioning yourself anywhere in the room then the main factor is to stay near to your speakers. Chapter 12 has a section on positioning your monitors, but as long as you're within a few feet of the speakers, you don't have to worry about audio delay or acoustic problems.
One thing that's always amazed me is that some DJs feel the need to set up their decks so that they're facing a wall. Try turning everything around so that you're looking out across the room. This positioning helps with visualisation, when you start to imagine yourself playing in a big club, but it also looks a lot more impressive when your mates come to see you show off your skills. You need to keep the cables tidy so they're not all hanging off the back of the desk, but this aspect gives you a much better feel of being in the DJ booth.
Chapter 3
Shopping for Equipment
In This Chapter
Trying out the right gear for you, and sticking to your budget
Making the choice between high street and the Internet
Choosing to buy new versus second-hand
Checking that your kit works properly
You've soul searched, and you've read ample magazines (and books, I hope!) and browsed enough websites to last you a lifetime on the subject, so now you're ready to take the plunge into buying equipment.
Buying equipment used to be straightforward. Your choice was limited to one specialist shop, a bit out of town, that would sell DJ gear. The guy running it would be a bit shifty, and you'd leave feeling ripped off and dirty.
The situation has now changed. With so much competition in the DJ equipment market, stores can't afford to put off the buyer, and with attractive package deals, free postage and good support, the days of the prickly, aloof salesman are long gone.
Taking Stock Before You Shop
Speaking from my own personal experience, people who have a dream don't want to listen to advice from others telling them to think carefully before spending their money. And if you feel as excited as I did when I got my first DJ setup, then I may not be able to convince you that doing so is important – but I'll try. Before you take the padlock off your piggy bank, do one last piece of investigation.
Trying before you buy
The first thing to consider is: are you ready to spend money on your dream? You're likely to be investing a lot of money into something that you don't know you'll be any good at (though by the time you've finished this book, you'll be great). So before you consider opening your wallet to buy your dream setup, try to find out whether you can go anywhere to use some DJ equipment first, or download a demo version of DJ software and have a play with that, so you can get used to the basics of DJing.
Ideally, you want to use the setup of a friend who has a couple of turntables and CD decks, a digital DJ setup and loads of records, CDs and MP3s ready for you to rifle through and have fun with. You'll get an idea of the equipment you need and how it works, but more importantly, you'll probably develop an affinity for one medium or another, which is a lot of help when choosing between CD and vinyl or whether to go digital. Your friend may not have this perfect setup though, so ask around and find out whether any other DJs you know will let you try out their kit too.
The friendlier DJ equipment stores let you demo some of their equipment if you look as if you're going to buy it, but not many of them have a room in the back with a full DJ setup for you to try out your skills. By all means ask the store for a prolonged demo, but don't hold your breath.
A big advantage when using other people's equipment, or a 30 day demo of DJing software, is that you'll have more time to save up for your dream setup. When you're happy that you know what you want and are bursting to buy, now's the time to blow the dust off your wallet or purse and go shopping.
Budgeting your money
How much money you have and how you spend it vastly alters the choice of equipment available for you to buy, including whether you opt for new or second-hand.
Have a realistic budget. You're not going to get good DJ equipment for £50 unless you know someone who needs to sell quickly. DJing isn't a bargain basement pursuit; set aside as much as you can and avoid going for the cheapest deal out there. Remember the saying 'Buy cheap – buy twice' when it comes to this kind of thing because if you get really cheap, unsuitable equipment now, you'll need to buy better equipment in a few months' time when you get better at DJing. Save yourself money by only shopping once for your DJ setup.
If you do have a very small budget to work with, the best way to make it work for you is to split it into two chunks: one large chunk for your turntables or CD decks (if they're the format route you're taking) and a smaller chunk for your mixer. It's more sensible to spend as much as you can on your input devices because even the best mixer in the world can't fix CD decks that skip, or turntables that don't hold a constant speed when playing. A basic mixer may be very basic, but is still sufficient when you're developing your initial skills as a DJ, and even if you do have to 'buy twice' for your mixer, it's far cheaper to upgrade the mixer than it is to upgrade two terrible turntables or CD decks.
A wide range of equipment is on the market, and I highlight a few popular manufacturers in this section, but of course they're not the only ones out there. Each budget level covers some broad options available to you when buying brand new turntables or CD decks. Remember, you'll still need to buy a mixer, no matter how basic.
£200+: You can buy a very basic mixer and a basic set of turntables or CD decks within this budget. If you have only £200, I believe that your best option is to pick up basic Numark, Stanton or Gemini direct drive turntables or CD decks second-hand. You can discover how to mix on these decks, but if they're very basic and have had a lot of use they may not be the most reliable decks in the world, meaning that they may eventually hold back your progress.
£400+: For around £400 you can get new, intermediate level turntables or CD decks. CD decks in this price bracket come with a better range of functions than the basic models, and you get a more reliable, stronger motor if you buy turntables. You won't have much money left after the decks, though, so you may still have to buy a very basic mixer.
£800+: By the time you've got £800 to spend on your DJ setup, I hope that you took my advice about trying out DJing on someone else's equipment first! That said, you can get some intermediate level turntables/CD decks and a good mixer for £800 or my preference of top level decks like Technics 1210 turntables or Numark's high-end range of turntables, or good Pioneer, Stanton or Vestax CD decks. Along with these, you should be able to afford a slightly better than basic mixer.
£1,500+: Budgets that stretch to £1,500+ open up the world to you. I prefer the top of the range turntables or CD decks from Vestax, Pioneer and Denon, which can cost between £700 and £3,000 for two. And my choice of mixers are by Pioneer, Rane and Allen & Heath, which cost between £500 and £1,500.
If you're about to spend six months' worth of hard-saved money on equipment, make sure you've got some left to spend on all the records and CDs you want to play on them. I spent about £40 per month on records when I first started DJing, but that soon ballooned to hundreds, so consider how this new hobby can affect the rest of your lifestyle.
Crossing over with digital DJing
If you're considering choosing a digital setup where you use a hardware controller or turntables, CD decks and a mixer to play and mix music on a computer, the previous budget considerations are just as important.
Not even counting budgeting for a computer/laptop if you don't already have one, you also need to set aside a large chunk of your budget to buy your chosen software title. This can range from £70 to £200 for the software, £200 to £500 if audio interfaces and control CDs and vinyl are on your shopping list, and well into the thousands if you're buying hardware controllers like the Allen & Heath Xone 4D.
Chapter 9 has more information about digital DJing and some of the different solutions to let you mix music with computers.
Buying Brand New
Buying your decks and mixer brand new has many advantages. As well as having the choice of the latest, greatest gear, your equipment comes to you untouched and working perfectly. If any problems crop up, the stores should replace faulty kit, and if your equipment fails after the end of their returns policy, you have the backup of a manufacturer's warranty to sort out anything that goes wrong. Not that anything ever goes wrong, of course . . .
The obvious downside to buying your DJ gear new is the price. But with high-street stores and online stores competing with each other, driving prices ever lower, if you hunt long enough and are patient you can find some great deals.
Resale value is the other downside to buying new. Consider a pair of Technics 1210 MkII turntables. Brand new, they cost around £700, but second-hand, you can find them for £400 or less, which is a considerable loss (but a bargain if you're the buyer!).
Cruising the high street
As DJing has become more popular, DJ shops have smartened up their stores and selling styles. Most cities now have at least one place that sells DJ equipment, and if you're in a large city you can find a few of them, all competing for your money.
Try before you buy and cry
I learnt a hard lesson regarding not trying before buying, and not paying enough attention to a magazine review. I was trying to choose between two very popular mixers and had read that although one of them had better features, the controls weren't laid out very well and were difficult to use (especially in the dark) because they were crammed too close together. I stood in the shop staring at both of the mixers, and didn't have the sense (or this book) to think to ask to try them both (even just to twiddle the knobs). I bought the more expensive, better featured one, of course, and assumed that the guy in the magazine must have fat hands.
The first time I accidentally hit the wrong switch the magazine review came crashing back into my mind! There's nothing like the silence of accidentally switching over to the line input to make you really regret some choices.
A high-street store offers three things you won't get anywhere else:
The chance to use a range of different equipment. The ability for you to have even a quick demo on the equipment in the shop sets local stores apart from online stores, and gives you the chance to compare many different pieces of kit.
You may have read in magazines and books that one style of turntable is better than another, or that single CD decks are better than twin units, but until you're able to stand in front of them, touch them and use them, you won't be certain yourself. Second guessing your choice after spending a whole load of cash on your kit based only on a review isn't ideal.
The personal touch of being able to ask a sales rep questions. There's no doubt about it, getting face-to-face, immediate advice from someone and being able to hold a conversation about what you want is extremely helpful when you're buying equipment. The guys or gals you're talking to at your local DJ store have sold a lot of kit in their time and typically really know their stuff.
Immediate gratification. I don't know if having immediate gratification is important to you, but it sure is for me. If I buy something as expensive as DJ equipment, I want it now. I want to be able to take it away with me and use it as soon as I get home. If the piece of equipment I want is only a small amount extra in a shop, and if I'm really jazzed about getting it, I'd much rather go into a shop, buy it and take it home there and then, than have to sit at home the next day hoping that every car that drives past the house is the delivery dude.
Opting for online shopping
Whether you use a high street shop that also sells online or an online reseller that doesn't actually hold any stock, you can expect dramatic price drops from online stores. With so many websites trying to get your business, a bit of patience and comparison can save you money.
Most sites have fantastic customer support and are really good at answering customers' questions via email. However, the drawback to online shopping is that you can't have a face-to-face conversation and get answers immediately to your myriad questions. Although some websites offer live web-chat or telephone assistance to try to get around this hurdle, they can't compete with you being able to walk around a store with a salesperson.
Ironically, even though an Internet store can seem faceless and anonymous, their after-sales customer service is usually as good, if not better, than high-street stores. An online shop is only as good as its reputation, and when shoppers start writing bad things, other people listen. The DJ community is a tight-knit one, and online stores need to avoid causing ill feelings, word of which can then spread like wildfire.
In addition to great customer service and attractive prices, Internet stores enable you to build your own package in an attempt to lure you away from high-street stores. A package is where the store offers you the turntables (or CD decks) and a mixer together at a reduced price. High-street shops typically can't mix-and-match packages quite so freely due to stock limitations. They can order other equipment in for you, but if you have to wait anyway, you may as well go online and get it cheaper!
Whether they physically hold the stock or not, Internet stores have access to every piece of kit available, which opens up the possibility to get any combination of turntables or CD decks and mixer you can think of. With access to an equally large range of headphones, amplifiers, cables, needles and so on, the choice and price you can get online, if you already know what you want to buy, is really attractive.
A number of manufacturers sell their own combinations of decks and mixer and aim them at beginner DJs. These can be convenient ways to buy basic kit on a small budget, but the downside to these packages is that you may outgrow the very basic equipment when your DJ skills demand more functions to help you work with the music. The safest option is to arm yourself with research and build your own package.
Many people are going into the high-street DJ store and asking all the right questions, finding out the best equipment for their use and then buying it all online through a cheaper store. No rule prevents this, just morals and a little dent in your karma. And if your local high-street store goes out of business, who are you going to talk to then?
Buying Second-hand
The advantage of buying your DJ gear second-hand is that you get a better standard of equipment for your money. Rather than needing to buy a basic set of decks and mixer brand new, you can afford a better set second-hand.
The disadvantage is that you don't know how well the person selling the kit has treated it. You can find some key things to look out for when buying second-hand later in the later section 'Making Sure That Your Kit Works', because you can never be too sure that the turntables haven't spent the last ten years of their use being drowned in beer and cigarette ash!
You can use three different places to source your second-hand equipment:
Auction websites
Classified adverts in newspapers, shop windows and online
Second hand and pawn shops
Bidding on auction websites
Auction sites like eBay are a great way to find a bargain, and the seller/buyer rating system gives you a relatively safe way to buy (or sell) your equipment. You need a little patience, but as long as you know what you want before you start looking, you can find some great deals.
When buying on an Internet auction site, you can be forgiven for worrying about two basic things:
The seller won't send the goods to you after you've paid.
The seller hasn't been accurate in the item description.
Looking at the feedback rating of a seller gives you an idea of whether you need to worry about not receiving your goods after payment. Take time to check out what previous buyers have written about a seller, and if you're not convinced that the seller has sold enough to warrant you dealing with him or her, be extremely cautious before handing over a whole load of cash!
Don't feel bad about emailing the seller to ask any questions that aren't covered in the item's description. Ask him or her to confirm the working order of the equipment, its general condition and whether they're prepared to accept responsibility for items that don't work correctly upon arrival with you. In the unlikely event of the seller 'bending the truth' with the item description, email evidence proves invaluable if you need to make an official complaint about the seller to the auction site.
The last point you need to consider when ordering anything from online auction sites is the postage and packaging costs. Two decks and a mixer need a lot of protection to survive being loaded into the back of a van in a cardboard box. You may think the postage costs are quite high, but the mountains of bubble wrap and foam required may be inflating the costs of carriage. Some sellers may try to make extra money by boosting the price of postage, though, so if you suspect anyone of attempting this practice on you, send a quick email asking the seller to include a receipt for the cost of postage.
Scanning newspapers
Newspaper classified sections have been hit pretty hard by auction websites over recent years, with people entering less items for sale. Fortunately, because not as many people look at newspaper second-hand sections any more, there's less of a chance that someone else spots and buys your dream DJ setup before you do. Also, because people normally sell items in newspapers at a fixed price or a 'nearest offer', you can secure the item immediately, rather than entering a bidding war!
Items sold in the classified section of a newspaper or shop window are probably quite local to you too. You can save a little money by picking up what you're buying rather than paying for postage, and you can take a look at the equipment first and see it working before handing over your money.
I'm getting all grown-up on you now, to warn you about the dangers of going to strangers' houses – be careful. Always let someone know where you're going, and try to take someone with you just in case the seller starts to raise the price, which can make the situation confrontational and even aggressive.
Internet classified websites like Craigslist and Gumtree offer a combination of the fixed price nature of a newspaper classified and the ability to search the entire country (or world) for someone selling a specific piece of kit. Caution still needs to be your watchword when buying something through these websites. Make sure what you pay for is what gets delivered to you!
Dipping into second-hand and pawn shops
Take advantage of people (sadly, DJs) who've fallen on hard times and go looking in a second-hand shop or a pawn shop. Over the past ten years a new wave of second-hand stores have appeared that have transformed the traditional murky pawn shop into a modern shop that rivals many high-street stores. They often have better displays, a large selection to choose from and a few even have expert salespeople who can help you with any questions you have.
Some second-hand shops aren't set up for you to check out the equipment before you buy, but I strongly suggest that you request to see as much of the equipment in working order as possible. I went to buy a mixer from a pawn shop once, and asked to see it working before I paid for it. They plugged it in, turned it on and a plume of smoke came out the back. So I went somewhere else, quickly.
Making Sure That Your Kit Works
If you're given the opportunity to try out the equipment before buying second-hand, try to be as thorough as possible, testing and checking all moving parts and any controls known to be vulnerable to malfunction.
Listen to the voice inside your head; your first impressions are nearly always correct. If you look at the equipment and can see that it's been well kept in a clean environment, chances are you'll find no problems. If it's dirty, dented and scraped, and been kept in the damp basement of a messy teenager, give the equipment a thorough test, as I describe in the following sections, before you part with your cash! (Rubber gloves are optional . . .)
Checking cables
Wiggle all cables and check all connections. On turntables, mixers, amplifiers and headphones make sure that you move the cables around and listen out for connection problems. You'll know if you have a problem because you'll hear crackling sounds or the music will cut out entirely for a moment.
Testing turntables
Here's how to test a turntable:
1. The first thing to check out on a turntable is the accuracy of the motor. (Chapter 6 covers everything you need to know about the workings of turntables.) The red light that shines onto the dots on the side of the turntable platter is a strobe light and helps you to check whether the motor fluctuates in speed when it's playing (see Figure 3-1). To test this, set the pitch control to 0, and look at how the dots on the side of the turntable move.
**Figure 3-1:** The power switch on a turntable, with the strobe light underneath it shining onto the calibration dots on the deckplatter.
At 0 pitch on Technics decks, for example, the row of dots second from the bottom should appear completely stationary; at +6 per cent, the top row of dots should appear stationary. If the dots move a little, you may be able to adjust the motor to fix this. If the dots move erratically, speeding up, then slowing down and then going in the opposite direction, the motor has a major problem.
2. Assuming that you're happy with the motor at the four calibration speeds (shown in Figure 3-1, next to the control: –3.3, 0, +3.3, and +6 per cent), start to move the pitch control smoothly from 0 pitch into the + (faster) region. As you increase the pitch, the second row of dots on the side of the turntable start to move from right to left, and as you increase the pitch fader even more, the dots start to move faster and faster. This change in the dots should indicate a smooth increase in speed; if the increase is erratic, something's wrong with the pitch control or the motor. Repeat this method for the slower pitch region.
3. As you check how the pitch control affects the speed of the turntable, try to notice how the fader feels as you move it. If it's sticking in places and is hard to move (apart from 0 pitch, where it clicks into place), the pitch fader is probably really dirty. You can buy degreaser spray that cleans out dirty faders, but start to ask questions about how well the owner maintained the turntable and why the kit is in such a state of disrepair.
4. The last thing to check on the motor is that the 45 and 33 buttons do their job. A few people have forgotten to check this, only to get the deck home and find that the turntable only plays at 45 no matter how hard they hit the 33 button with a hammer.
5. If you have the time, lift off the deckplatter (the bit that turns around with the record on it) so you can take a look underneath. If that area is really dirty then you may find that the motor is dirty too. Ask whether you can unscrew the cover and take a look at the motor if this is the case – although you may annoy the person who's selling the turntable with this rather invasive request.
6. Take a look at the deckplatter while you've got it in your hands, and make sure that it's not warped or bent. Place it on a flat surface to check that the platter makes contact with the surface all the way round. If (heaven forbid) you're looking at belt-driven decks, take a look at the belt too, which is located under the deckplatter. Check carefully for signs of stretching or damage. Belts are easily replaceable and don't cost much, but damage and wear indicates that the turntable has had a lot of use over time.
7. Finally, examine the tonearm (the arm that holds the needle over the record). The biggest problem you may find is a wobbly tonearm assembly. If the seller is a chatty chappy, you may have already found out how he used the decks. If the seller used them in clubs and took them to the clubs in cases, be extra vigilant when checking the tonearm. Though a turntable case is a nice sturdy item, it doesn't actually offer much protection for the tonearm, which is the most delicate part of the turntable.
You have two basic ways to check the tonearm for damage. In both cases, if the tonearm has a height adjustment control, make sure that it's locked (see Chapter 6 if you want to know more about the height adjustment feature):
• Wiggle it. Be very gentle, but try moving the assembly. Does it move while you wiggle it? If it does, it's likely to be damaged.
• Float the tonearm. This method is the more precise way to check for damage to the bearings in the tonearm assembly. You may want to remove the needle from the cartridge, just in case you get this bit wrong; even better, ask whoever you're buying from to do this check.
With the antiskate control (used to cancel out the pull of the tone-arm towards the centre of the record) set to 0, turn the counterweight (the weight on the back of the tonearm) so that the tone-arm floats in mid air. (For more information on how to do this check out Chapter 6.)
Move the tonearm toward the middle of the record and once there start to increase the antiskate control. As you increase the antiskate, the tone-arm should start to move back toward its resting place. If it doesn't move, or if it jams in one place, the tonearm assembly is likely to have serious and expensive problems.
If the turntable's tonearm fails either test, run for the hills. The repair job for this fault is very expensive and troublesome, and not one you should undertake yourself.
8. While you're looking at the tonearm, have a quick peek at the needle and cartridge. You can replace needles, but you may not want to pay for a new one so soon, so if it's bent or squashed, ask for a little money off the price. On the cartridge, look at the wires that connect into the headshell. Check for signs of corrosion or loose connections.
If you're willing to buy decks that have been quite heavily used, you may want to think about getting them serviced. A good technician can usually get everything back to normal again, but that comes at a price, so be warned that the cost of repair added to the cost of the turntable may just cost the same as a brand new turntable!
Vetting CD decks
Checking how the pitch control affects the playback speed on CD decks is harder than on a turntable, because you don't have a visual reference like the strobe light on a turntable. However, CD decks don't tend to suffer from the same motor problems as turntables, so you really only need to check that the pitch control and pitch bend functions work properly and are free of dirt.
Here are a few tips for checking out CD decks:
Make sure that the pitch control increases and decreases the speed of the tune in a constant, smooth way and that the pitch bend buttons temporarily change the pitch when you press them, and the pitch of the tune returns quickly to the set pitch when you release the buttons.
Try to use every function on the CD unit. If you researched the CD deck well enough before choosing to buy it, you probably know what functions to expect. To be on the safe side, bring a checklist for that particular model and make sure that the functions all work.
Inspect the CD loading system. If the CD deck loads with a tray, make sure that it's not bent, that no bits are missing and that it goes in and out smoothly. If the CD slots directly into the deck, try inserting a CD a few times and make sure that the deck doesn't spit your CD back at you. (Although, maybe it just doesn't like the music you're playing . . .) If the CD deck uses a top-loading method to accept the CD, make sure that the deck closes properly, and as with the other loading methods ensure that the CD plays properly when it's in there!
If the CD deck has a good antiskip function (which prevents the CD from skipping when there are a lot of vibrations), get a demonstration of that working properly. Ask the seller to do this demo, rather than thumping the deck with your fist a couple of times or throwing it across the room. Make sure that you're satisfied with the antiskip, and that it does actually prevent the CD from skipping when faced with vibrations.
Monitoring mixers
Make sure that you get a chance to see the mixer turned on and in action – you don't want to get it home and see smoke pouring out of it! (Turn to Chapter 10 for more on mixers.)
Before you play anything through the mixer, connect the turntables/CD decks to the mixer and listen. If you can hear any kind of electrical hum from the equipment or through the speakers, turn off the decks so only the mixer is on, and if you can still hear a loud hum, check the connections (especially the earth connection) for any problems. The noise may be a harmless operational hum given off by the mixer, but if you're not convinced that this sound's good, it probably isn't harmless!
After you've listened to the mixer with nothing playing through it, put on a record/CD and check that all the controls do what they're supposed to. The master level, the gain control, the EQs, the channel faders, the cross fader, the booth controls and effects section; absolutely everything needs to be checked for each channel on the mixer. Listen for any signal (sound) dropout or any crackling sounds as you turn knobs and move faders.
When checking the faders, pay particular attention to the cross-fader. The cross-fader should have a smooth fluid motion from one side to the other, and you need to check for faults in the fader's control of the audio.
The first thing to listen for is any crackling as you move the fader from one side to the other, but more importantly, listen for any music bleeding in from the other channel. If you're playing music into channel 1, and nothing is playing on channel 2, move the cross-fader over to channel 2, where you'd expect it to be silent. If you can still hear channel 1 playing faintly while you should have silence, you've got a problem with the cross-fader.
Depending on the mixer you're looking at, you may still want to buy it if the mixer has a user-replaceable cross-fader. Ask the seller to knock off some money so you can buy a new one. A worn cross-fader may be a sign of extensive wear and tear to the mixer, but then again, it may just be a worn cross-fader after months of use by a scratch DJ. Go with your instincts.
If you have headphones and a microphone available, try them out with the mixer. Wiggle the cables of the headphones and microphone while they're plugged in and listen for any loose connections causing the signal to cut out.
Use all the headphone cue controls, making sure that you get a good, clear sound from each channel, and if the headphone section includes a headphone mix or split cue, test them to make sure that you don't have signal cut out here either. Plug in the microphone and check that the controls and the inputs are clear of any crackles, and if the mixer has a talk-over function, which dips the level (volume) of the music so you can be heard talking over it, be sure that it works properly.
For mixer outputs you'll probably see a Master Out, a Record Out and, if you're looking at a good mixer, a Booth Out or Zone Out. Test all three of the outputs through the amplifier, and make sure that no breaks in signal occur when you wiggle the wires.
Don't overlook the Line/Phono switches when checking out a second-hand mixer. Ensure that the switch from Line to Phono for each channel works without crackling, and check for silence when you switch to either Line or Phono when they don't have an input. For example, if you have turntables plugged into the mixer, when you switch to Line, make sure that you can't still hear the turntable playing.
If the mixer has any of the other features that I mention in Chapter 10, such as BPM counters, cross-fader curve adjusts, punch buttons or hamster switches, check that they all work too.
Assessing headphones
If the gear you're buying includes headphones, listen carefully to them at varying volumes. Move the cable around to make sure you don't hear any breaks in the signal, and check the connection of the cable to the mixer to ensure that it's securely fitted to the ear pieces, and if you move around a lot that you don't lose sound.
Turn the volume up in the headphones for a few seconds. Be careful not to play the music so loud that you may damage your hearing, but still try to play the sound at a volume loud enough to check whether the music distorts. Distortion can naturally occur on headphones when you play music too loud, but they need to take a lot of volume before starting to sound fuzzy.
Sounding out amplifiers and speakers
Look at the amplifier and speakers (if provided) in the same way you did the mixer and headphones in the previous section. Check that you don't get a loud hum coming through the speakers, check that all the controls are working properly on the amplifier and make sure that the speakers don't distort at moderate sound levels. As always, give the cables a little wiggle and check that the connections don't crackle or the signal cuts out.
If the speakers are in an open cabinet that lets you view the drivers (another name for the actual speaker), then inspect them for tears, dents or even stains. If the cone on the speakers is ripped or badly dented, this damage can cause the music to start distorting really quickly and the speakers may fail completely if you play the music too loud, so don't even consider buying them. If you see stains, liquid may have got inside the speaker, which as well as weakening the speaker cone may be on its way to corroding cables and circuit boards inside.
Chapter 4
Retro Chic or PC Geek? Buying Records, CDs and MP3s
In This Chapter
Buying your tunes the smart way
Considering the legalities of MP3s
Caring for your CDs and records
If your decks, mixer and headphones are the tools you use as a DJ, consider your records, CDs and MP3s as the nails, screws and glue you need in order to perform your best work.
In this chapter, I cover what to look for when buying your tunes, how to make sure that your hard-found records and CDs stay in great condition for as long as possible and how to keep on the right side of the law with MP3s.
Sizing Up Records, CDs and MP3s
Music is expensive, so you need to make sure that you're buying the right tunes, by the right people, from the right place. Therefore, you need to consider all options when you're about to spend your hard-earned money.
Circling around vinyl formats
Records (circular discs made out of vinyl) come in a few different formats:
7-inch singles: Not as popular as they were a few years ago, but still hanging in there, 7-inch singles tend to have the main release on one side (the A-side) and a different tune on the other, B-side. The A-side may be a specially edited version of the original tune for radio (known as a radio-edit), which cuts it down to a minimum length and content, and this process could remove parts of the tune that you'd really want the crowd to hear. The B-side may contain a tune that you don't like or don't want to play to a crowd.
7-inch singles are small, so they're quite fiddly to work with, and the cut-down version of the main tune on the A-side combined with the lack of remixes of the tune mean that club DJs don't often use this format. However, many northern soul, ska and reggae DJs still find that the 7-inch is king for releases of their music.
LPs: An LP (long play) is a larger record (12 inches in diameter) that contains an entire album by an artist. Wedding and party DJs who still like to use vinyl can use LPs because the album version of a tune is more than likely the one most people are familiar with, and there may be a few tracks on the LP that the DJ would like to play.
The downside to using LPs is that they're quite hard to use when beatmatching or scratch DJing due to the amount of space dedicated to each song. With only an inch or two's worth of vinyl available to play the entire track, you may find that the map of the tune (see Chapter 14), which the different shading of the black rings creates, is fairly difficult to see, and the tightly compacted groove is more prone to picking up scratches, pops and crackles.
12-inch singles: These singles are designed and produced with the DJ in mind. Typically, you get two or three remixes of the same tune on the one record, offering a lot more choice and versatility with how you play the tune. There may be a different tune on the B-side too – but not often.
Remixes are variations of the same tune, sometimes by the producer who created it or sometimes by other producers who change the sound of the original tune entirely (like Tiesto did to Sarah McLachlan's 'Silence'). The layout changes record to record, but often the main mix that the record company feels may be most popular sits on an entire side of a 12-inch single, with the remixes on the B-side.
Polishing up on CD options
CDs can come in different sizes too, the most common being 12 centimetres in diameter, but a smaller version (originally marketed as a CD single) comes in at only 8 centimetres. CDs this size find their place as CD-ROM business cards and promotional, gimmick CD releases. The full size, 12-centimetre diameter CD comes in a few different flavours:
The party DJ: Sticking with familiarity
The great thing about being a party or wedding DJ is that you only need to play the tunes (and the mixes of the tunes) that everybody knows. Playing a deep house remix of 'Brown Eyed Girl' is probably just going to throw people off the dance floor, so you don't need to spend the time looking for rare mixes of tunes that club DJs do.
Go to a record store, buy a few compilation CDs, bolster your collection with tunes that you can't source on a good compilation CD and you'll have a great set list for a fantastic night.
CD singles: CD singles are like the middle ground between a 7-inch and a 12-inch single. CD singles normally contain the main release of a tune (often still the radio-edit), the full mix of a tune (if appropriate) and the B-side that would be on the 7-inch single, but most importantly, CD singles regularly contain one or two of the remixes that you find on the 12-inch versions.
CD albums: Albums on CD are similar to LPs in that they give you more songs from the artist, but they only give you one mix (the original) of the tune to play. Unlike albums on vinyl, however, size and reliability problems aren't an issue with CDs, so if you're happy using an album from an artist, nothing's stopping you doing so on CD.
Compilation CDs: Compilation albums with 20 or more separate, individual tunes from different artists on them can help the party or wedding DJ build a large music collection for a small amount of money.
One compilation CD can contain the entire track list for an evening. Buy two copies of the same CD so that you can mix from one to the other, and you'll have a record collection for £20, whereas the individual tunes together would probably cost you £100!
One point to be careful about when buying compilation CDs: the tracks on them might be the dreaded radio-edited versions, not the full length tunes that you want to play.
Mixed CD compilations: Whether you're looking for pop music, commercial dance music or rock and pop tunes, you may come across a lot of premixed CD albums that contain a whole load of tracks that you'd like to get your hands on.
The problem with mixed CDs is that lifting only one tune out of the original DJ's mix to use in your own set is hard to do because of the overlapping between the intro and outro of tunes. If, for example, a mix CD contains 'Jump' by Van Halen and the DJ mixed Foo Fighter's 'Everlong' into it, the end of 'Jump' and the intro of 'Everlong' will mix together. If you want to play Everlong in one of your mixes, and choose to start it from the very beginning, you'll still hear Van Halen playing. You need to have a clean version of Everlong (just the tune on its own) in order to keep this a nice-sounding mix, which you don't have on a mixed compilation CD.
Byting into MP3s
The Internet plays a huge part in your life, changing the way you receive music, movies and television. MP3 has firmly taken hold as the way to listen to and buy music. Available throughout the Internet on pay sites (and, unfortunately, illegal sites), MP3s are a quick and cost-effective way to get your music, and with iPods and iPhones becoming style icons, MP3 is the fashionable way to listen to music.
Considering compression
On a typical CD you can fit only 74 minutes of CD-quality music. If you burn your MP3s onto a CD at 192 kbps (kilobits per second) stereo, which is the best trade-off for sound quality versus file size (although I prefer 320kbps), you can get over 500 minutes worth of good quality music stored onto a CD. If taking a wallet filled with CDs instead of massive record box to a club is an eye opener (and weight off the shoulder) for vinyl DJs, just think what MP3 CDs mean! You can walk into a club with a pair of headphones and just two CDs filled with hundreds of MP3s, and be a DJ!
MP3s are able to cut the file sizes down by compression, throwing away sound frequencies that don't make much of an impact on the sound quality of the music. This method is perfectly acceptable to a lot of people, and with a good pair of headphones on your iPod you soon get used to this drop in audio quality and your brain adjusts to accept this level as the standard sound of the music.
But the compression in MP3s can have a huge effect on how the music sounds in a club. The low, sub-bass frequencies and the very high frequencies are the main casualties of MP3 encoding. The higher frequencies help with the clarity of the music, but more importantly, the sub-bass is what makes your whole body shake as the bass beats thump.
Sub-woofer amplifiers and careful attention to EQ settings can emulate sub-bass information from the frequencies left in the compressed tune, but the key to keeping MP3s sounding good on the dance floor is in the compression setting. MP3s compressed at 320kbps are preferable, but try not to go lower than 192kbps and you should be okay.
Staying on the right side of the law
Explaining the legalities of downloading and using MP3 tunes is very simple. If you go to somewhere like iTunes or Beatport to buy and download your MP3s, you're doing so legally. If you use peer-to-peer software to share MP3s, downloading a few gigabytes' worth of music without giving any money towards the artist, you're doing so illegally.
From a moral standpoint, as a DJ you're an artist yourself and you need to share responsibility with your fellow artists. Take an example of (imaginary) new producer DJ Steve who's just released his first single. Suddenly, the single's a smash hit and tens of thousands of DJs all over the world are downloading his track to play in nightclubs, but he doesn't have a strong financial foundation to absorb such a loss of revenue. All this time, you're getting paid to play his music that you didn't pay for, while he starves . . . Okay, maybe I'm being a little heavy handed here, but as a DJ who gets paid to play, you'll be treading on very thin ground by playing stolen music, both legally and morally.
Depending on the country you live or perform in, you may need to investigate digital DJ licences. Check out whether you need a licence to stay legal, so investigate what you need to do as a DJ and check that the bar, club or any other venue you play at owns any legal licence required. In the UK, an organisation called PPL (Phonographic Performance Limited) deals with this; see www.ppluk.com for more information. Search for 'digital DJ licence' online to find out whether you need one in your country.
Researching and Buying Your Tunes
In many cases, the place you research what tunes to buy and where you buy them from are exactly the same place. Online download sites and high street stores can all give you lots of information about the music available.
Buying MP3s
MP3s have taken over as a music format, not only for the DJ but also for a huge amount of the population, for the simple reason that because you most commonly buy them online, they're easy, instant and cheap to buy.
Downloading iTunes software from www.apple.com/itunes and accessing the iTunes store is a fantastic way to purchase and download a wide variety of popular and rare genres of music. The great benefit is that you can buy single tracks on an album you like instead of the entire album. Spending 99p on one track you like instead of £15 on an entire album saves a lot of money in the long run.
Avoiding musical holes
If you're relying on a review or recommendation to pick out a tune you haven't heard, or have only heard a preview of online, try to find a way to listen to the whole thing to make sure that it doesn't have a 'musical hole' in the middle. (Radio shows, clubs and online stores may help with this.)
What I mean by a musical hole is that a tune can be beautiful for the first couple of minutes, but then turn to musical mush in the middle. For some ungodly reason, the artist decided to kill everything and play 20 seconds of a car alarm going off.
This point has further implications if you're buying tunes to play that evening in a club or at a party. Unless you really trust the person who's recommending the record, be sure to listen to it from start to finish, just so you know that 'Merry Christmas Everyone' isn't going to suddenly start playing halfway through. I'm not kidding; I played a record that did that. In the middle of summer. I could have curled up into a ball and cried . . .
For a similar approach aimed more towards the electronic dance music DJ, download sites such as Audiojelly (www.audiojelly.com), DJ Download (www.djdownload.com) and Beatport (www.beatport.com) work in a similar way to iTunes and have a large range of dance tunes available.
Most online music download sites enable you to preview the track before buying it, just to make sure it's the tune or mix that you want to buy – and that you like it! These previews are usually a small snippet of a tune, so if you haven't heard the entire thing, be careful – you may be running the risk of it going somewhere strange! A little research (see 'Choosing what to buy', later in this chapter) can help with this, however.
Purchasing CDs and records
Three avenues are open to you when it comes to buying records and original CD releases:
High street music stores
Online music stores
Auction websites
Following record store etiquette
Unfortunately, some people don't treat records in stores very well. Here's my guide to good record store etiquette:
Use the dedicated listening post record or CD if a copy's available in the rack, rather than opening a shrink-wrapped, un-played copy.
Replace records and CDs where you got them from.
Put the tunes back in the same state you found them (don't bunch them up in the inlays, and clean records if you get them dirty).
Handle vinyl carefully – remember, you don't own it yet. Now is the time to handle your records like your mum always told you to, by the edges – no fingerprints please.
Take all the time you need to listen to your tunes, but don't take a pile of 50 tunes and monopolise the only listening post in the shop.
If the turntable or CD deck at the post is a cheap one, don't think that breaking it or treating it badly doesn't matter.
Be careful with the needles on turntables; most stores would rather remove the listening post than replace a needle.
Handle headphones with care. The store may only provide cheap headphones, but don't break them just because they're cheap. Be careful with the headband, which can snap if mistreated.
Visiting high street music stores
High street music stores may have suffered a decline in recent years due to the number of online stores that are able to sell the same music for a lot less, but you'll still find them in busy shopping malls and city centres. The CD DJ can find new releases in these stores more easily than the vinyl DJ. If you're looking for new releases on vinyl, you need to hunt for some specialist stores that cater for DJs like you in or near to where you live.
All good record stores have a listening post (a spot in the store with a turntable/CD deck and a pair of headphones for you to listen to records and CDs before buying them), or they have a deck sitting in the back, on which, if you ask nicely and look as if you're going to buy something, you can review your music choices.
Don't feel as if you have to rush listening to the record just because someone's standing over you, waiting to listen to CDs and records. You're about to spend quite a lot of money, so take your time to ensure that you're spending it wisely. Listen to as much of the record as you can, and check for scratches and dirt on the surface of the CD or vinyl – be aware that a lot of people don't know how to treat records properly, especially ones they haven't bought yet.
Surfing into online record stores
The Internet's a wonderful thing. I've found everything from poker chips to a house online. For the DJ hunting down new releases on vinyl and CD, or if you don't have a record store nearby, the Internet is a treasure trove. In the years before the Internet, the poor DJ would trudge from store to store and hunt through the Yellow Pages trying to track down a few elusive CDs and records. Now all you have to do is boot up, sign in and surf for it!
Using the Internet as a store front is an exceptionally convenient way to sort through a store's music stock, and as a result, hundreds of high street stores are on the Net.
Prices are usually cheaper than the high street store because online retailers don't have as high overheads. You may miss out on the personal touch when you compare shopping online with going into your local, specialist record shop, but you can get over this downside by ensuring that you do your research first.
Specialist websites like Hard to Find Records (www.htfr.com) and Juno Records (www.juno.co.uk) carry huge back catalogues of stock as well all the latest tunes. If you're also hunting for commercial and popular tracks don't pass by websites such as Amazon (www.amazon.com), Play (www.play.com) or HMV (www.hmv.co.uk). Most of these sites have options to let you preview the tunes before buying them, and many of them are also MP3 download sites.
With every online store, whether you're browsing for shoes, garden furniture, rucksacks or iPod accessories, getting reliable customer service for buying and receiving items is the most important aspect of the store. If you find you have difficulty buying a tune because you can't navigate the site well enough, you won't return to it or buy anything. If delivery takes a long time, is too expensive or – heaven forbid – the store sends you the wrong item, you'll think twice before returning to that store.
With many online stores, if you order enough then delivery is free. Even when you do have to pay a postage cost, the overall cost of what you're buying online can amount to what you would've paid in the store anyway. And by the time you add on money for petrol and parking or a train fare, and consider the time spent looking for the tune in a store, you're probably happier to wait a day or two for it to arrive. Most online stores post to anywhere in the world, so you have to wait only a day or two for your goodies. But make sure you know your currency conversions!
Using auction sites
Sites such as eBay (www.eBay.co.uk) are a great resource to find tunes that you thought were long gone. As with buying anything online, however, try to make sure that the records (and CDs) are in proper, playable condition. Be sure that:
You don't get ripped off by postage.
The seller has good feedback.
The CD is an original and not a copy burnt to a recordable CD.
You get some kind of assurance that the seller does have the record or CD (I've sadly been stung this way when buying a rare promo record).
See eBay For Dummies (Wiley) by Jane Hoskyn, Steve Hill and Marsha Collier for loads more about using eBay.
Choosing what to buy
You can find a lot of music on the market, and you need a way to find the good eggs and avoid the bad. Start reading music and DJ magazines and pay particular attention to the record reviews. You may make a couple of mistakes and go on wild goose chases, but eventually you're likely to find a reviewer with the same taste as you. You can trust what he or she says about a new record so you can pay particular attention to that tune next time you go shopping. You needn't die by a reviewer's advice, but write-ups are a good place to start.
Try listening with an open mind to specialist radio shows, such as Pete Tong, Judge Jules and Zane Lowe on Radio 1 (www.bbc.co.uk/radio1) where you can listen again to the show online and read the tracklist. Going back and listening to the show again is a good idea because you can get distracted the first time around and miss the little hook in a tune that turns it from okay to wahey! And face facts, sometimes the DJ says the title or artist a bit too fast to catch so you need to hear it again, or read an online tracklist.
Online DJ charts (such as those at www.dmcworld.com/charts) can give you a great deal of information about what's popular in a variety of different genres. DJ homepages, online forums and MP3 download sites like Beatport contain charts from popular DJs too, so you can take a look at what your favourite DJ is currently playing and pick out tunes you might like to play.
Eventually, to supplement the advice you get from radio shows, magazines and websites, you may end up standing in front of a huge rack of records or CDs, or navigating an online MP3 store library, reading the blurb the store has written about a tune and trying to decide whether you'll like it or not.
You can supplement what the store writes about a tune by considering the label and artist. When you've bought enough music, listened to enough radio shows and read enough magazines, you'll start to show an affinity toward certain labels and artists. If most of the records you like are released on a similar range of labels, always focus on them first. Even the big labels sign a few turkeys, but going back to a familiar label is a good way to thin out a lot of rubbish that gets released.
If you've liked the last five or six tunes by an artist, there's a good chance you'll like the newest one on the rack in front of you too. But as well as your favourite artists' own work, check out who's done the remixes of their tunes. If you look at other tracks remixed by these producers, you may find that although you've never heard of the main artist, you really like the tune, whether it's the original or the remix.
Eventually, your selection of artists, labels and remix producers all create links to other labels, re-mixers and artists that sprawl out like a web of knowledge, helping you pick out tunes that you wouldn't normally look at.
The guidance of a knowledgeable guy or gal behind the counter can prove invaluable for getting hold of the latest, greatest tunes, and when you spend enough money (and time) in a specialist record store, the staff there can get to know your tastes, recommend tracks and start handing over the tunes that they reserve for their preferred customers.
Weighing up Classic and Current
The genre of music you're DJing with has a great impact on how you build your music library. Wedding and party DJs need to play a mixture of new music along with a lot of older tracks to keep varied guests interested. It helps to go to a few parties and weddings and take notes of the kind of things they're playing, or look at online catalogues for inspiration when building your arsenal of tunes. Rock, indie and pop DJs play a lot of current tracks, but throw in older, classic tracks to get the dance floor rocking.
House and trance DJs can fall between the tracks when it comes to building a library. If you've grown up with certain tunes, quite possibly the ones that made you want to be a DJ, you'll want to own them for yourself to play and mix, which is great. As a beginner, owning records that you're familiar with, that you love to hear and that mean a lot to you is a positive thing. Especially if your progress with beatmatching has hit a plateau, you still love listening to the music you're playing, and that can keep you pushing on to get better.
However, you do need to think about what happens when you try to get work as a DJ – how many places are going to be happy for you to play only old tunes? Depending on the club or pub where you end up playing, they may demand set-lists comprising only current music, and you'll play any classic tunes in your library only at home, for your own amusement.
I was lucky. My first DJing gig was called 'A Decade of Anthems', which meant that I could play whatever I wanted, new or old. But if your sights are set on the big clubs that only play the newest, greatest tunes, you may end up spending a lot of money on old music that you'll never play live.
If you get the chance to drop in a classic tune once in a while during a set, it can be very effective. Check out the crowd to gauge their reaction to what you're playing (see Chapter 21 for more info on reading the crowd), and ask yourself whether they seem like a knowledgeable bunch that would respond to a classic tune. If the answer's yes, try playing a really good, older tune, but be careful because reading the crowd wrongly can clear a dance floor faster than a good night in a bad curry house!
If you don't have a paying DJ job yet, think hard about the tunes you're buying; don't buy anything just because it's brand spanking new and top of the charts, or it's the big tune at the moment. You'll play it once or twice at home, include it in a couple of demo-mixes and then demote it to the bottom of the pile because its initial appeal has completely worn off.
No matter whether you're a rock, party, pop or trance DJ, when you start to get more work, you need to buy and play tracks that are popular or get played frequently in clubs. However, if you don't think that you'll ever play a track when you're yet to perform outside of your bedroom, don't buy it just because it's popular.
Of course, you can't know which tunes are going to stand the test of time. Some tracks may surprise you by lasting a while, but if you feel you're compromising your musical integrity by buying a tune, you can bet that you won't be playing it after a month or two.
Protecting Your Records and CDs
You may have the best DJ setup in the world, the best turntables, needles, amplifier, mixer, effects units and CD players ever made, but if your records and CDs are scratched and dirty, they'll sound just as bad on top-quality equipment as they would on basic equipment.
Storing records
How you store your records when you're not playing them is extremely important for keeping them clean and protecting them from getting scratches. Put your records back in the inner and outer sleeves, and if possible store the record so that the opening doesn't point upwards, because dust and dirt that floats through the air makes a beeline towards the record (due to static electricity and gravity).
If you have the patience, go one step further by rotating the inner sleeve by 90 degrees inside the main sleeve, so even if dirt and dust did get into the main sleeve, the opening of the inner sleeve is on the other side and dust can't get in to dirty the record.
Cleaning CDs, records and needles
Think of your records and CDs as you do your teeth. If you can prevent damage occurring by cleaning them before and after use, they'll last a lot longer and you won't have that feeling of doom when everything starts to go wrong. (I'm a hypocrite by the way; I always put off going to the dentist, waiting for toothache to make a visit necessary . . .)
CDs: CDs are easy to clean. A soft, lint-free cloth wiped in a straight line from the centre out removes any dust on the disc. If you've spilt something on the CD, you may want to give it a clean by wiping the CD (in the same direction) with weak soapy water. Then wipe it with clean water to rinse and pat it dry with a soft cloth.
Try to stay clear of CD cleaning machines, which clean the CD in a circular motion. I don't recommend cleaning them in that way; always wipe from the centre of the CD outwards in a straight line.
Prevention is the best cure, so always return your CDs to the CD case or wallet after use. Don't be lazy and leave your played CDs lying around the DJ booth, where people can spill beer onto your hard-found music.
Records: Various cleaning solutions are available for keeping your records sparkling, and a few promise that if you clean the record once with the solution you'll never need to clean it again. Some people swear by using lighter fluid to clean the record, others say that alcohol or soapy water (rinsed very well afterwards) works wonders.
I find that a wipe with a carbon fibre brush (designed for this purpose) in a circular motion round the record before and after playing is more than enough. In truth, though, in the middle of a darkened DJ booth, a quick wipe with your T-shirt is probably the best your record can look forward to!
Needle: The reason you need to be so careful about keeping your record clean is because of the friction caused by the needle travelling through the record groove, which creates a lot of heat (up to 150 degrees centigrade). This heat softens the vinyl, and dirt in the groove gets welded onto the side of the needle and gouges its way through the walls of the groove. This chain of events is the major cause of all the pops and crackles that can appear on your beloved records. Well, that and throwing your records onto your bed when you've played them . . .
Repairing vinyl
If one of your tunes has a scratch that makes the needle jump, you're probably better off looking for a new copy. But if you really want to try to salvage the record, you can try a technique with a sewing needle before throwing the record in the bin. I was taught this about 18 years ago by a friend who scratched my Van Halen album, and it's stuck with me ever since (though the friend wasn't so lucky . . .). All you need is a small sewing needle, a magnifying glass and a lot of care and patience to do this without ruining your record even more. Here's what you do as a last resort option:
1. Play the record to locate the exact position of the scratch and look closely at whether the needle jumps forward or backward.
If the needle jumps to a previous part of the record, the scratch runs from right to left. If it skips to a part you've not heard yet, the scratch goes from left to right across the record.
2. Take the record off the turntable and place it on top of a soft, protective cloth on a flat surface.
In a well-lit room, look through the magnifying glass to see where the scratch is on the record. Now pick up the sewing needle. (You may want to wind some tape around the needle so that you can hold it more securely.)
3. Drag the sewing needle along the groove from one or two centimetres in front of the scratch to one or two centimetres behind it.
Drag in the opposite direction to the scratch. If the needle jumps backward when you're playing the record, you need to drag the sewing needle in an anticlockwise direction. (And if it jumps to a point later in the tune, drag the needle in a clockwise direction.)
While dragging the needle along the groove, apply a little pressure as you start, increasing to a moderate pressure as you reach the scratch and then releasing the pressure for the next couple of centimetres. Any reduction in audio quality is less noticeable by a gradual change in pressure. You may have to go through five or six groove lines to cover the entire scratch.
Note: If you're at all clumsy, this method isn't for you.
Instead of carefully dragging through a needle, some DJs simply press down pretty hard on the turntable's cartridge while slowly playing the record through the scratch to achieve a similar effect. If the scratch isn't too deep, this technique can repair it. However, if the scratch is too deep, it can just make things worse, so it's a bit of a lottery really!
Fixing warped records and CDs
Your records and CDs can become pliable under heat, which can cause them to warp. Vinyl can also warp just through stress, so your records are likely to warp when left at a strange angle with weight on them. Some compounds in vinyl and CDs aren't affected by heat, making repairs quite difficult, but if you can't play them anyway then you may want to try the following method, which was first adopted for vinyl but works just as well for CDs that become pliable under heat.
1. Clean the record/CD.
2. Place it between two clean sheets of glass.
Make sure that everything is clean before doing this, or you may fix the warp only to find that you've scratched the record!
3. Warm up the record or CD when it's inside the glass sandwich by using a hairdryer or leaving it out in the sun.
The hairdryer is better because you can work out how long and how hot you need to get the glass in order for this technique to work. You can't be too sure how much heat the sun gives off (I live in Scotland, and the sun's not that hot here!) so you can't guarantee replicating the same temperature using the sun when treating other warped tunes.
4. No matter how you heat it up, after it's warm apply an even weight on the glass over the record/CD and leave it for a few days.
5. Come back to it and see whether the record or CD is flat again.
Another similar method involves putting a record in the oven to generate the heat. I tried it once. The results weren't pretty . . . Be careful with how much heat you apply; too much and the record will look like Salvador Dali made it.
If you want to test out fixing warped tunes before having a go on your precious records and CDs, go to a second-hand record store and search (or ask for) a couple of warped records or CDs that you can use as test cases. After you've perfected the technique with them, you can fix your own.
Repairing scratched/cracked CDs
Record stores carry many products that you can use to protect your CDs from scratches in the first place, or repair them if they've been scratched. Just don't try to be smart like me and use Brasso to clean the CD. That idea doesn't work too well . . .
Some people swear by fluids and gizmos that remove part of the protective surface of the CD to smooth out the scratches. I'd be very careful using this approach, though: you don't want to run the risk of removing too much of the surface – your CD player may not be too happy playing thin CDs.
If you've accidentally cracked one of your CDs and you don't want to buy (or can't find) a replacement copy, you may still be able to play the CD. You probably can't play the parts of the CD that are cracked (and remember, a CD plays from the inside-out) but the rest of it may still be okay. Be careful, though: if the cracks are too plentiful then when you play the CD it may disintegrate.
Some audio-ripping software has an advanced error correction built into it, which may let you archive broken discs before throwing them in the bin, but in the end you may find that buying a new copy of the CD is easier, or if you can't find it on CD, you could find it as an MP3 to then burn to a CD.
Backing up digital libraries
No matter whether you're a PC or a Mac user, don't rely on the promises of operating systems to look after all your MP3s and digital music for you. Every week, or after every major import of music, back up your tunes and your library database to an external hard-drive, and keep it somewhere safe. If possible store your backup in a different room (or building) from where you keep your equipment and music library, just in case your DJ room goes up in flames or gets flooded.
I have my music library on an iPod, which I use to listen to all my tunes. The added bonus of this is that it functions as a backup for all my tunes, and I email myself my library database once a week so I have an online backup of it in case anything goes wrong. See Chapter 9 for more about digital DJing.
Part II
Stocking Up Your DJ Toolbox
In this part . . .
You need to make an informed decision about which equipment is best for you and your DJing style and, more importantly, how it all works when you get it home! Part II takes a foray into format considerations, covers the features and functions of turntables, mixers, CD decks, headphones, and amplifiers, as well as explaining the different designs of needles and cartridges for turntables, the wonders of slipmats and ways to be a digital DJ.
To wrap up this part of the book, Chapter 13 is dedicated to how to set up and connect all of your equipment, and how to troubleshoot the connections if something goes wrong.
Chapter 5
Keeping Up with the Tech-Revolution: Format Choices
In This Chapter
Looking at the blurry line between CD and vinyl
Diffusing the argument with hybrids and computers
Cain and Abel, the Capulets and the Montagues, Apple and Microsoft, Britney and Christina; throughout time, history and literature have told of the wars between two similar sides; wars that exist because of what the two sides have in common, not because of how different they are. When CD decks first came onto the scene, vinyl purists all over the world cried foul. CDs were seen as a great threat to the vinyl DJ and DJs started to take sides between the standard vinyl method of DJing and the CD upstart.
If you're unsure what format to use as a DJ, this chapter covers the major differences between DJing with CDs or vinyl and then suggests how utilising your computer destroys those differences.
Clashing CDs against Vinyl
The argument for using turntables or CDs boils down to two different things: functionality of equipment and the availability of the music you want to play.
Finding your format
You may dream of being a vinyl DJ using two turntables, a mixer and a box of records to create your sets, but unfortunately, the genre you want to play may not let you. During the 1970s and '80s this wasn't an issue, because music was released across all formats: vinyl, tape and then CD. But as records became less popular, CD and MP3 downloads became the main way to buy music and the availability of records you could buy reduced considerably.
Reflecting on vinyl
As sales for the home consumer market have fallen over the years, vinyl has been aimed almost exclusively at the club music market because of its long associated history. Music genres such as house, trance, drum and bass, hip-hop and techno still release the majority of their tunes on vinyl.
Some rock, classical, folk and country music is still released on vinyl, and a bit of a resurgence is going on in the indie/alternative scene in the UK for 7-inch singles, but when you compare the range of music that's released across all the different genres, only a tiny percentage of it is available on vinyl.
Unreleased music was one of the big areas in which vinyl reigned strong. Record companies would send promotional recordings (known as promos) to DJs in hopes that they would get early exposure and gain popularity at gigs. Recently, however, CDs and MP3s have become more popular for promos because they're cheaper and more convenient to send out than pressing a thousand records. Record companies still hand out vinyl to the chosen few, and you know that you're in a position of reckoning when you're a working DJ who receives promos on vinyl.
Keeping up with CDs
Record companies release hardly any music nowadays that isn't available on CD. Every music genre – rock, folk, classical, country, pop – is waiting for you on a shiny, 12-centimetre disc. Even if it's not available to buy in store on CD, you can buy an MP3 online, burn it to CD and play it immediately.
As a CD DJ, if you receive any promos on vinyl, or a small label has only released a test pressing of a tune on vinyl, you can easily transfer them onto CD. All you need is a good quality, direct-drive turntable that plays accurately at zero pitch (refer to Chapter 6), a good set of needles and a computer with a soundcard and CD burner and you can transfer all your records to CD. You may even want to incorporate the turntable into your DJ setup for some variation!
If you have lots of vinyl that you're transferring onto CD and you're a beatmatching DJ, use a BPM (beats per minute) counter to set the BPM for each tune in the same genre to the same BPM as you transfer them (125 for house, 135 for trance and so on). This way, when you play back tunes with a similar genre from CD, beatmatching is really easy because you won't have to change the speed of your tunes by much (if at all) in order to match the beats. (Check out Chapter 15 for more about beatmatching.)
Unfortunately for the vinyl DJ, recording from CD to vinyl doesn't work out quite as cost effectively. If, for instance, you're a rock DJ, you'll find that most of the tunes you want to play aren't available on vinyl; so to be a rock DJ who uses vinyl, you need a way to transfer the music you want to play onto vinyl. Vinylium make the Kingston Dub Cutter to add onto a standard Technics turntable or you may be able to find the Vestax VRX-2000, both of which etch the music into blank 12-inch records. But at around £5,500 for the Dub Cutter and more than that for the Vestax, you'd better be making a lot of records to get your money's worth!
Choosing Analogue or Digital
Analogue audio (which you encounter as a DJ when you play records on turntables) played through the right sound system may sound warmer (more pleasant with a feeling of depth) than an original CD played through the same sound system. But the fragility of vinyl, which suffers through time from cracks, pops, skips and jumps, is a flaw that (in my opinion) gives music released digitally on CD an edge over analogue audio.
The only time a CD release sounds different is when you use a different sound system to play it. A CD never wears out, it never degrades and, as long as you take care to prevent deep scratches on the surface of the disc, you don't need to worry about the CD skipping or jumping.
MP3s burnt to CD are a different proposition. To keep the digital file sizes small, MP3s are heavily compressed, removing some of the higher and lower audio frequencies that aren't too audible in the first place.
How good the music ends up sounding is down to the level of compression. If you heavily compress the music and remove too many audio frequencies to keep the file size small, the music can sound as if it's been recorded underwater. But with the correct compression setting (I recommend 192 kbps (kilobits per second) stereo as a minimum, but 320 kbps stereo is preferable) and a good sound system, it can be hard to tell the difference.
You can burn an MP3 to CD in MP3 format, which fits a lot more music onto the disc (check whether your CD deck can play MP3 CDs first) or you can 'up-convert' MP3s and burn them as a traditional CD. However, this up-conversion doesn't transform an MP3 into CD quality music. All it does is allow you to play MP3s on a normal CD player – if it sounded bad before, it'll still sound bad . . .
Functionality: My Way Is Best!
If you get the chance to compare a record and a CD (an original CD release from a store, not an MP3 burnt to a CD-R) in a club environment, there's very little to choose between them, and it can be hard to tell the difference when listening back to recordings of mixes too. So if you had enough money to buy any equipment on the market, only a few sensible arguments are left when choosing between formats.
Turntables and records are heavy and cumbersome
Turntables are solid and heavy for a good reason; if they weren't, the needle would skip with all the booming bass you play through the club's sound system.
Having lugged around a couple of bags and boxes filled with vinyl to clubs, I'll concede that a wallet with 100 CDs inside is a lot lighter than the same amount of tunes on vinyl, but I could do with losing a few pounds anyway, and look upon 'night club weight training' as a booster to gym visits.
On an affectation level, I'm embarrassed to say that I felt really cool walking into clubs with two big boxes filled with records. Everyone I passed in the crowd knew I was the DJ (and if they didn't, I'd make sure to bash their knees with the record boxes a couple of times). If you walk into a club with a little wallet filled with 100 CDs, the crowd may think that you're just there to read the meter!
I was kidding about the boxes and the knees. I'd never do that . . .
The shifting sands of time and development
Early CD decks were based on the domestic CD player, and although they added a pitch control and a jog wheel to search through the tunes, they weren't anywhere near as versatile or functional as turntables. Since those early models, technology has improved the CD deck so not only does it compete with turntables in all areas, but it leads the way in functionality and creativity. Options like pitch bend, master tempo, scratching, seamless looping, hot cues, effects and mixing between two tunes on the same CD have all shifted the dividing line that once existed between vinyl and CD.
CD DJing is firmly mainstream. Back in 2007 Judge Jules (one of the UK's biggest DJs) said he'd only use CD DJ decks when playing in clubs because the effects and controls give him enormous creativity in the DJ booth. Add to this the ability to remix a tune on a laptop en route to a gig, burn it to CD and play it that evening and he's able to provide an incredible, entertaining and unique performance each night.
Turntables don't have built-in effects
Until CD players included built-in effects, this point was never an issue. If you wanted effects, you'd buy a separate effects processor like the Pioneer EFX-1000 or you'd get a mixer with built-in effects. Personally, I'd much rather have the effects externally, or on the mixer rather than on the turntable or CD player, but my opinions aside, effects, loop controls and multiple cue points (places to start playing from) make CD decks more versatile than a single turntable. See Chapter 8 for more on these functions.
You can't see the music on CD
The great thing about vinyl is that all the different shades of grey and black rings on the record let you see where you are in the tune. If you look closely at the changes between the darkness of the rings, you can work out how long it will be until the breakdown, chorus and so on, and you know when to start your mix accordingly.
As a CD (which is a shiny disc without shading information) just spins around inside the deck, you have to take the time to discover the structure of your tunes, remembering when changes happen, and read the time display in order to make perfect mix placements. Unless, that is, you have a CD deck with a waveform display.
Manufacturers realised that this issue was a big flaw for the beatmatching DJ, and have started to show a representation of the music's waveform on readouts of CD decks (see Figure 5-1). The waveform is larger for loud parts and smaller for quiet parts, so you can tell by the dips and troughs when the tune is about to change to a quieter or louder part. You still need to know the structure of the tune, and the waveform is more of a ball-park reference than a precise guide, but it has transformed mixing on CD from blind memory of a tune structure to a visual trigger of your memory.
**Figure 5-1:** The peaks and troughs show the quieter and louder parts of the tune.
Using CDs lacks aesthetic performance
On expensive, professional CD decks like the ones made by Pioneer and Denon, with large platters and vinyl emulation, this isn't really the case any more. For those who like to see a DJ do more than just press a couple of buttons on cheaper CD decks, these professional CD decks give the DJ creative flexibility, all with loads of visual flair when working the controls.
Personally, the sight of a DJ teasing a record out of its sleeve, cleaning it on his or her T-shirt, placing the needle in the groove and then man-handling it to get the beats matched still does it for me. But as the design, control and versatility of CD decks evolve, the argument about the lack of aesthetic performance isn't as strong – provided you spend the money.
Bars don't have turntables for DJs any more
As vinyl has become less popular and more DJs shift towards CD DJing, sadly a lot of bars realise they can claim back space by removing bulky turntables and replacing them with twin CD units. If you're a vinyl DJ, you can't do much about this unless you're allowed to bring along your turntables. One option is to transfer your entire collection onto CD for occasions like this, but that can take a lot of time.
Whether clubs still have turntables depends a lot on the genres that they play. House/trance clubs should still have a set of turntables waiting to be used, but if you're a rock, pop or indie DJ, you might not be so lucky.
Turntables are more expensive than CD decks
This all depends on what you're buying. I've found that one of the most expensive vinyl-only turntables is the Technics SL-1210M5G, which is around £700; but one of the most expensive CD decks on the market is the Pioneer CDJ2000 at £1,500 each! Even the industry standard CDJ1000MkIII from Pioneer is around £850. Compare money with features, though, and turntables can still be a lot more costly than CD decks.
A pair of £100 turntables will probably be belt-driven, have motors that won't hold their pitch very well, will most likely cause feedback when you play them too loud due to the thin plastic bodies and you'll probably get fed up with them in a year or so and want to buy a different pair. On the other hand, if you have £100 to spend on a CD deck you should find one that gives you a reliable pitch control and pitch bend with possibly a loop function too. The antiskip on them might not be the best, but these basic functions on a cheap CD deck can give you more control and confidence mixing the music than a cheap, belt-driven turntable ever could.
If you have £200 to spend, you find that the features on the CD decks you look at outclass what's on a turntable of the same price. Although the turntable you can afford now has a high torque (power), direct-drive motor like the one on the Numark TT500 and may offer a pitch bend and large ranges of pitch variance (sometimes over 50 per cent faster or slower), I still don't think that a turntable competes with a CD deck in the same price range.
For starters, at £200 you can afford twin CD decks, so you'd only have to pay £200 to get both of the input devices instead of paying £400 for two turntables! Or I recommend that you get something similar to the Numark AXIS 9, with loads of built-in effects, multiple cue points, a beat counter, seamless looping and the chance to do some scratching on CD too!
If you compare the £700 Technics SL-1210-Mk5G mentioned previously to a CD deck in a similar price range, you find that the CD deck still beats the turntable hands down on features. For £700 you can get the Denon DNHS5500CD, and this thing rocks. It's got a motorised deckplatter, so it can feel like using a turntable, built-in effects, ability to connect external hard-drives and iPods to play MP3s and it can even mix into itself with the two-decks-in-one feature.
So if you want to compare top prices, CD decks are more expensive but you get a lot more bang for your buck. Refer to Chapter 3 for more on buying and budgeting for equipment.
Can't We All Just Get Along?
Two factors blow the whole CD versus vinyl argument completely out of the water.
Hybrid turntables let you have it all
Hybrid turntables, which play both CDs and records on the same unit, have blown the wind out of the sails of the CD versus vinyl argument.
These turntables come at a hefty price (between £500 and £700), but Numark and Gemini have both brought out hybrid turntables that let you use the deckplatter like a giant jog wheel to control CDs as if they were vinyl, and when you want to play a record you do so on the same piece of equipment.
If you're thinking of going down this route, bear in mind that you'll rarely find hybrid decks in a pub or club. Not too much of a problem for vinyl DJs, because it's a skill that's easily transferable between turntable models; all that changes is the feel and response of the platter and the pitch control. But the CD controls on these hybrid decks may be nothing like those you use on CD decks in a pub or club, so be sure to do some research first, before standing in the DJ booth with a look of horror on your face!
You can say the same no matter what CD decks you use, but a bigger difference in controls may exist if you're used to using hybrid decks. Chapters 20 and 21 have some guidance into what to look for in the DJ booth.
The new kid: Digital DJing
Digital DJing's most explosive feature is that it can let you use your turntables or CDs to control music stored on a hard-drive using special DJ software. With digital DJing, the two dividing factors between CD and vinyl that I mention at the beginning of this chapter (the availability of music and deck functionality) become irrelevant.
By storing music on your computer's hard-drive and controlling it with your choice of turntables or CDs (or both!), you have almost no limitation to what music you can play with your chosen format. If you want to use turntables to DJ with but the music you want to play isn't available on vinyl, find the music online at an MP3 download site, load it into the DJ software and use your turntables to play the music as though it were on a record in front of you. Genius!
From a functionality point of view, most of the special features that CD decks have that turntables don't, like effects, BPM counters and loop controls, are contained within some of the DJ software programs. This gives you access to exactly the same creativity tools using your turntables and DJ software that CD DJs have, and means that in the right hands, with the right software, turntables are on an equal playing field with CD decks.
On my journey through formats I started as a vinyl DJ, but I moved to CD when the music I wanted to play was too hard to find on vinyl. But now I use a digital DJ setup, using my turntables and mixer to control Native Instruments 'Traktor' playing music stored on a laptop. As a result, I haven't even switched on my CD decks at home for over a year . . .
I cover digital DJing in detail in Chapter 9.
Chapter 6
Getting Decked Out with Turntables
In This Chapter
Finding out about the basic parts of a turntable
Keeping up to date with new innovations
Caring for your turntables
All turntables are equal in that they play records but, like most things in life, some are better than others. Whether you're using turntables to play loads of different records, or want to use them to control MP3s in software, playing the same two records over and over again (see Chapter 9), you need a turntable that can cope with the physical demands of DJing. In this chapter, I go through the functions you need to look for when purchasing, setting up and servicing turntables.
Avoiding Cheap Turntables
Deciding what turntable to buy and use is largely based on your budget. When you go shopping don't go for the cheapest option so that you can save a little money. Investing in a better quality turntable puts you straight on the road to becoming a quality DJ. Actually, maybe reversing the point makes this clearer: the worse your turntable, the harder it is to become a good DJ. And this advice isn't aimed at just the beatmatching DJ. If you're a rock, indie or party DJ, and you're planning to use turntables, it's just as important to buy quality turntables that won't skip or feedback in loud environments.
The main things to watch out for on cheap turntables are that they tend to have belt-driven motors rather than direct drive motors (see the following section), and they often skimp on essential DJ features such as removable headshells, tonearms with adjustable counterweights and long pitch sliders.
Spend as much money as you can on the turntable – only then think about purchasing the rest of your equipment. Great decks remain great decks no matter what mixer and headphones you use, but not even the best mixer or the clearest headphones can make cheap, belt-driven decks better.
Motoring in the right direction
Belt-driven decks do seem like an attractive option when you're looking to become a DJ because they're so much cheaper than their direct-drive big brothers. Of course, some people claim that their belt-drive decks are fine to mix with, scratch with and so on, and I'm sure that they think they are. But the first time these folks use a good direct-drive deck, they change their minds and (reluctantly) accept that they've been thinking only with their wallets or purses and have been fooling themselves. (A few people still stand by their belt-driven decks, but they're either stubborn as a mule or have super-human powers of adaptability.)
Belt-driven turntables
Inside a belt-driven turntable is a small motor with a rubber band linking it to the underside of the deckplatter (the part you put the record on). It's similar to how turning the front cog with your bike pedals makes the back wheel turn. This method of powering the turntable results in low torque (power to the turntable), meaning that the deckplatter often grinds to a halt when you hold the record stopped.
The other downside is that the speed the turntable plays at can fluctuate, speeding up and slowing down. If you're a DJ who'll be trying to beatmatch the bass beats of two different records (see Chapter 14), the fluctuation of speed makes keeping the bass beats playing at the same time, for anything over ten seconds, extremely difficult. You may blame your own beatmatching skills rather than realising it's the turntable's fault.
Direct-drive turntables
Where belt-driven turntables have a rubber band transferring power from the motor to the deckplatter, which then spins around a centre spindle, in direct-drive turntables the centre spindle is attached directly to the motor.
The improved torque that this results in means start-up times of well under half a second, and the power from the motor is more than enough to keep the turntable spinning under the slipmat as you hold it still, preparing to start a tune or when performing complicated scratches.
The turntable speed is solid and reliable on a direct-drive turntable. Though you can get pitch wobbles around the zero pitch mark (see the sidebar 'The Bermuda Pitch Zone exists'), you can be confident that any beatmatching errors are your errors, not the fault of a weak transfer of power through a rubber band. You may regard this fact as a double-edged sword – but the moment you realise you can't make excuses and blame your performance on bad turntables, your DJing skills start to improve!
Watching out for pitch control design
Watch out for cheap turntables that use a small (2-inch/5-centimetre) pitch fader or rotary knob to adjust the pitch of the record. You won't often find either on direct-drive decks, but super-cheap belt-driven decks sometimes have them. These pitch faders are too small to make the fine adjustments you need to keep the beats of your records playing in time, and this can make beatmatching insanely difficult.
Look at the standard design of a turntable (the Technics 1210 in Figure 6-1) and notice the large pitch control down the side of the deck that lets you make minute adjustments to the pitch. Make sure that the turntable you buy is based on a similar design.
**Figure 6-1:** The Technics 1210 DJ turntable.
Short-term gains, long-term pains
If you're happy doing things the hard way, you may find that at least one good thing comes out of learning to DJ on belt-driven turntables. In the short term, you'll become an extremely accurate, attentive DJ when beatmatching.
I've found that beginner DJs who start by using top of the range turntables from Technics, Vestax and Numark can have a really easy time. The motor is so powerful and reliable that they don't need to worry about speed fluctuations throwing off their beatmatching skills. When these DJs have to use a poorer set of turntables at a party, for example, they may find that their concentration and levels of attention aren't as good as those DJs who were forced to develop on bad decks, and may have difficulty keeping their beats matched because they're not used to the problems of bad decks.
I must stress, however, that eventually, the good DJs develop attention and accuracy just through time spent practising and developing their own skills – no matter what turntable they use – so this isn't an excuse to buy cheap, belt-driven decks.
One club that I worked at developed a problem with their turntables due to a customer of the club spilling beer over them. While they were getting repaired, the club owner decided to hire a pair of belt-driven turntables. Due to the heat of the club, the belts started to stretch, causing the decks to be even worse at holding their pitch, which made beatmatching extremely difficult.
Fortunately, I was used to decks that played in this way, because one of the pubs that I'd worked at had decks with motor problems, which felt just like shoddy belt-driven decks and really used to annoy me. From using those decks frequently I developed the intuition and concentration to hear beats slipping out of time before they were noticeable to the dance floor, and wasn't too fazed by such a problem when it happened in the club that night.
The other DJ wasn't quite so lucky . . .
Identifying Key Turntable Features
A DJ turntable has many key features. Some of them are similar in function to a home hi-fi's record player, but added functionality to these controls and designs is what truly separates a DJ turntable from a hi-fi's record player. This section covers what these features do so that you not only buy the correct turntables but also know how to make use of them.
Start/Stop
Automatic hi-fi record players start playing when you place the needle on the record and only stop turning when you take the needle off and replace the arm on the rest, or when the needle gets to the end of the record and automatically returns to the rest.
This isn't helpful for the DJ – you need manual control of how the motor starts and stops. You sometimes need to stop the turntable but still leave the needle at a specific place on the record. This is usually when you've taken time to find the place to start the record from (the cue point) but don't want to start the tune for a couple of minutes. The Start/Stop button gives full control over how and when the turntable starts and stops. Pressing Stop when the record is playing can be a great DJ technique too (see Chapter 16).
On/Off
The On/Off switch on a DJ turntable is normally on the bottom-left corner of the deck, next to the Start/Stop button. The switch is raised above the deckplatter, and a strobe light is positioned underneath (see later sections in the chapter for information about the deckplatter and strobe light). Though used mostly for the mundane task of turning the turntable on and off, you can also use the switch creatively in the mix (see Chapter 16).
33/45/78 RPM
Nothing's particularly special about the RPM (revolutions per minute) button on your DJ deck; when you press 33 and the pitch control is set to zero, the record makes 33 revolutions in one minute, and when at 45, the record revolves 45 times in one minute. If you don't know what speed you should set your turntable to, look at the record label or cover, which tells you whether to play it at 33 or 45 RPM. Or simply try listening to the record. If you're playing Barry White and it sounds like the Chipmunks, you're playing the record too fast; try pressing the 33 button!
If you have older records set to play at 78 RPM, some turntables have a sneaky hidden setting: when you press the 33 and 45 buttons together, the turntable plays at 78 RPM. If you need this feature, check that the turntables you're looking to buy has it before parting with your money.
Strobe light
The strobe light is the soft red light at the side of the turntable (normally bottom left corner, integrated as part of the On/Off switch). It's not just a pretty red light – it's a strobe light that you use to calibrate and check the accuracy of the turntable's motor, as I describe in detail in Chapter 3.
Deckplatters
The deckplatter is the part of the turntable that spins round and is what the slipmat and the record sit on. Home hi-fis have a rubber mat firmly glued onto the platter, which is useless for DJing with, because the deckplatter needs to be made of smooth metal to let the slipmat slip (see Chapter 7 for what a slipmat is and how to make it slip better).
When you buy Technics decks they come with a thick rubber mat sitting on top of the deckplatter, which fortunately isn't glued down. If your decks came with a similar thick rubber mat on top of the metal deckplatter, simply lift it off, exposing the deckplatter, and keep the rubber mat somewhere safe. I find down the back of the wardrobe is a safe enough place.
Target light
The target light (shown in Figure 6-2) sits on the edge of the deckplatter and shines a light along the grooves of the record where the needle traces, enabling you to see the grooves more clearly. Why do you want one? Apart from letting you see where the needle is (or where you'd like to put it), the target light helps you locate different parts of a tune. If you take a look at a record under good light, you can see groups of different shaded rings on the record. These rings are the map of the tune: the darker rings are the quieter parts and the lighter rings are the louder parts. Being able to see where the needle is in the record can help you work out when new parts are about to kick in, helping with perfect mix placement (see Chapter 16).
Like your health, you don't really think about this little pop-up target light until you don't have it. If it's broken, or the decks you have don't come with one, it can be hard to see these rings in a well-lit room, let alone in a dark DJ booth.
Pitch control
The pitch control adjusts the rate at which the turntable turns. If you move the pitch control into the + area (towards you on a standard DJ turntable), the record plays faster; and if you move the pitch control towards the – area (away from you), the record plays slower. Different turntables have different ranges, but you typically find that pitch adjustment ranges are between 8 or 12 per cent in either direction.
**Figure 6-2:** The target light on a Technics 1210. A helpful little fella.
Although the record plays faster the more you increase the pitch control, it's called a pitch control, not a speed control, so the more you increase the speed, the higher the pitch of the music gets. So you may start to beatmatch two tunes you think will sound great together, but when you increase the pitch on one of the tunes, the two tunes may sound out of tune, like your dad singing in the shower along with the radio. See the section 'Master Tempo/Key Lock', later in the chapter, for one way around this issue (and take the batteries out of the radio to stop your dad singing in the shower).
The numbers
The numbers on the pitch control can be confusing. These numbers don't refer to BPMs (beats per minute, the usual measurement of tempo) of the music you're playing, but rather a percentage difference of the speed of the turntable. The only time the numbers correlate exactly with the BPM is if the tune you're playing has a BPM of 100. If you move the control to +1, you increase the pitch by 1 per cent of 100, which is 1 BPM; and the same for the other numbers (5 per cent would be 5 BPM and so on).
If you're playing a 150-BPM tune and decrease the pitch to –1 per cent, then the tune now plays at 148.5 BPM (1 per cent of 150 is 1.5). A 130-BPM tune with the pitch set to +5.5 per cent increases by 7.15 BPM – so you can assume that tune now plays 'around' 137 BPM, and adjust the pitch on other tunes so they play at the same speed too.
The Bermuda Pitch Zone exists
The decks that I learnt on used to change the pitch the wrong way for a 1 per cent region; if I moved the pitch fader to +1 per cent, the music slowed down, and the music sped up if I moved the pitch fader into the – region. Fortunately, after the +/–1 per cent area, the pitch control went back to normal – otherwise, I'd have gone mad!
Even my Technics 1210s suffer from this problem, but not as pronounced as with the decks I learnt on. The 1210s just hover around zero pitch between +/–0.5 per cent, and then go back to normal again.
Fortunately, turntable manufacturers have noticed and rectified the problem – first Vestax and then Technics on their 1210 MkIII have made the pitch fader completely smooth, with no click point as you pass through zero pitch to cause this problem.
You can 'hack' your turntables to disable the quartz lock feature that's the cause of the problem, but you'll have to search on the Internet for these hacks because I don't want this book to create an epidemic of broken turntables!
Unfortunately, the pitch control isn't an exact science. The difference that even 1 millimetre of change can make to the speed of your record is enough to throw off your beatmatching. Even though the fader sits somewhere near the 2 per cent area, you may actually be playing at 2.2 per cent, and that 0.2 per cent can make a huge dent in your beatmatching skills. So use your ears and listen to what the beat is doing, rather than only relying on the numbers on the pitch control.
For more about how calculating BPMs can help with beatmatching, check out Chapter 14. The Cheat Sheet at www.dummies.com/cheatsheet/djinguk has the mathematical calculation for working out BPM percentage changes.
Accuracy
The other problem with the pitch control is that through time its accuracy starts to shift, so when you set the pitch to 4.5 per cent the turntable is actually only running at 4 per cent. But even worse is the area around the zero pitch mark on the turntable (what I like to call the 'Bermuda Pitch Zone', because it's easy to get lost in there for days!). On problem decks, when you set the pitch control to zero the control clicks into place. When you move the pitch control away from this zero pitch click point the motor sometimes has trouble knowing which way you're moving the pitch control, and can do the opposite of where you're setting it, or sometimes belligerently remains at zero pitch for a short distance either side of the click point.
Counterweight/height adjust
The counterweight is a metal weight that rotates on the back of the tonearm, which, when turned anticlockwise to add weight, increases the down pressure of the needle on the record, making it less likely to skip when you're moving the record back and forth, either to find the start point of a record (the cue), or when scratching. You can find detailed information on calibrating and using the counterweight properly in the later 'Counterweight' section.
The higher you set the tonearm, the steeper the angle at which the needle points down into the groove, exerting even more down-force and making it even less likely to skip. A lot of scratch DJs adopt this setting to give increased needle stability. Be careful, though – if you've set your tonearm height to the top and the counterweight on at full, you'll wear out your records and your needles really fast.
You may have read about or heard of DJs who like to put the counterweight on back to front, to get a little more down pressure onto the needle; this action is very bad for your needle and your records, damaging and wearing them out really quickly. For the scratch DJ who accepts accelerated wear as part of the consequence of scratching, this is fine. But as a beatmatching, mixing DJ, never put on more weight than the needle manufacturer suggests. If you need to add that much weight, chances are your technique is wrong, your needles are already damaged or dirty, or you're using the wrong needle altogether (Chapter 7 covers these issues).
Antiskate
When a record plays forwards, a centripetal force pulls the needle in the groove in toward the centre of the record. Antiskate cancels out this pull by adding an equal force that pulls the needle out toward the outer edge of the record, keeping the needle in the middle of the groove with no sideways force to wear out the walls of the groove.
Although antiskate helps to keep the home listener's vinyl copies of Mozart in pristine condition, when DJing the function can be redundant because you don't only play the record forwards; between scratching and back cueing, you also do your fair share of playing the tune backwards. When you play a record backwards, the force that normally pulls the needle into the centre of the record when playing forwards is now pulling out toward the edge of the record (it's become a centrifugal force). If an antiskate setting is already pulling the record out to the edge, more force than normal is acting on the needle, making it even more likely to jump out of the groove. All this really means is that most DJs tend to leave antiskate set to zero.
Removable headshell/cartridge
The needle you use is very important depending on the style of DJing you do. DJs who want to scratch need to set up their needles for maximum stability, and beatmatching DJs need to ensure that they get the best sound and versatility from their needles and cartridges. The ability to adjust the angle at which the needle points into the groove or change the entire headshell from (for example) a standard Technics design to an all-in-one Concorde design are important factors for achieving individual DJs requirements that separate the DJ turntable from the home hi-fi record player, which typically doesn't allow this kind of customisation.
From a practical point of view, removable headshells can be a life-saver if you damage a needle during a set in a club. If something happens to the needle on the turntable, and you have a spare headshell to hand, instead of fiddling around trying to remove the needle from the cartridge to replace it in a dark, loud DJ booth, while under pressure to get the next tune ready to mix in, you can whip off the headshell containing the damaged needle and screw on a new one, all within five seconds. For more information about needles and cartridges, head to Chapter 7.
45 RPM adaptor
In the days before CD and hard-disc jukeboxes, 45 RPM, 7-inch singles were crammed into a jukebox. Manufacturers produced these records with an extra large hole in the middle (25 millimetres in diameter, compared to 5 millimetres on 33 RPM LPs) so that you could mechanically move them from the rack and sit them securely on the unit that played the record in the jukebox. Because the singles used in jukeboxes were the same as those on sale to the public, a 25-millimetre adaptor placed onto the centre spindle increased its diameter so you could play the record properly on home turntables that had a 5-millimetre centre spindle.
Now relegated to a recess in the top-left corner of the turntable, this shiny piece of metal has become (virtually) obsolete due to the demise of traditional jukebox records. However, if you play older records (ska or northern soul stuff especially), or newer reggae/ragga 7-inch singles, you'll find that you may still need to use this adaptor on some of those records.
Customising Your Sound with Advanced Turntable Features
The basic features on a turntable enable you to play a record and change the playing speed. For most DJs, that's more than enough. But for some, gadgets, buttons and switches all go hand-in-hand with creativity and individuality and personal styles, so they look to turntables with enhanced features.
When you look at the gadgets and controls on your turntables, just bear one thing in mind – where are you going to be DJing? If you only ever intend to make mix CDs and run your own parties using your own equipment, then feel free to go nuts, but if you're planning on playing in clubs, have a quick think about how much you use these add-ons and the likelihood of them being available on the clubs' setup.
This argument is similar to the one about relying on beat counters to develop your beatmatching skills (see Chapter 10). The advanced functions such as reverse play, quartz lock, digital displays and pitch bend/controls with 50 per cent variance are all useful, adding a nice dimension to your mixes when at home, but because 97 per cent of clubs still use Technics 1210s (with nothing more than a pitch control that's a bit wonky around zero pitch and an otherwise rock-steady motor), ask yourself whether your advanced turntable DJ skills will travel well to these clubs. If you can only mix well on advanced turntables, you're in for a tough time when you can't use any.
I'm not saying don't get turntables with advanced features on them. I'm not even going to lie and say that you'll never work in a club that has decks with these features, but in the same vein as beat counters, don't rely on these advanced features to make you a good DJ.
Pitch range options
Once upon a time, your choice of pitch range was limited to 8 per cent faster or slower (unless you opened up and started screwing around with the innards of the turntable); that was when Technics 1200/1210s ruled the roost. But things have moved on. Now 12 per cent pitch variance has become a standard on many turntables, but advances in pitch control mean that the DJ can have 50 per cent pitch variance on offer, or more!
Simplicity is reliability
I believe that the Technics 1200 and 1210 MkII turntables have gained popularity over the years in no small part because they're extremely reliable. They're reliable because there's very little in them to go wrong – just a motor, a few electronics to control the power and speed of the motor, and the audio output.
Adding extra features to turntables can increase the chance of breakdown and malfunction. However, in my opinion, manufacturers such as Gemini, Vestax and Numark have elevated turntables to another level of functionality by offering the DJ extra creativity (for a price), while ensuring a long life-span for the equipment by increasing reliability and build quality.
You aren't likely to play a tune at 50 per cent that often, but you're certain to want to play a tune faster than 8 per cent. Some scratch, funk and drum-and-bass DJs like to over-pitch their tunes, making them sound completely different. (Try to steer away from using tunes with vocals when you do this, though, because the vocalist will sound as if she's been inhaling helium!)
Sliding the pitch control up or down to 50 per cent at the end of a tune is a good technique to use (sparingly) to get from one tune to another, but increased pitch options are more about offering the DJ another level of creativity than about everyday use.
Pitch bend and joystick control
Pitch bend was first introduced on CD decks. When beatmatching, if the beats start to slip out of time, instead of temporarily speeding up or slowing down the turntable by pushing the record, spinning the spindle, touching the side of the deck or briefly boosting/cutting the pitch fader setting by 4 or 5 per cent, you get two buttons on the turntable, or a joystick, which control small bursts of speed. When you use the + or – pitch bend buttons or controls, the turntable speeds up or slows down by a small amount. When you release the buttons, the deck returns to the original speed setting.
CD DJs, who are used to using buttons instead of using their hands to control the speed bumps on their tunes, welcome these controls when they first use vinyl. You still need to set the pitch control and start the record at the right time, but if you're more familiar using buttons to correct the speed of CDs, the concept and the technique of using the turntable's pitch bend is the same, making the migration from CD to vinyl all that bit easier for the CD DJ.
Predictability
The knack of adjusting the speed of the record with your hands is something that you pick up after a few hours, but sometimes you come across a record that feels stiff to move or flies away too fast and turns a lot faster than you thought, almost spinning out of control as you try to speed it up. The constant, definite change that you always have to hand as you press the pitch bend buttons, no matter what record you use, means that your mixing is easier, quicker and sounds better.
Cleaner records
Pitch bend is also a good alternative to pushing or slowing down the tune with your fingers because it protects your records from excessive fingerprints and grime. As a DJ you're actively encouraged to touch your records, but a method that keeps your records as clean as possible is a good thing.
When you're considering buying turntables with pitch bend, try to see the feature in action first. Some turntables have a really clumsy control over the speed boost/lag, and can zip up the speed of your tune by too much, too fast, sometimes rendering the control pointless because you can never make small enough adjustments to get the bass beats back in time.
Tempo Reset/Quartz Lock
Earlier in this chapter, I describe the 'Bermuda Pitch Zone', which is where the pitch control goes a little wonky through the zero pitch range on turntables that click into place when set to zero. To get around this problem, turntable manufacturers started to make turntables with clickless pitch faders that glide through the zero pitch area, moving smoothly all the way through the entire pitch range. The problem with a clickless fader, though, is that you can't be sure when you're at exactly zero pitch any more. Some turntables still show a green light as you pass zero, but a better option is the Quartz Lock or Tempo Reset button, which resets the pitch to zero pitch, no matter where you set the pitch control.
Some people use this Quartz Lock almost like a pitch bend when the record is playing too fast. Hit the button once to slow the tune down temporarily and then again to bring the tune back to the speed you set it at. This technique is a bit hit and miss, though, and not as accurate as a pitch bend or using your hands. I like to use it by slowing a record right down by 50 per cent (or more) to really drag out the last couple of beats of a breakdown, then I use Quartz Lock to instantly return to zero pitch rather than an acceleration as I move the slider. The downside to this is if I was playing the tune at 5 per cent before slowing down to –50 per cent, the tune will now be playing at zero per cent, 5 per cent slower than before.
Master Tempo/Key Lock
Master Tempo – first available as an add-on to turntables by a company called Vinyl Touch, then available on Pioneer CD decks and now an option on a number of advanced, digital turntables – enables you to change the speed of a tune, but not its pitch.
The pitch control isn't just a speed control. As you increase or decrease the pitch control, the pitch of the music gets higher or lower as a consequence of the tune playing faster or slower. Pressing the Master Tempo button means that you can affect only the speed, leaving the pitch of the music as it was recorded.
Some decks take this a stage further, like with the Key Lock on the Numark TTX1 turntables. You can use the pitch control to select whatever music pitch you want the tune to play at, press the Key Lock button and then adjust the tempo while retaining your original pitch setting. Check out the info on harmonic mixing in Chapter 16 for more.
These controls can be quite temperamental, though – not just on turntables, but on CD decks and in software too. If the pitch setting is more than 4 or 5 per cent and you activate Master Tempo or Key Lock, you can sometimes add digital noise to the music, making the track sound as if it's playing underwater. Tunes with strong vocals tend to suffer the worst from this problem, whereas simple, musical tracks can withstand quite a large change.
You won't find any hard and fast rules for using the Master Tempo and Key Lock features, so you simply need to keep experimenting to work out how far you can push each of your tunes.
Digital display of pitch
The pitch control is an essential tool on a turntable, but its analogue nature means that you can't be 100 per cent sure that when you set the pitch to 3.5 per cent it's has actually changed by 3.5 per cent. Sometimes the smallest pitch change is all you need to make the beats of two tunes play at the same time; with a pitch fader that has no display you have to guess whether the pitch changes at all when you move the fader by a millimetre.
A digital display on the turntable shows you exactly where you've set the pitch, and whether you've adjusted the pitch by a small enough amount to make the beats play in time. This info helps you mix with confidence, taking away some of the guesswork that comes with analogue pitch controls.
Adjustable brake for Start/Stop
Traditionally, when you press Stop on the turntable, the record stops in about half a second. Some decks enable you to adjust the brake, which changes the time that the record takes to stop, giving you more control if you decide to use Stop as a mixing technique (see Chapter 16).
The half-second Stop is really nice, but even prolonging that to one bar of music (which equals four beats) can add another dimension to the mix, or you can set a really long brake time and emulate the power-off as I describe in Chapter 16.
In some instances, you can tighten the brake up so much that when you press Stop the record plays backwards!
Reverse play
Instead of adjusting the brake to make the turntable play backwards on advanced turntables, sometimes turntables have a handy little button (often located next to the pitch control) that does exactly the same thing. Simply press the Reverse button and the deck plays backwards. You get a slow-down-to-stop, start-up delay as you do this operation, but if your timing's right when pressing this button, it sounds great.
Some CD decks give you the option of instantly reversing the direction of the music, rather than needing to account for this delay as the record changes direction. See Chapter 8 for information on DJing with CDs.
Different shaped tonearms
For years the standard shape of the tonearm on a turntable was an S shape. The S-shape creates a variety of different forces upon the needle as it's pulled into the centre of the record – a tracking force, an inside force and a vertical force – which not only adds to the wear on the record but also, due to so many different forces, you can understand why the needle might jump out of the groove when scratching. In the late '90s Vestax pioneered the ASTS straight tonearm for DJs, which only has a tracking force affecting the needle. By cancelling out some of the lateral forces, the turntable achieves maximum stability, and the needle is less likely to skip out of the groove when you're in the middle of a really complicated, frantic scratch move.
The straight tonearm isn't aimed at only the scratch DJ, though. The reduction in forces acting on the needle in the groove means that you get a lot less wear on the vinyl, your records last and sound good for much longer and the needle is less likely to pop out of the groove when you're trying to locate the cue point in the record.
A lot of turntables come with only an S-shape or only a straight tonearm, but some decks from companies such as Numark now include both styles in an interchangeable format, so you can change the design of tonearm as often as you change your socks.
Turntable modification companies can create a fixture similar to the headshell joint that enables you to easily swap from one design to the other, depending on your mood (or that day's style of mixing).
Removable cabling
For years turntables came with the RCA cables (you may know them as phono cables) hard-wired into the electronic gubbins inside the casing. This setup meant that any damage to the cables involved opening up the casing and re-soldering the connections (if possible) or sending your precious turntable off for repair.
When equipment manufacturers realised that this was problematic for DJs, they started to make turntables with RCA plugs on the back, just like the inputs on the mixer. These turntables now have removable cables that you plug between the turntable and the mixer, and if anything happens to damage the cables they're easy to replace. The new design can also prevent further damage to your turntable because if you drop something on the cable, instead of the tug on the cable pulling the turntable onto the floor, the RCA plugs may act as a shock release, unplugging themselves through the force on the cable and saving the turntable from damage.
Digital outputs
As well as addressing the mechanics of the cabling on the back of the turntable, manufacturers also looked at the range and quality of output connections that they offer to the technology-driven DJ. Not content with the analogue signal sent through the RCA outputs, digital outputs such as USB and S/PDIF (which I describe in more detail in Chapter 13) are now on offer for you to connect turntables to a mixer or PC with a similar input.
Battle or club design
Look into the history of DJing and you see that club DJs have the turntables positioned as per the manufacturers' expectations, but scratch DJs turn them around 90 degrees, anticlockwise. The reason that scratch DJs turn their decks around is so that the needle is clear of their hands as they move like lightning from deck to mixer to the other deck and back again, all in the blink of an eye.
The downside to this orientation is that the power control, pitch control and Start/Stop button (all of which scratch DJs love to use) are now awkwardly placed. Companies such as Numark and Vestax saw a gap in the turntable market and designed turntables with Start/Stop switches at both corners, and pitch faders that you move from one side of the deck to the other, making it more comfortable for the scratch DJ to use the decks.
If you're a beatmatching DJ with no interest in scratching, turning up to a club that has the turntables set up with this 'vertical alignment' for scratch DJs can be extremely annoying. It's not as easy to access the pitch control, it's a bit harder to take the needle on and off the record and it simply isn't as comfortable to beatmatch with the turntables set up like this. Some time spent using turntables with this orientation soon gets you over this hurdle, so when you research a venue where you're due to play be sure to look at how the turntables are positioned and put in any required practice at home with this setup if need be.
Built-in mixer
Okay, I'm going out on a limb here: I believe that the Vestax QFO (see Figure 6-3) is the ultimate in advanced scratch turntables. Suggested, tested and tweaked by DJ QBert (a famous scratch DJ), this turntable is a feature-packed single deck aimed at performance scratch DJs, with a built-in mixer for performing scratches, reverse play, Quartz Lock and a straight tonearm. But best of all, you can take off two of the feet, put a strap on the remaining two feet and wear it like a guitar!
How practical the QFO is as a turntable for everyday use (especially at the cost of £750) is questionable, but if you're looking for the ultimate turntable gadget then this is it.
**Figure 6-3:** The Vestax QFO turntable.
Setting Up Turntables
The various features I describe in this chapter can make turntables appear to be complicated creatures if you know nothing about them. Whether you're using your turntables to play loads of different records, or just the same two over and over again when controlling music in software (see Chapter 9), you need to set up three different elements before use:
Deckplatter
Tonearm
Peripherals
Deckplatter
If you're using direct-drive turntables, all you have to do is make sure that you've removed the thick rubber mat that may have come with the turntable and then place the slipmat directly on top of the deckplatter and the record sits on top of the slipmat.
If you've just bought brand new belt-driven turntables, you may find that the belt hasn't been linked between the motor and the deckplatter. Carefully lift off the deckplatter and look underneath; if the belt isn't linked to the motor, it's probably taped to the underside of the deckplatter. Stretch the belt between the motor's capstan (the bit of the motor that turns) and the underside of the deckplatter. If in doubt, check the manual for instructions!
Tonearm
The tonearm holds the needle. If you set the tonearm up poorly, the needle can jump out of the groove when you're trying to find the cue point (see Chapter 14). Worse than that, though, a poorly set up tonearm can permanently damage the needle and your records.
As well as leaving the antiskate set to zero for DJ use, the tonearm may require adjustment in two different ways:
Counterweight
Height
Counterweight
The counterweight is a weight on the back of the tonearm that controls how much down-force the tonearm applies to the needle to keep it in the groove. The amount to add is suggested by the manufacturer of the needles and cartridges that you're using (Chapter 7 tells you more about needles and cartridges, and has a table of common counterweight settings).
The key to achieving your desired setting begins with a technique known as floating the tonearm (Figure 6-4 shows the correct, floating position; notice how the tonearm is completely parallel to the deckplatter, pointing neither up nor down).
To float your tonearm, follow these steps:
1. Remove any records from the turntable.
2. Starting on one of the turntables, carefully lift the tonearm off its rest towards the middle of the deckplatter.
3. While holding the headshell to keep the needle from crashing down onto the slipmat, turn the counterweight clockwise with your other hand so that it starts to move towards the back end of the tone arm.
4. As you move the weight backwards, frequently check to see whether a shift in weight has caused the tonearm to point up instead of down.
**Figure 6-4:** The tonearm perfectly balanced, with the needle removed from the cartridge to avoid damage.
5. When the tonearm starts to point up, turn the counterweight anticlockwise by a small amount in order to find the setting where the needle floats in mid air, neither pointing up nor down, as shown in Figure 6-4.
6. After you've found this floating point, return the tonearm to its rest and use the tonearm clamp to lock it into place.
7. Now hold the silver part of the counterweight and use two fingers to grip the black ring on the front of the weight. The ring, which has numbers on it, turns independently to the rest of the counterweight.
8. Turn only the black ring until the line pointing down from the number zero lines up with the line on the tonearm beneath it. Figure 6-5 shows you how to control the black ring.
The tonearm is now set to the floating position and has been zeroed. If your needle manufacturer suggests that you add 3 grams of counterweight onto the tonearm, turn the entire counterweight (so the black ring also turns) anticlockwise until the number 3 on the black ring lines up with the mark below it on the tonearm.
**Figure 6-5:** One hand supports the back of the counterweight while the other rotates only the numbered ring.
Height
The height adjustment on most decks is a ring at the bottom of the tonearm assembly that raises or lowers the tonearm as it turns clockwise or anticlockwise. A small mark on the assembly shows you how much height you've added, and unless you're a scratch DJ who uses a raised tonearm height to add even more down-force to the needle, your best bet is to follow the height suggested by the makers of the needle and cartridge you're using.
When you're altering the height of the tonearm, leave the tonearm in the tonearm rest with the clamp on to hold it in place. Otherwise, one wrong move and the needle may bounce across the record/slipmat/deckplatter.
Look out for the lock switch on the tonearm – without releasing this lock, you can't change the height, and if you try to force the ring, thinking it's stuck, you may do permanent damage to the tonearm assembly. Also be aware that when left in an unlocked position, the tonearm moves slightly and may fool you into thinking that you've damaged it.
Peripherals
The last items to attend to when setting up your turntables are the feet and the lids. Keeping the lids attached to the turntables when you're mixing is a bad idea; they get in the way and you may knock them, causing the needle to jump. Don't be lazy: take them on and off each time you use your decks.
The rubber feet on your turntables don't act as mere vibration dampeners. Because the feet screw in, adjusting how tightly they're attached affects the height of each of the four corners of the turntable, which is ideal when compensating for the badly built DIY furniture that your decks sit on. Grab a spirit level if you want to be precise, and adjust the feet to make sure that your decks are level. If they're not level, the needles may skip.
Servicing Your Turntables
Make your turntables last as long as possible by showing them a little bit of care and attention from time to time. You can find information all over the Internet for fixing various broken parts on your decks, but a little cleaning and lubrication can keep the gremlins at bay.
As a general rule for all your equipment, when you're not using it, keep it covered. If your turntables have plastic lids, put those back on when you're not using the turntables. If you keep the decks in flight cases, put the lid back on. If you have neither of these, put a clean bed-sheet (or something soft, clean and lint-free) over the decks when they're not in use, to catch any dust before it gets a chance to settle on your faders, motor and tonearm.
Motor: If you keep the motor properly lubricated, it can run smoothly for years. All you need to do is remove the deckplatter and put a small drop of sewing machine oil on the centre spindle. Use lubricating oil such as sewing machine oil rather than covering the entire insides of your deck with a slobbering of WD-40 spray!
After you've lubricated the motor, replace the platter and spin it round with your hand. You can use the turntable immediately, as long as you didn't pour half a can of oil all over the inner workings of the deck.
Tonearm: You need a can of compressed air and a can of degreasing lubricant to thoroughly clean and lubricate the tonearm assembly (the degreaser dissolves any dirt you can't clean by hand or air alone). Don't worry if you think these sprays are expensive; you're going to need them for your mixer too (see Chapter 10).
Cover the rest of your equipment with a sheet you don't mind getting dusty and then spray the tonearm assembly with the compressed air to remove any surface dust (the sheet is so you don't just move the dust from one deck to another). Spray the grease dissolver over the bearings in the tonearm to remove any ground-in dirt and keep them lubricated.
Pitch fader: Use the compressed air to blow any dirt out of the pitch fader. Use the cleaning lubricant to dissolve any dirt residue in the fader if you think that you have a problem, but using the compressed air is usually adequate to clean the fader.
Headshell: If you ever suffer from signal dropout from the cartridge (which is when the music starts to break up and cut out), use a pencil or a pin to clean any dirt off the contacts. I've heard of DJs licking the contact points on the headshell and the cartridge to try to clean off any dirt, but as well as being disgusting, your saliva (mixed with the beer you've been drinking) ends up damaging the contacts in the long run.
Check that the screws holding the cartridge are tight, that the needle is clean of any dirt build-up and that it sits securely inside the cartridge.
Under the platter: If your turntable comes with a removable deckplatter, lift it off and wipe around the underside with a lint-free cloth, and make sure to pick up any dust or dirt that may get trapped underneath. Using the spray can of air may be a bad idea because you can blow the dust farther inside the deck chassis. Although a little dirt may not cause a problem with the electronics, it's not a good idea to keep forcing more and more dust inside the turntable.
Chapter 7
Perfecting Your Decks: Slipmats and Needles
In This Chapter
Understanding what slipmats are for
Making sure that your slipmats slip
Knowing the differences in needle designs
Picking the right needle and cartridge for your DJing style
Prolonging the life of your needles (and records)
When choosing a turntable to DJ with, Chapter 6 encourages you to look for one with a good pitch control, an adjustable tonearm, a strong motor and a solid design – qualities that set the DJ deck apart from a home record player.
However, you still need to look at two more areas before your turntable is a true DJ tool: slipmats, and what types of needles and cartridges to use.
Sliding with Slipmats
As well as acting as an antistatic device, the slipmat is a key factor in transforming your new turntables from just a really good pair of record players to fully functional DJ decks.
The slipmat is the same shape and size as a 12-inch record, and sits between the record and the deckplatter (the part of the turntable that rotates to make the record rotate). Slipmats are normally made out of felt, and if you've taken my advice in Chapter 6 about making sure that your turntables have a smooth, metal deckplatter, you find that the low friction between the felt and the metal keeps the deckplatter turning underneath the record when you hold it in a stopped position. This simple function of the slipmat is extremely important when you want to start a record playing at an exact time, and is essential for successful beatmatching.
If the deckplatter has stopped turning underneath the record, when you let go of the record to start playing it again it can take almost a second to get up to full speed, meaning you've started the record later that you'd planned. With the slipmat helping the deckplatter continue to turn under the stopped record, the record takes little or no time to get to full speed, and your records start exactly when you want them to.
This friction-free slip is also essential for the scratch DJ so that he or she can move the record back and forth easily, without the drag and inertia of the full weight of the deckplatter moving backwards and forwards with the record.
The setup you want to achieve with the slipmat goes like this:
The deckplatter (the part with the bumps on the side that turns round) is at the very bottom.
The slipmat goes on top of the deckplatter.
You place the record directly onto the slipmat.
When you first buy your turntables, they may come with a thick, heavy rubber mat on the deckplatter with the slipmats placed on top. Remove this big rubber mat so you have the same setup I describe in the preceding bulleted list. If you leave the rubber mat on, the slipmat won't slip over the rubber mat, and the deckplatter will grind to a halt when you try to hold it stopped.
Choosing an appropriate slipmat
The two design concepts that affect how well your slipmat slips are its thickness and weight, and what kind of design is printed on it.
The best slipmat is made from a smooth, compacted felt, and is thin and light. If the slipmat is too thick and heavy, and the felt too rough (or too fluffy), the extra friction drags on the deckplatter, making it turn a lot more slowly under a stopped record, or making it stop completely.
The image printed on the slipmat can be a great expression of your personality. Search any online record store and you find a whole load of slipmats with different logos, designs, photos and colours printed on them. Slipmats like these are great to look at, but try to steer away from cheap versions that are covered in print because, depending on what technique the printer uses, your slipmat may stick to the record and cause drag problems, or the design can wear off and look bad, and may actually harm your records.
My first set of slipmats came second-hand (as did the turntables), and the print had started to come away and go slightly brittle, which ended up scratching some of my beloved tunes. I got around this problem by turning the mat upside-down, so the logo was in contact with the deckplatter and the felt touching the record. This method had the added bonus of reducing the friction even more, and made the slipmat a lot more . . . slippy.
Winning the friction war
When you hold your record still, the power of the motor (known as torque) directly affects how easily the deckplatter continues to turn underneath. If you have a weak motor or (gasp) you chose belt-driven turntables (Chapter 6 has more on choosing a turntables), the motor may have a hard time keeping the deckplatter turning even with the best friction-killing slipmats.
If you do find that your turntables grind to a halt when you hold the record stopped, before laying blame on your decks take a look at your technique. You don't need to press down hard on the record to hold it stopped: just rest one or two fingers towards the outer edge and that should be enough. Too much pressure adds resistance, stopping the deckplatter turning.
If you're convinced that it's a friction issue between the slipmat and the deckplatter and need to reduce the friction, you can buy commercial products such as Flying Carpets, which you put between the slipmat and deckplatter. However, before you spend even more money, try out this home remedy using some wax paper instead.
A circular piece of wax paper, cut to the same size and shape as the slipmat and then placed between the slipmat and the deckplatter, is a great way of reducing friction and resistance. If you don't want to go out and buy wax paper for this purpose, take a look through your records and look at the inner sleeves that protect them. You may find a sleeve made out of wax paper with one of your records. Just remember to keep that record protected with something else if you take away its inner sleeve.
Here's how to make a friction-killer:
1. Place the wax paper or inner sleeve on a flat cutting surface.
Carpets, dining room tables and the bonnet of your car are all suggestions of surfaces not to use.
2. Using your existing slipmat as a template and a sharp utility knife as a cutting tool, cut a 12-inch (30-centimetre) circle out of the wax paper.
3. Mark the centre of your cut-out by putting a pen through the centre of the slipmat, then cut a tiny hole at that point for the centre spindle on the turntable to go through.
4. Place this wax cut-out between the deckplatter and the slipmat, and try it out.
You'll find that the record slips more easily now.
Getting Groovy with Needles and Cartridges
The needle is the part on the turntable that sits in the groove of the record. As the record plays, various bumps and ridges inside the groove cause vibrations in the needle that the cartridge translates into electrical signals, which are then sent from the turntable to the mixer, and you hear music. This is how the groove makes you groovy.
You need to know what the different kinds of needle and cartridge are, and how to pick the correct ones for your DJing style. The needles you use as a DJ are a lot stronger than the ones you find in home turntables because they need to take a fair bit of abuse. Back cueing (playing the record backwards while trying to find the place to start), scratching, the inevitable whoops when you rip the needle right across the record and repeatedly taking the needle off and placing it somewhere else on the record with a thump can all take a toll on even the most robust of needles.
The good news is that any needle and cartridge designed for DJs can go on any turntable. You don't have to use Stanton needles and cartridges on Stanton turntables; you don't have to use the Technics headshell that comes with Technics turntables. Manufacturers of DJ turntables have been smart enough to design a universal connection from the cartridge to the tonearm, so that you can use any cartridge on any turntable. This flexibility stands as long as you haven't just bought a basic, cheap, hi-fi turntable with an all-in-one, moulded tonearm and cartridge, or gone for a high-end design that uses different connections. Figure 7-1 shows the back of some cartridges with the same connection.
**Figure 7-1:** The same connection on the back of different cartridges.
Your cartridge and needle considerations come in pairs (fitting, because you usually buy them in pairs). Firstly, there are two main designs for how the cartridge eventually attaches to the tonearm, and then you also have to choose between two different styles of needle:
Headshells with the cartridge and needle screwed on: This design is the one that nearly always accompanies your turntables when you buy them. This doesn't mean it's a poor design, it's just the design that covers all bases. One of the most popular and enduring scratch DJ needle setups is a Shure M44-7 needle and cartridge attached to this headshell, and you find the Stanton 500AL (see Figure 7-2) in clubs and bedrooms all over the land.
The top of the cartridge is screwed to the headshell, and the needle plugs into the cartridge (the needle is the front, white part shown in Figure 7-3). Four coloured cables make the electrical connection from the cartridge to the headshell, which then plugs into the tonearm to make the final connection.
**Figure 7-2:**
A Technics headshell with Stanton 500AL attached.
**Figure 7-3:**
A disassembled needle and cartridge with a Technics headshell.
Built-in headshell: This design does away with the separate headshell; instead, the cartridge, which is the main body of this unit, plugs directly into the tonearm. The needle is still separate, and easy to remove and replace, but the sleek all-in-one design makes this cartridge a very attractive part of your turntable.
This style of needle and cartridge has a strong link in clubs for the beatmatching DJ, but is just as suitable for scratch DJs. To name only two, the Numark CC-1, pictured in Figure 7-4, is the signature model of the Scratch Perverts, and the Ortofon Concorde QBert was developed through DJ Qbert (both world-class scratch DJs).
**Figure 7-4:** The Numark Carl Cox needle and cartridge.
After you've decided on the design of your needles and cartridges, the next thing you have to think about is whether to buy elliptical or spherical needles. A lot of manufacturers supply both shapes for the same cartridge, and you can get them for both the designs I mention in the preceding bulleted list, so the choice is down to your preference rather than availability.
Spherical: A spherical needle has a rounded tip that only makes contact with the straight sides of the groove, so the contact between the needle and the groove is extremely small (see Figure 7-5).
**Figure 7-5:** The small range of contact with the groove when using a spherical needle.
The small contact area creates a very strong tracking force (the force created between the needle and the sides of the groove) so the needle puts up a fight against jumping out of the groove, making spherical needles an excellent choice for scratch DJs. However, the concentration of the tracking force means that the record wears down more quickly, and the small contact area with the groove means less of it causes the needle to vibrate, resulting in reduced sound quality.
Elliptical: Elliptical needles make more contact with the sides of the groove because of their cone shape (shown in Figure 7-6), producing much better sound quality because they can pick up more information from the groove. However, the trade-off for this improved sound quality is that the tracking force is now spread out over a larger surface area, making it easier to knock the needle out of the groove. This makes elliptical needles unsuitable for really vigorous scratch moves (see Chapter 17), but they're perfect for the beatmatching DJ who demands great quality of sound.
**Figure 7-6:** The larger range of contact with the groove when using an elliptical needle.
Digital DJs who use timecoded vinyl to control music playing on computers (see Chapter 9) are usually safer with elliptical needles. Although sound quality isn't an issue, because the needles only need to carry a simple high pitched timecode signal, spherical needles would cause excessive wear to the groove and would be a great cause for concern because these DJs play the same two control records over and over again for the entire set.
If you're buying new turntables, find out whether they come supplied with needles and cartridges. Most stores include the basic Stanton 500AL cartridge and needle set with turntables, but do check – never assume. Imagine this scenario: you're waiting excitedly for your decks to be delivered, but when they arrive you find that needles and carts haven't been included, so you have to wait before you can use your new decks – and all because you forgot to check when you ordered.
Feeling the Force with Counterweight Settings
The counterweight affects the tracking force of the needle in the groove. The heavier the counterweight, the stronger the force, so the more secure the needle is in the groove – but the quicker your records wear out.
In Chapter 6 I describe how to set up your tonearm properly for DJ use, and how to add the correct amount of tracking force with the counterweight. Firstly, needle manufacturers dictate how much counterweight you add on the tonearm. The documentation you receive with the needles and cartridges tells you the suggested tracking force and suggested tonearm height for the needles you've bought. However, some of these figures aren't aimed toward DJ use, where you need stability; they're sometimes calculated for the greatest longevity of your records instead.
As a brief guide for you, here are the most popular counterweight settings for common DJ needles:
Needle | Counterweight (in grammes)
---|---
Stanton 500AL II, Stanton Discmaster II, Stanton 605SK | 2–5
Shure M44-7, Shure Whitelabel | 1.5–3
Numark CC-1 | 3–6
Ortofon Concorde DJ S | 2–4
Ortofon Concorde Night-Club S | 2–5
If you find that the needle still skips when you're scratching or trying to find the start point of the record, first check your technique. If you're quite rough as you move the record with your hands, it may be that you're the one making the needle jump out of the groove. You don't have to be forceful to move the record; you can move it back and forth just as quickly with a light, fluid motion as with a harsh, rough, jerky movement. When you push and pull the record, follow the curve of the record, rather than pushing and pulling in a straight line. This straight line force is a common cause for the needle popping out of the groove.
If you think that the needle is jumping because not enough counterweight is on it, try gradually increasing the counterweight until the needle stops skipping. Take your time and increase the counterweight by small amounts each time. And when the needle does stay securely in the groove, try taking a little weight back off again; you'll probably find it's still okay.
Though vinyl is designed to be long-lasting and not wear out too quickly, if you find you've had to use the full counterweight on the needle to keep it from jumping out the groove, you must understand that the added tracking force will wear out the record and the needle quicker than usual.
Nurturing Your Needles
Knowing when you need to change your needles requires a mix of professional help and general knowledge. The only way to truly know whether your needles are worn out and in need of replacement is to look at them through a microscope. Not many people have a microscope sitting next to their turntables, so you may want to do a bit of research now and get in touch with some of the specialist stores in your area to see if they can check your needles for you.
However, you can look for the following simple things yourself:
Are the needles picking up lots of dirt from records?
If you play a quiet part in a record, the next time you play the record does it pop and crackle because of damage caused by a worn needle?
Do the high frequencies (especially the hi-hat cymbal sounds that normally play in between bass drum beats) sound fuzzy?
Have you had your needles longer than a year, and used them for a couple of hours nearly every day?
Does you gut instinct tell you that your needles need replacing?
If you can answer yes to half of these questions, especially the last one, then the chances are you need to replace your needles. If you're using relatively cheap needles such as Stanton 500ALs, trust your instinct and buy some new needles. But if you're using something like the Ortofon Night-Club E, which cost £45 each, get them checked out first by a professional, rather than immediately going out to spend £90 on a pair of new needles.
Because you plan to DJ with these needles, their lifespan is inevitably shortened, but you can do a couple of things to extend their usefulness:
Keep your records clean. You'd think that if Mr Diamond and Mr Dust got into a fight with each other, Mr Diamond would win. Unfortunately, that's not the case with your diamond-tipped needle and the dust in the groove of your record. If you consider that by the time you play three or four records, the needle has played through a couple of miles' or more worth of record groove, if a piece of dirt is constantly grinding away on the diamond tip, the needle's going to wear down much more quickly than if it were playing on a clean record.
Keep the weight down. The more counterweight you add, the quicker the needle wears down. It's as simple as that.
Your needles and your cartridges are literally the first point of contact for the music you're playing. Take care of your needles, and make sure that you replace them when they're worn. No matter how good the rest of your equipment is, if your needles aren't picking up all the information they should from the record, your music won't sound as good as it can.
You can only make poop from poop. Bad sound in equals bad sound out. Enough said.
Chapter 8
Spinning with CDs
In This Chapter
Considering designs of CD decks
Locating the right tune and cue point using different CD deck controls
Starting the CD and making pitch corrections
Trying out additional CD deck features
The great thing about mixing with CDs if you beatmatch is that the only way the beats of two tunes can drift out of time is if you haven't correctly set the pitch. When the pitch is right and the beats are in sync, all you have to worry about is the mix, not dodgy motors on cheap turntables.
This chapter discusses the various controls on CD decks and how CD DJs use them to do the same thing as vinyl DJs, and use them to take mixing to another level of creativity.
Knowing the Requirements of the DJ's CD Deck
A CD deck meant for DJ use is different from the one that sits sandwiched in a home hi-fi system. The main differences are:
The layout of the CD deck
Controls and displays to help you search and find exact start points in tunes
Pitch controls that enable you to alter the speed at which the CD plays
Rugged designs that prevent the CD from skipping
DJ CD decks have many more improvements (see the later section 'Taking Advantage of Special Features') but these design features are what separates domestic from DJ.
Laying out the design
CD decks come in a few different designs, and although the functions and ease of use vary depending on the layout of the CD deck, these various designs allow you to mix music no matter what genre you play. Rock, pop, indie, house or wedding DJs can use any of the CD decks I mention in this section. The only DJ who may demand something specific is the scratch DJ.
Twin CD decks
Twin CD decks (shown in Figure 8-1) are split into two halves. The top part is a control panel, with two sets of time displays, playback and cue controls, a pitch slider and pitch bend, and a jog wheel for each deck to help search through music on the CD. Together, these controls let the DJ find the right place in the track, start it playing, set the pitch controls to match beats if beatmatching, return to the cue point, start the tune with a press of a button and adjust the speed briefly with the pitch bend if the beats aren't properly matched.
The control panel is linked by a cable to the other half of the unit: two CD players that use a 'tray' system (like a home CD player) to take the CDs in and eject them when you're done.
Image 8-1: The Numark CDN22 Twin CD deck.
Twin CD with a built-in mixer
Twin CD decks like the Numark CD MIX series (shown in Figure 8-2) take the twin CD design one step farther; instead of a separate twin CD unit and a mixer, everything comes together as one piece of equipment. This design is good on paper, but as the mixer that's included with this kind of setup is quite basic (especially in the case of the CD MIX), you limit yourself in creativity by going down this route.
This design is good for the party/wedding DJ, who only uses the mixer to set the volumes of both the CD players, and performs a very simple, very quick mix from one CD to the other. But because the mixer is basic (mainly because of a lack of EQ controls) it doesn't give you full control over the sound of the mix.
This CD and mixer combination does look good financially when you start as a DJ, but beatmatching DJs will soon yearn for a new mixer, and this is a problem because even though you can send the outputs of the CD decks on this combined CD player/mixer unit to another, separate mixer, you're still stuck with the original mixer lumped together in a big box of plastic and metal with the CD decks. The mixer is always part of your setup, whether you use it or not.
Image 8-2: Numark's CDMIX 1; good value unless you want more.
Single CD Decks
Single CD decks don't tend to use the tray design that the twin units use. Older CD decks used a top-loading design, where the top of the deck was hinged and opened up for you to insert the CD, but the newer CD decks use a slot on the front of the unit, which automatically takes in and spits out the CD using motors (similar to the CD player you may have on your car stereo).
The controls on offer on single CD decks are similar to the twin units, except the pitch slider may be a lot longer (which offers you finer control) and the jog wheel is bigger, helping you find cue points (start points) on the CD with ease. Single CD decks may also have a host of other controls to enhance the mix such as loops, reverse play and hot-cues (see 'Taking Advantage of Special Features', later in this chapter).
Scratch DJs and CD Decks
Innovations in CD technology have given the scratch DJ an avenue to scratch on CD, but doing it well, with ease, comes at a price.
The first thing that affects how well you're going to be able to scratch on the CD deck is the size of the jog wheel you use to perform the scratch. Scratch DJs need large jog wheels that they can scratch on as though they were normal records. This means that the jog wheels on twin CD decks, which are sprung and only turn 90 degrees left and right, aren't suitable for the scratch DJ.
In the same way, I've found that single CD decks with relatively small jog wheels, although still used by scratch DJs, make it a lot harder to perform complicated scratches.
The most important thing the scratch DJ needs from a CD deck is for the CD to sound like a record when being scratched. Unsuitable CD decks just stutter and stop when the DJ turns the jog wheel, but the ones suitable for scratch DJs sound identical to a record player when you play the music backwards and forwards with the jog wheel.
Many scratch DJs prefer the pro level CD decks that come with large jog wheels, such as the affordable Stanton C.304, or the more expensive Pioneer CDJ-1000MkIII (shown in Figure 8-3) and Denon DN-S3500.
Image 8-3: The Pioneer CDJ-1000 MkIII single CD Deck.
Navigating the CD
The biggest difference between vinyl DJing and CD DJing is how you find a start (cue) point in a tune, and then how you start the tune playing. With vinyl, finding the cue is easy: pick the right side of the record that your tune is on, look at the groove, place the needle near to where you want to start, move the record backwards and forwards to hear the precise cue point and then hold the record stopped at that point. The hardest part when DJing with vinyl, especially beatmatching, is starting the record at the right time so the beats play in time with the beats on the other tune instantly.
CD DJing is the complete opposite. After you've found the correct cue point, starting the tune in time is extremely easy; all you need to do is press the start button, and if you're beatmatching just press it in time with the other beats. Locating the precise cue, however, can be a bit more difficult. Finding the cue on a CD means locating the right track on the CD, scanning (fast-forward or rewinding) through the track to find the general area you want to start from and then fine-tuning the cue by playing the CD forwards or backwards by the smallest of amounts.
Although this doesn't sound particularly difficult, CD decks don't have a visual reference other than the time display to help you know where (or when) you are in the tune in order to set the cue. Wave displays, which have a series of peaks and troughs to show the louder and quieter parts of the tune, can help with this problem, but you only find them on the more expensive CD decks such as the Pioneer CDJ1000MkIII as shown in Figure 8-4.
**Figure 8-4:** The Wave display on the CDJ1000 MkIII.
Keep the inlay covers or written tracklists with your CDs to help you find what the track number for a certain tune. Don't just print on the CD itself, though – reading what's on the CD when it's spinning inside the CD player is rather hard! Putting all your CDs together in a case with the tracklists makes reading the track names and numbers easier, and saves time and frustration when trying to find the track you want to play next in the mix.
Different CD decks have slightly different sets of controls to find the cue, using one or (more commonly) a mixture of the following designs:
Buttons
Jog dials
Platters
Buttons
CD decks with very basic controls only use buttons to navigate the CD. You use one pair of + and – buttons to go through the track numbers on the CD to locate the correct tune to play and a second pair to search through the CD and fine-tune the cue point.
The longer you hold down search buttons, the faster the CD plays in either direction. If you just tap the search button, the CD plays frame by frame (a frame is the smallest time change that the CD deck can give you), which enables you to locate the exact cue.
Repeatedly tapping the search button makes the music play in slow-mo, but because the CD deck repeats each frame you stop on over and over again until you move on, the sound you hear is like a broken CD. This digital noise can initially lead to difficulty in hearing where you are in the tune, making it hard to set a precise cue. Listen out for a change in the sound that's playing; when the sound has more bass to it, you're likely to be on the bass drum. (The cue point you want to set is likely to be one of the bass drums in the tune – see Chapter 14.)
Using buttons to find the cue is quite laborious and takes patience and a good memory of the tune to do quickly. However, developing the knack for finding the cue this way doesn't take long, and although the cheaper, budget CD decks tend to use only buttons, as long as you can find the precise cue when you need to then nothing's wrong with this basic design.
Jog dials
The jog dial on a twin CD deck is between 7–12 centimetres in diameter, and is normally made of two parts: an outer ring and an inner disc (see Figure 8-5).
**Figure 8-5:** The jog dial on a twin CD deck.
CD decks with jog dials still tend to use buttons to find the track you want to play on the CD, but a sprung outer ring on the dial replaces the search button you find on cheaper CD decks to find the general area in the tune you want to start from. How far you turn the ring left or right changes how fast the tune searches backwards or forwards. When released, the ring returns to the centre position, playing the music at the speed you set with the pitch control.
An inner disc inside the outer, sprung ring makes fine-tuning the cue a lot easier. Most of these CD decks are designed so that their inner disc gives a little click as it turns, with each click representing a frame in the music. By spinning this disc backwards and forwards quickly, you can play the music in slow-mo and then turn the disc more slowly to play the music more slowly and find the exact frame. When scanning through the track frame by frame, you do still hear a digital repetition of the frame you're on, so this still takes concentration, knack and a good ear to hear properly, but it's a lot easier than only using buttons to do the same thing.
The jog dial on a twin CD deck is small and quite fiddly to use, but single CD decks that use a similar, sprung jog dial tend to have much larger dials because the top of the deck has more room – and this increased workspace makes fine-tuning the cue easier.
Platters
CD decks used to try to keep up with and emulate turntables, but the introduction of large control platters now means CD decks have matched and surpassed the functionality of the vinyl turntable, revolutionising the world of CD DJing.
Motorised, rotating platters (as found on the Denon DNS3500 – see Figure 8-6) or manual platters that only turn and affect the music when you touch the platter (as found on the Pioneer CDJ1000MkIII that I use) help CD DJs find the cue in the same way as a vinyl DJ, by controlling the CD just like a record on a turntable, spinning the platter back and forth to find the general area of the tune. But more importantly, when locating the cue, these decks emulate the exact sound you'd hear if you were using vinyl rather than the stuttering, digital, broken CD sound you get on other CD decks.
You can still use track Skip and Search buttons to locate the general area in a specific tune, and then use the platter to fine-tune the cue point like you would with a record on a turntable, playing it backwards and forwards until you find the exact place.
**Figure 8-6:** The Denon DNS3500 platter.
Adjusting the Pitch
As with vinyl DJing, locating start points and starting the tune in time is only part of beatmatching. The other important part is using the pitch control to adjust the speed to make the bass beats of the new tune in the mix play at the same time as the one currently playing through the speakers.
The good news is that the pitch slider on CD decks acts in exactly the same way as on a turntable (refer to Chapter 6). Pitch controls have improvements, such as adjusting the range from 4 per cent to 100 per cent or more, but the principle is the same: moving the slider towards you (into the + area) makes the tune play faster; away from you (the – area) makes the tune play slower. (Check out Chapter 14 for more on the basics of using pitch control when mixing.)
However, if you set the pitch control slightly too fast or too slow and the beats start to drift, you can't push the CD like you can with a record (even if you could touch it, the CD would skip). So pitch bend controls are on hand to get the tracks back in time. These controls may be different depending on the CD decks you're using:
Buttons: Usually found on twin CD decks but sometimes used on single decks, two buttons (one marked + and one marked –) temporarily speed up or slow down the tune when you press them. The longer (and sometimes harder) you press the button, the greater the pitch bend you achieve. When you let go of the button, the CD returns to the speed you originally set with the pitch control.
Small jog ring: Found on a number of twin CD decks, there's usually a button or switch that changes the function of the sprung outer ring from 'search' to 'pitch-bend'. You turn the jog ring to the right to go slightly faster, and to the left to go slower. How far left or right you turn the ring affects how large a pitch bend you get. When you return the ring to the centre position, the CD plays at the set pitch again.
Large jog wheel: Depending on your CD deck, the large jog wheel may work in exactly the same way as the small jog ring. In the case of the expensive CD decks with platters, you can temporarily adjust the speed that the tune plays at as if it were a piece of vinyl.
With vinyl, if you need the record to run faster you can make the record turn faster, or if you need to slow it down you add some resistance to the side of the deck. It's exactly the same with CD decks like the Denon DNS3500, which have motorised plattters: push the platter to play it faster, or run your finger along the side to slow it.
The Pioneer CDJ1000 uses a ring around the edge of the platter as a pitch bend. Turn it clockwise to speed up the tune, or anticlockwise to slow it down. Importantly, it's only when the ring moves that any change happens to the CD and how fast you move the ring directly affects the amount of pitch bend. So quickly spinning the ring forward or back by a couple of inches is normally all it takes to get the beats back in sync.
No matter what method you use to adjust the error in beat sync, remember to change the pitch control to reflect your adjustment. If you needed to briefly slow down the tune and the beats are drifting further and further apart, make sure that you reduce the pitch control slightly, and increase it if you needed to speed up. Otherwise, because you haven't set the speed of the tunes exactly in time, you'll need to keep using the pitch bend to get the beats back in time. If it was just a starting error you needed to fix, just use the pitch bend and don't worry about altering the pitch control unless you hear the beats starting to drift out of time.
Smoothing Out Vibrations
The good news is, you don't need to do or know much when it comes to dealing with vibrations caused by loud bass sounds and physical knocks.
When you buy your CD decks be sure to do a little research and make sure the ones you're choosing have a good antiskip feature. Nearly all CD decks designed for DJing have some level of antiskip; you can hit or throw some CD decks across the room without the CD skipping; others can deal well with sound vibrations, but if you're too rough with them the CD judders and skips.
When you've chosen your CD decks, consider where you place them. The first thing to consider is what they'll sit on while you use them. Choose something heavy and solid that won't transfer any sound vibrations into the chassis of the CD deck, which may cause it to skip. Also try to put the decks somewhere you won't easily bump into them. (Sitting them so they overhang your desk at waist height is asking for trouble.)
Lastly, put some thought into speaker location. Avoid placing your speakers on the same piece of furniture that your CD decks are on, because bass vibrations may travel through the solid surfaces and cause the CDs to skip.
Working with the Cue
No matter what format you use to DJ with – CD, vinyl, computer software or an app on your iPhone – the basic concepts of DJing and of beatmatching remain the same: find a precise starting point (the cue); if beatmatching, set the pitch control so that the beats of your tunes play at the same speed; start the tune playing; and then make sure the beats play at the same time if you're beatmatching. The choice you make about what format to use only affects the mechanics of how you go about each stage.
I describe how to use the pitch control and pitch bend function to beatmatch on CD decks in Chapter 14, but finding the cue, starting from it and returning to it on CD needs a dedicated explanation.
The four steps to properly work with the cue are:
1. Locate the cue.
2. Store the cue.
3. Check the cue.
4. Start the tune from the cue.
Locating the cue
No matter what controls your CD deck has (see 'Navigating the CD', earlier in this chapter), you need to locate the precise cue. If you often start from similar parts of the track, take note of what the time display reads and write that info next to the track title on the inlay sleeve.
Some CD decks (like the CDJ1000 and CDJ2000) have memory cards that can save the cue points that you set on your CDs. This means that you can return to a stored cue point almost immediately after you pop the CD into the deck.
If you haven't written down or stored a cue point for a tune yet, here's how to use the controls to find the cue:
1. Use the search controls to get close to where you want to set the cue, and if the tune doesn't automatically start playing when you release the search control, press Play so that you can hear the music.
2. When you're near to the cue point, press Play again to pause the music, then use the jog controls (buttons, dials or platters) to slowly go through the tune to find the exact start point of the first bass drum of a bar or phrase, or whatever piece of music you want to start from.
When fine-tuning the cue, if you want to start on a bass drum you'll hear the sound change to have more bass frequencies as the drum hits. Experiment with setting the cue before or on this sound, to see how this affects your timing when you press play. It may only be 100th of a second difference, but it can make all the difference between starting beats in or out of time.
Storing the cue
After you've found your cue point, you need to store that position to the CD deck. On some CD decks, when the CD is in pause mode and you've located the exact cue, you simply need to press Play to set the cue point, and if you ever need to return to it, just press the Cue button again. Pioneer CD decks are different in that you press the Cue button to store the cue when you've found it. Interestingly, the Denon DNS3500 CD decks have a button that lets you choose between either of those methods, so you can set the cue in the way that's most familiar to you. Read the manual that comes with your CD decks so you know what method you should use to store the cue.
Checking the cue
Start your tune, and if you find that you haven't set the cue accurately enough, return to the cue point and use the jog controls to fine-tune the cue and store this new, updated cue.
After you've found and successfully stored the preferred cue, you need to return the CD to that cue point, ready to start the tune in the mix. This may just be a case of pressing the Cue button, but sometimes the state the CD deck was in before you pressed Cue affects what happens afterwards. On some CD decks, if you're in play mode when you press Cue, the CD returns to the cue point and restarts playing from there, or if you're in pause mode then pressing Cue returns you to the cue point and the CD stays paused. However, on Pioneer CD decks, pressing Cue in pause mode resets the cue to where you are at that instant.
This is why it's exceptionally important that you learn how your CD decks operate. Read the manuals that came with your CD decks so you don't accidentally press the wrong button at the wrong time!
Starting the tune
Starting tracks on CD is a lot easier than on vinyl. When the tune that's playing through the speakers gets to the part you want to start the new tune, press Play on the new tune and then go to the mixer to mix between them.
If you're beatmatching, listen to the bass beat from the other tune. Try to block out the rest of the music and focus on the boom from the bass, almost like meditation – helping you press Start on the new tune at the same time as the one that's currently playing. Pressing the button exactly on the beat takes practice, but it's nowhere near as hard as starting tunes on a turntable.
If you prefer a challenge, and still want to start tunes like vinyl, CD decks with motorised platters can let you do this. Find the cue point, hold the platter still and then let go, or give a little push to start the tune.
Taking Advantage of Special Features
DJ CD decks improve on home CD players by including pitch controls, rugged designs and better navigation, but that's not where the improvements end.
MP3 playback
As music becomes easier to buy and download online it makes sense that a lot of the music you'll purchase as a DJ will be files you download from iTunes or other online stores like Beatport or Audiojelly (see Chapter 4 if you need tips on buying online).
CD players that allow you to play downloaded music that you've burnt to writable CDs (CD-R or CD-RW) aren't unique to the DJ CD deck – home and car CD players have been able to do this for a long time. However, a feature that negates the need for a CD disc and reads music directly from USB hard-drives, iPods and flash cards is a great addition to DJ CD decks.
CD decks such as the Pioneer CDJ2000 (pictured in Figure 8-7) and the Denon DNHS5500-CD still allow you to play CDs and CD-Rs, but connecting external hard-drives give you access to thousands of tunes, all without needing to worry about ejecting and storing individual CDs.
**Figure 8-7:** The CDJ2000 is packed full of features including MP3 playback.
The important thing to investigate when looking at this kind of CD deck is how well the display and controls let you navigate the large library you're using. If you have a CD with eight tracks burnt onto it, it's hard to get too lost finding a track; even if you're unsure what one you need to play, you only need to skip through eight tracks to find it. If you've just connected an iPod containing 6,000 tunes, it might take a little longer to go through them one by one . . .
Most CD decks that allow connection of external hard-drives account for this, though, and have large screens to help you sift through your library in even the darkest, dingiest of DJ booths.
Master Tempo
Master Tempo isn't unique to CD decks; it's available on a lot of turntables too. It enables you to speed up or slow down a tune without changing the key that the music was recorded in. So if you play Barry White and pitch him up (speed up the tune) by 16 per cent, he still sounds like Barry, whereas decks without Master Tempo make him sound like a chipmunk.
Some CD decks do this better than others. The more you speed up the track, the harder it can be for some CD decks to keep the pitch the same, and some can suffer terribly from digital noise problems if you try scratching with Master Tempo turned on. If you think you'll use this feature a lot, be sure to get a demonstration of it working on the CD deck you're buying.
Hot Cues
Normally labeled 1, 2, 3 or A, B, C, Hot Cues are extra cue points that you can set on-the-fly, which means that you don't have to stop or pause the CD in order to set them. Doing so takes a little hand/ear coordination, but setting and then returning to these cue points is very simple.
You can then use hot-cues to jump around the CD, instantly playing different parts of a tune, or even jump to a Hot Cue that you've set in another track on the CD! Repeatedly pressing the same Hot Cue button returns to that cue point each time you press the button, playing the same part over and over.
Loop
The loop function plays a discreet part of a tune from an in point (that you can set anywhere in the tune) to an out point (that you also need to set). When you hit the Loop button, the music plays from the in point to the out point, then in to out over and over again, until you stop the loop.
Looping intros and outros or sections of a tune can extend the mix and subtly remix the tune to make something different, or looping part of a buildup to extend it adds variety to the mix. If the buildup is a drum-roll, set it as a loop and edit the length of the loop so it gets shorter and shorter; the shorter the loop gets, the more frantic the breakdown sounds and you can work the crowd into a frenzy before finally ending the loop or hitting a Hot Cue button and crashing back into the powerful beats of the tune.
Loop controls vary in their ability to help you get it right. If you're looping one bar of beats, and haven't hit the in and out points exactly on the beat, you'll hear a stutter/jump of beats each time the loop restarts. Some CD decks automatically adjust the loop for you; others let you edit the loop points and fix any issues; whereas with some CD decks you need to get it right first time, every time.
You can use loops creatively to keep a good part of a track repeating, or you can use this feature as a safety net. If you haven't had time to set up the next track in the mix yet and you're approaching the end of a tune, you can repeat a section of the end of the tune, giving you the time to set up and mix in a new tune. (This shouldn't ever happen, but you might spend too long talking to the wrong person and run out of time.)
If you're the type that always runs out of tune, you could try saving a Hot Cue earlier in the track and then trigger it to jump back and repeat the last minute. This can be easier than using loop controls, because if you're about to run out of tune it's easy to get flustered and begin to panic, which can make it difficult to set accurate in and out points in a loop – but you do need to plan ahead.
Sample banks
Similar to the loop function, instead of setting in and out points, you can record a section of the music into sample banks (memory contained on the CD deck) to play back as and when you like.
You can use these samples in as many ways as you can think of. You can loop them or play them on their own, and on some CD decks you can also play them over the CD that you took the sample from, letting you remix a track or mix into another tune on the same CD deck! The creative possibilities are endless.
Reverse play
Reverse play is possible, and a nice gimmick with vinyl, but CD decks give you a lot more control. For starters, some CD decks let you choose whether you want the CD to go into reverse just like a turntable or instantly. If a record is at zero pitch at 33 revs per minute (rpm), it needs to slow down from 33 rpm to zero and then accelerate from zero to 33 rpm in reverse. Some CD decks offer the same de-acceleration and acceleration sound, but also the choice to instantly reverse the tune without any delay. The Denon DNS3500 gives an incredible level of control over reverse playback.
BPM counters
Instead of needing to buy an external BPM counter or a mixer with beat counters built into it, many CD decks calculate and include the BPM of a tune you're playing in the time display area.
Like any BPM counter, it can be easy to rely on this calculation rather than use your ears when beatmatching. Try to avoid falling into this trap, otherwise the first time you use equipment that doesn't have a BPM counter you won't be able to beatmatch very well.
Digital DJ software control
Denon, Numark, American DJ, Pioneer and many other DJ CD deck manufacturers have models that can control music playback in software that supports MIDI (musical instrument digital interface) and USB connections, instead of relying on timecoded control discs. Check that the digital DJ software you use allows this before buying CD decks for this purpose.
Having Fun Experimenting
Many more features are available on CD decks, and each year a new piece of equipment with a brand new innovation escapes into the DJing community, so it's easy to lose track of what your CD deck is capable of.
If you're unsure about what your CD decks can do, or how best to utilise their functions, read the manual, go to clubs to see them in action and check out video clips on websites. Between reviews on manufacturers' websites and personal reviews on magazine websites and on YouTube, you should be able see the deck you love doing all the things you didn't know it could do.
Or just toss the manual under the bed and experiment for a while. Then, after you're thoroughly confused, try to find that manual again . . .
Chapter 9
Bits and PCs: Digital DJing
In This Chapter
Discovering various digital DJ setups
Choosing and controlling the right software for you
DJing on the move
In my opinion, digital DJing – using computer software to play music stored on a hard drive – is as big a revolution to DJing as when someone realised that using two turntables and a mixer could keep the music playing all night with no gaps.
With digital DJing, the equipment the DJ uses no longer restricts the music available to play. Vinyl DJs who previously needed to tirelessly hunt out music available on vinyl can now download tracks to their hard drives and use their turntables to control the DJ software. CD DJs can take charge of their libraries, binning the countless CDRs they've strewn across the DJ booth by keeping all their music on one hard-drive instead.
Alongside greater access and control of music, the creativity and accessibility that digital DJing opens up is outstanding. Whether through a vast host of built-in effects, loops and samples to enhance the sound of a mix for creative DJs or an auto-beatmatch function that can keep new DJs inspired if they hit a plateau while learning how to beatmatch properly, digital DJing is helping to create and motivate a new generation of DJs.
Designing Your Digital DJ Setup
The three things you need to consider when putting together a digital DJ setup are:
A computer
Any external hardware to control computer software
The software for DJing
Processing computer hardware
The computer is the heart of your digital DJ setup and as such it's vital to make sure it's as powerful, stable and capable as possible.
Mac versus PC
If you're lucky enough to be shopping for a new computer to use for your digital DJ setup, the decision to use a Mac or a PC probably comes down to what you're more familiar with and which one you prefer. I've used a Windows laptop and a Macbook Pro in my setup, but have stuck with the Mac.
The more popular, market-leading DJing software titles that I describe later in this chapter, such as Traktor, Serato and Ableton Live, release their programs for both Windows and Mac operating systems. However, some DJ programs (like PCDJ and BPM Studio) only work on computers with Windows operating systems, so if you've decided on the software you want to DJ with before thinking about the computer you'll use it on, do some research to check whether you'll be forced into using a Mac or PC by the software specifications.
Few DJing programs don't work with Windows, so this caution is aimed more at the Mac user, but Windows users still need to check that the software works with the installed operating system. Some titles have been slow to adopt Vista and Windows 7; others need at least Windows XP Service Pack 3 or later; and if you've still got that old Windows 95 PC, it might be time to dust off your wallet and go shopping for a new one.
Desktop versus laptop
The most common design of computer to use in a digital DJ setup is a laptop/Macbook style due to its portability and compact nature. Full size work-stations, PCs and Mac Pros work just as well as laptops – sometimes better due to a larger screen, increased memory and faster processor speeds – but they're not very portable when hopping from club to club, and finding room for a separate keyboard, mouse and monitor might prove tricky in a DJ booth or in your bedroom setup.
Memory and processor considerations
If your computer is old, check that you have enough processing power and RAM along with suitable hardware (such as supported soundcards and USB ports) to run the software you want to use.
For PC DJs, most software recommends a minimum of a 1.5GHz processor (how fast your computer can 'think' and do what you want it to do is measured in Hertz – Hz) and 1Gb (gigabyte) of RAM (think of RAM like a car-park: the more spaces, or RAM, your car-park has, the more cars can go about their business; but with fewer spaces, less cars can park, or less applications can run smoothly on your computer, and a bottleneck will build, slowing down traffic and your computer).
PC DJing software usually needs Windows XP Service Pack 3 or later to run properly. For most DJing programs, Mac users need an Intel Mac with similar processor and RAM minimum requirements as the PC DJ. The most recent OSX operating system is likely to work fine, but check the software requirements to be sure no compatibility problems exist.
If you can choose a computer that has features well above the recommended minimum of the software, you'll find you have a smoother DJing experience. You might want to record your mix as you perform or have an Internet browser window open at your chosen MP3 store, in case you need to buy a tune to play to the crowd in front of you. Increased memory and processor power lets you do this without risking glitches and sound problems in the DJing software. It's like giving you more floors to your car-park, and getting the cars moving around faster.
Stability
Stability largely depends on how fast your computer is, how well you maintain it and what other programs and processes are running in the background. But whether you're buying the DJ software on its own, or a new computer too, do some research on Internet forums (and on the specific DJ software websites) to make sure the software works in harmony with your hardware.
I experienced problems with my HP laptop where if I had the Wi-Fi card turned on the music would cut out intermittently – which doesn't go down very well in the middle of a club! I don't tend to hook into Wi-Fi during a set to download music to play (or update my Facebook status like a few DJs I know), so it's not an issue for me. But loads of DJs (especially party and wedding DJs who get wide-ranging requests) love having the option to download any music to play instantly, so Wi-Fi access can be an important complement to their music library.
Macs aren't immune to hardware problems either. Earlier Macbook Pros required you to connect USB soundcards to the socket closest to the power input in order to maintain enough power to keep the music from cutting out.
Do some research before and after you buy your setup to avoid being plunged into silence during a DJ set. Software websites are usually very good at giving setup and troubleshooting advice. The Native Instruments website has a comprehensive list of tweaks for Vista and XP operating systems; go to www.native-instruments.com/support and search for 'tuning tips', or just search their forum and knowledge base. Even if you're not using their Traktor software, the troubleshooting ideas on their website may solve any problems you might be experiencing with the DJ software you've bought.
Controlling the Digits
Digital DJing is based around software running on a computer with a common layout of the software display similar to what you'd see in a DJ booth: at least two decks to play the music, with a mixer in between, and a library of your tunes underneath it all (see Figure 9-1). However, what makes digital DJing so fascinating is that you aren't shackled to a keyboard and mouse to control the software.
**Figure 9-1:** The Traktor Scratch Pro interface – two decks, a mixer in between and the library of tunes below.
Mouse clicks and keyboard strokes are the most basic way to navigate and adjust the various controls and options in DJing software. However, by adding some external hardware, digital DJing evolves into a true performance, for your experience as the DJ and for the people on the dance floor too.
Setup options available for the digital DJ include:
Use a laptop only (or a computer with keyboard, mouse and display) with DJing software installed – you control everything with the keyboard and mouse.
Add a better soundcard and a DJ mixer to the laptop, leaving the mouse and keyboard controlling only playback of the music.
Use a DVS (Digital Vinyl System) to control the playback of music using any turntables or CD decks, with the option of adding an external mixer too.
Combine control over playback of the music and a mixer in an all-in-one piece of hardware.
Connect CD decks via USB or MIDI (musical instrument digital interface) to control playback of the music. Adding an external mixer minimises keyboard and mouse use.
Laptop/computer only
By far the simplest setup is in Figure 9-2. Install software, connect the output of your computer's soundcard to an amp and navigate the music library, adjust playback of the music and control the mixer all with the mouse and keyboard.
**Figure 9-2:**
A simple setup between your laptop and amplifier.
Nothing's wrong with DJing this way – you can do everything that any other digital DJ can do. You just might need a little more time to navigate menus, click and drag cue points back and forth, find the right key to press to activate an effect and then to move the mouse slowly enough when controlling the cross-fader and EQs on the internal mixer in the software so that the mix still sounds good. And in my opinion, a DJ just using a mouse and keyboard to perform the mix gives a bit of a lacklustre performance. For all I know, I'm looking at a manager checking email, not a DJ mixing up a storm!
The connections and requirements for this setup are relatively simple. All you need is:
A laptop (or a computer with a display, mouse and keyboard) with a soundcard so you can output to an amplifier
DJ software
Music files
Amplifier and speakers
A cable to connect the soundcard output to the amplifier (check the connections on your setup)
A downside to this option is that the output of a laptop is likely to be just a headphone socket. This can be a low level sound output that needs amplifying more than a normal Line level output and could result in a lot of interference and noise being amplified too.
The bigger downside, however, is that as a DJ you want to be able to send the main mix sound to an amplifier, but also be able to listen to the next tune you want to play in your headphones (without it being sent to the amplifier too; check out Chapter 12 if you need more information about why this is important). A laptop-only setup is unlikely to let you do this because it probably has only one output (the headphones) and even if it has a Line output and a Headphone output, it's unlikely that you can play a different tune through each one through the software. In order to make this happen, you need to add some hardware.
Enhancing the basics by adding hardware
You can buy a new soundcard (most likely to be an external, USB soundcard) that can split two different signals sent from the DJ software and that has at least two outputs, one of them being a headphone connection. With this more advanced soundcard, you'll be able to send the main mix to the amplifier and listen to the next tune in the headphones, as Figure 9-3 shows.
**Figure 9-3:**
A laptop with an external soundcard. You can connect the two outputs to an amp and headphones, or both to a mixer.
Adding this kind of soundcard to your laptop setup also means you can add a DJ mixer to your setup too. This means you can mix between tunes using traditional DJ hardware with a lot more control (and performance value) compared to using only the keyboard and mouse.
By using a soundcard that can accept two input signals from the DJ software and that has two outputs, you can send Deck 1 of the software to Channel 1 of the DJ mixer, and Deck 2 to Channel 2 of the mixer. You mix the music from both decks using the mixer like a conventional DJ would, and the output from the mixer is then sent to the amplifier to rock the dance floor!
It's rare you'll find DJ software that can't send two output signals to a soundcard, but if you're unsure about the functionality of your chosen software title, or if it has any specific recommendations for what soundcard to use, do some research on the program's website or on Internet forums first.
DVS using records and CDs
DVS ((Digital Vinyl System) is how digital DJing has found its place and exploded into clubs and bedrooms all over the world.
DVS setups are similar to the arrangements I explain in the previous sections, except instead of needing to use a keyboard and mouse to control and adjust playback of the music in the software, you can use traditional turntables (or CD decks) to do the same thing, as Figure 9-4 shows. If you use a mixer in this setup, the only time you need ever go near the laptop's keyboard or mouse is to select the next track to play or to enable any effects. Even then, adding hardware controllers like the Kontrol (see the later section 'Adding Hardware Controllers') means that you don't even need to do that either!
**Figure 9-4:**
A timecode-controlled DVS setup. Shown using turntables, this works just as well with CD decks.
The DVS option in Figure 9-4 is based around records or CDs that play special timecode data into a special soundcard. The DJ software reads the timecode data and matches it to the music you want to play. So if you move the needle on the record one minute in and start it playing, the track you've loaded into the matching deck in the software starts playing from one minute in. If you stop the record turning, the music stops playing too, or if you play the record backwards, the music playing from the computer plays backwards.
Nearly all software that you can use in a DVS setup has fantastic vinyl emulation sound (whether you're using CDs or vinyl), so not only does the music stop playing or play backwards, but also it sounds exactly the same as if the music were playing on that record instead of from a computer. This enables scratch DJs to scratch with DJ software and it sounds no different to if they were scratching a record with real music on it instead of timecode squeal.
In a DVS digital DJ setup, a separate mixer isn't essential, because you can still use the software's built-in mixer (if it has one) to mix the music. But most DJs with a DVS setup won't stop at using only CD decks or turntables; they'll add a mixer to their setup too, so it faithfully emulates a traditional DJ setup.
Connections and requirements
Nearly all DJ software that you can buy as a DVS setup uses a specific soundcard designed by the software manufacturer. For example, I use the Audio-8 hardware interface (what they call the external soundcard) when DJing with Native Instrument's Traktor, and then have to unplug it and connect the Serato SL made by Rane when using Serato to DJ with (see 'Picking Out the Software', later in this chapter, for more about DJing software choices).
Unfortunately, in most cases, you won't be able to buy just the software, a cheap soundcard and a few cables and then use your turntables to play MP3s on your laptop. With wide-ranging price ranges between different DJ DVS setups, though, you should be able to find one within your price range, so hopefully the rigid hardware specifications don't become too much of a problem.
Connections are important but can seem complicated, with the external soundcard acting as a connection junction between turntables, CD decks, the mixer and the computer. You connect the outputs of the turntables (or CD decks) to the soundcard (using RCA to RCA cables) and the soundcard to the computer via USB, transferring the timecode data from the CD or record to control music playing on the computer. The music is then sent back to the soundcard, and you connect the outputs of the soundcard to the mixer, with the output of the mixer sent to an amplifier. It may sound confusing, but once you work out the chain of what's happening, and look at the writing on the soundcard, it's not that bad!
Some soundcards (like the Serato SL) have two inputs and two outputs so you can control and send only two tunes from the computer to the mixer using these connections (just as if you'd connected two turntables or CD players directly to the mixer playing normal records or CDs).
The Audio-8, used with Traktor, has four inputs and outputs, which in my case means I can use both of my turntables and both of my CD decks at the same time, controlling four tunes and mixing between them with my four-channel mixer – not something I do often, but it's nice to have the option!
DJ software manufacturers realise that you may have a large library of normal CDs and records, so they usually have a function that lets you bypass the software to enable you to send the music from real records and CDs directly to the mixer to use in the mix. If you want to use existing records and CDs in your DJ sets, check that the software, hardware and cables let you do this before spending loads of money only to leave your old library useless.
Adding Hardware Controllers
Although DVS pushed the boundaries of digital DJing, external controllers are probably the most fast-moving and exciting side of digital DJing hardware now.
All-in-one hardware controllers
Simplifying connections and equipment needs, hardware controllers from the likes of Behringer and Hercules (and many more) release you from a reliance on the keyboard and mouse to control software in the same way a DVS setup can, but mean you only need a laptop, some software and the controller.
Combining playback control, a mixer, effects and the audio interface, these hardware controllers are incredibly convenient and sometimes cost-effective ways to DJ. Different makes and models offer different levels of functionality. Lower priced offerings from Behringer or the Hercules DJ console offer an affordable yet full level of control, and more expensive mixers like the Allen & Heath Xone:4D, which controls similar functions to the cheaper alternatives, give greater flexibility and options for creativity.
Most of these hardware controllers allow you to add other input devices too, so not only can you play music stored on the computer, but if someone hands you a CD with music he wants you to play, you can throw it into a CD deck (if you have one with you) and mix it into music playing from the computer.
Control and effect
A hardware controller like the Kontrol, which is designed to work best with Traktor (shown in Figure 9-5), gives you full control over the effects in the software but also has a section to control playback of the music. DJs with DVS setups who want to be able to control effects with hardware instead of mouse clicks can make great use of this kind of controller, as can laptop DJs who want to expand their control over the software but don't want to be saddled with a cumbersome all-in-one controller.
**Figure 9-5:** Traktor Kontrol.
Putting CD decks and mixers in control
Instead of using timecoded records or CDs to control music playing in software, special CD decks like Pioneer's CDJ400, 900 and 2000 along with Denon and Numark CD decks connect to DJ software directly via MIDI or USB to control playback of the music. With no CD or record to play, stability and reliability is 100 per cent locked in when using these pieces of kit, with internal gubbins inside the CD decks themselves doing all the controlling.
You still need to decide whether you want to use the internal mixer in DJ software or an external one (I suggest using an external mixer), and you need to make sure your CD decks work with the software you want to use.
This method takes a lot of the confusion out of the connections of equipment. USB connections to the computer control the music in the software, and standard audio outputs of the CD decks are sent to a mixer in case you want to play a real CD instead. You still need a soundcard to connect the music from the software to the mixer, but overall the connections are nowhere near as complicated as the DVS connection method.
Your way is the best way . . . for you
The decision whether to add hardware to your DJ setup is entirely up to you. If you can still create a great sounding mix with your chosen setup, and you love using it, then it's the right one for you.
The kind of DJ you are may affect how big your setup is. Party DJs may be happy with just a laptop; DJs who work in a bar and want a bit more control but still keep things compact may just add a mixer to the laptop. Club DJs are likely to want to use the more expanded options, using hardware controllers or DVS setups for full control and performance reasons.
Picking Out the Software
Pick the right software title for you depending on how much money you have in your pocket and how you much control you want over the software.
Keeping it simple with jukebox software
Although most DJs want to use DJ specific software, if you don't really need or want to get too involved in the mechanics of mixing, you can easily set up jukebox programs like iTunes, Windows Media Player or SilverJuke, which offer different levels of control.
From a hardware point of view, this is the most basic digital DJ setup: just a laptop connected to an amplifier. Load all your tunes into the music jukebox program, create a playlist of music you want to play, enable any cross-fade options that may be available so that the songs overlap a little (in iTunes, check 'Crossfade Songs' under the Playback preference) and then walk away. iTunes takes care of everything, randomises the order in which the tunes play, mixes them together and even keeps the overall output volume the same if you enable Sound Check.
If you want a little more control over the playlist, get hold of the latest version of iTunes and select the DJ option. This lets you add tunes and change the order of play while the music's playing. You still don't need to worry about sound control or mixing the tunes together – you just have greater control over what music plays and in what order.
As good as it is, the iTunes approach is in danger of putting a lot of DJs out of work as bars decide it's cheaper and more reliable to have a pre-loaded computer at the end of the bar playing a set list of tunes than a DJ who has an opinion. Stop these bar managers in their tracks by being the best DJ you can be!
Software designed for DJs
From free titles like Mixx and Zulu to expensive, industry-standard options like Traktor and Serato, most digital DJing software titles tend to have interfaces designed around the same basic setup shown in Figure 9-1, earlier in this chapter.
What's added to this basic design separates DJ software titles from one another. Very basic software just has the players (with pitch controls and cueing section), a mixer and the library, with no effects, no waveform display to help you find the beats in the music and no option to connect external hardware to control the software.
However, recent software releases address these issues, with features packed in to help you create a fantastic sounding mix. Even Mixx and the free version of Zulu have built-in effects, auto-beat-sync and a waveform display to help you with cue points and beatmatching.
Considering auto-beat-sync
Auto-beat-sync is a very seductive feature. By automatically dealing with beatmatching for you, and sometimes even finding perfect placement points so that bars and phrases match, it's all too easy to simply let the software take over so all you have to do is move the cross-fader to mix between tunes (and most software can take control of this too!).
If you're busy adding effects, dropping in samples and scratching up a storm, and want to give yourself more time to be creative by removing the mechanics of beatmatching, auto-beat-sync is a useful tool. If you're not doing any of this and have loads of time to beatmatch properly, but your constant reliance on auto-beat-sync means all you do is move the cross-fader from side to side every four minutes, leaving the computer to take care of beatmatching and placement, you're cheating yourself out of learning a great skill. You're still DJing, but you're only half a DJ.
Waving for help
A waveform (shown in Figure 9-6) is a visual representation of music. When the music is loud and powerful, the waveform is bigger; when it's quieter, it's smaller. So bass beats (which are loud and powerful) show as sharp spikes in the waveform. By looking at the waveform and spotting where these big spikes are, you can work out when bass beats are going to play. For example, in Figure 9-6 a section of music has no bass beats for a short period, but when you see the big spikes, that's when the bass beats start to play.
Waveform displays do more than let you know what's about to happen in the next few seconds. By zooming out and viewing the entire waveform for a tune, you can tell where the music changes through its different parts of structure (check out Chapter 15 for more about the structure of your music). This way, you can make sure the next tune you want to mix in starts at the correct place to allow for perfect placement (see Chapter 16).
**Figure 9-6:**
A tune's waveform in Traktor Scratch Pro – the peaks are bass beats.
Serato aids beatmatching by showing the waveforms of two tunes playing side by side. Spikes of different frequency in the music are a different colour in the waveform, which means you can see what's a bass beat and what's a combined bass/snare beat. Looking at how closely similar colours of the waveform play next to each other when you're adjusting the pitch of the cued tune (the next one you want to add to the mix) can help unlock the mystery of which tune is playing faster than the other. And when similar coloured spikes are locked side by side, you'll hear that the beats are matched, with the bass beats playing at the same time. It takes a little getting used to, but with enough practise, it's easy to do.
Perfect placement, getting bars and phrases matched, takes more attention, and still needs you to listen to the parts of the tune that work best together, but the two waveforms side by side can give a boost to the DJ who's struggling to grasp beatmatching.
The waveform isn't just for beatmatching DJs; scratch DJs benefit from it too. You can locate the sample that you want to scratch by looking at the waveform. By watching the waveform move back and forth while scratching, you can ensure you're returning to the correct sections of that sample (Chapter 17 has more on scratching).
Taking Control
What can make you lean towards one software title or another is how you can control it. Software that you can only control by a mouse or keyboard can be quite hard to use quickly and creatively, but software that lets you use external controllers, or even your turntables or CD decks to play the music, open up great options, both creatively and as a DJ performance in front of a crowd.
Most software works with USB hardware controllers from Behringer, Hercules, Vestax, Denon, Pioneer, Numark and many more, but check first before buying the software and hardware, just to be sure.
A growing number of options also allow DVS control (see 'DVS using records and CDs' earlier in this chapter), and this is what most DJs look to use. The two leading lights in my opinion are Serato and Traktor. Both titles are sweeping through clubland as clubs install the hardware you need to use them properly into their DJ booths.
I have both Serato and Traktor, simply so I'm never stuck if I'm in a club that uses one or the other, but at home I use Traktor because of the expanded functionality. Without the link to Live (see the next section), Serato is designed as an easy-to-use, reliable music playback and mixing title, giving little added value like effects, whereas Traktor has built-in effects and unending customisation to help you set it up to create the best mix you can.
Livening up software choice
DJ solutions that emulate a twin CD setup are great for traditional DJs who want to mix from one tune to the other, add samples, scratch and add effects to the music, but Live by Ableton (for Mac OS and PC) uses more of a sequencer approach to put the mix together, taking mixing on computer a step further by allowing you to remix any of the tunes live during the mix.
You can use Live through each stage of the musical process; so you create the music and then perform that creation to the crowd as a DJ. The software is so versatile that you can remix the tunes on-the-fly, live to the crowd, and add MIDI controllable instruments to the mix, to create a completely unique remix and a DJ set that nobody else has ever heard or may ever hear again.
You need to do a fair bit of prep-work before you can beatmatch with Live, which is one argument that some people have against using it to DJ with. Instead of having a pitch control to affect the speed of your tracks, Live uses a warp function that helps to change the tempo of the tune. The warped songs in Live link to the program's internal beats per minute (BPM) clock, so changing the BPM of a tune from 135 BPM to 138 BPM is effortless, and takes no time at all during a performance. For this technique to be effortless, though, you need to give the software reference points to know how to adjust a tune's BPM quickly. In Live, these are called warp markers, which you add to the waveform display in the Live software.
The setup process sounds quite complicated, but it isn't. If you ripped your entire CD collection into Live for a mix, you'd only need to take a little time to analyse the tracks and prepare each of the songs with warp markers in order for Live to be able to change the BPM when you're beatmatching.
In the past, some people have accused Live DJs of cheating, lacking the skill to beatmatch, and say that sets performed on Live are preconceived and no better than a mix tape played through the sound system. However, Sasha, John Digweed, and Gabriel & Dresden are typical of the DJs that use Live: they've all proven that they're already masters of their craft, and use Live to expand their creativity rather than cheat the DJ skills. Because the beatmatching is essentially done for you by Live, DJs are left to focus more on what tunes they want to mix, and how they put together mixes between tunes and create the effects and track layering that build up a unique sound to the mix.
A whole host of controllers and options are available for whatever stage of the music process you use Live for, so you aren't faced with a DJ staring at an iMac, clicking a mouse. With audio interfaces and controllers for making music, and mixer and output interfaces to control Live for DJ performances, you can't accuse anyone of lacking in aesthetics when using a computer with Live and a few controllers attached to it. Check out www.ableton.com for more information.
Bridging the gap
One of the most exciting developments in recent times for Live is its partnership with Serato. Using software called The Bridge from Serato, you can use Serato to mix tunes together using a DVS setup (see the earlier section 'DVS using records and CDs') but also utilise the remixing capabilities of Live to turn the mix into something incredible. This union of Serato and Live using The Bridge turns Serato from a rock-solid playback title into a must-have for the creative DJ.
Exploring Alternatives
Huge digital DJ setups incorporating two CD decks, two turntables and a mixer might be good if you're looking to perform a big, complicated mix, but other options are available, ranging from the very simple DJ option on iTunes to mixing with iPods, iPhones and MP3 gadgets. Unfortunately, DJ Hero on the Xbox or PlayStation isn't really DJing . . .
DJing with iPods and USB drives
If you'd like to keep a toe in the digital DJing waters, but don't really want to go as far as lugging a computer around with you, try these alternatives.
DJing with hard-drives
You can use USB hard-drives that hold thousands of music files in a few different ways.
If you DJ using software on a computer you can use an external hard-drive to expand your storage space. If your internal hard-drive is only 50Gb in size, you can store around 10,000 tunes. By adding a 1Tb (1,000 gigabytes) external drive, you now have the ability to store approximately 200,000 more tunes!
It's not only DJs who use DJing software who can gain from this expansion of music storage. CD decks like the Pioneer CDJ2000, the Denon DNS1200 and many more from the likes of Numark, Gemini and Citronic allow you to connect a USB drive and play, control and (if applicable) effect the music on the hard-drive in the same way as if you'd inserted a CD into the player.
The iBooth
An iPod is, in essence, just an external hard-drive. However, the music library database it contains is what makes this a lot better than a simple USB hard-drive that has 200,000 tracks placed in one folder.
You have a few iPod solutions, the most basic being using two iPods connected to a mixer, but because this doesn't allow you to change the pitch of the music (which you need to do when beatmatching) it isn't the ideal choice.
DJ equipment manufacturers have come up with several solutions to DJing with iPods that range from a simple connection that uses the iPod in exactly the same way as an external USB hard-drive to connecting the iPod to a CD deck or mixer and allowing access to the library of music, but with limited playback capability.
However, for functionality versus cost, Numark's iDJ2 (shown in Figure 9-7) leads the way in iPod DJing in my opinion.
**Figure 9-7:** The Numark iDJ2 offers a digital solution for iPod DJing and regular DJing.
The future's bright . . .
I imagine the ultimate design for a digital DJ hardware setup is something that encompasses all needs: a Swiss-Army knife of DJ mixers and controllers that would allow the DJ to stay digital, or continue to use turntables and CD decks if so desired. Although combinations of functionality exist already, the ultimate mixer for a digital DJ would be something that allows full control of DJ software, the ability to play, navigate and have full control over music from hard-drives and iPods, a mixer section comparable to the most expensive Pioneer or Allen & Heath mixer, with everything linked together via simple single cable connections instead of complicated patch and splitter cables.
Although something like the Numark MixDeck comes close, the ultimate mixer isn't out there quite yet. But believe me when I say it won't be long!
The most impressive feature the iDJ2 offers is the ability to play two tracks from the same iPod at the same time. With an LCD screen helping to navigate and manage your iPod's library, a complete mixer with EQ controls, cue controls, metering (to make sure you keep the sound output at its best) and a cross-fader curve adjust, it helps the iPod DJ create stunning mixes.
The ability to connect turntables and CD decks as well as USB hard-drives to the iDJ2 means that it's ideal for DJs who want loads of music and format options available to DJ with. Check out www.numark.com/idj2 for more about the iDJ2.
Though still functional for a lot of DJs, be aware that the previous model, the iDJ, didn't allow you to alter the pitch of the music – vital if you want to beatmatch your tunes. So if you want to beatmatch, and you're shopping for one of these iPod solutions, make sure you get the iDJ2, not the iDJ.
Mixing on the move
DJs no longer need to be chained to a DJ booth in order to mix up a great set. Portable, handheld DJ devices and applications (apps) on smart-phones won't replace the traditional DJ booth, but for short, sharp, entertaining DJ sets, they've opened up the glass door to let the DJ perform outside of the booth.
A few DJ gadgets are out there, but in my opinion the Tonium Pacemaker is one of the most fun and effective portable mixing consoles available. It has everything you need to beatmatch, mix, effect and record your mixes jammed into a handheld device along with storage for over 15,000 tracks. It's incredibly intuitive and creative to use, and the end results, I think, are stunning.
For something a bit more substantial, but just as portable, the Nextbeat by Wacom can either be desk mounted for standard DJ booth use, or if you want to add a performance aspect to your DJing it has a removable controller that lets you walk out onto a stage, into the crowd or just over to the bar, and mix a fantastic set while ordering a drink.
iPhone apps can help you pick a restaurant, magnify the menu, book a taxi home and then track a bike route to help you burn off all those calories the next day! Even better than that, though, if you hunt through the App Store (you'll need to download iTunes from www.apple.com/itunes to access this) you'll find apps that let you emulate the DJ booth with your iPhone.
Apps like Quixpin DJ (see Figure 9-8) have loads of features, with two input decks, a full featured mixer with cross-fader curve adjust and all important pitch controls to aid beatmatching. A comprehensive set of different output modes through the headphones let you listen to the next tune before you add it into the mix (see Chapter 12) and if you utilise an audio splitter out of the headphone socket you can connect your iPhone to a DJ mixer and use it as two separate decks!
**Figure 9-8:** The Quixpin DJ app for the iPhone.
iPhone apps aren't just about the full mix experience either. Apps that work as BPM counters, virtual single turntables (so you can add a third device and do some scratching with it), music production apps and even controllers for software like Serato and Traktor have all helped to turn the iPhone into the third hand that you sometimes need in the mix.
And these apps aren't just for iPhones: Windows Mobile and Android phones have a few apps available that are capable of DJing too. Search on the Internet to see whether any applications exist for your phone.
As with the bigger Digital DJ setups, audio connections are very important when using portable devices to DJ with. Before parting with your money, check that you're able to connect your device to an amplifier, but also check you can connect headphones to listen to the next tune without people hearing it through the amplifier.
Other things to keep an eye out for are that your portable device is fully charged if running on batteries, and if it relies on Bluetooth or Wi-Fi connections to operate or send/receive music, test all the connections before trying to mix in front of a crowd. Otherwise, you'll just be someone standing on a stage in front of a crowd holding a phone with a panicked expression.
You could phone a friend for help while the phone's in your hand, though . . .
Chapter 10
Stirring It Up with Mixers
In This Chapter
Finding out about the mixer's most common features
Looking at the advanced options available
Choosing the right mixer for your DJ style
Keeping your mixer in tip-top condition
Mixers are a very demanding breed of animal. They come with many functions and features, and can manipulate the music in many ways. But in the end, mixers only do what you tell them to do.
This chapter explains how the vital controls on a mixer function and how they relate to your DJ mixing style. Understanding that much sets you on your way to buying the right mixer.
Getting Familiar with Mixer Controls
In your journey as a DJ, you'll come across a vast range of mixers. Some you may already know about, and some you won't ever have seen before. If you understand what the features are on a mixer, and how to use them, you need never accidentally press the wrong button and cut out the sound.
Well, never may be too strong a word . . .
Inputs
The common DJ mixer accepts three different input methods:
Phono inputs for turntables
MIC inputs for microphones
Line inputs for everything else
Professional digital mixers also have S/PDIF, USB and Firewire inputs to connect digital sources (such as CD, MiniDisc and PC inputs) and keep the music playing at the best possible quality. For information on how to connect these, and the standard inputs in the list, head to Chapter 13.
Phono inputs
Records are recorded in a special way in order to fit all the information onto the vinyl. The mixer needs to translate the signal it receives from the turntable in a completely different way to a CD player or any other device, and it's the Phono input you use for this translation.
Line inputs
All other equipment (CD players, MP3 players, MiniDisc players, the audio output from your computer and DVD player and so on) sends out a Line signal to the mixer. When you want to use any of these, you use the Line input on the mixer.
On a two-channel mixer, both channels have a Line and a Phono input connection. This means that you can connect two turntables and two CD players to a two-channel mixer, and use the Line/Phono switch to select the CD player or turntable input for either channel.
Mic inputs
As well as accepting playback devices like turntables and CD players, most mixers also have XLR or quarter-inch jack inputs for connecting a microphone. There's usually a separate volume and EQ (equaliser) control to affect the bass, mid or high frequencies in your voice so that you can sound great speaking to the crowd.
Outputs
Basic mixers usually have two outputs, with better mixers having at least three outputs.
Master Out connects to an amplifier. The LED display on the mixer relates to how strong a music signal you're sending out of the Master Out to the amplifier. The stronger the signal, the less you have to turn up the amplifier. Too strong a signal, though, and you may cause the sound to distort because the amplifier can't process it properly.
Record Out is for sending music to a recording device like a CD burner, digital recorder or computer. The output LEDs on the mixer have no bearing on how strong a signal you send to the recording device through this connection. Only the channel-faders (the vertical faders) and the gain control (which changes how strong a signal comes in from the turntables or CD players) affect how strong a signal you send to a recording device.
Booth Out sends a signal to a separate speaker in the DJ booth so that you can hear the music too! This is vital in a large club where the main speakers are far away. The delay in sound between those speakers and your ears can make beatmatching very difficult.
For more on each of these outputs, and how to connect them to their intended recipients, check out Chapter 13.
Multiple channels
Although you can have two turntables and two CD players plugged into a two channel mixer and flick from Line to Phono, having a dedicated channel for each input is more convenient. You also need more than two channels on your mixer if you want to use three CDs or three turntables, because you can't plug a turntable into the Line input and you can't plug a CD deck into the Phono input on a mixer.
A mixer with three or four inputs can cater to most DJs' needs, and if you need more than four channels to use all your equipment, I'd be more worried about the electricity bills than where to plug it all in!
Cross-faders
The cross-fader (see Figure 10-1) is a simple horizontal slider that enables you to change the music played out of the mixer from one input device to another. The cross-fader is a lot like the control on your shower that lets you adjust how much hot and cold water comes out. You can have only cold, only hot and many, many different combinations in between.
**Figure 10-1:**
A cross-fader on a mixer.
After you've towelled off thoroughly, go to your DJ setup. Tune A plays into Channel 1 on a two-channel mixer (and is usually the turntable or CD deck positioned on the left side of the mixer) and Tune B plays into Channel 2 (on the right-hand side of the mixer).
With the cross-fader positioned to the far left, you only hear Tune A. When the cross-fader is all the way to the right, all you hear is Tune B.
However, the cross-fader comes into its own when it's anywhere in between. If the cross-fader is in the middle, the output of the mixer is both Tune A and Tune B, and if the cross-fader is to the left of middle, you can hear more of Tune A than Tune B (and vice versa).
How much louder Tune A is than Tune B is dictated by something called the cross-fader curve. The cross-fader curve controls how quickly one tune gets louder as the other one gets quieter when you move the cross-fader from side to side. The following figures show some common cross-fader curves you'll encounter. Figure 10-2 shows a simple cross-fader curve.
**Figure 10-2:**
A simple cross-fader curve.
At Position 1 marked on the cross-fader, Channel 1 is at full and Channel 2 is silent.
By Position 2, both tunes are playing at around 90 per cent of their loudest volume.
By Position 3, Channel 2 is at its loudest and Channel 1 is silent.
The cross-fader curve in Figure 10-3 helps to stop both your tunes blaring out of the speakers simultaneously at near to full volume.
At Position 1, Channel 1 is full and Channel 2 is off.
At Position A, Channel 1 is still full; Channel 2 is starting to come in (playing at about 10 per cent of its full volume by this stage).
At Position 2, both tunes are at 80 per cent of their normal volume.
By Position B, Channel 2 is now playing at full volume and Channel 1 is playing at 10 per cent volume.
And by Position 3, Channel 2 is playing at full volume, with Channel 1 silent.
**Figure 10-3:**
A faster cut-in on the cross-fader curve.
Although this curve is similar to the first example, the straight line in this 'curve' gradually brings in one tune while removing the other one, whereas the swooping curve in the first example kept the tunes playing together for longer at a higher volume level.
Figure 10-4 shows the cross-fader curve preferred by many scratch DJs due to the speed at which you can cut in (make audible) the second tune at full volume.
Position 1 shows Channel 1 playing full and Channel 2 is off.
At Position A, both channels are playing full volume, and it only took a small amount of cross-fader movement to get there.
This situation stays constant until Position B.
At position 3, Channel 2 is full and Channel 1 has been removed.
**Figure 10-4:** The more immediate 'scratch' curve for the cross-fader.
You can also get a straight X-shape curve, which fades one tune out while bringing the other tune in at exactly the same ratio throughout the move. If Tune A is playing at 10 per cent, Tune B is at 90 per cent – if Tune A is at 73 per cent, Tune B plays at 27 per cent, and so on. (That's likely to be the cross-fader curve of your shower control too.)
A number of mixers come with just one kind of cross-fader curve, but most mid- to high-range mixers have a way to change the cross-fader curve by selecting pre-defined curves with a switch or with a control that enables you to create any kind of curve you like.
Channel-faders
Channel-faders are the up and down faders that control how loud the music comes out of the mixer when the cross-fader is all the way over to one side, allowing the full power of a channel to play.
Taking another visit to your bathroom, think of channel-faders like the taps on the bathroom shower. Even though the water mixer (the cross-fader) is set to only let out cold water, if you don't turn on the cold tap, nothing comes out. So although the cross-fader lets you mix hot and cold water to the right temperature through the showerhead, the channel-faders control how much hot and how much cold water is available to mix together in the first place.
Getting back into the DJ booth then, the ability to vary the volume of the two channels, as well as mixing with the cross-fader, gives incredibly precise control over the mix. If you use the channel-faders in conjunction with the cross-fader to their extremes, you get the kind of curve shown in Figure 10-5.
**Figure 10-5:** The cross-fader curves are unlimited when you use the channel-faders as well as the cross-fader.
Chapter 16 covers how to use your channel-faders to help your mixes sound really professional.
Headphone monitoring
The headphone section on the mixer is simple, but extremely important. Plug your headphones into the quarter-inch jack socket (if you're using a mini-jack, similar to the one on the end of your iPod headphones, you need a converter from the mini jack to quarter-inch jack to do this). Use the headphone volume control (which you don't need to set to full, please) along with the cue controls to listen to individual channels on your mixer (or a few of them together at the same time).
Headphone cue controls are split into two functions:
Choosing what plays into your headphones
Controlling how you hear the music in your headphones
Each channel on the mixer has a Cue or PFL (pre-fade listen) button assigned to it. When you press it, you can listen to the music in that channel without needing to play it through the main speakers. This function means that you can listen to any combination of any of the channels on the mixer at any one time. You can listen to Channel 1 on its own or with Channel 2 playing at the same time – or have Channels 1, 2, 3 and 4 all playing in the headphones. That might not sound very good, though.
You use headphones to find the start point of the next tune you want to play (called the cue), but beatmatching DJs also use them to make sure that the beats of both tunes are playing at the same time. This is called beatmatching, and it's the fundamental concept of house/trance DJing. Go to Chapter 14 to discover how DJs use headphones to match beats, and how the following ways of listening to music in the headphones can give you more control over the beatmatching process:
Headphone mix enables you to play both tunes in stereo in your headphones, and a mini cross-fader or rotary knob gives you control over how loud each tune plays over the other (exactly like a cross-fader, except for your headphones). Headphone mix is especially useful because you can check how the two tunes sound playing together before letting the dance floor hear, and check that the beats of both tunes really are playing in time without anyone else hearing.
Split cue sends one selected channel into the left earpiece of the headphones and another one into the right earpiece (as if you're listening to one tune in the headphones and have one ear to the dance floor). Split cue is a lifesaver when you don't have a monitor (speaker) in the DJ booth and the delay in sound from the dance floor speakers makes it hard to check whether the bass beats are playing at the same time.
EQs and kills
The EQ controls on a mixer enable you to increase or decrease three broad musical frequency bands: high, mid and low. The amount of change is measured in decibels (abbreviated as dB), and although mixers let you increase the EQ bands by +12 decibels or more, the amount they take out is actually of more importance to the DJ.
A cut setting on an EQ pot (a professional term short for potentiometer, which describes a rotary knob) removes the EQ frequency band from the tune completely. So when you cut the bass from a tune, all you hear is the tinny hi-hats (the tchsss tchsss sound made by the cymbals on a drum kit) and the mid-range (which carries the vocals and main melody of a tune).
The difference between an EQ pot and a kill switch is that an EQ enables the DJ to vary the amount of frequency to cut out, from just a little to the entire band, whereas a kill switch instantly removes the bass frequency at the push of a button, and then puts it back in when pressed again. No grey areas here!
EQs on a mixer serve two purposes. Firstly, they let you make the tune you're playing sound great; if the bass is too loud through the speakers, you can reduce it using the bass EQ, and if the music sounds a little too shrill, reducing the high and mid controls can fix the problem.
But apart from sound processing, EQs are essential for the seamless mix DJ who wants the transition (mix) between tunes to be as smooth as possible. If you get a chance to study DJs such as Paul Oakenfold, Tiesto and Sasha closely, you see just how much they use the EQs to aid their mixes. Chapter 16 has a whole section dedicated to using EQs to create seamless mixes, and Chapter 21 has a section about sound processing with EQs.
Input VU monitoring
Your mixer has a VU (volume unit) display to show the strength of the signal going out of the mixer, and an important enhancement of this feature is the option of checking the strength of the signal coming in to the mixer.
The normal output display on a mixer is two lines of LED lights, one showing the strength of the left-hand side of the stereo music, the other showing the right-hand side. Some mixers offer the DJ an option to change this display into the left line of LEDs showing the input strength of Channel 1, and the right line displaying Channel 2's input strength. Or, in the case of mixers like Pioneer's DJM-600, a separate line of LEDs next to each channel's EQ controls shows the strength of the input signal – leaving the Master Output display to always show how strong a signal you're sending out of the mixer.
Gain controls
Gain controls aren't just another volume control. Don't regard them as a way to affect the volume going out of the mixer: look at them purely as a way to affect the music coming in to the mixer.
If the input level LED for Channel 1 is at zero decibels, occasionally flashing into the red +3 decibel area, and Channel 2's LEDs show that its input signal is well below zero decibels, you use the gain control to increase the input level of Channel 2 to match Channel 1. If you mix from Channel 1 to Channel 2 without matching the input levels, you'll notice a drop in volume even with both channel-faders set to full. Gain controls (and input level LEDs) let you get this level right at the input stage, instead of panicking at the output stage when it's too late.
If your bass EQ is set to cut or kill when checking the channel's input level, it can appear a lot weaker than it really is. When you then bring the bass frequencies back into the music, your speakers won't be very happy with you, because you'll be playing far too loudly, and you may damage them (or at the very least, your reputation!). For more information on how to use input levels to create an even volume to the mix, head to Chapter 13.
Balance and pan controls
The balance control alters which speaker the sound comes from. When the control is to the left music only comes out of the left speaker, the reverse for the right-hand side and when the control is in the middle music comes out through both speakers, much like the balance on your home stereo.
However, some mixers have balance controls (sometimes called pan controls) on each channel rather than having a control that affects the mixer's Master Output. Why do you want balance controls on each channel? Sometimes (for example) if you have one channel panned all the way to the left and another all the way to the right, and bring the cross-fader into the middle, the effect of having one tune playing in one ear and another in the other ear can sound really good (if you've chosen the right tunes and both bass beats are playing at the same time). This feature works well with plain beats, especially if you constantly change the balance settings during the mix.
Hamster switch
Mixers used by scratch DJs often have a hamster switch, which simply reverses the control of the cross-fader (but the channel-faders remain the same). So instead of hearing Channel 1 when the cross-fader is all the way to the left, you now hear Channel 2, and vice versa. Check out Chapter 17 for more information about scratching and why the hamster switch exists – and why it has such an odd name.
Punch and transform controls
If you have the cross-fader completely on Channel 2 (what I call closed off onto Channel 2), pressing the Punch button changes the output to Channel 1 until released. Note, however, that some mixers don't take account of where you leave the channel-faders, only where you set the gain controls, so make sure you set those gain controls properly otherwise you may experience a huge drop (or rise) in volume when you punch in the other channel!
Transform controls were designed as an advancement to the technique of cutting a mixer's channel in and out of the mix (quickly hearing it, then not hearing it) using the Line/Phono switch. When using turntables, flick this switch over to Line and the music cuts out (for CD, flick it to Phono). The problem is that you often hear a clicking or popping sound when you switch, so transform controls were designed to do the same thing but won't pop or click when you use them. (The Punch button does the same thing as the transform controls if nothing is playing through the other channel).
Built-in effects
Although some mixers offer sound effects such as sirens and horns, I don't really mean this type of effect. Rather than having to use an external effects processor, mixers like the Pioneer DJM-600 have built-in effects like flanger, echo, delay, transform, pitch, loop and reverb assignable (able to add the effect) to each channel or the Master Output. These effects are a great way of adding a new sound to the music, or during the transition between tunes.
The most common effects you find on mixers are as follows:
Delay repeats a selected part of the tune while the rest of the tune is still playing. Especially useful for repeating musical hooks in quieter parts of tracks or for doubling-up bass beats to play three bass beats where only two would normally play.
Echo is similar to the delay feature, except the music fades away when repeating to create an echo effect. Useful again in quieter parts of the tune (or at the very end of your DJ set).
Auto pan swaps the music from the left to the right speaker (and back).
Transformer cuts the entire sound in and out at a speed you set. A good way to create a stuttering effect as the music builds up or during a scratch (see Chapter 17 for how to manually perform a transform).
Filter manipulates the sound frequencies of the music to alter its tonal quality by removing and then replacing a range of frequencies. The filter isn't the same as using the EQs on the mixer to kill and replace frequencies, though, because a specific sound is also added to it.
If you've ever been to the beach and held a shell to your ear, the ambient, resonating sound you hear from the shell is similar to the sweeping effect as the filter removes and replaces frequencies in the music – as if the shell had a tiny DJ crab inside it . . .
The filter effect doesn't always sweep in and out. Certain filters enable you to select a range of frequencies, add the resonating filter effect and then keep the music in that same state until you turn off or alter the filter.
Flanger makes a 'swooshy' sound like playing music through a jet engine as it climbs and falls, while retaining the full frequency range (and usually boosting the bass frequencies) of the music. The most over-used effect ever (but really cool the first time you use it!).
Reverb adds reverberation to the music so that it sounds as if you're playing in a massive hall. Turn it up to full and the sound is like listening to music inside the toilets at a club.
Pitch shifter can change the pitch of the music. Useful to try to match the pitch of another tune, but mixers vary in their ability to do this well.
You encounter other built-in effects, as well, of course. I took this list of effects from the Pioneer DJM-600 that I use.
Effects Send and Return
The Effects Send and Return enables you to send just one channel from the mixer to be processed by an external effects processor (like the Pioneer EFX-1000, for example), to add whatever groovy effects you want, and then it's returned in the blink of an eye for you to use it in the mix. All the while, the other channels on the mixer are unaffected. A detailed description of Send and Return connections with an effects processor is in Chapter 13.
Built-in samplers
Samplers are great because they enable you to take a short vocal sample or a few bars of beats from a tune and extend or introduce a mix by playing these samples. DJ mixers with built-in samplers can record short samples – for anything longer, you need to buy a separate sampler.
An example of how you can use a sampler is with the 1990s song 'Nighttrain' by Kadoc. At the very beginning of the record, James Brown says 'All aboard, the Nighttrain'. By recording that vocal sample into the sampler, and playing it a while before you start the mix, you create anticipation of what's yet to come. I used to do this as a scratch (see Chapter 17 for how), but the sampler made this a lot easier and simpler to do.
The better samplers have loop controls on them, where the sample you take is looped seamlessly over and over again, meaning you can really extend the mix. A good use of this technique is to record four bars of beats into the sampler and loop them to extend the outro of a tune, or to add beats over a breakdown to keep the energy going to the dance floor.
Built-in beat counters
Beat counters give you a visual display of how many beats per minute (BPM) are in a tune you're playing. Two channel mixers with built-in beat counters may have a counter for each channel. Multiple channel mixers can have a counter for each channel, or two counters that you can assign (choose to use) to any channel you like. This can be helpful for beatmatching DJs. By visually comparing the BPMs of two tunes, you know how much to speed up or slow down the next tune to match the BPM of the one currently playing.
A beat counter that displays the BPM to one decimal point (for example, 132.7 BPM) is more accurate than one that only shows whole numbers. If one tune is playing at 131.6 BPM and another is playing at 132.4, and the counter simply rounds up and down those figures to show them both as 132 BPM, it's wrong by 0.8 BPM, which is a huge difference when beatmatching.
Beat counters can be a real help to the beginner to let you understand what's happening with the beats and tune your ear to gauge when a tune is running too fast or too slow, but they can also be a real hindrance. If you're going to refer to a beat counter as you develop your beatmatching skills, you need the discipline not to rely on it. Otherwise, the first time you stand behind a mixer that doesn't have a beat counter (which is going to be quite often in clubs), and are expected to beatmatch using just your ears, you'll find it very hard and possibly get into a lot of trouble!
Beat light indicators
Beat light indicators are little LED lights that flash in time with the beat of the tune. By looking at the lights of two tunes flashing together (or not together), you can tell whether the beats are playing at the same time.
Beat light indicators are very nice to watch in the dark, but personally, I think that they're next to useless when compared to your ears.
MIDI controls
Although MIDI (musical instrument digital interface) can connect a mixer to an effects processor, allowing control over how you activate these effects, the biggest application of MIDI control has become how it helps to control various aspects of software on a computer directly from the DJ's mixer.
Using MIDI connections, you can trigger samples, control effects and playback and locate cue points on the mixer instead of via the mouse and keyboard (or other separate hardware). The capabilities of MIDI on a DJ mixer grow with each new equipment release and have become limited only by the scope of the software.
Choosing the Right Mixer
Different mixers suit different kinds of DJs. If you're looking to spend a lot of money on your mixer, make sure that you're buying one with the right functions on it depending on your mixing style:
The seamless mix DJ needs a mixer that helps every mix sound perfect by controlling the sound levels and the sound frequencies of each tune during the mix.
The scratch DJ needs to chop and change from track to track using a slick cross-fader on the mixer.
The effects DJ isn't content with the sound of the tunes as the original producers intended, and wants the option to add a series of different sounds and effects to the music, making a new sound unique to that performance.
The wedding DJ uses a mixer as a means to change between a wide range of different styles of music.
The seamless mix DJ
The club or house mixer is used by house DJs, trance DJs, drum-and-bass DJs – anyone who wants full control of how the music sounds when they're mixing to create the best transition from one tune to another. So another name for this type of DJ is a seamless mix DJ.
If you're a seamless mix DJ, the important features you need on a mixer are:
EQs to fully control the sound of each tune, with the ability to cut or kill the frequencies to help tidy up the mix.
Multiple channels so that you can use more than two CD decks, MP3 players, or turntables at the same time.
Headphone monitoring, which needs to be as comprehensive as possible, with headphone mix, and ideally split cue for when no DJ booth monitor is available.
Easy-to-use (and see) metering that shows the input level strength as well as the mixer's output level.
Beat counters and built-in effects, though not essential, are a great tool for the seamless DJ.
The house mixer can be quite large, and has the controls spread out to remove the risk of accidentally pressing something if the mixer controls were crammed together.
The scratch DJ
Although scratch DJs can use same mixers as seamless mix DJs, battle mixers are designed specifically for scratching. With only two channels, they make good use of space to allow the DJ unobstructed control of the channel-faders and of a robust, fluid cross-fader.
Although by no means essential, extra controls such as Punch and Transform buttons, along with hamster switches and cross-fader curve controls, are becoming standard tools for the scratch DJ. You can find built-in effects and BPM counters on a lot of scratch mixers, though I think I'd fall over if I had to use all that lot and scratch at the same time!
The design of the battle mixer is as important as the features it offers (see Figure 10-6). Because the most important controls on a scratch mixer are the cross-fader and the channel-faders, these three controls take up a lot of space and are kept clear of any obstructions. To this end, the headphone input is located on the front of the mixer (often along with the cross-fader curve adjust) so it's not poking up from the mixer, where you're going to smack it with your hands one day!
The most important part of any battle mixer is the cross-fader and how it performs. Because you make a lot of fast movements with the fader when scratching, any resistance on the cross-fader is not a good thing, so you need to have as slick and fluid a cross-fader as possible.
Scratching is incredibly taxing on a cross-fader, so it needs to be durable and replaceable (or at least cleanable until you can afford a new cross-fader). New designs of non-contact, optical and magnetic cross-faders from manufacturers such as Rane and Stanton are increasing the lifespan, durability and ease of use of the cross-fader. But don't worry, the standard cross-fader on a battle mixer is good enough for developing the basic skills.
**Figure 10-6:** The Vestax VMX-002XL. Note the headphone socket on the front (bottom right).
The effects DJ
The EQs and design of the club mixer for the seamless mix DJ are perfect for the effects DJ, although frequently, the effects DJ demands more than the built-in effects available on the club mixer.
In this case, the Send and Return function on the mixer may be especially important because it enables you to send individual channels to an effects processor and add whatever effects you want, without having to affect the entire output of the mixer.
However, the effects DJ is becoming more likely to embrace the effects processing built into software in a digital DJ setup than needing to use an external sound processor. In this instance, a mixer with good MIDI capability on it will be of great creative benefit, giving instant access to effects in the software and enhanced control over playback of the music.
The rock/party/wedding DJ
The music these DJs play is more important than the way they mix it together. A lot of creative DJs out there play this kind of music that demands features similar to the seamless and effects DJ, but a large number of these DJs care more about the music and just want to be able to fade from tune to tune. As such, an expensive, feature-laden mixer isn't required for most party DJs. Multiple channels can be useful if you're going to use more than two CD players, MP3 players or turntables, but normally a simple setup requiring two or three input channels at most suffices.
Controlling the sound using EQs when mixing from tune to tune to make it seamless isn't such an important feature for the party DJ compared to the seamless DJ. However, EQs can help remove some bass or add some high frequencies when you're trying to overcome bad sound in different sizes of venues. A global EQ on the amp, which just affects the entire sound output, is probably enough, but you may also consider the option to change the sound for each tune played and therefore need EQs for each channel on the mixer.
EQ controls on the microphone are important to help to sharpen your voice as you talk over the music, enabling you to control the evening with clarity.
It goes without saying that the microphone you use should be a good quality one in the first place. One of the workhorse microphones that (in my opinion) you'll never go wrong buying is the Shure SM58; it sounds great, is simple to connect and it's almost indestructible (though please don't try to prove me wrong).
Built-in beat counters are all but redundant, because the party set list has wide-ranging BPMs. From Tom Jones' 'Delilah' at 64 BPM to Ricky Martin's 'Livin' La Vida Loca' at 178 BPM, the variance is so large that it's near impossible to beatmatch them! Check out Chapter 16 for a good trick on how you can manage this, though.
As to built-in effects, apart from using the reverb effect on your voice when speaking to the people on the dance floor, they won't be of much use to a lot of party DJs. Although I'd love to hear a flanger effect running through 'Build Me Up, Buttercup' . . .
Servicing Your Mixer
Although your turntable or CD player is the piece of equipment with the most moving mechanical parts, the piece that's most likely to suffer from problems first – if you don't keep it clean and treat it well – is your mixer.
You need to look at two things in order to keep your mixer in proper working condition. Clean all the dust away from the rotary controls, and clean and lubricate the faders.
You need the following tools to clean your mixer properly:
A can of compressed air
Lubricant
A screwdriver
Follow these steps to clean your mixer:
1. If you can, pull the knobs off the rotary controls on the mixer.
Take them all off at the same time, place them next to the mixer and lay them out in the order that they've come off, so that you can replace each knob back onto the control it came from.
2. Spray around each of the controls with the compressed air to blow away any dust that may be lodged in them.
You may also want to wipe the mixer carefully with a lint-free cloth to remove any stubborn dust particles after spraying.
3. If you have a mixer that enables you remove the channel- and cross-faders, use a screwdriver to take them out one at a time (so you don't mix up where to replace them).
Dirt that may have worked its way in can cause crackles and sound bleeding (hearing the music quietly when it should be silent). To clean out dirt and dust, blow the compressed air into every crevice in the fader. Then spray the fader with a lubricant and replace it in the mixer.
However, sometimes your faders still make crackle noises, are too stiff and start to malfunction, in which case many mixers are designed to allow you to buy replacement faders from your preferred DJ store.
4. If your mixer doesn't have removable channel-faders and they sound crackly, try spraying compressed air and then cleaning lubricant into the slot in the mixer where the channel-fader pokes through.
However, you may be too late, and may not be able to reverse the damage yourself, meaning you'll have to send the mixer to get repaired – or more likely, buy a new mixer.
To keep this servicing to a minimum, keep your mixer clean and free of dirt, keep it covered when not in use and give the faders a quick lubrication every couple of months.
Chapter 11
Ear-Splitting Advice about Not Splitting Your Ears: Headphones
In This Chapter
Knowing what makes a good set of headphones
Stopping to think about headphone and amplifier volumes
Protecting your ears when faced with excessive volumes
The funny thing about headphones is that they're probably the most important part of your DJ setup because you can't mix properly without them, but, strangely, many DJs treat them as an afterthought.
The only time I've ever really panicked in the DJ booth was when I couldn't hear clearly through the cheap headphones I was using. I couldn't hear any bass, couldn't hear how the beats were playing together, and was effectively mixing 'blind' (or should that be 'deaf'?). If you've followed the same cheap path that I did, when you do start to demand more and want to get more suitable headphones, put some thought into what you need, and don't just get caught up in current fashion trends.
And no, your iPod earbuds won't do . . .
Choosing a Good Set of Headphones
As you advance your DJ skills you start to become aware of all the things that are holding you back from progressing. Cheap decks and a basic mixer are nearly always the first things to upgrade, but consider what your current headphones sound like. Can you hear a good, solid bass thump? Or are the mid-range frequencies drowning out the rest of the music so you can't find cue points for your rock tunes? Better headphones will improve your mixing and beatmatching a lot faster than a new mixer can.
The following six factors can help you when deciding what to buy:
Weight/Comfort: Ideally, you're looking for headphones that are lightweight so they don't hurt your ears after sitting on your head for a couple of hours. That's not to say that lightest is best, though. If the headphones are too light, they may fall off when you lean forward to look down at the mixer, or they may be so light that they don't sit tightly over your ears, letting in a lot of external noise as a consequence.
Because you may be wearing them for four hours at a time, the ear cups need to be soft and sit comfortably on your ears. The headphone band that joins the two ear pieces needs to be comfortable when worn on your head in a normal position, but still be just as comfortable when you twist the band backward to free one of your ears to hear the monitor (speaker) in the DJ booth.
Closed-back: Closed-back headphones, like those shown in Figure 11-1, have seals around the outer parts of the ear cups so they don't let as much external sound through to your ears. In the DJ booth this enables you to clearly hear the next tune you want to play in the headphones despite the noise coming from the dance floor.
The best style of headphones are closed-back and sit nice and tight on your ears, a bit like ear mufflers but with speakers inside!
**Figure 11-1:** The Technics RPDH1200 headphones with the closed-back design to the ear cups.
Wide frequency response: At school you were probably taught your hearing ranged from 20 hertz (the deep, deep bass sounds) to 20,000 hertz (really high, hissy sounds). In reality, your hearing is closer to 20 hertz to 16,000 hertz, although children and dogs can hear up to 20,000 hertz.
Quality DJ headphones typically cover the frequencies from 5 hertz to 30,000 hertz, so they cover the bass and sub-bass ranges all the way through to the stuff only dogs and sound engineers can hear!
Low impedance: If you don't know anything about impedance, it's okay, you don't need to, but it's all about electrical resistance. You only need to know to try to match the impedance of your headphones as closely as possible to the impedance of the mixer you use. A large mismatch can lead to distortion, unwanted noise and sometimes a drop in the maximum volume your headphones can play (all things you really don't need when DJing).
Fortunately, this isn't something to lose a night's sleep about, because most DJ equipment manufacturers are well aware of this issue and design their equipment within the same impedance range.
High sound pressure level: Sound pressure level is just a way to describe how loud your headphones (and speakers in general) can play. You want your headphones to be able to play loud to let you cope with noisy DJ booths, but please remember you don't have to turn up your headphones too loud (see 'Remembering that the Volume Doesn't Have to Go Up to 11', later in this chapter).
Have a realistic budget when upgrading your headphones. If your current pair only cost £10, you won't benefit much by getting a pair for £30. Save up more money and start looking to spend around £100 on a set of Sony, Sennheiser, Technics or Pioneer headphones, which I think are the market leaders. Don't be fooled by fashion. Few people (apart from fellow DJs) care that you have the latest, best-looking headphones; they only care about the music!
Realising no one cares about headphones
I remember one night when Alex P did a guest spot at a club where I had a residency, and the other DJ (Dave Armstrong) and I were left wandering through the club, feeling a bit bored while waiting for him to finish (because, remember, DJs don't dance). At this time, the new Sony MDR-V700 DJ headphones had just come out, and they were the fashionable choice of the discerning DJ – including the two of us.
Thinking we were being really cool and funny, we both put on our headphones and wandered around the club, talking to people we passed, and had a bit of a laugh. I look back at the image now of two guys with matching headphones on their heads in the middle of a nightclub, with Dave trying to chat up all the girls, and I cringe. That said, I think Dave got some phone numbers . . .
These considerations play a major role in deciding what headphones you eventually buy, but other features are available that may yet swing your decision from one pair to another.
Single-sided, coiled cords
Coiled cords are the curly ones that you sometimes see guitarists use (Brian May from Queen uses a coiled guitar lead). By coiling the cable, manufacturers are able to offer a lot more length to the DJ without the danger of a long, dangling, straight cable that can bunch up on the floor and trip you up. You attach single-sided cables to only one earpiece, and the cable travels from one ear-cup to the other through the headband.
Only after spending an evening in the DJ booth with a pair of headphones that don't have single-sided cabling do you realise why this simple design is so important. By the end of the night's mixing, after repeatedly putting on and taking off your headphones, putting them down, picking them up, dropping them under the decks and so on, you'll have spun the cable round enough to almost strangle yourself as the two cables twist around your neck. A single-sided cord has nothing to wrap around, and stays out of the way, keeping you breathing happily for the rest of the evening.
A single-sided, coiled cord, such as the one on the Technics RPDJ1210 headphones that I use, is perfect for giving you a long, coiled cable, which allows you to move around in the DJ booth, and the single-sided cord means that you don't end up garrotting yourself by the end of the night!
Swivelling earpieces
Sometimes the headband on the headphones can feel slightly uncomfortable when you pull one of the ear cups back behind your ear to listen to the live sound. Swivelling ear cups mean that you can pull the ear cup behind your ear, but the headband stays across the middle of your head.
This setup is advantageous not only because of comfort, but because it reduces the stress on the headband. Cheap, plastic headphones (like the cheap ones I started with) can snap after you twist them backwards too many times.
User-replaceable parts
Sennheiser's HD25 and HD25SP headphones are designed to be completely modular, with each piece user-replaceable. This design means that you need never stress about these headphones breaking or malfunctioning. Provided you have the spare parts in your DJ bag, all you have to do is replace the broken part, and keep on mixing.
Having been in the position where someone wrenched the cable out of my headphones one evening when he stood on them (my fault for leaving them on the floor), the opportunity to instantly replace the cable would've been fantastic. But because I didn't have headphones with user-replaceable parts, I had to mix with only one ear working for the rest of the night.
Sticking it to your ears
Figure 11-2 shows an example of a 'stick' headphone that has only one ear cup. By wedging the cup between your shoulder and your ear, you can cut out more external sound and hear the music a bit more clearly through the one earpiece. However, I still prefer traditional headphones, which let you do exactly the same thing and still give you the choice of hearing the music in stereo – and you won't end up with a strained neck from craning it to one side. DJs such as Fatboy Slim and David Morales have used this style of headphone with great success, and their heads don't loll to one side, so absolutely nothing is wrong with this design.
**Figure 11-2:** The Stanton DJ Pro 3000 STK 'stick' headphones.
Remembering that the Volume Doesn't Have to Go Up to 11
Please forgive the Spinal Tap quote (check out the film This is Spinal Tap if you don't understand the 'Up to 11' reference!), but the only person who knows you're playing the headphones at full volume is you – you can't show off to anyone because no one else can hear. You don't need music to be loud to enjoy it, and you certainly don't need to look forward to wearing hearing aids in your future.
As a drummer from age 10 who also used to go to loud rock concerts, someone who used to go to clubs at least four times a week (and dance right next to the speaker, because it was somewhere to keep the drinks!) and a DJ from age 21 through to the current day, I've always surrounded myself with loud music. I pay the price for that now by having a constant ringing in my ears (something called tinnitus). Although it doesn't affect what I hear, you don't want to wake up in the middle of the night and just hear a ringing in your ears, believe me. Do everything you can to protect your ears. You are not invincible.
In addition to causing irreversible ear damage, if you play the music in your headphones too loud, you'll find mixing a lot harder. Beatmatching and finding cue points (see Chapter 14) are easier when you find the perfect level to listen to the headphones while the amp is still blaring out at 130 decibels.
When beatmatching you need to listen to two tunes at the same time to work out whether their bass beats are playing at the same time. The most common technique (single ear monitoring) involves listening to one tune in one ear through the headphones and the other tune in the other ear from the speakers or monitor in the DJ booth. Playing one tune so that it plays louder than the other makes it harder to concentrate on the bass drums from both tunes.
For more information on the single ear monitoring technique, and guidance on how to check that you've set the levels (volumes) of both the amplifier and the headphones correctly, go to Chapter 14.
Using Earplugs
Earplugs can make a world of difference to your future hearing and the quality of your mixing. I encourage you to use earplugs when practising in the bedroom so you're used to using them when it comes to DJing in a club. I only wear one earplug during a mix, protecting the ear that listens to the music from the monitor, while the other ear has some protection from the headphone that's covering it.
The decibel level in a club can be upwards of 100 decibels (decibels, abbreviated as dB, are a way of calculating how loud sound is), and as a DJ who gets work four or five times a week (if you're lucky) you're exposed to this level more often than any clubber. So although I recommend using one ear plug in your ear open to the monitor when you're mixing, I strongly suggest that you plug the other one in when you've taken the headphones off, in order to protect the other ear.
Even though I don't have an earplug in my headphone monitoring ear, that ear benefits from the protection given to the other ear. Because the earplug reduces the loudness of the music that enters the ear that's open to the monitor, you can reduce the volume at which the headphones are playing. If you didn't lower the volume of the headphones, it would be harder to concentrate on the music from the monitor, making it harder to beatmatch.
The noise levels and acoustic sound inside a club can make hearing specific parts of a tune quite difficult, no matter how good the monitor in the DJ booth is. Maybe you want to hear a subtle change in the melody, or you want to hear the hi-hat cymbals as they change, or you just want to hear the bass drum beats stand out from the rest of the tune. You can sometimes have difficulty picking out these parts with the combination of sound from the dance floor and the monitor, and you may (wrongly) consider turning up the monitor in the DJ booth to try to hear the music better.
You experience this difficulty because the sound waves from the dance floor and from your monitor in the booth mix together, making it harder for you to pick out and concentrate on the parts of the song you need to. Using an earplug means that the sound waves have to travel through the foam or rubber before they get into your ear canal, so the music sounds a lot clearer. Wearing an earplug is like running a brush through tangled hair. It's much easier to separate the hair if it's been brushed (or filtered in the earplug case), and pick only the parts you'd like to concentrate on. (Just make sure that the person whose hair you're stroking is happy with this!)
The basic foam earplugs that you get from the chemist cost about £1 for three pairs and aren't designed specifically for listening to music. They're designed more for getting to sleep when the person sleeping next to you is doing an impression of a sawmill. They do a very good job at cutting out high volume levels but aren't good at retaining the quality of the music (they don't let through the high frequencies very well, so they're like sending the person with tangled hair to get it all cut off to fix the problem).
If you think that the cheap foam earplugs aren't letting you hear what you need to hear in the music, you have two options – buy more expensive ear plugs off the shelf or get some professionally made for you:
Off the shelf: You can find lots of great designs for earplugs that try to maintain the quality of the sound that enters your ears; like Elacin Er-20s (which I use) or Hocks Noisebrakers (shown in Figure 11-3). Noisebrakers embrace the laws of physics to bounce the sound coming into the earplug back out again, which has the effect of not letting anything over 80 decibels into your ears without sacrificing the quality of what you're listening to. They cost about £15, so are a step up in price from the basic foam ones, but they do work well, and save your ears while still making it easier to mix.
**Figure 11-3:** Hocks Noise-brakers earplugs.
Custom made: Custom-made ear plugs from companies such as Etymotic and Advanced Communication Solutions (ACS) are costly (around £165 for the ACS ER-15s), but they have a superior ability to maintain sound quality while reducing the volume level (see Figure 11-4). The company uses an impression of your ear cavity to make an earplug that fits snugly into your ears, and your ears only.
**Figure 11-4:** ACS custom-made ER-15 earplugs.
For more information about earplugs, check out www.earplugstore.com, and for more information about tinnitus and taking care of your ears, check out www.deafnessresearch.org.uk.
Chapter 12
Letting Your Neighbours Know That You're a DJ: Amplifiers
In This Chapter
Choosing the right amplification for your wallet and environment
Getting to grips with connecting it all up
Keeping the sound down to save your hearing, and your neighbours' sanity
Each stage of the DJ equipment chain is vital. Without the amplifier and speakers, you'd be the only person to hear how good a DJ you are. In this chapter, I cover the various methods of amplification, the best way to connect and place your speakers, and how to play at a volume that won't get you ejected from the neighbourhood.
Choosing Suitable Amplification
You need to choose a method of amplification that's suitable to the size of room you're playing in, and also for the size of your wallet – which are both important factors. The key word here is suitable. If you're just in your bedroom practising at a moderate volume, you won't have much need of a £3,000, 1,000-watt amplifier and set of speakers, so save your money!
The different ways you can amplify the signal from the mixer so you can hear it through speakers are via:
Your home stereo: For the bedroom DJ who has a good-sounding stereo with a spare input into which you can plug the mixer.
Powered speakers (each speaker has a built-in amplifier): If you don't have a home stereo, or the one you have doesn't have a spare input, powered speakers are perfect as an all-in-one solution.
A separate amplifier and speakers: This combination is the best choice if you have a large room/hall/club that you need to fill with music.
Settling on your home stereo
Your home stereo (or hi-fi) is probably the easiest and cheapest route to go down when you're just playing in the bedroom for practise, because you probably already own one. As long as you have a spare input channel on your hi-fi, and you can position the speakers close enough to your DJ setup that you can get a good sound from them, your home stereo is a very good option. Though a hi-fi may not be as loud as a separate amplifier, if you're playing in a modest-sized bedroom, it should be more than loud enough.
Don't sneer at the idea of using a hi-fi. They can have great sound quality, produce very loud volumes and may have a built-in recorder to record your mix sessions.
If you get the chance to buy a new hi-fi for this use, search for one that has a manual graphic equaliser on it, rather than relying on some pre-set nonsense about Hall, Big Hall, Stadium and Bread Bin to approximate the different sounds that those areas would make. A manual EQ (equaliser) lets you adjust the sound to your taste, by controlling a range of different sound frequencies individually. If you plan to use the hi-fi to record your mix, full control of the sound is especially important (see Chapter 19 for guidance on recording great sounding mixes). Even if it means another £20, you won't regret your choice. Hi-fis with pre-set EQs are great for domestic, easy listening at home; but you're a DJ – you're far from domesticated.
The hi-fi also needs a spare input on the back of it to plug in your mixer. If you only have CD and Phono inputs on the back, you have to use the CD input (Phono inputs are only for direct connection of a turntable). If you already have a CD player plugged into the hi-fi, you'll need to unplug the CD player and plug in your mixer each time you want to use do some DJing, which can get tiresome, so try to pick a hi-fi with a separate AUX (auxiliary) input to plug your mixer into if buying a new one.
The length of the cable between the hi-fi unit and the speakers can also affect your choice of purchase. For example, I have a Sony hi-fi with less than a metre's worth of speaker cable between the base unit and each of the speakers. I have no plans to use it with my decks, but the length of cable provided is useless for DJ use because I can't get the speakers either side of the decks without needing to sit the base unit on top of my mixer!
Purchasing powered speakers
If you don't have an amplifier or don't want to tie up an input on your hi-fi with your mixer, powered speakers (also knows as active monitors) are a good alternative. Powered speakers are the same as normal speakers, except they don't use a separate amplifier; each speaker has its own, built-in amplifier so you can connect the output of the mixer directly to the speakers.
Consider power needs if using this kind of amplification. You may need to connect each speaker to its own power supply, or power both speakers from one power unit. Make sure that wherever you intend to sit the speakers you have a power point close by.
If at all possible, to maintain audio quality don't cross the power cable over any of the audio cables, because this may cause electrical interference. You probably won't have any problems if you do, but if you can get into the habit of properly laying the cables between two pieces of equipment now, you'll know to keep the speaker cable away from power leads if you're ever connecting a lot of speakers and amplifiers for a party or club night. The volumes involved at those events may reveal the electrical interference.
Powered speakers are very popular in the DJ booth as booth monitors. The volume control for this monitor is usually situated somewhere accessible on the side or back of the cabinet, which is perfect because you can turn it up or down whenever needed (especially if the mixer doesn't have a separate booth level control on it). Powered monitors in the DJ booth also don't tie up an entire amplifier for the sake of one speaker, making good financial sense. See 'Working with Monitors', later in this chapter, for more about booth monitors.
For bedroom use, powered speakers can range in quality (and price) from budget monitors such as those by Ion and Numark, which cost around £40 a pair and have an acceptable sound (though to my mind they're lacking a bit in bass thump), to great-sounding powered speakers such as those made by KRK, Alesis, JBL and RCF, which can cost anywhere between £300 and £6,000 for a pair!
Good quality, surround-sound powered speakers that you usually use with computers can sometimes be an option too.
Opting for separates
A powerful amplifier with huge separate speakers can be overkill in the bedroom. Five hundred watts of music can be more than you need even in a large hall, so if you buy a high-rated amplifier and speakers and turn up the volume to full, don't be surprised if your neighbours come knocking on the door!
Both the amplifier and the speaker have a power rating, which is measured in watts (abbreviated as W). The higher the number of watts, the louder you can play the music. Generally speaking, the rating on the back of your amp (short for amplifier) tells you the maximum sustained output that the amp can produce. On speakers, however, you may see two ratings, the average and the peak rating. The average rating (also known as RMS) refers to the maximum sustained output that your speakers can handle. The peak rating refers to how much power they can handle momentarily without risk of damage.
In non-tekky talk, think about a trampoline. How low the membrane on a trampoline is to the ground when you're standing still on it would be the average rating: it's happy at this level, and nothing's really going to go wrong with it. When you start jumping on the trampoline, as you land the membrane gets a lot closer to the ground momentarily. How close the membrane can get to the ground before suffering damage is the peak rating of your trampoline.
The peak value is always higher than the average value, and is why manufacturers like to print the peak in their documentation – it makes the speaker look more powerful.
When matching up an amplifier for use with your speakers, it's safer to make sure that the power of the amplifier is less than the average rating of the speakers. No matter how loud the amp goes, it shouldn't be able to blow the speaker this way. If you do want to choose an amp that's more powerful than the average output of the speaker, make sure not to buy an amp that's more powerful than the peak rating of the speaker. Even if you make a promise to yourself that you'll never turn the amp up to ten, you can't say the same for your friends, or your drum-and-bass-loving cat.
Allowing a power margin for error
Choosing the power rating of the amps and speakers, especially when considering a lot of power for a hall, or club setup, takes a little forethought and margin for error.
If you're looking to buy a setup that would give you 200 watts of power, the best option isn't buying a 200-watt amplifier and speakers with an average rating of 200 watts, nor is it buying two 100-watt amplifiers to make up a total of 200 watts of sound.
The preferred way to set up this amount of power is to buy three 100-watt amplifiers and three sets of 100-watt speakers, and run them all at two-thirds of their output level. Running two amplifiers at full volume for too long is running the risk of one, or both, breaking down – but three amps at two-thirds of their power will run happily for a long time. And even if one of them did blow, you'd still only lose one-third of the power, instead of all or half of the power in the other two examples.
Table 12-1 is a general guide to the room size, occupancy and power rating you may need for different situations. This guide isn't a set-in-stone rule, and you may want more than suggested to give you a little 'headroom' of power, in case you want to go louder.
Table 12-1 Amplifier Power Needed for Different Room Sizes
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Room and Occupancy | Power Needed
Empty(ish) bedroom (you, your bed, your decks and the cat) | 20–40 watts
Full(ish) bedroom (a few friends came for a visit) | 40–60 watts
Big room or small, half-full hall (back room in a pub) | 80–150 watts
Large hall, half full (local Scout hall, and so on) | 150–300 watts
Large hall, lots of people (phew, they came!) | 500–800 watts
You may have noticed that the number of people in the room affects the amount of power you need. People are very greedy. Not only do they raid your fridge for beer and food, but their bodies also absorb sound waves, robbing some of the volume from the room. The more people that turn up, the louder you have to play the music to be heard at the same volume! The good thing is that even though you have to turn up the sound a bit, the soaking of the stray sound waves by the crowd can improve the sound on the dance floor.
As well as counting the people on the dance floor, when you're choosing the amount of amplification for an event take a look at what's around you; the decor and the floor are just as important as the size and capacity of the room. A room with wooden floors and wooden or mirrored walls bounces sound waves around the room, making the music sound a lot louder. A room with carpet flooring that has big, thick curtains in it does just the opposite, absorbing a lot of the sound waves; so you may need a touch more power.
If you want to know how to connect multiple sets of speakers into your amplifiers (which is essential knowledge for club systems and some mobile DJs), check out www.recess.co.uk.
Working with Monitors
Your booth monitor is your link to what's really happening on the dance floor and can make the difference to your night going well, or going to you-know-where. Without hearing the exact audio that's coming from the mixer at the exact moment it comes from the mixer, you'll have a really hard time beatmatching. In the bedroom, the 'dance floor' sound and the music you hear in the 'monitor' are the same thing (usually because they are the same thing), but in a club, the two sounds are a bit different.
The booth monitor is like your health. You don't miss it until you don't have it any more. It not only lets you gauge how the music sounds playing to the dance floor, but also helps with the accuracy of your beatmatching.
Working with the speed of sound
This is where the DJ booth monitor comes in. The monitor is often a pair of speakers either side of the DJ, but in some cases, is just a single speaker positioned to the left or right of the DJ. A monitor right next to your ears cuts the audio delay from 1//16 th of a second to 1//256 th of a second (if it's a metre away), which is more than acceptable.
Positioning your monitor
Unless you live in a mansion, you're unlikely to have to deal with any delay in the bedroom from your speakers to where you have your decks set up. If you do live in an oversized room that's causing delay similar to working in a club, ask your butler to bring one of the speakers closer to you. Sarcasm aside, if bringing a speaker closer to you isn't an option, then you can hook up a separate booth monitor (maybe a powered speaker) to play right next to your DJ setup, or you can add another pair of speakers to your existing setup and place them next to your homemade DJ booth.
The monitor needs to be close enough to counteract any delay from the dance floor, but also overpower any music from the dance floor that you may still hear in the DJ booth. Keeping the speaker close and facing you gives you the best clarity. Too far away and you may find it harder to pick out a solid bass thump or the crisp hi-hats and snare drum that you use as reference when beatmatching (see Chapter 14).
The perfect position for a monitor in the DJ booth is 1 to 2 metres from the mixer, slightly in front of you, at head height and with the speaker turned in to point directly at you. Assuming that your speaker has the bass driver (the big speaker) at the bottom and the tweeter (which plays the high frequencies) at the top, this position is perfect for getting the best sound quality from your monitor.
If the monitor is too high, the bass driver dominates the tweeter, drowning out a lot of the high frequencies from the music. If the monitor is too low, aimed at your waist, the bass is lost, leaving a shrill, unclear sound dominated by the high-frequency tweeter that's at head height. Turning the monitor on its side so both the tweeter and bass driver are at the same height helps to prevent either eventuality.
For your bedroom setup you may not have as much room or control over where you can put the speakers. The two things to keep the same as in the club DJ booth are that the speakers are in front of you and pointing toward your ears, and that you try not to set the speakers on the same piece of furniture that your decks are on. If the vibrations from the speaker cause the turntable to vibrate, you'll generate feedback. If you're using CDs, you may cause the CD player to skip with the bass vibrations.
Noise Pollution: Keeping an Ear on Volume Levels
Many reasons come to mind as to why you shouldn't play your music loud all the time, but hearing damage (which I cover in Chapter 11), neighbour relations and the quality of your mixes are paramount.
Protecting your ears
Keeping the volume of your monitor at the lowest functional level protects your ears and reduces any risk of distortion from the headphones or the monitor.
One of the most popular ways to cue up the next tune (get it ready to play) and match the bass beats of two records is to use a technique called single-ear monitoring. This technique is when you have one ear open to the music from the monitor, playing the live sound from the amplifier, and the other ear has one of the headphone cups on, listening to the cued song that you wish to play next. (For more information on this, check out Chapter 14.)
The volume of the music that comes into your head from the monitor needs to match the volume at which the headphones are playing into your other ear. Due to the proximity of the headphone to your ear, this is about perceived volume rather than trying to match the actual decibel level coming from the monitor in the DJ booth – because to do so would make you go deaf.
You only have to play the monitor loud enough to drown out the music from the dance floor, which helps the accuracy of your beatmatching. You may be surprised at how little it takes. After you've reached that level, try not to increase the volume, even if you're really getting into the music!
Neighbourhood watch
Keeping the music at a sensible level so that you don't go deaf or harm your mixing skills is important, but you also have your sense of social responsibility to think of. Not only may the rest of the people in your flat, house or building start to get a little irked when you play pounding bass beats at full volume for hours at a time, but the people in surrounding buildings may soon get fed up with the dull thudding noise coming from your house.
Getting spooked into turning down the bass
When I lived at home with my mum, I had a huge setup in my bedroom with six 100-watt speakers dotted around the room, which was on the ground floor of the house (no wonder with all that noise!). I used to spend hours playing my tunes, working out new mixes, having fun and improving my skills. I didn't always play the music really loud, and I hardly ever played it at full volume, but I had a huge subwoofer that made a heck of a thump every time the bass drum pounded.
Understandably, my next-door neighbour got fed up feeling the vibrations of the beats through the floor in his house – 30 feet away! Because a dual-car garage linked the houses, the vibrations travelled through the foundations of my house and into his house. All this disturbance led to him banging on the window of my room for ten minutes, getting increasingly frustrated while waiting for me to turn around and notice him. When I eventually did turn around and saw a (less than happy) face staring in through the window, it scared the life out of me! I thought it was a ghost against the window. I turned the bass down after that fright.
Realising that you only need one speaker
When you're DJing at home, you really only need the one speaker, and that's the one you use for the 'live ear' when using single ear monitoring to beatmatch (your equivalent of a DJ booth monitor).
When a neighbour pointed out how annoying the bass of my subwoofer was, I put switches on all of my speakers so I was able to leave only the monitor speaker running. This meant that I could play the music just as loud as before, but because only one speaker was playing the volume that other people could hear was a lot lower, yet my perceived volume of the monitor stayed the same. Turning off the unnecessary subwoofer helped a lot too!
If you only have two speakers, you may not need to add switches to isolate one speaker. If your amplifier (or hi-fi) has a balance control, just pan the music so that the music only plays out of your preferred speaker (though if you use a hi-fi to record your mixes, this may result in the recording only playing out of one speaker too).
If you're thinking of adding switches to isolate your speakers, do some research into the best switch to use. I must admit, I used light switches, but they're not designed for audio signals and can add too much resistance to the signal from the amplifier to the speaker, even when just passing through the circuit. This resistance may only cause a drop in sound quality or volume, but in the worst case it may break your amplifier. Something as simple as the Hama LSP 204 (shown in Figure 12-1) can do the job a lot better for up to 100 watts of sound.
**Figure 12-1:** Hama LSP204 is a great way to control four different speakers.
Chapter 13
Plugging In, Turning On: Set-up and Connections
In This Chapter
Setting up and connecting your turntables properly for DJ use
Connecting everything to your mixer, and your mixer to everything
Troubleshooting why you're not hearing what you should be hearing
You've spent a heap of cash on your new turntables, CD decks and a mixer, bought an amplifier loud enough to deafen the back row in a stadium and everything's turned on and ready to go – except you can't hear anything.
You simply have to know the chain of inputs and outputs to check that you've plugged all your equipment into the right place.
This chapter assumes you're connecting turntables, CD decks or MP3s directly to the mixer – digital DJ setups are a bit more complicated, so be sure to read Chapter 9 for information about these connections.
Getting Familiar with Connectors
Before you connect your equipment together, getting familiar with the connections you're using is a good idea. The most common connection types you come across are RCA (also called Phono), XLR and quarter-inch jacks (also known as TRS). In order for music to play in stereo, you mostly encounter two of each of these for connecting your equipment. One cable and connector carries what you hear out of the left speaker; the other carries what you hear out of the right speaker. Quarter-inch jack plugs are also available as a single, stereo connector (as seen at the end of your DJ headphones).
Some turntables, CD decks and mixers use digital connections to keep audio quality at maximum. In order to make use of them, your mixer must have a digital input too. USB (universal serial bus) and Firewire are connections you see on computers, and along with S/PDIF (Sony/Philips Digital Interface Format) these digital connections combine both sides of the stereo sound and send it through one cable. The mixer then separates out the stereo sound and plays it back at crystal clear quality.
RCA/Phono connections
RCA connections are also known as Phono connections, but I'll continue to call them RCA to stop any confusion with the Phono/Line terminology for inputs on the back of the mixer.
RCAs are the most common connections you use as inputs and outputs to your DJ mixer. They come in pairs, one for each side of the stereo signal, and each of them is a different colour. The left signal cable is usually white, though it can be yellow or black, but the right-hand side of the audio signal is always red. The two 'R's make remembering which cable plugs into where easy; simply remember that Red = Right.
S/PDIF digital connections on DJ equipment often use the same RCA style of connection. These are usually coloured yellow (just to add confusion!).
XLRs
Used for amplifier connections and microphones, XLRs are the preferred connection for professional audio equipment because they're capable of reducing interference when using long cables, and because they lock into place so they can't accidentally pop out if a drunken customer falls on them.
XLR connections (see Figure 13-1) come in two different flavours:
Unbalanced XLRs are the more common pro-sumer (a mixture of professional and consumer) XLR connection. An unbalanced XLR simply sends the audio signal through the cable, and any unwanted electrical or radio interference that's picked up by a long cable is carried along with the music to the speakers or recording device.
Balanced XLRs are used in professional audio equipment, and attach to the cables in a way that cancels out the unwanted sound interference.
XLR microphone (mic) inputs and master outputs on DJ mixers often work with cables and connectors that are both balanced and unbalanced, but when buying a new microphone, amplifier or mixer it's best to check the specifications of the equipment you use if you're unsure of the connections.
**Figure 13-1:** Two XLR connectors; one for the left, the other for the right.
Quarter-inch jack
A quarter-inch jack (also known as a TRS jack), is what you find at the end of your DJ headphones (though not the one on the end of your iPod headphones; that's a 3.5-millimetre jack). Quarter-inch jacks also come in balanced and unbalanced varieties. Balanced connectors are mono, so you need two of them, but an unbalanced connector can carry a stereo signal so it only needs one cable and jack plug. If you need to know whether the jack you're holding in your hand is mono or stereo, look at the black bands on the tip; one band means it's mono, two bands mean it's a stereo jack, as shown in Figure 13-2.
**Figure 13-2:** Left: A mono quarter-inch jack (TRS) connector. Right: A stereo quarter-inch jack connector.
It's not always the clubber's fault
Blaming an accident on the customers of the club that you play in is quite easy, but as a DJ you have to be careful of doing things that can break connections yourself. I remember one evening while playing at a bar I had the lid of the record box neatly balanced on the DJ booth. I knocked it with my hand and it fell down the back, bounced onto the cables coming out of the mixer, pulled out the Master Output cable and plunged the place into silence for about three minutes while I tried to work out what I'd done. Thank goodness I worked there as a barman; otherwise they'd have thrown me out on my ear for being so careless! Soon after, the bar started using XLR connectors that locked into place.
Plugging Into the Mixer
The first time you take a look at the back of a mixer, it can look quite daunting with all the different inputs and outputs, but after you've plugged in a couple of pieces of equipment you find out just how simple it is back there. For more information on mixers and any functions you may be unsure of that I mention in this section, refer to Chapter 10.
Connecting turntables to a mixer
Turntables are unique in their connection because they're the only item of DJ equipment that plugs into the Phono input on the mixer and they have a thin ground wire (also called an earth) connection that you need to connect to prevent electrical hum and static from the turntables.
Connection is simple:
1. Take the two RCA cables that come out the back of the turntable and plug them into the Phono input on the mixer.
The red RCA is the right-hand side of the music signal, and white is the left-hand side (see the earlier section 'RCA/Phono connections').
If your turntable uses detachable cables, connect the RCA cables to the correct colours on the turntable outputs as well as the mixer inputs.
2. After you've connected the cables properly, set the Line/Phono switch on the mixer for the channel you've just plugged into to Phono.
3. Connect the ground (earth) wire. It's usually a thin cable with a piece of bare wire exposed at the end, or a thin U-shaped metal hook.
Your DJ mixer will have something similar to a thumb screw on the back to which you connect the ground wire. Cinch the ground wires from both turntables between a washer on the screw and the body of the mixer (as shown in Figure 13-3).
Be sure that you have a secure connection for both turntables to this ground point by checking that the metal ends of the wires make connection with the ground point's metal washer or screw. You'll know if you haven't properly grounded the turntables because you'll hear static or a really nasty, loud hum playing through the speakers.
**Figure 13-3:** Two ground wires screwed to the back of the mixer.
Connecting CD decks to a mixer
CD decks usually use two RCA outputs to connect to the mixer's analogue Line RCA inputs.
However, if your CD decks have digital outputs and your mixer has a digital input (both are usually an RCA connection), use a single RCA cable to connect the CD deck to the mixer and keep the music digital.
When connecting CD decks to the mixer through the analogue outputs and inputs (a pair of red and white RCA cables), be sure not to plug one of them into the digital connection by accident. If you hear only one side of the music and you have a digital input or output, this mistake could be why.
Connecting iPods and personal MP3s players to a mixer
Unless you're using one of the Numark iDJ mixers or another mixer specifically designed for mixing with iPods, you need to use a cable that converts the output of your iPod (or any other MP3 player) to two RCA plugs. You can get a cable that's based on the dock connector of the iPod that splits into two RCA plugs (this is how a lot of people play their iPods through a home hi-fi) but without that, and for most of the other MP3 players, you need a cable that splits the headphone output into two RCA plugs.
You can buy these cables from most electronic spares stores, or simply type '3.5 mm stereo jack to RCA' into any search engine or eBay (www.ebay.co.uk), and you'll find one for about £5. Just make sure that the jack on the end of the cable you go for is stereo (it'll have two black bands on the tip), and that it's a 3.5 millimetre jack, otherwise it won't fit into the MP3 player's headphone output.
As with the CD decks, simply plug the RCAs from this cable into the Line input on the back of the mixer, making sure that the channel you use for this input on the mixer is switched over to Line.
Headphone outputs are normally weaker than a typical Line output, so you may have to set your MP3 player to a high volume or increase the gain on the mixer by more than normal in order to play a strong signal through the mixer, so you can keep the volume of the MP3 music similar to the music from your CDs and turntables.
Connecting a computer as an input device
To connect the audio outputs of a computer to the mixer so that you can mix the computer music with your CD players and turntables, you use the computer's soundcard output. The soundcard processes the digital music data and converts it to a Line signal to be sent to the mixer (the reverse also happens, see 'Connecting a Mixer to your PC/Mac', later in the chapter).
If you have a soundcard with analogue RCA outputs, use a cable with two RCA connectors on each end and connect the RCA outputs of the computer's soundcard to the RCA Line inputs on the mixer. If you have RCA style digital S/PDIF outputs on the soundcard and a matching input on the mixer, use one RCA cable to connect between them both. If the soundcard has a 3.5-millimetre jack output marked 'Line', you'll need the stereo 3.5-millimetre lead to RCA cable I mention in the previous section 'Connecting iPods and MP3s to a mixer'.
If you're using a laptop or have a computer with a very basic soundcard, you may notice that the only audio connections you have are a headphone output and a microphone input. You can use the headphone output as long as you have the RCA to 3.5-millimetre jack cable, but like the MP3 player headphone output you'll need to adjust the gain on the mixer to get a strong signal.
A wide range of analogue to digital USB and Firewire converters are also available to buy. Edirol (shown in Figure 13-4), Alesis, Behringer and a whole host of other makes have products at varying prices (and quality) if you don't have a good enough soundcard on your computer.
**Figure 13-4:** The Edirol audio to USB by Roland with analogue inputs and outputs connected to a USB connection.
If you want to connect your computer directly to an amplifier, the connection is identical to connecting to a mixer. Connect the output of the soundcard to an available input on your amplifier.
Always check the software and computer hardware you use for any special input or output connection instructions to enable it for DJ use. Manuals are there for a reason: don't start disconnecting and screaming at cables only to find out you were meant to click 'Out' in the software!
Choosing your mixer inputs
If you just use two turntables, CD decks or MP3 players, and have a two-channel mixer, connection is simple. Connect the CD deck/MP3 or turntable to your left to Channel 1 and the one on your right to Channel 2.
If you have more than two channels on your mixer, take a look to see whether any of them are aimed at a certain input device. Channels 1 and 2 on a four-channel Pioneer DJM600 mixer have specific connections for Pioneer CD decks as well as standard Line/Phono inputs. They have the connection for Pioneer's fader start controls that make the CD start when you move the fader. So if you want to use that function on your Pioneer CD decks, you'll need to connect to Channels 1 and 2. The Pioneer DJM800 has fader start connections on all four channels, but turntables only connect properly to Channels 2, 3 and 4.
If your mixer doesn't have any specific channel requirements or functions, you can connect to any two channels on the mixer, though it's still an idea to connect the left deck to a lower channel number and the right deck to the higher number (for example, use 1+2, 2+3, 3+4, 1+3, 1+4 or 2+4).
If you use two CD decks and two turntables, and have a four-channel mixer, you may want to connect in the same way the decks are arranged in front of you. Suppose that you arrange your equipment in this order:
Turntable 1 – CD 1 – Mixer – CD 2 – Turntable 2
A simple setup is to connect Turntable 1 to Channel 1, CD 1 to Channel 2, CD 2to Channel 3 and Turntable 2 to Channel 4 on the mixer, which may cause less confusion about what channel controls what equipment. Just make sure that you switch the Line/Phono switch to Line for the CD decks and Phono for turntables.
The mixer you're using may have other ideas! For instance, with the special CD control inputs on the Pioneer DJM600, if you want to use fader start controls you need to connect to Channels 1 and 2 for CD decks and 3 and 4 for turntables.
If you only have a two-channel mixer, you can still use two turntables and two CD decks. Plug Turntable 1 into the Phono input on Channel 1, and CD 1 into the Line input on Channel 1. Then plug Turntable 2 into Phono on Channel 2, and CD 2 into Line on Channel 2. You then just need to switch the channels from Phono to Line (or vice versa) to use the right piece of equipment. However, it's important to remember that you won't be able to mix from Turntable 1 to CD 1 or mix from Turntable 2 to CD 2 because even though they're different machines, they're both playing into the same mixer channel.
Your headphone jack isn't a headphone rest
Please don't get into the habit of hooking your headphones over the headphone jack when you're not using them. A club I worked in had the mixer at an angle and also had very little room in the DJ booth, allowing hardly any room to put anything down. So when I wasn't using my headphones I'd hook them over the headphone jack, which seemed sensible to me. That was until I aimed a bit high and hit the power switch with the headband from the headphones, plummeting the club into silence, and I almost blew a speaker when I turned the mixer on without turning the volume down . . . oops. Also, the weight of hooking headphones over the jack connection can cause damage to both the mixer and the headphones, which may lead to sound problems (the headphones may cut out and go silent).
Plugging in your headphones
Plugging in your headphones is as simple as finding the hole marked 'headphone' on your mixer and plugging them in, but I want to mention it here so that I can bring up the use of 3.5-millimetre adaptors. These adaptors let you convert headphones with a small 3.5 millimetre jack into the big, 6.35-millimetre (1//4 inch) size that your mixer needs.
A 3.5 millimetre jack is the same as the one on your iPod earbuds. Though it may be tempting to use your earbuds for DJ headphones, they're not really suitable because they don't sound too good when played very loud, and they let in a lot of external sound from the dance floor and DJ booth. For more about picking suitable DJ headphones, check out Chapter 11.
Some mixers have the headphone connection on top of the mixer; others have it on the closest side to you, or even both. Choose your connection and plug in. Simple.
Connecting effects units to a mixer
You can connect effects units to the mixer in two ways:
Between the mixer and the amplifier: Direct connection is the most basic, and easiest way to connect your effects unit. Take the Master Output of your mixer (two RCAs) and plug them into the Line input on the effects unit. Then, take the output of the effects unit (still two RCAs) and plug them into the input of the amplifier.
The drawback to this method of connection is that the entire audio signal will be effected by the effects unit; you won't be able to play one channel from the mixer clean (without effects) while the other one gets a whole load of crazy effects applied to it.
With Send and Return connections: You can send music from an individual channel on the mixer to an effects unit using the Send and Return option. With this, you can apply an effect to only one channel, leaving other channels to play unaffected through the speakers.
You can send the signal from the mixer to the effects processor (and return it) in two different ways:
• If the effects processor can accept multiple inputs, you can use a mixer with a separate Send and Return for each of the channels. Controls on the effects processor (and sometimes on the mixer) let you choose what channel on the mixer to apply the effect to. With the correct controls, you can 'effect' any number of channels while 'un-effecting' any number of channels. This method is by far the most versatile approach to using an effects processor, but does tend to require a large mixing desk instead of a compact DJ mixer.
• Some DJ-specific mixers with multiple channels may have only one pair of Send and Return connections but have a control on the mixer that assigns what channels are sent. The DJM-600 that I use lets you send any one of the four channels or the entire Master Output to an effects unit, so though it's not quite as versatile as the option to include or exclude any number of channels, this way can still give you clean audio from one channel while 'effecting' another, which is good enough for me.
The connections for Send and Return vary, but on the DJM600 it's a pair of mono quarter-inch jacks for each direction. One pair connects from Send on the mixer to the input of the effects unit, then another pair connects from the effects unit to Return on the mixer. You may find some units use RCAs for this purpose or stereo quarter-inch jacks, so take a close look at your mixer and the effects unit so that you know what cables you need.
Connecting mixer outputs
After you have all the inputs connected to the mixer you need to look at how to connect your mixer to an amplifier in order to hear the music, and maybe also connect to a recording device (tape, MiniDisc, CD, PC and so on) so that you can capture the moments of greatness you'll achieve in the mix.
Your mixer has two (or sometimes three) outputs:
Master Out is the connection to use when connecting to an amplifier. Using a stereo RCA cable, connect one end to the Master Out on the mixer and the other end to an input on the amplifier. If the amp has more than one input channel and you're also sending items like a TV, PlayStation or another CD player to it, you may want to add sticky labels to change the normal 'Input 1, Input 2' labels that'll be on the amp, to help you remember what channel lets you hear what.
More expensive, professional mixers may use a second Master Output that uses XLR connections rather than RCA connections.
The Master Out is affected by the Master Level Control on the mixer, so if you turn that down, the volume of the music from the mixer reduces.
Record Out is reserved for outputting to recording devices. The reasons you use this output rather than the Master Out are because
• The Master Out is probably going to an amp anyway.
• The Record Out bypasses the Master Level Control, so if you turn the Master Output down (maybe to take a phone call), the music level you send to the recording device won't change.
Like the Master Output, connect the Record Outputs to the recorder's inputs using a stereo RCA cable, making sure to continue to plug the red RCA output to the red RCA input and the white output to the white input. (For information on how to set the record levels on your recording device, see Chapter 19.)
Booth Output is where you feed the mixer into a separate amplifier and speaker in the DJ booth, known as the Booth Monitor. Chapter 14 has important information about setting the volume of the Booth Monitor and the headphones to allow you to mix properly.
The connection is the same as Record Out and Master Out: connect one end of a stereo RCA cable to the Booth Output on the mixer and the other end to the Booth Monitor's input.
Connecting a mixer to your home hi-fi
Connecting to your home stereo (hi-fi) is similar to connecting to an amplifier. You make the connection using a stereo RCA cable from the Master Output on the mixer to the hi-fi – but you need to pay attention to the input you choose to use on the hi-fi. On the back of a hi-fi you probably see some of these inputs: Line, CD, TV, DVD, Aux and, if you have an old (or really good) hi-fi, a Phono input too.
If a CD or MP3 player is already connected to the hi-fi, a TV is connected to the TV input, and the DVD input is in use too, you're left with Aux (Auxilliary) or Phono (which is meant for turntables only). Therefore, you should use the Aux input to connect your mixer. Even though the music may be coming from turntables, by the time it's played through and outputted from a mixer, the signal's transformed into a Line level signal.
Of course, if you don't have a CD player or TV plugged into the hi-fi, you can use the TV and CD inputs too. Just stay away from the Phono input unless you're connecting turntables directly to the hi-fi.
Connecting a mixer to powered speakers
Sometimes powered speakers only have a jack input (like the headphone output on your mixer), so check whether you need to buy an RCA (the output from your mixer) to jack cable for each of the speakers (left and right).
You can find more information on using amplifiers, powered speakers and home hi-fis to play your music in Chapter 12.
Connecting a mixer to your PC/Mac
Whether you're using the computer as an amplifier or plan to record the mix to edit it or upload it to the Internet, the connection between your computer and your mixer is similar to all the other equipment you'll connect. Connect the output from the mixer to the input on the computer's soundcard (see 'Connecting a computer as an input device', earlier in the chapter, for detailed information on the connections and what you use a soundcard for). Use the Record Output if you're only using the computer for recording and the Master Output if using the computer as an amplifier (this frees up the Record Output for a recording device).
If your soundcard came with instructions and software for setting up the computer to be able to accept a Line input, please refer to the manual carefully. If it's a Windows controlled soundcard, you can activate the Line input through the Volume Control or Recording Devices window – found either by double clicking the speaker icon in the taskbar or through the Hardware/Sound properties in the control panel. Mac users can access audio input controls through the Sound section of System Preferences.
You may want to turn off any other recording inputs (de-select them in the Record Control) or mute other playback devices in the Volume Control Window (by selecting Mute) to make sure that Windows system sounds or sounds from other programs aren't accidentally combined with the sound from your mixer. Nothing's worse than being halfway through a great mix only to have Homer Simpson say 'D'oh!' over the music when you get an email. Come to think of it, that might be quite cool . . .
Troubleshooting Set-up and Connections
Sometimes you're sure that you have everything plugged into the right place, you've turned everything on and everything's playing, but you just can't hear anything. To wrap up Part II of this book, and the equipment information as a whole, the following is a list of troubleshooting issues that may help to answer any of your connection and turntable setup problems.
Everything's connected, a record (or CD) is playing, but I can't hear any music through the amplifier
Ask yourself the following questions:
Are the LEDs on the mixer flashing up and down to show that the mixer is receiving some music? If not, there's currently no signal.
Have you used the correct inputs on the mixer for your MP3/CD players or turntables and set the Line/Phono switches accordingly? (Line for CD and MP3, Phono for turntables.)
If you're currently playing one channel of music, have you made sure that the cross-fader is on that side and the channel-fader is up at least to 75 per cent? And if the cross-fader has an assign function to control any of the channels, is it switched to control the correct channel?
If the mixer LEDs are flashing, have you made sure that you've connected the mixer's Master Output to a Line input on the amplifier?
If the amplifier has the capability for multiple inputs, have you made sure that you've set the input switch or button to the correct input?
Are the Master Level and the Input Level on the amplifier set at a point where you should hear music?
Are the speakers connected?
Have you tried connecting something else to the amplifier to check that it isn't a problem with the amplifier or the input channel you're using?
I can hear the music from the amp now, but I can't hear anything through the headphones
Try the following steps:
Firstly, check that you have your headphones plugged in, turned up and switched to monitor the correct channel.
Try turning all the headphone cue switches on. If you can hear music now, you were pressing the wrong cue button or you've connected your equipment to a channel you didn't intend to use.
Plug your headphones into another piece of equipment with a headphone socket (such as the amplifier) to make sure that this problem isn't a malfunction with your headphones.
One of the turntables sounds really bad: it's distorting and the high frequencies sound fuzzy
The first thing to do is to look at your needles. Are the needles caked in dirt? (Carefully remove the dirt from around them.) Are they really old? (Replace them.) Are they inserted into the cartridge properly? (Check and re-insert them.)
If you think it's a malfunction, try swapping the headshell from one turntable to another or try swapping the needle from one headshell to the other. In case you have a connection problem rather than a needle or headshell problem, try swapping round the turntable connections to the mixer.
Why do my needles keep jumping when cueing?
If you're having a problem with your needles jumping around, try working through these possible solutions:
Refer to manufacturer guidelines on where to set the height and counterweight of your tonearm. If you're given a range of numbers to set the counterweight within (between 3 and 5 grams, for example), set the counterweight to the lowest number first and then gradually increase the weight until the needle stops skipping.
Check the settings provided with the needle and cartridge for the height of the tonearm and make sure that it's completely parallel to the record. If you need to set the weight or height to more than the recommended amount, your technique or needles could be at fault:
• Make sure that you're cueing the record back and forth in the curved direction of the record. If you push and pull horizontally, rather than in a curve, this action may make the needle jump.
• Old, worn needles are more prone to skipping.
I hear a really strange humming noise coming from my turntables
You may not have connected the ground wire. Make sure that it's securely attached to the earth/ground connector on the back of the mixer.
Why is everything distorting badly when I play a CD?
Check whether you've inserted the outputs of your CD decks into the Phono inputs of the mixer by accident. This causes distortion. Plug into the Line input.
Why is everything really quiet when using my turntables, even when everything is turned up to maximum?
Make sure that you've plugged your turntables into the Phono input. If you've put them into the Line input, they'll be very quiet.
Everything sounds nice through the mixer, but distorts through the amp
Ask yourself the following questions:
Have you turned up the input level on the amp too high? Turn it down a bit; see whether that helps.
How strong a level are you sending out of the mixer? Take a look at where the LEDs on the mixer are flashing; try not to play the music above + 5 decibels on the scale because it may cause some nasty distortion.
Have you plugged into the Phono inputs of the amplifier by accident? Change the connections to plug into one of the Line inputs.
Music is playing through the mixer, but I can't get any music into the PC
Try the following steps:
Make sure that the speakers on your computer are turned on and all volume controls (including the computer's) are turned up.
Check the connections and ensure that you've plugged the output from the mixer to the Line input of the soundcard. You may find a Mic input right next to the Line input, so double check that you didn't plug into the wrong place when you were fumbling behind the PC.
Check the meters on the recording software. They'll be bouncing up and down if they're receiving a signal.
Check the Record Control (which you can access through the Volume Control icon on the taskbar). Double check that you've selected Line input and that the input level is set to at least 75 per cent.
Have a quick read of the manual that came with the software and the soundcard to see whether you need to do something special.
The meters are flashing like mad in the software, I'm able to record what's going in, but nothing is coming back out of the PC
Check that you've connected the Line Out from the soundcard and not plugged into the Mic or Line In by accident.
Check the Volume Control found in the taskbar. Make sure that you haven't accidentally checked the mute box thinking it was the select box from the Record Control (I do this all the time).
Why doesn't my recording device seem to record anything when connected directly to the mixer?
Have a look at your connection. There's a good chance that you didn't connect the Record Output to the Line In on the recorder.
Ask yourself three questions:
Did you accidentally use the Booth Output to send to the recording device, but turned the Booth Output volume off? If so, switch the cables over to Record Out, which is preferable to turning up the Booth Output.
Is the input level control on the recording device switched to accept the Line input, and turned up to an appropriate level?
Does your recording device need to be in Record mode in order to register any input? This isn't a common case on home tape and MiniDisc recorders, but on a lot of professional equipment if a CD/DAT/MiniDisc is in the machine then you need to press the Record button on its own to get the device into record mode (the machine only starts recording when you press Record and Play together). This tells the electronics to accept a signal in rather than just play a signal out.
Part III
The Mix
In this part . . .
DJ skills are two-fold. Beatmatching is the core skill of the electronic dance music DJ – all DJs who play this genre of music need this skill. Chapter 15 in this part tells you all you need to know about beatmatching. Chapter 16 covers further mixing skills, including mixing music from other genres.
The second part of your DJ skills are the most important, and apply to all genres of music – choosing the tunes to play, the order to play them, and how and when to mix between them.
If you want to add another layer of creativity and performance to the mix, scratching is covered in Chapter 17, with guidance on how to start your journey as a creative DJ or a dedicated scratch turntablist.
Chapter 14
Grasping the Basics of Mixing
In This Chapter
Discovering the essence of club DJing
Working out the tempo of your tunes – beats per minute
Finding the first beat of a tune with confidence
Starting your tunes so the beats play in time
Using the pitch control to match tempos
Getting to grips with headphone cueing techniques
DJs play music. They play music that people want to dance to, and play music that keeps people on the dance floor. As a DJ, if you can't do that simple thing, you're not going to be a big hit with the crowd.
House and trance DJs employ a technique called beatmatching, which makes the bass drum beats of two different records play at the same time. That way, when they change from one record to another, the people on the dance floor don't have to adjust their dancing rhythm.
In this chapter, you discover all the tools and skills you need to beatmatch. The secret of successful beatmatching is simple: good concentration and lots of practise – no special tricks required. The great news is that after you've made the investment of devoting your time and concentration to mastering beatmatching, the skill sticks to you like glue.
Knowing What Beatmatching's All About
Matching beats is a very simple concept, but it's an important core skill. Although certain kinds of music don't lend themselves to beatmatching (rock music, for example, tends only to use beatmatching once in a while as a special trick), if you want to play in a club where the DJ's expected to beatmatch records to mix them together, you'd better develop the skill!
The reason beatmatching is so essential for the trance and house DJ isn't only to aid with smooth, seamless transitions from tune to tune, but also for the physical effect on the people on the dance floor.
When these DJs progress through the set, playing different tunes and different styles, the music gradually plays faster and faster until it reaches what I call the sweet spot. This sweet spot occurs when the bass beat from the music matches the speed of the heartbeats of the people dancing. This speed can be anything between 130 and 145 beats per minute (BPM) for most music, but can be more depending on the music genre.
When the speeds of the pounding bass beats and the thumping heartbeats get closer and closer, the combination of pulsating rhythms begins to do strange things to the body and emotions of the people on the dance floor. With time, this euphoric moment is commonly signified by a hands in the air moment on the dance floor. It makes me sweat a bit, but that's just me . . .
Importantly, even if you consider this phenomenon as some kind of voodoo mind control, you need to understand that you should play at a tempo where people are enjoying themselves and comfortable dancing on the dance floor.
Other genres of music can affect the people on the dance floor too – but usually only on a song by song basis. The right rock tune at the right speed can really blow off the roof – but this isn't the same thing as the pounding, pulsating beats of a series of great trance tunes putting the people onto the dance floor into a euphoric, trance-like state.
Discovering How to Beatmatch
Your choice of format doesn't matter – CD, vinyl, MP3 or anything else – the mechanics of beatmatching are the same. It's just the controls that are different.
In this chapter I describe how to perform beatmatching with reference to vinyl and CD DJing. However, please check Chapter 6 if you need more information about using controls on turntables, and Chapter 8 if you need more details about using CD decks. Digital DJs may find the on-screen layout and controls very similar to a CD deck, but check out Chapter 9 for more on digital DJ setups, so you can be sure you know what to do depending on your equipment.
Choosing skills over thrills
As technology advances, especially with digital DJing, the option to let technology take care of the skill of beatmatching rather than doing it yourself is available more and more, and can be very tempting.
One school of thought says letting technology take care of the hard stuff means you can concentrate on the music you're playing, but trust me, beatmatching is only hard at the beginning. When you get good at it, you'll be able to beat match two tunes in 20 seconds or less.
Setting up your equipment
A few basic settings and requirements can help you master the fundamentals of mixing comfortably (jump back to Chapter 10 if you're not sure about some of the mixer controls):
Make sure that your DJ setup is switched on and hooked into an amplifier (check out Chapter 12 for more on connecting up). Don't worry about headphones for now; you get to them later.
Use two copies of the same tune (preferably something that has a simple, constant beat from the very beginning). The reason for using two copies of the same tune is that when both pitch controls on the turntables are at zero (known as the green light area), both tunes play at exactly the same speed. This fact means that you don't have to worry about one tune playing faster than the other, and makes getting to grips with starting your tunes and keeping them in time a lot easier.
Set your mixer so that you can hear both records at the same time and at the same volume. (Typically, this requirement means moving the cross-fader into the middle, and setting both of the vertical channel-faders to maximum, with the gain and equaliser, or EQ, controls set the same on both channels). The reason you set the mixer to hear both records at the same time is so that you only have to worry about working with the tunes – you don't waste time and concentration trying to adjust the controls on the mixer. This method may sound messy at first, and your dog may leave the room in protest, but don't worry – you'll move on to proper mixing soon, and the dog needed some exercise anyway.
By using two copies of the same tune, you may experience a phenomenon known as phasing. When two identical sounds play over each other, their sound waves combine and cancel each other out to make it sound like your music is playing through a jet engine. This can seem a little distracting at first, but as you begin to hear this phasing sound, you're getting the bass beats closer and closer to playing together, so you eventually realise that this is a great help when learning how to beatmatch. When you move on to using two different tunes, you won't need to worry about phasing any more, unless you want to use it instead of using a phaser or flanger effect on a mixer (check out Chapter 10 for information about effects on mixers).
Locating the first bass beat
Every journey begins with a step, and every beatmatch begins with a beat. To start with, find a tune with a solid, clear bass beat right from the beginning. (In a perfect world, all records would start with a constant bass beat, making beatmatching a lot easier.)
'For an Angel' – for a new DJ
For years I've used the same record when helping people develop their DJ skills: Paul Van Dyk's 'For an Angel'. It's quite an old tune now and my two copies were getting very worn before I went digital (especially at the beginning of the record). The reason I love to use this track is that it has really clear, solid-sounding bass drums throughout, and they start from the very beginning.
Whether you've chosen a record with the beat at the beginning or picked a record that has its first beat 45 seconds in, the following points can help you locate the first bass beat so that the needle is cued up (ready to play) or the CD is waiting at the very instant the first beat is about to play:
Listening for the beat: The first option is to simply start the tune from the beginning and wait until you hear the first beat. When you hear the first beat, place your finger on the record to stop it and slowly play it backwards by hand. As you play the record backwards, you hear the part of the record you've just heard playing in reverse. (Don't be overly concerned about revealing any Satanic messages when doing this; dance music doesn't tend to contain any.) If you use a tune that starts with a beat from the beginning, the last thing you hear playing backwards is that beat. The instant the beat goes silent is where you want to leave the needle.
CD DJs: Pause the CD when you hear the first beat and then play the tune backwards (your CD deck will have a certain way of doing this; check out Chapter 8 for more) until you get to the beginning of the bass beat. Then store that point as your cue (start) point – often by pressing the Cue button, but check what to press on your CD deck in order to do this.
Winding to the beat: If you're impatient or in a rush, you can turn the record around really fast with your finger until your hear the brrrrrrrrrrrp noise of beats playing really fast and then play the record backwards until you find the very first of those beats.
CD DJs: If you have a CD deck with a large rotating platter that emulates the sound of a turntable, you can do the same as vinyl DJs. If you only have buttons that skip through the tune, press and hold the Search button until you hear the bass beats starting to play very fast, and then play the tune backwards until you locate the first of those beats.
Looking for the beat: Take a close look at a record and you can see a lot of different shades of grey and black rings (the target light on your deck shows up this shading). The darker parts of the record means that it doesn't have as much information cut into the groove and is likely to not contain a beat. Look at the beginning of the record where the rings change from dark to light – the lighter shaded area contains more sound information and is probably where the beat starts. Place the needle where the dark and light rings join. If you can hear the beat, spin the record backwards until the beats stop, or if you still hear the introduction, play the record forwards until you find the first beat.
CD DJs: If you have a wave display on your CD decks or software, which has a series of peaks and troughs to show the louder and quieter parts of the tune, refer to your wave display to find where the big peaks begin – that's likely to be where the beats start.
Starting your tunes in time
When you're happy with finding the first beat in a tune, choose a deck and get ready to start. (I'm left-handed so I seem to always start on the left.)
Vinyl DJs:
1. Place your finger on the outer inch of the vinyl.
Notice I didn't say press – just place your finger, you only need a little pressure.
2. Press the Start button.
Due to the wonder of slipmats, the turntable turns underneath the record while you're still holding it (if it doesn't, shame on you for buying cheap equipment).
Now the easy part.
3. Take your finger off the record.
Glorious bass drums should now flood through your speakers.
CD DJs: No need for three steps for you – just press Play!
Deciphering drum patterns
Although most house/club music follows a pounding bass beat, not all dance music has this simple and basic rhythm. Drum patterns are as varied as the music they accompany, ranging from a simple bass/snare beat to the complicated patterns of dubstep, drum and bass and jungle. You can often distinguish different music genres as much by their drum pattern as by the music. The drum pattern alone is enough to be able to recognise breakbeat, R&B or two-step garage.
If you're interested in finding out more about drumming and drum patterns, I heartily recommend Drumming For Dummies (Wiley) by Jeff Strong.
4. While the tune is playing, listen to it. Don't simply hear it – take a moment to really listen to what's happening (this is called listening with an active ear). Really concentrate on listening to the bass drums.
You should pick up that the bass drum has two different sounds. One of them is just a bass drum on its own, and the other one is normally the bass drum combined with another sound (sometimes a clap – or a snap sounding drum called a snare drum). Listen – notice the difference in emphasis between the first beat of the bass drum (represented by B in my DJ beat notation that follows) and the second beat of the bass drum (represented by BC to show that's B combined with another sound):
B BC B BC B BC B BC
5. When you're comfortable with the sounds of the beat, move over to the other deck and check that the pitch is set to zero. Vinyl DJs: go back to the previous steps 1 and 2.
The first beat that you've located on your tune and are ready to start from is normally the bass drum on its own. What you're about to try is starting this first beat at the same time as the single bass beat plays from the tune that's currently playing through the speakers.
Have a listen again. Make sure that you know what bass beat sound you want to start on. At this early stage, you may find that counting the beats in your head is helpful: '1 – 2, 1 – 2, 1 – 2' or 'bass – snare, bass – snare, bass – snare'.
The record is poised, ready to go; the deckplatter is still spinning underneath; you're now sure that you know the sound of the beat you want to start on.
6. Let go of the record (CD DJs: Press Play).
Chances are, one of three things happens.
You get it right first time – both beats play at the same time. Well done! Give it a few more goes to make sure that you've really got the knack.
In your haste, you let go/pressed Start too early and the two bass beats sound like a galloping horse when they play together. Don't worry; it's easily done. Take the needle off (CD DJs: Return to your cue point; check out Chapter 8 if you're unsure how), head back to Step 1 and have another go.
You're over-cautious, wait too long, start the tune too late and the beats sound like a train-wreck together. Again, very easily done. Just go back to the first step and try it again.
The good news is that a small timing error may not be all your fault. Before you get too frustrated at not getting your tunes to start in time, check out a couple of external factors:
Give a little push. When using vinyl, you may find that waiting too long happens more often than not, which is common and happens to the best DJs. The good news is that the delay may be nothing to do with when you let go of the record but more to do with the motor in the turntable.
In your attempt to start the beats in time, even though the slipmat does its job and the deckplatter still turns underneath the record, if you just lift your finger off the record to start it playing, the motor can still take a fraction of a second to get the turntable up to full speed (known as lag).
The more powerful the turntable's motor, the quicker it gets up to speed, but even the best of decks can introduce a tiny delay. (All you CD DJs are allowed a smug smile at this point.)
To get around motor lag, don't just let go of the record – give it a gentle push too. How much of a push you have to give the record is just as much a knack as starting it at the right time, but like everything else with beatmatching, you'll get the knack with practice.
Make sure that you've really got that beat! The other common cause of not starting the beat in time is not having the needle or CD cue point at the very beginning of the first beat.
For CD DJs this is just about listening properly to the sounds of the beats as you try to find the very beginning of the bass beat. For vinyl DJs and CD DJs who use deckplatters with vinyl emulation, to get used to finding exactly where the beat is play a second or two duration of the tune backwards and forwards, as if you were scratching slowly. The beat will make a boom – woomp – boom – woomp noise as you rock it back and forth.
To improve the timing when you eventually release the record, perform this rocking (scratching) motion at the same time as the other tune plays its bass beats. Scratch forward when the other tune only plays a bass beat, and backwards as the other tune plays the bass and snare/clap beat. Then, when you want to start the tune, just let go instead of continuing to scratch to the beat.
With all the noise around you in a DJ booth, you can have difficulty hearing the first bass beat if it isn't a solid thump. By rocking a record back and forth through the needle, you're giving your brain more information to help it pick out the bass sound from all the other noise.
Try this rocking technique a few times as you practise starting the record in time. You'll be amazed at how quickly you get used to working the vinyl (a fancy-pants way of saying using and touching the record).
Your parents may have told you never to touch records and to treat them with care, which is right for their Beethoven LPs but not for DJing. Moving the needle off and on the record, finding the first beat and starting it playing at the right time are skills that go toward making you more comfortable with your DJ tools. Just keep your hands clean and show some care (don't drop the needle from a great height or rip it right across the record) and your tunes will be with you for a long time.
Adjusting for errors
When you make a timing error starting the beats, starting over again is perfect when you're developing your skills, but it's not how experienced DJs deal with theses errors.
Try starting the beat again – but from now on, if you make a timing error, use the following methods to bring the bass beats back in time (make them play at the same time):
Starting too soon: If you started the new tune too early, its bass beats will play before the bass beats on the tune to which you're trying to match the beats. So you need to temporarily slow the new tune down a little to get it in time.
CD DJs should have pitch bend controls on their CD decks which do exactly this. If you have pitch bend buttons, press and hold the – pitch bend button until the beats play in time, and then release the button to return to the correct speed. If, like me, you use something like the Pioneer CDJ-1000 with an outer ring that you rotate to make the tune play faster or slower in short speed bumps, spin it backwards to slow down the tune.
Vinyl DJs can place a finger on the dimpled ring running around the side of the spinning turntable to add a little friction. This added friction slows the speed at which the turntable turns and eventually slows the record down enough so that the beats play at the same time. When the beats now play in time, take your finger off the dimples to return the record to normal speed. The amount of pressure to add to the dimples takes a little getting used to, and if you're ticklish try not to giggle – it doesn't look professional!
Starting too late: When you start the tune too late, and the beats on the new tune play after the one to which you're trying to match, vinyl DJs can try a couple of methods to speed up the record:
• Tightly grab the turntable's centre spindle that pokes through the record with your thumb and middle fingers and turn that around to make the turntable turn faster than normal.
• My preferred method is to place your finger lightly on the label at around the 6 o'clock position, and push that round to help the record play faster.
CD DJs: Use your pitch bend controls to temporarily speed up the tune.
A technique some DJs use to fix starting errors on CD decks or turntables is to use the pitch control as a pitch bend. Briefly boosting or cutting the speed using the pitch control works well at this stage, because you only need to return it to zero in order to make the tunes play at the same speed again, but by the time you start using the pitch control to play your tunes faster or slower (see 'Using the Pitch Control', later in this chapter), it'll be a lot harder to return the control back to where you originally set it.
Nerves and carelessness don't mix
I remember my first night playing live in front of real people (eek!). I was so nervous that when I tried to speed up the record by pushing the label, my hand slipped and I ripped the needle right across the record (which is why I now start at the 6 o'clock position, nowhere near the needle!).
Fortunately, you tend to only do this kind of thing once . . . it's incredible how quickly being that embarrassed helps you learn from a mistake like that!
Experiment with all the methods and find the one that you're most comfortable with. Importantly, you need to find the error adjustment method that suits you the best, giving you consistent, positive results.
No matter which method you use, try to be gentle when making these timing adjustments. If you press down too hard on the side of the turntable, it'll grind to a halt! Or if you push the label around too hastily, you may knock the needle out of the groove or zip forward through the tune by 20 seconds. Some CD decks pitch bend more the harder you press the button, so work out how heavy-handed you need to be.
Knowing which record to adjust
When you need to alter the speed of a tune to make the beats go back in time, you almost always adjust the tune that isn't playing through the speakers yet – the cued track, which you normally listen to in your headphones. If you were to speed up or slow down the live track that people can hear, they'll start shouting 'Sack the DJ!' (a phrase that strikes fear into the heart of any DJ). If both tunes are playing through the speakers when you're in the middle of mixing one tune into the other, adjust the quieter of the two tunes.
There are cases (usually a tune with a constant note playing) where speeding up or slowing down the quieter tune sounds terrible because of the pitch hiccup to the notes playing, but practice gives you the experience to know which one to change.
Using the Pitch Control
After you're comfortable starting your tunes in time (see the earlier section 'Starting your tunes in time'), the next step in beatmatching is to follow the same process using the same two tunes, but this time one of them starts off playing at a different speed to the other one so you can get used to working with the pitch control.
At this stage of getting to grips with beatmatching, the advantage of using the same two tunes as the first exercise is that you can compare the pitch controls of both decks to help match the speeds. The downside is that you still play the same tune over and over. Don't worry, you'll move on to other tunes soon.
Understanding BPMs
In order to use the pitch control correctly, it's useful to know how it affects the speed of the music, and how to calculate these changes of speed.
Beats per minute (BPMs) are a way to describe how fast (known as the tempo) your tunes play. The name gives it away; the BPM is the number of beats that occur in one minute.
As a very broad generalisation, house music is recorded with a BPM between 110 and 130 BPM, trance music ranges mostly between 130 and 145, and hard-house/happy hardcore can be well in excess of that. Other genres of music, like rock, pop, jazz and so on, have wider ranges of BPM. Even looking at just one artist like Aerosmith, 'Crazy' is a ballad at 54 BPM, whereas 'Young Lust' rocks out at 189 BPM!
Calculating BPMs
When you try to beatmatch two different tunes, knowing the BPM of each one helps you to make an educated guess about how much you need to adjust the pitch control.
You can adopt two main approaches for calculating BPMs:
Use a beat counter. A beat counter is a useful DJ backup tool that automatically calculates and displays the BPM of the tune for you. Stand-alone beat counters can cost between £70 and £200. If you're thinking about BPM counters and you haven't chosen your mixer yet, it makes good financial sense to look at a mixer with built-in BPM counters. Instead of buying a basic mixer and an expensive stand-alone BPM counter, use the combined money to afford a really good mixer with built-in BPM counters.
Calculate the BPM yourself. The free approach. It doesn't take long, and is easy to do. Set the tune to zero pitch and get a stopwatch ready. Hit start, and count how many bass beats you hear for 30 seconds. If you counted a beat as you started the watch, subtract one and double the figure – that calculates the beats per minute for that track.
For example, if you counted 67 beats in 30 seconds and counted a beat as you hit Start, the BPM would be 66 × 2 = 132. If you counted 60.5 beats in 30 seconds, and started counting from the first beat after you started the stopwatch, the BPM would be 60.5 × 2 = 121 BPM.
You can count the beats for an entire minute of course, but you'll probably find that the difference between the 30 second and 60 second count isn't noticeable enough to warrant doing it for longer.
If you can get into a routine of calculating the BPMs of your records as you buy them, you'll always be on top of your calculations.
After you've been DJing for a few months and your skill develops, you'll find you don't have to worry about knowing exact BPMs any more. Quite quickly, you'll not only develop the skill to tell instantly whether a tune is faster or slower than the one playing, but you'll find you've developed an incredible memory of the general tempo of your records before you play them and won't need to refer to calculations.
Matching the pitch setting
The numbers on the pitch control don't in fact show how many BPMs you may add or subtract. The pitch slider on a turntable is numbered to show the percentage increase/decrease of the turntable rotation, and therefore the percentage change of the original BPM of the tune. On Technics 1210mkII turntables the pitch slider is zero when in the middle, +8 when moved closest to you and –8 when moved away from you to the farthest point (assuming you don't have your turntables sideways for scratching – see Chapter 17).
If you play a 130 BPM tune and set the pitch control to +4, you're not adding 4 BPM, you're adding 4 per cent to the original BPM. Four per cent of 130 is 5.2, which means the 130 BPM tune now plays at 135.2 BPM.
Don't count your life away
I used to spend a full minute calculating the BPM because I wanted to be sure that I was really accurate. Eventually, I figured that by the time I'd counted 120 records, I'd used up an extra hour of my life for no real reason! I'd rather have spent that hour mixing.
Here's an example of how to calculate where to set the pitch control on the cued track (the track you want to play next) in order for it to match the live track that's currently playing through the speakers to the crowd:
The live track is a 130 BPM track with its pitch set to +2 per cent. This data means that the record is running at around 132.5 BPM (2 per cent of 130 BPM is 2.6, which I round down to 2.5 BPM).
The cued track is 138 BPM. You therefore need to slow this tune down by around 5.5 BPM to make it close in BPM to the live track. Because it's best to deal in rough estimates with the first adjustment to the pitch control (see 'Taking your eyes off the pitch control', later in this chapter), this means taking the pitch control down to around –4 per cent to slow it down enough, and then you just need to do some fine tuning.
All hands (back) on decks
Enough theory – go back to your decks and try the following method, still using two copies of the same tune:
1. Slide the pitch control on your live track to about +3 per cent.
(The numbers on Technics turntables go up in twos, so set the pitch slider between 2 and 4 if you have one of these.)
2. Leave the pitch setting on the cued track at zero and start its first bass beat at the same time as the live track's single bass beat.
You'll notice that the beats start to drift apart and play out of time very quickly.
3. Change the pitch to +3 per cent.
Fortunately, you can cheat for now. Because you can see that the live track is set to +3 per cent, you know that you need to set the pitch on the identical cued track to the +3 per cent mark in order to get the beats playing at the same speed.
4. Have another go at starting the beats in time, but this time don't stop the cued track when it's playing too slowly.
Treat it in the same way as a starting error. You know (for now) that you need to set the pitch control to +3 per cent, so do so, and then use your chosen error correction technique (see 'Adjusting for errors', earlier in this chapter) to get the beats to play at the same time again.
You may get lucky and set the pitch precisely the first time, but most often you'll probably find that the beats start to drift apart after ten seconds or so, because even though you've moved the pitch control to the +3 per cent mark, the pitch control may not be totally accurate.
This is all just for practise of course – when you use two different tunes with different BPMs you won't have the option to cheat by just looking at the pitch control on the other turntable to know whether you need to speed up or slow down the new tune. So things start to get a little trickier. You need to be able to tell whether the cued track is running too fast or too slow in order to make the beats play in time again, using your ears, instead of your eyes. You work this out by listening to the sound that the bass drums make together.
Playing too slow or too fast
If you can hear that a record is slipping out of time before anyone else can and if you can react to it and fix it before anyone hears it, you'll be as good at beatmatching as any top-class DJ. However, knowing whether a tune is playing too fast or too slow is by far the hardest part of DJing. How to know this is the question I most commonly get asked, and the hardest thing for a lot of new DJs to figure out.
The reason people new to DJing have difficulty making this judgement is that they haven't spent the time training their ears to listen out for the audio clues that provide the answer. Spend time practising the following method, and listen to and concentrate on the sound that plays when a tune is running too fast or too slow.
In order to be able to tell whether your cued track is playing too slow or too fast, you need to change your mixer setting so that the live track's channel-fader is set to about three-quarters of the volume of the cued track's channel. You make this change because you need to be able to identify the cued track's bass beats while both tunes are playing through the speakers. If both tracks played at full volume, you wouldn't know which beat was playing first (especially because at the moment they're currently both the same tune!). Having one tune louder than the other helps you distinguish one from the other.
The reason I suggest this setting is that it's similar to how I set my headphones when beatmatching. I have the cued track playing loud, and assuming the mixer has headphone mix where I can also play the live track in the headphones, I play the live track at a much lower volume at the same time. See 'Introducing Your Headphones', later in this chapter, if you want to know why that's my preferred setting.
I've discovered that the best way to describe what to listen for is by using onomatopoeic words (words that you can associate with sounds): l'Boom and B'loom. (Please bear with me here . . . I haven't gone mad.)
Simply, when the cross-fader is in the middle, the cued tune is beating away at full volume: Boom Boom Boom Boom . . . The live tune is playing quieter than the cued track; instead of sounding like a loud Boom, it's a softer loom sound: loom loom loom loom. (Honestly, bear with me, it does makes sense when you put this into practice, I promise.)
This means that the two sounds you hear that let you know whether to speed up or slow down the cued track are:
B'loom: When the louder 'Boom' tune (in this case, the cued tune) plays too fast, you hear its beat first – and the sound you hear is B'loom, B'loom, B'loom, B'loom
l'Boom: When the cued tune is too slow and plays after the live track, it sounds like l'Boom, l'Boom, l'Boom, l'Boom.
Being able to hear the sounds of both bass drum beats with all the rest of the music playing takes a fair bit of concentration, but some spend time practising and you'll realise that I'm not as mad as I sound. It's slightly easier when using two different tunes, because the bass drums will probably sound different anyway, but regardless B'loom and l'Boom are your beatmatching buddies.
Go back to the previous step of playing the live track at +3 per cent and, starting at zero per cent, adjust the pitch on the cued track so the speeds are similar. Listen carefully to the sound that the bass drums are making when the beats are almost matched. Listen especially for l'Boom or B'loom, and try to work out whether your cued 'Boom' track is running too slow or too fast.
If you got it wrong and have slowed down a track that was already playing too slow, that's okay! Just remember the sound that you heard that made you think that the track was running too fast and re-associate that with running too slow.
This technique takes practice and concentration, and you may want to adopt a trial-and-error approach for a while. Go back to zero pitch on both of the tunes, slow one of them down and listen to the sound the bass beats make – then speed one up, listen to that sound and take note of the difference.
Taking your eyes off the pitch control
When you're used to hearing the different sounds that beats make when they're playing too fast or too slow, the next step is to match the beats by adjusting the pitch control without looking at where the other deck's pitch control is set, using only your ears as your guide.
Using identical tunes, increase the pitch control on the live one but this time with something covering the reading, so you know that it's increased but you can't cheat by looking at where the pitch control is set to. A bit childish I know, but from now on your cheating DJ days are over.
To match the pitch control on the cued tune to this new setting, I consider four different ranges of adjustment:
Large, rough adjustments to get somewhere close
Medium adjustments (about 1–2 per cent on the pitch slider) to get closer
Small adjustments (about 1//4 of 1 per cent) to finalise it
Minute adjustments (millimetres) for fine tuning during the mix
For example:
If the cued tune starts to play too slowly immediately, increase the pitch control by about 4 per cent and perform your preferred error correction method to get the beats playing at the same time (see 'Adjusting for errors', earlier in this chapter).
If you then hear B'loom when you stop the error correction (which means you've sped up too much, but the beats aren't drifting apart as fast as they were in the last step), reduce the pitch a little, by about 1 per cent.
If the beats now take about ten seconds to play noticeably too slow, and you begin to hear l'Boom sounds this time, increase the pitch by about 1//4 of 1 per cent.
If you're almost there, but after 20 seconds you start to hear B'loom again (the louder, cued tune is playing too fast), correct the error and decrease the pitch by the tiniest amount. Nudging it to move by only a millimetre is sometimes all that it takes.
Practising happy
Always think about the fact that you're spending the time practising because you want to be a DJ – and you want to be a DJ because, as well as a lot of other things, DJing really is a heck of a lot of fun.
If you start to get a little frustrated as you try to develop any of your beatmatching skills, stop. Take five minutes away from the decks. Get a glass of water (anything stronger may inflame matters!), and come back to your setup with one thought in mind – to have fun. Don't worry about any of that pesky learning/skill stuff. Don't record yourself, don't try to be something you're not, don't sweat it. Just play some music and smile like you mean it! In fact, this is almost the one time I'd say an auto-beatmatching function on your decks would be of help, so you can pretend you're really the one doing it, get your groove back and get rid of any negativity.
Introducing Your Headphones
When first developing your beatmatching skills (see the preceding section), playing both tunes through the speakers at the same time makes it a lot easier to hear clearly and instantly whether you've managed to get the bass beats to play in time. Sadly, you don't get that option when mixing for an audience or when recording a demo CD because, as you'll already know, it sounds awful. So I think that it's time to take the stabilisers off and start to work out whether the beats are in sync (play at the same time) through your headphones from now on. Your neighbours and dog will thank you for this.
Switching over to headphone control
In order to start making the best use of the headphones, you need to set up your mixer so that you only hear the live track playing through the amplifier's speakers, and you only start to hear the cued track playing through the speakers when you move the cross-fader toward the cued track's channel.
Set your mixer to these settings:
Cross-fader all the way over to the live track's side
Headphone cue buttons set to hear the cued track in the headphones
Gain controls and EQ settings on both channels set identically (so both records play at the same volume, with the same amount of bass/mid/high frequencies playing)
Both channel-faders at maximum
The last setting is for ease of use while you're developing your skills because this, along with the EQ and gain settings, maintains an identical play-out volume for both identical records. As you get better as a DJ, though, you'll find that setting the channel-faders to maximum can cause volume problems instead of prevent them. (See Chapter 16 for more information.)
If you're unsure of how any of these settings affect the sound through your mixer, or for detailed explanations of the different cueing options, refer to Chapter 10.
Cueing in your headphones
Making the pitch adjustments to the cued track in the headphones while listening to the live track through the speakers isn't an easy thing to do at first. Cueing in your headphones (finding where you want to start in a track and also setting the pitch control during the beatmatching process) is another key skill of beatmatching that once gained stays with you forever. At first it can feel a bit like patting your head and rubbing your tummy, or juggling four chainsaws while singing – though not quite as dangerous.
Cueing with single ear monitoring
The most popular way to cue in the headphones is called single ear monitoring. Quite simply, you cover only one ear by the headphones playing the cued track, leaving the other ear clear to listen to the live track through the speakers. This way, you can hear both tracks and compare them in your head.
Cueing with headphone mix
You can use a headphone mix to help hear the B'loom, l'Boom sounds (see the earlier section 'Playing too slow or too fast') when single ear monitoring, or cover your ears with both cups of the headphones to check that the beats are playing in time.
When single ear monitoring with the cued track playing at a good volume in your headphones, the headphone mix lets you play the live track quietly over it (what I call bleeding in) so you can hear the B'loom, l'Boom bass beat clues in your headphones. If you hear B'loom, the cued track is running too fast; if you hear l'Boom, your cued track is running too slow. See the earlier section 'Playing too slow or too fast' if you need to go over this technique.
When you get halfway through the mix, and the cued track is now the louder tune through the speakers too, you may wish to swap the headphone cue controls so that the cued track now becomes the live track and is now the quieter one, and the tune that was the live track now plays louder in the headphones and becomes the cued track. What this means now is that when you hear B'loom, the tune you're mixing out of (which is now the cued track) is running too fast, and when you hear l'Boom, it's running too slow.
Apart from helping to spot the l'Boom and B'loom indicators, the other advantage of a headphone mix is that you can do a trial mix with both ears of your headphones on before letting anyone hear it. Some records just don't play well with others, and listening to a mix first in your headphones can be a great safety net for preventing a poor choice of tunes to mix together.
You may even find that the B'loom and l'Boom indicators are easier to hear through both ears, rather than single ear monitoring and you're happier with both ears of the headphones on when checking the beats are playing in sync.
If you're going to check the beats and maybe even perform the mix with both of your ears inside the headphones, periodically take them off, just so you can hear the music playing to the dance floor. You may think that you're performing the best mix in the world, when in reality the people on the dance floor can only hear distortion and noise.
Headphone mix isn't a vital option on the mixer, but every little bit helps – especially when beginning your beatmatching development!
Cueing with split cue
Another headphone monitoring option is split cue, where one ear of the headphones plays the cued signal and the other ear plays the live signal.
This technique is almost identical to single ear monitoring, where one ear is in headphones and one ear open to the live sound, except that the live sound is a lot clearer through headphones than from the speakers on the dance floor.
There's no right or wrong method for cueing in your headphones. The headphone cueing section on your home mixer can have an enormous effect on your cueing style, as can the room or club you're playing in. I suggest that you practise how to beatmatch with single ear monitoring first because it's the most common technique, but choose the method you prefer and make sure that you're 100 per cent happy with it.
Knowing how to use all three kinds of headphone cueing makes you a well-rounded DJ. If you can only mix using single ear monitoring, for example, the first time you play in a club that doesn't have a monitor in the DJ booth and you get a delay that's caused by the distance between the main speakers and the DJ booth, you're going to struggle. If you're faced with that occasion and if the mixer has the option, if you know how to mix with a split cue in the headphones, you're prepared for such a problem.
Centring your head with stereo image
Listening to two tunes at the same time and comparing their bass beats to see whether they're playing at the sam e time takes a lot of concentration. Your brain isn't normally in situations where it needs to listen and react to two things at the same time, so at first it tries to shut one of them out, meaning listening to two tunes at the same time may take some getting used to. The trick to getting this method right is how you set the volume in your headphones.
When you put your headphones on both ears just to listen to some music, you should notice that the music seems to be playing in the middle of your head. This sensation is known as the stereo image and is the voodoo magic of stereo sound.
If you monitor the live and cued track using single ear monitoring, the perfect volume at which to set your headphones is when you've created a similar stereo image in your head between the live speakers and the headphone as shown in Figure 14-1.
**Figure 14-1:** The joy of stereo: balancing the headphone and speaker volumes gives a perfect stereo image, as though both cups of the headphones were on your head.
DJs who use split cue can use the gain control to match the volume of the cued track in one ear of the headphones to the live track in the other ear. See Chapter 10 if you want more information about gain controls.
If the headphone or the loudspeaker is louder than the other, it becomes the more dominant sound, throwing off the balance of the stereo image, and your brain finds it much harder to concentrate on the bass beats from both records. Figure 14-2 gives you an idea of this imbalance.
**Figure 14-2:** When the loudspeaker is louder, the music ends up off centre. If the headphone was too loud, the stereo image would be off centre in the other direction.
You can adopt this technique in reverse, which is why you turn up the TV volume when you're being nagged at home – when the TV is louder, it's harder to hear the person nagging you!
When listening to two copies of the same record, you really get the chance to discover what I'm saying in regards to stereo image. Set both records to zero pitch, start them playing at the same time (you're great at that now, I trust) and adjust the headphone volume louder and quieter. Close your eyes and listen to where the sound appears in your head. When you have a balance of volume between the live speaker and the headphone, the music creates a near-perfect stereo image in the middle of your head.
You won't often have the need to mix the same tune into itself, though, and when you play different tunes they won't create the same perfect stereo sound in your head. However, the bass beat is the key and is what you need to concentrate on. Even though the rest of the tune is different, all you need in order to create a stereo image in your head is the bass beat.
If you're having difficulty concentrating on the bass beats, or if the tune you're playing doesn't have a solid Boom Boom Boom Boom bass beat, listen to the bass and snare/clap combined beat instead (see 'Starting your tunes in time', earlier in this chapter). The snare drum or clap adds a sharper, clearer sound that some people find easier to pick out from the rest of the tune.
Practising with your headphones
To get used to using your headphones to monitor your tunes, go back to your DJ setup and, if you haven't already, set the mixer so you can hear the live track through the speakers and the cued track through your headphones.
Then go back to the beginning of this chapter and work on the basics of starting beats and matching pitch settings, from the basics of how to locate the bass beat to starting it at the right time, working out when you need to speed up or slow down a tune in order to match pitch settings and listening out for the l'Boom, B'loom indicators, all the time listening to the cued track in your headphones and the live track through the speakers.
When you're confident with cueing in the headphones and can comfortably tell whether the beats are in time this way, you can start creating long mixes without the beats of the tunes drifting apart, and will give yourself more time to spend creating impressive, professional-sounding mixes.
Using new tunes
At last. The confidence you've gained matching the beats of the same two tunes in your headphones means you can easily move on to beatmatching two different tunes.
Practice makes perfect
Practice makes a huge difference when developing your beatmatching skills. If you practise for two hours a night, you should be 75 per cent as good as anyone else at beatmatching by the end of one week – it's the last 25 per cent, perfecting it, that takes time to develop.
As a general timescale, when you become more comfortable with your music and your chosen DJ tool, be it CD, vinyl or digital DJing, by the end of a month practising beatmatching you'll find you'll be able to get the beats matched quickly without having to rush it or guess in order to start the mix before the other record runs out.
You may take months, maybe even years to perfect beatmatching and be confident that 99 per cent of the time you have the beats matched accurately and that they'll stay locked together for the duration of the mix. Just remember that during all that time spent practising, you get to listen to the music you love and the music you want to hear.
You may still want to use one of the tunes you've been practising with, but throw a new tune on the other deck. The good news is that you've already developed the skills and the ear to be able to match the beats of this new tune to the older one. The only things you have to think about are the sounds of the bass beats on this new tune, and whether its BPM means you need to speed up or slow it down in order to match the bass beats of both tunes.
If you take a while to get beatmatching right, that's fine. Tying to concentrate on two completely different tunes is a little more difficult, but give yourself time to practise and focus on what you're doing, and it'll fall into place very quickly.
Quick Beatmatching
I've left this technique until the end of the chapter because it's a last minute, emergency method for beatmatching when you don't know the BPM information that would normally help you with how to adjust the pitch control, and you don't have time to work it out.
You can use this method right at the beginning of your development when learning how to beatmatch, with both tunes playing through the speakers at the same time, or in a more traditional DJing situation, monitoring in the headphones. The outcome is just as effective.
1. With the live tune playing through the speakers, set the pitch control on the cued tune (the next one you want to play) to maximum.
This takes all the guesswork out of knowing whether you need to speed up or slow down the tune to get the beats matched. Because you're starting the new tune way too fast, you know you'll just have to slow down the tune.
2. With the cued track playing a lot faster than the live track, perform your chosen error correction method to slow the cued tune down enough that the beats are playing at the same time (or as close as you can get it). At the same time as you're performing this error correction, reduce the pitch control.
As you reduce the pitch control, you'll find you won't have to press quite so hard on the side of the turntable or press the pitch bend button quite as hard/long on CD decks to keep the tune playing slow enough to keep the beats matched.
3. The closer you get to the correct pitch setting, the lighter and lighter your error correction needs to be.
4. When you feel you no longer need to error correct, stop – and stop adjusting the pitch control.
5. Make tiny error corrections and adjustments to the pitch control in order to keep the beats playing in sync.
When you stop hearing B'loom and l'Boom, which let you know your beats are out of sync, the beats will be matched.
Using this method, you should be able to get from Step 1 to Step 4 in about ten seconds. Step 5 may still take a little bit of time, but when you're in a rush, or just don't know your tunes well enough, this is an incredible quick fix for beatmatching.
Some people use this method for every mix they do, and nothing's wrong with that. However, in time, when you become more experienced with beatmatching and can easily remember more about the speed of your tunes, you won't need such a 'hail-Mary' approach to beatmatching.
Chapter 15
Picking Up on the Beat: Song Structure
In This Chapter
Understanding how songs are constructed
Introducing beats, bars and phrases – and a certain sheep
Working out where you are in a tune
Relying on your memory and instincts
Trying out your skills on a sample structure
Being a good DJ means getting yourself a split personality. One half of you plays great tunes in the perfect order, and the other half of you creates the perfect mix from tune to tune.
You need more than straightforward beatmatching to create the perfect mix, especially if you're mixing rock, indie or party tunes, which don't lend themselves to beatmatching. How you adjust the EQs (equalisers) and overall sound level changes the dynamics of a mix (see Chapter 16 for more info), but the most important factor is choosing which parts of your tunes to mix over each other, and listening out for when your tunes progress from introductions to verses to choruses and to their outros.
Your knowledge of beat structures kicks in at this stage. Starting from the simple bar, which grows into a phrase, which blossoms into a verse, songs are mapped out in an extraordinarily ordinary fashion.
When you crack the code of how a tune is constructed, your instincts take over, you don't need to think and you can effortlessly create smooth transitions through your set that gets you praise for your skills.
Why DJs Need Structure
The simplest of mixes involves playing the introduction (intro) of a new tune over the last part (the outro) of the tune you wish to mix out of. In order to start this mix in time, the DJ needs to know when the outro is about to start. By analysing how beats and bars are put together to make up verses, choruses, introductions and outros (all of which I describe in detail in the section 'Studying Song Structure', later in the chapter) you won't miss a beat.
Knowledge of beat structure is vital for all kinds of DJs. Whether your style is to create minute-long, seamless transitions from tune to tune, or you simply start one tune as another ends, an understanding of how a tune is put together enables you to mix without any risk of gaps in bass drum beats, drops in the fun and energy of the night, or even worse – silence.
For more information on how different parts of tunes overlap to alter the sound and energy of the mix, check out Chapter 16.
Multiplying beats, bars and phrases
Just as a builder constructs a wall from hundreds of bricks layered on top of each other, and then adds that wall to other walls to make a house, a songwriter groups together the beats in a tune and adds these to further groups, and then joins these groups together to make larger structures, all of which are part of a bigger whole – the song. But before you start looking at how walls make a house (or how verse and choruses make a tune) you need to know how to build a wall – or create a chorus – out of beats and bars. If you can count to four, you can easily deal with beat structure, because the building blocks of nearly all tunes you'll encounter are grouped into fours:
Four beats to a bar
Four bars to a phrase
Four phrases to a verse (normally)
Although typically made up of four phrases, the length of a verse can change depending on the decision of the songwriter.
The easiest way to explain how four beats become a bar and four bars become a phrase is with song lyrics. Unfortunately, I'd have to pay a lot of money if I wanted to use the lyrics to a recent, famous song, so I use the nursery rhyme 'Baa, Baa, Black Sheep' to show how the magic number 4 multiplies beats into bars and phrases.
To demonstrate the principle that you get four beats to a bar, look at the first line of the nursery rhyme, which is 'Baa, baa, black sheep', and lasts one baa, sorry, bar in length. You sing each one of these words on a different beat of the bar, and the first word has more emphasis than the next three.
A simple drum beat that accompanies this bar follows a basic pattern of 'bass' – 'bass/snare' (check out Chapter 14 if you need more information on drum patterns), as you can see in the following:
Beat 1 – Baa (bass drum)
Beat 2 – baa (bass drum and snare)
Beat 3 – black (bass drum)
Beat 4 – sheep (bass drum and snare)
Moving further into the nursery rhyme, this first bar is the first of the four bars that make up the first phrase:
Bar 1 – Baa, baa, black sheep,
Bar 2 – Have you any wool?
Bar 3 – Yes sir, yes sir,
Bar 4 – Three bags full.
This first phrase is grouped together with three others to create 16 lines (and therefore 16 bars) and create a full section.
Baa, baa, black sheep,
Have you any wool?
Yes sir, yes sir,
Three bags full. (End of Phrase 1 – four lines/bars in length)
One for the master,
One for the dame,
And one for the little boy
Who lives down the lane. (End of Phrase 2 – rhyme is eight bars to here.)
Baa, baa, black sheep,
Have you any wool?
Yes sir, yes sir,
Three bags full. (End of Phrase 3 – rhyme is 12 bars to here.)
One to mend the jerseys
One to mend the socks
And one to mend the holes in
The little girls' frocks. (End of Phrase 4 – total rhyme duration is 16 bars.)
Take another look at the 16 lines in the nursery rhyme. Although four different phrases make up the entire rhyme, you can group together the first two and the second two phrases as two different parts of the rhyme. Both halves start with the identical 'Baa, baa, black sheep, have you any wool, yes sir, yes sir, three bags full' phrase, but the next phrase is different.
You find the same principle in music: the second half of a verse may sound very similar to the first half, but in the final, fourth phrase, the sounds, drums and energy of any vocals or instruments increases to let you know that you're approaching the end of the entire verse rather than the end of the first half.
Hearing the cymbal as a symbol
Not all songs have lyrics to follow that let you know where you are in the tune. Even though music without lyrics sometimes has a change of the melody through the different phrases, you may need a little more guidance to help you pinpoint your position. If you've just dropped the needle, or started the CD at a random point with a view to starting a mix, you need to know how to work out where you are in a four-phrase (16-bar) pattern.
Luckily for DJs, record producers are very kind people and leave end-of-phrase markers (commonly cymbal crashes) at or after the end of phrases.
The four phrases given in the 'Baa, Baa, Black Sheep' example have three key, different types of endings:
The end of the first and third phrase (probably identical)
The end of the second phrase (the halfway point)
The end of the fourth phrase (the final and most powerful point)
The ends of the first and third phrase are likely to have a cymbal crash as a simple punctuation point (often on the fourth beat of the fourth bar), but nothing too special.
The end of the second phrase, the halfway point, has a little more to it, because that first half exists as a discreet part of the story. This ending may have a small change to the drums, such as a mini drum roll, and end with a cymbal crash on the last beat or the first beat of the next (ninth) bar.
The end of the fourth phrase is the important one. This end-of-phrase marker lets you know that the tune is about to move onto a new section, from a verse to a chorus, a chorus to a breakdown or a breakdown to a verse, and so on. It's similar to the halfway marker, but more pronounced and powerful. The drum roll is longer, the vocals have more depth and the energy is a lot higher, swelling up to move onto the next section.
Everything changes
Markers at the end of each phrase are common in some genres of music, but don't rely on this fact; songwriters don't always provide markers at the end of Phrases 1 and 3. Knowing your tunes inside out really helps you at this stage.
If the tune has lyrics, then recognising the lyric cues for the end of phrases – when you've listened to the tune enough times – is relatively easy.
For a tune without lyrics, listen to how it changes from phrase to phrase, even without these end-of-phrase marker points. The main hook may start over, the melody may have a key change, another instrument may be introduced, another drum sound or synthesised sound may be added or you may pick up on a general shift in the volume or power of the music made by the addition of filters/compressors, a feeling to the music rather than something that you can actually hear and define.
Clever producers try to bend the rules and play with what you expect to hear, but in most tunes out there something changes or is added every four bars.
Counting on where you are
Start one of your tunes playing, listen to it and try to hear how the beats build into bars, bars build into phrases, phrases into halves of verses like the nursery rhyme and then how the verse moves into the next part.
To help you get to grips with this, start from the very first bass beat, and as the music plays count along with the beats, as shown in Figure 15-1.
**Figure 15-1:** Counting along with the beats.
Count the bar number as the first beat of the bar. The point of counting this way is simply so that you know which bar you're on.
The first beat of the bar has more emphasis to it, so when you're counting the beats, put more energy into saying the first number; 'ONE two three four – TWO two three four', and so on.
At the end of the first phrase (four bars) of the tune you're playing, listen to what happens. On beat 4 of the fourth bar, or beat 1 of the next bar, you're likely to hear a cymbal crash or some kind of sound that acts as the end of the phrase. The marker sound for this first phrase is likely to be the same for all the first phrases of a section throughout the rest of the tune.
Carry on counting and listening to how each phrase ends, and take special care to compare how each of the phrases end and how this indicates where you are in the 16 bars.
Keep listening to the entire tune because the opening section (the intro) may only be eight bars long. As you listen to the rest of the tune, use your knowledge of phrase lengths and remember the different end-of-phrase marker styles to help you decide what makes up the intro, verse and the chorus, all of which I describe in detail in the later section 'Studying Song Structure'.
Actively listening to your tunes
Be an active listener; really listen to what's playing. Rather than just sitting back and enjoying the music, concentrate on the sounds that you're hearing: drums, vocal samples (an 'Oh yeah' at the end of a bar is a good indicator!), changes in melodies or the bass line, any strange whoosh or other electronic noises – any of these sounds can be the markers that the songwriter has left to let you know where you are in the tune. Even the absence of a marker at the end of Phrases 1 and 3 can be the very marker you're searching for! Listen hard and you'll uncover the secrets of markers.
When you've cracked the beats/bars/phrases formula of how a tune is built, when you can identify the different end-of-phrase markers and when you've developed these instincts to be able to tell when the music is about to change, you find that you no longer need to count out beats and bars.
I can't stress strongly enough that you should try to move away from counting beats as quickly as possible. Developing a reliance on beat counting in order to mix well can stifle your creativity and may end in disaster. Not only do you risk looking like Rain Man when you count the beats and bars as they roll by, but if something happens to throw your concentration and you don't know where you are in the tune, the potential to create a nightmare mix is too big. Dedicate the time and concentration to develop the memory and the skill that enable you to listen to a track halfway through and know where you are within one or two phrases.
Studying Song Structure
The people on the dance floor aren't really interested in how songs are made, although they do anticipate and respond to the different parts of the music – just as you need to, too. As a DJ, you have to know when the tune is playing a verse, a chorus or a breakdown – even if the song has no lyrics – in order to create seamless, error-free, professional-sounding mixes.
Introductions, verses, choruses, breakdowns and outros are the different groups of bars and phrases that go together to create an entire tune:
Introduction (or intro): The part at the very beginning of the tune before the main tune kicks in. It can be as long or as short as a piece of string, but usually consists of a multiple of eight bars in length, with normally a change or addition of instrument or sound every four bars. At the end of the intro, the song includes an end-of-phrase marker (build up, drum roll or cymbal crash sound), letting you know that it's about to end.
The most DJ-friendly intro for beatmatching DJs lasts for at least 16 bars, and is made up of just drum beats for the first 8 of them. The second set of eight bars may start to introduce music such as the bass line to the tune. Chapter 14 tells you why this is so useful for beatmatching DJs, and also describes how to deal with different types of intros.
Verse: In tunes with lyrics, each verse usually has different lyrics. If the tune has no lyrics, the verse is harder to discern, and though it may contain the main musical hook (the catchy part of the tune that you hum in the shower), it won't be too powerful and energetic. In most cases, the verse lasts for 16 bars (four phrases), and is split into two sets of 8 bars where the melody repeats itself but builds up through to the end of the 16th bar.
Chorus: The part in the tune that normally has the same lyrics each time it plays. The chorus is usually based around the melodic hook and it's the most energetic, catchy and powerful part of the tune. It's shorter and more powerful than the verse sometimes at only eight bars (two phrases) in duration and lifts the energy of the track (and the dance floor). You may find that the song includes a marker cymbal to crash between the two phrases, and it has a build-up out of the second phrase.
Even music without lyrics has a verse and chorus. What you find is that the main hook that runs through the tune is quite subdued in one part, and then powerful, energetic and obvious in another part. The subdued section is the verse of the tune, and the more powerful, full-on section is the chorus.
Breakdown: The part where you can have a little rest. It's a transition/bridge from the end of the chorus to the beginning of the next part.
To create a nice bridge out of the chorus and back into the next verse, breakdowns tend to be less powerful. The bass drums drop out, and the bass melodies and a reduced version of the hook to the tune play. The last bar has a build-up, like the end of a chorus or verse, and you may hear an indicator on the last beat of the bar or the first beat of the next bar, to let you know that it's changed to a new part.
If the track includes a breakdown very early on, it's likely to be quite short, lasting four or eight bars, and is known as a mini-breakdown.
The main breakdown occurs around halfway through a tune, and probably lasts twice the duration of any mini-breakdown already heard. It's typically 16 bars in length and follows the same sound design as the mini-breakdown, but has longer to get in and out, probably has less sounds and instruments to begin with and includes a crescendo (a build-up, like a drum roll with the instruments getting louder and faster) for the last two bars or entire last phrase.
In indie/rock/party music, a breakdown in the middle of the tune is more commonly called a middle 8. It can follow the same principle I described in the preceding paragraph, dropping power only to build back into the tune. But often the middle 8 is a twist to the tune, lasting eight bars (hence the name) and building back into the main, familiar tune again when finished. The effect is the same, giving a break from the main sound of the tune, but the method can be different, compared to trance/house music.
Outro: The last part of the tune. Chances are, the last major element before the outro is a chorus. This chorus either repeats until the end (which is a DJ-unfriendly fade out) or you have a DJ-friendly outro.
The best kind of outro is actually a reverse of the intro. The intro starts with just beats, introduces the bass line and then starts the tune. If, after the last chorus, the music distils into just the drums, the bass melody and a cut-down version of the main melody for 8 bars, and then the next 8 bars are the drums and maybe the bass melody, you have 16 bars on hand that make mixing into the next tune easy (head to Chapter 16 for more).
Outros can last for a long time, though – going on for minutes! Every eight bars, the tune may strip off another element, until all you have is the hi-hat and the snare drum. Rather than a waste of vinyl (or bytes), this outro is extremely useful if you like to create long, over-lapped mixes.
Repeating the formula
The main blocks of the song are linked together by repetition, and even more repetition, but with subtle changes throughout the tune:
The next verse and chorus tend to be much the same as the first two. If the song has lyrics, different verses have different sets of lyrics, but the chorus probably won't change.
Although the structure, melody and patterns remain the same, the music may introduce new sounds or effects processing to the original verse/chorus to create a new depth to the tune (changing the sound slightly gives the listener a feeling of progression through the tune).
As the breakdown or middle 8 drops the energy of the tune to its lowest point, a lot of songwriters like to follow it with a chorus – the most energetic part of the tune. Once again, the song may introduce more instruments and sounds to give the chorus a slightly newer feel.
Depending on how long the tune is, the main breakdown may be followed by more verses, choruses and mini-breakdowns.
Accepting that every tune's different
You'd soon get bored listening to tunes that were designed to the same structure, even if the music was all different. In music production, altering the length of an intro, adding verses or choruses, adding breakdowns and mini-breakdowns, changing their length and extending outros are all part of what makes a tune unique when still following the basic four beats to a bar, four bars to a phrase structure.
The brain is an incredible organ. When you listen to a track with an active ear, after three or four run-throughs your brain remembers the basic structure of the tune, and then relies on triggers (such as the end-of-phrase markers, vocals or even just looking at the different shades of rings on the record) that help you remember the structure of that track along with the 1,000 other tracks in your collection.
The trick to getting your brain to work for you is to listen to your music a lot. You can't expect to know the structure of a tune immediately; you need to listen to it a few times. Practising your mixing skills gives you an opportunity to get to know your tunes, but I recommend copying your tracks to an iPod/tape/MiniDisc/CD so that you can listen to your music at any time.
Always listen with an active ear to the structure, the melody, the hook and the lyrics. Your brain stores all this information in your subconscious, calling upon these memories and your knowledge of how a tune is constructed from bars and phrases, ensuring that you never get confused during the mix.
Developing your basic instincts
Your memory and instincts for your music develop in the same way as they do when you drive a car. When driving, you don't have to think 'Accelerate . . . foot off a little . . . steer . . . straighten up . . . brake . . . clutch . . . check mirror . . . change to third . . . clutch . . . change to second . . . accelerate . . .' and so on, you just do it. You develop your instincts as a driver through practice and experience. It's exactly the same with DJing.
You know that the first beat of the bar is emphasised, you know that the melody or line of a lyric is likely to start on the first beat of a bar and from listening to the tune you know the kind of end-of-phrase markers that a certain tune uses at the end of a phrase, at the end of half a phrase and when it's about to change to another element like a verse or chorus.
In the 'Baa, Baa, Black Sheep' example in the earlier section 'Multiplying beats, bars and phrases', when you hear 'Have you any wool?', your instincts tell you that you're in the second bar of either Phrase 1 or Phrase 3, because you know the lyrics so well.
The lyrics in the phrase that follows tells you what half of the verse you're in, so if the next phrase begins 'One for the master', you know that you're only in Phrase 2 – but if you hear 'One to mend the jerseys', you know that it's Phrase 4.
However, try to listen for the different end-of-phrase marker that can tell you if you're just halfway through the verse or about to enter a new part of the tune, so you don't have to rely on remembering a vast range of lyrics. Songs without lyrics still follow structures; you just have to listen for the changes in music and instruments, rather than the changes of lyrics.
Listening to a Sample Structure
After you know how beats become bars, and bars multiply like rabbits (or sheep for that matter!) to become verses and choruses, the best thing you can do is to go through the structure of an entire tune, and then describe each part in a bit more detail.
In my website to accompany this book (www.recess.co.uk), you can find a section that contains some audio examples. When you finish reading this chapter, I recommend that you download one of the tunes. Listen to it, and try to hear not only what happens to mark the change from the larger parts of the tune, but also what happens every four and eight bars.
The following structure may help you discern the structure of the sample tune:
Intro: 16 bars
Verse 1: 16 bars (four phrases)
Chorus 1: 8 bars (two phrases)
Mini breakdown: 8 bars
Verse 2: 16 bars (four phrases)
Chorus 2: 8 bars (two phrases)
Breakdown: 16 bars
Chorus 3: 8 bars (two phrases)
Verse 3: 16 bars (four phrases)
Chorus 4: 8 bars (two phrases)
Chorus 5: 8 bars (two phrases)
Outro: 16 bars
And remember – try to develop the skill to intuitively pick up beat structure through time and experience. Don't count bars!
Chapter 16
Mixing Like the Pros
In This Chapter
Selecting the best placement points in your tunes
Using your mixer's controls to their full potential
Reaching the next level of beatmatching
Mixing tips for different genres
In this chapter, you build on your beatmatching skills (refer to Chapter 14) so that you can mix tunes at their correct points, and use the controls on the mixer to make the transition from tune to tune as smooth and skilful as possible. The mixing techniques in this chapter take time, experimentation and practice to get right before you can use them creatively. Understand the core concepts, but don't be bound by them, and discover the moments when breaking the rules is a good thing.
Recording your practice sessions when experimenting with the following techniques can be useful. In the heat of the moment, you may think that something didn't work, but when you listen back, it actually turned out great! Try anything, and if it sounds good to you then others may like it too.
Like all the techniques in this book, it doesn't matter what format you use – be it CDs, turntables, digital DJ setups or even MP3 DJ gadgets like the Pacemaker, the Nextbeat or an iPhone. It's not about what you use, it's about how you use it. The controls on these different pieces of equipment may be different, but beat structure and a need for perfect mix placement remains the same. Check out my website (www.recess.co.uk) for examples of the techniques I mention throughout the chapter.
Perfecting Placement
From Van Halen to Van Morrison, Silicon Soul to Soul to Soul, most tunes that you play follow the basic building blocks I describe in Chapter 15: four beats to a bar, 8 bars to a phrase and multiples of 8 bars to a section (a section is an entire intro, verse, chorus and so on, and typically lasts for 8 or 16 bars). One tune may have more choruses than another, or a longer intro, monster length breakdowns or extended outros, but this structure knowledge makes creating the perfect mix easier for you.
The perfect mix begins with perfect placement. Placement is simply the choice of what parts of the tunes you mix over each other. Perfect placement occurs when both tunes start or end a section at the same time – not only do the beats of both tunes match, but their structural changes match too. If the tune you want to mix out of (Tune A) is about to change from a chorus to its outro, an example of perfect placement would be to start the new tune (Tune B) so that its change from intro to verse happens on the exact beat that Tune A changes from chorus to outro.
Intros over outros
If Tune A has a 16-bar outro and Tune B has a 16-bar intro, simply overlapping the intro and outro is an option, but often intros and outros have no melody and are just a simple bass drum and hi-hats (the tchsss-sounding cymbal sound). Sixteen bars of that, though, can sound dull, unprofessional and boring. Figure 16-1 shows an example of a better sounding transition, where Tune A has two eight-bar choruses before the outro. You can create an overlap with the 16-bar intro of Tune B playing over the two choruses (marked Chorus 1 and Chorus 2) of Tune A. Then the outro of Tune A plays over the verse of Tune B.
In all the figures in this chapter, numbers in italics mean that the tune is at a lower volume, and numbers change size as the music fades in or out (gets gradually louder or quieter). Bold numbers mean playing at normal volume.
**Figure 16-1:**
16-bar intro of Tune B playing over the last two choruses of Tune A.
If both tunes had vocals in the chorus and verse, if you mixed between them so that the vocal on Tune A ended and Tune B's vocals started instantly, it may seem a little too quick. In this case, create a little rest, or an anticipation of what's to come. To introduce this pause, start Tune B at the end of Chorus 1, as Chorus 2 begins. This later starting point creates an eight-bar rest while the outro of Tune A mixes with the intro of Tune B, and then the verse of Tune B begins (see Figure 16-2).
**Figure 16-2:** The outro of Tune A mixes with the intro of Tune B.
Ideally, the outro of Tune A or the intro of Tune B is more than just plain drum beats. A bass melody or subtle background noise is enough to keep interest going in this mix for eight bars. A four-bar rest is better if you only hear drum beats. As with all these techniques, experiment to get the best results.
Melodic outro
Not all tunes have pounding bass beats from start to finish. Some have moody, beatless, melodic outros that sound great over an intro with a strong beat.
In Figure 16-2, the intro was slowly faded up to sneak into the mix. However, if you want to keep a constant beat going by mixing 16 bars of beat intro over 16 bars of beatless melodic outro, you have to start Tune B so that it instantly plays at full volume.
If Tune B has a good build-up out of the intro and into the verse, you can keep Tune A's outro playing at near to full volume until the end and then fade it out on the last beat before Tune B's verse starts (check out Figure 16-3).
**Figure 16-3:**
16-bar intro of Tune B playing over the last two choruses of Tune A.
Mixing beat intros over beatless melodic outros means you can't afford to make a starting error – you have to start the beat precisely in time. If you use turntables, spend lots of time practising starting records so you hear them instantly, to develop the confidence to start the beats on time, every time, without needing any error correction. (If you need to go back to the basics of starting tunes, check out Chapter 14). Waiting one or two beats to check that you're in time and then quickly moving the cross-fader to the middle (or worse, fading in the beats) sounds terrible, is unprofessional and usually ruins a mix (and your reputation). This technique is a lot easier for CD DJs who don't have to worry about motor start-up times like vinyl DJs. They just need to press a button in time with the beat to get it right.
If you're not confident with the instant start or don't want to mix the full 16 bars of intro over outro, start the beats of Tune B at the beginning of Chorus 2 (eight bars before the outro of Tune A begins) to make sure that your timing is immaculate. Then move the cross-fader to the middle after eight bars, as Tune A hits the outro (see Figure 16-4).
**Figure 16-4:** Using the cross-fader to fade out Tune A's outro over the verse of Tune B.
The faint-hearted who need a safety net can slowly mix in Tune B's intro beats over the beats of Tune A's Chorus 2 using the EQs (equalisers) to smooth the transition (see 'Balancing it out with EQs', later in the chapter), which is far preferable to fading up the beats over a beatless outro.
Melodic intro
The reverse of melodic outros is a bit tougher, because mixing an intro with no beats means that with no drums to keep time when beatmatching, when the beats in Tune B eventually start you risk them playing at a completely different time to the beats from Tune A.
If the intro has a melody or a very soft rhythm, concentrate on that. Tapping your feet with this rhythm can help to keep your concentration. Practise this mix as much as you can, because when you do it live all the noise and distraction in the DJ booth can mean that you end up with a train wreck of a mix!
Mixing Breakdowns
You don't have to play a tune from the very beginning to the very end. Mixing two breakdowns over each other or an intro over a breakdown can sound great, and lets you shorten a really long tune. (Chapter 15 has more on breakdowns and mini-breakdowns.) Here are a few combinations to try:
Breakdown over breakdown: No matter whether your breakdowns are 8-bars or 16-bars long, if both are the same length, start Tune B's breakdown as Tune A's breakdown starts, then gradually fade and EQ out Tune A so all that's left is Tune B's breakdown, which is about to build up into the beats again (see Figure 16-5).
**Figure 16-5:** Two breakdowns mix over each other to skilfully introduce the new tune.
Mini-breakdowns: As breakdowns are normally at least halfway through a tune, you may not want to start Tune B at that point because it'll cut out so much of the tune. If you're lucky, there may be an eight-bar mini-breakdown in the first half of Tune B, probably after the first chorus, or it may be right after the intro, used as a way to emphasise the start of the main tune, in which case try my suggestion in Figure 16-6).
**Figure 16-6:**
A mini-breakdown introduces a new tune early on rather than halfway through.
Adding pace: If you start Tune B eight bars earlier so that you mix out halfway through Tune A's breakdown, you add a feel of urgency and pace to the mix (see Figure 16-7).
**Figure 16-7:**
By not letting Tune A finish its breakdown before mixing fully into Tune B, you achieve a great sense of urgency.
Beat intro over breakdown: This method, shown in Figure 16-8, is identical to starting a beat intro over a melodic outro (see Figure 16-3). You need the confidence to start Tune B with the cross-fader open to carry the beats through the breakdown. However, because this is a natural breakdown in Tune A, rather than an outro, you can fade in Tune B's beats if you use the EQs to kill the bass before starting the fade (see 'Controlling the Sound of the Mix', later in this chapter). The hi-hats from Tune B keep a rhythm going and you can quickly bring the bass in halfway through the breakdown. How well this method works and how good it sounds greatly depend on the tunes that you're using.
In that example, if you're still not confident starting the beats with an open cross-fader, start Tune B in the same place, wait until the end of the eighth bar and then quickly move the cross-fader to the middle. But if this sudden introduction of beats sounds a bit jarring, try killing the bass and gradually fade Tune B in over the first eight bars of Tune A's breakdown.
**Figure 16-8:** Beats from Tune B start instantly as Tune A enters its breakdown.
These examples are the simplest, most basic placement principles to take into consideration when mixing tunes. You can mix your tunes in thousands of different ways depending on where you start Tune B from, and where in Tune A you start the mix. Change where you start Tune B back or forward by 8 or 16 bars, and experiment with how soon or late to mix out of Tune A.
Listen to your tunes with an active ear for all the audio clues and markers (refer to Chapter 15) that let you work out the best places to mix in and out of your tunes. Two tunes may have the perfect mix – you just have to find it!
Controlling the Sound of the Mix
After you've mastered the mechanics of beatmatching and know the best places to mix in and out of your tunes, your true artistry comes from controlling the sound of the mix. The cross-fader, the channel-faders and the EQ controls on your mixer are the salt and lemon to your tequila, the candlelight to your dinner and the chocolate to your chilli; they all add extra zest and finesse to the mix. (I'm not kidding; add a little dark chocolate to your chilli – it's lovely.)
Bringing the cross-fader into play
How fast you move the cross-fader from one tune to another can dramatically alter the power of a mix. Smoothly moving from one tune to the other over the course of 16 bars can be very subtle if you're beatmatching, or extremely messy if you mix the wrong rock tunes together. Chopping back and forth from tune to tune adds a sense of immediacy, which can be really powerful at the right moment. These methods work with the right tunes, and can be the main way to mix for a lot of pop, rock, indie and party tunes. But as a beatmatching DJ, if all you do is whip the fader across quickly for each mix, you'll come across as a DJ who can't hold the beats matched for a long time and needs to mix out quickly.
Every mix has two halves. No matter how fast you move the cross-fader, you're not only bringing in a new tune but you still need to take out the old tune. Apply the same care and attention when moving the cross-fader to fully mix out of a track as you do when mixing in the new track.
A cross-fader move that lasts four beats or less is hard to get wrong – just time the move from one side to the other to last four beats (you'll be at the halfway point by the second beat). Moves that last longer than four beats when beatmatching need a bit more of a pattern and control to them.
The way to approach longer mixes is to move the cross-fader so that the increases occur on the hi-hat tchsss sound in between the bass drums. This method helps to hide the increase in volume from the new track, and makes taking out the old tune less noticeable.
Cymbal crashes and build-ups are great places to hide larger moves of the cross-fader. When something like that from either tune adds impact, move the cross-fader a farther distance than the move before. Be aware of a mix that starts to sound messy, though. If you're moving the cross-fader too fast, move it back a bit and let the music play for a bar without any increase (provided you have time in the tunes to do so).
You can also use crescendos and temporary bass beat drop-outs to disguise your cross-fader moves. Crescendo is a fancy way of saying build-up. A four-beat crescendo is over quite quickly, so you may want to have the two tunes mixed together for a couple of phrases beforehand with the cross-fader still favouring Tune A (the outgoing tune). Then, during the four beats of the crescendo, move the cross-fader over so that the new tune is dominant, at the end of the four beats, with the old tune playing in the background. When to finish the mix is up to you, but it's likely that this will be quite a fast mix.
The opposite is just as appropriate. Instead of a build-up, the last four beats of a phrase in Tune A may have no bass drum beat (but the rest of the music is still just as loud). Instead of mixing Tune B lightly into the background, keep it silent and then just as the last beat of Tune A's opposite-build-up plays (at the end of the phrase), quickly move the cross-fader over to the new tune. Moving the cross-fader all the way over in one beat can be an incredibly powerful mix, or you can move the cross-fader so that it favours the new tune (about three-quarters of the way across) and kill the bass on Tune A to keep it subtly playing in the background (see the section 'Balancing it out with EQs' for info on EQ control).
Unleashing channel-faders
Channel-faders are lonely little fellows. Lots of DJs put them up to full and leave them there forever. But these vertical faders have a secret, undercover role that many DJs don't tap into.
The primary role of the channel-fader is to work in conjunction with the gain control to control how loud the music from a channel plays out of the mixer. (If you're unsure of how to make this adjustment, check out Chapter 10.) With the input levels matched for both channels, you need to decide where to set the channel-faders when you want the tunes to play at their loudest.
DJs quite commonly set up their mixer so that the channel-fader needs to be set to its highest point (sometimes marked 10) for this optimum play-out volume. For beatmatching DJs who try to keep the volume of the mix a smooth constant from start to finish, this isn't the best setting. For scratch DJs, this highest-point setting is correct, and very important so that they can just flick up the fader to be at full volume.
Some DJs advise setting channel-faders to full so you won't accidentally knock them and increase the volume by accident. I say, be as careful about not knocking your channel-faders as you are about not ejecting CDs or taking off records while they're playing. You may do it once – but you learn quickly to be more careful.
The best way to set up your mixer is so that your channel-faders are set at three-quarters of the way to maximum (around 7 if your fader is marked from zero to 10). Using this technique means that when you mix in the next tune, if the tune is a bit too quiet even though the levels looked correct, you can quickly raise the channel-fader to compensate for the lack of volume.
Letting you in on a big, curvy secret
Cross-fader curves affect how much one tune gets louder and the other one gets quieter as you move the cross-fader from side to side (you can find examples of cross-fader curves in Chapter 10). However, sometimes the curve isn't subtle enough for a smooth, seamless mix and can cause the two tunes to play too loudly over each other, sounding messy and unprofessional. So you need to find a way to gain more control over the output of each tune during the mix. The channel-faders release you from the strict constraints of the cross-fader curve.
For a simple mix that gives you precise control over each tune's volume try the following:
1. Set the channel-fader on the new tune (Tune B) to one-quarter of its loudest point.
2. When you're ready to start mixing in the new tune, move the cross-fader into the middle, following the techniques I describe in the section 'Bringing the cross-fader into play', earlier in this chapter.
3. Start to raise Tune B's channel-fader, continuing to increase it in time with the hi-hats. (The cross-fader is still in the middle.)
4. Keep an eye on the output meters and an ear on the sound of the mix, and as the Tune B gets louder slowly lower the channel-fader of the outgoing tune (Tune A) until Tune B is dominant and Tune A is playing at a volume that's best for that moment in the mix (likely to be similar to where the Tune B's channel-fader was when you started it).
5. When you want to fully mix out Tune A, move the cross-fader all the way over to Tune B's side.
How you change the positions of the channel-faders, and the time you take to do so, is up to you. You can simply raise one fader while lowering the other, or wait for Tune B's channel-fader to be halfway up before you start to lower Tune A's fader. Make the adjustments depending on your own personal style, the output levels and what sounds best with the two tunes you're using.
If you prefer, you can leave the cross-fader in the middle (or do what I do and turn it off if you have that function) to bypass the cross-fader function altogether. This option gives you ultimate control over the individual volumes of your tunes during the mix. The only difference to the previous method is that you start with the channel-fader at zero for the incoming tune (Tune B), and end with the channel-fader at zero for the outgoing tune (Tune A).
Balancing it out with EQs
As with channel-faders, EQs have multiple roles. The first role is sound control: affecting how the music sounds on CD or to the dance floor. You can also use EQs to add some variation and spice to a tune (check out the section 'Cutting in', later in this chapter). But their most useful role is in smoothing the sound of the mix.
Good EQ control can't do anything about a poor choice of tunes to mix together, but great EQ control can turn a passable mix into an incredible one.
Smoothing a transition with the bass EQ
The bass EQ is the one that you use most to create an even sound through the mix. When both tunes play with their bass at full, even if one tune is quieter than the other, the bass drums are too powerful and the bass melodies combine to sound messy.
The simplest but most effective technique is to kill the bass (reduce it to, or near to, its lowest point) on the incoming tune when you start to mix it in, and when you want to make this tune the dominant one increase the bass EQ at the same time as decreasing the bass EQ on the tune that you're mixing out of. This manoeuvre means that the amount of bass you hear through the speakers stays the same, but it comes from different tunes.
With the right tunes, taking your time over this swap can create a subtle, unnoticeable mix. Or swapping the EQs in one beat can cause a hands in the air moment by introducing the bass line from a tune that you know the crowd will love, emphasising a change in key (see Chapter 18), changing the power of the mix or punching in a change in genre.
Taking the edge off with the mid-range and high-end
Despite the fact that the high frequencies aren't as loud and obvious as the bass frequencies, they're just as important in controlling the sound of the mix. Two sets of loud hi-hats playing over each other can sound just as bad as two sets of bass drums and bass melodies. The technique is exactly the same as the bass EQ, except you don't need to cut the high EQ nearly as much. For example, on my Pioneer DJM-600 mixer I find that the 12 o'clock position is usually the best place to leave the high EQ for normal play-out. When I want to cut out the high EQ to help the sound of the mix, I only need to move the knob to around the ten o'clock position (rather than the seven o'clock position for the bass EQ).
Because the mid EQ covers a larger range of frequencies, how much you use it with this technique depends on the tunes you're playing. You may not need to swap over the mid EQs if you don't notice a clash of sounds, or you may find that rather than cutting the mid EQ, you want to boost it. Sometimes, when the outgoing tune is playing quieter, I boost the mid EQ to play those frequencies louder than normal. If you have a melody or sound repeating in the background of the tune, this emphasis can lengthen and strengthen the mix, and even more so if you add effects to the music (see Chapter 10).
Always keep an eye on the meters and an ear on the sound of the mix while you're swapping any EQs. Strive to keep an even sound as the two tunes play over each other. If one tune is too loud, or both tunes have too much bass or high frequency, you may create a cacophony of noise.
Using Mixing Tricks and Gimmicks
Tricks and gimmicks are great to use once in a while because they add surprise and a little pizzazz to your mix. Avoid over using tricks, however, because the listener may think that you only use them because you can't mix between tunes properly. Use the gimmicks as transitions to increase energy, change the musical genre or key, or even just help a change in tempo.
With each of the following techniques, experiment with how long you take to move the cross-fader and where you position the cross-fader when you start the trick. Start by setting the cross-fader so that you can't hear the next tune until the start of the move, and then find out what it sounds like if you have the cross-fader in the middle when you start the move. Give thought to volume control as well because some of these tricks really don't work well with the channel-fader at maximum – you may deafen the dance floor or blow a speaker!
Spinbacks and dead-stops
Try out a technique called a spinback: beatmatch and start a mix between two tunes with perfect placement (see 'Perfecting Placement' at the beginning of the chapter) so that the tune you want to mix out of (Tune A) ends a section (probably a chorus or powerful outro) as Tune B (the new tune) begins the first phrase of a section. On the very last beat before this change, place your finger on Tune A and spin the record back, sharply. As the tune spins backwards, close the cross-fader over to Tune B within one beat, as shown in Figure 16-9 (SB stands for spinback).
**Figure 16-9:** The spinback is performed on the fourth beat of the fourth bar and then instantly mixes into Tune B.
The spinback isn't exclusive to turntables, but you'll need a CD deck with a vinyl mode in order to make this sound right. CD decks without this mode just judder and stutter if you try to skip them backwards. A CD deck with vinyl mode activated should sound just the same as a record being spun-back.
To perform a dead-stop, instead of spinning the record back in the example in Figure 16-9, press the Start/Stop button on Tune A (the one you're mixing out of). This action makes the tune stop playing in about one beat (unless your decks have a function to change the brake speed and you've set it to last longer). As with the spinback, move the cross-fader over to Tune B by the time it plays the first beat of the new section (so the move only lasts one beat).
Similar to the spinback, the CD deck you're using affects how well the dead-stop works. A CD deck with vinyl mode works perfectly if you set the brake correctly, but one without just stops instantly when you press Stop.
Power off
A power off is when you turn off the power to the turntable (normally located bottom left with the red strobe light underneath it). When you turn off the turntable, it gradually gets slower and slower, until it stops.
If you have a CD deck with vinyl mode and can adjust the brake speed, set it to its longest amount and this does the same thing. If you don't have vinyl mode, don't try turning off the power . . . everything just turns off.
Power off is a great trick in the DJ booth if you have good lights and someone who knows how to use them. Ask your partner-in-mayhem to kill the lights slowly at the same time as you do the power off. Chances are, everyone will think 'Power cut!'. After a few seconds, slam in the next tune at the most powerful point, at full volume, as the lighting jock floods the dance floor with as much light as possible. It's a gimmicky, cheesy trick, but can take the dance floor by surprise, and – you hope – really jazz them up. It's very clichéd, but at the right time, works a treat.
A cappella
If you have an instrumental track that you think would sound better with something else over the top of it, look for an a cappella, a separate vocal track without any instruments behind it.
The problem with using vocals is that you need the vocal to be in the same key as the instrumental you want to play it over, otherwise it sounds out of tune. This makes speeches and other spoken words a great alternative. I have a copy of JFK's inaugural speech that I love to mix over long instrumental tracks. The line 'Ask not what your country can do for you . . .' is an incredible introduction into the most powerful parts of a tune.
Don't get so involved in your new creation that you forget to mix in the next track. Your blend of a 'Learn Italian' lesson over a great instrumental may be going down really well, but if you run out of time to beatmatch and mix in the next tune, you've wasted your time.
A third input device like an extra CD deck or turntable, or an MP3 player or laptop, lets you play the a cappella over the instrumental tune, beatmatch the next tune and start the mix with the a cappella playing the whole time. Or you can use audio software to pre-mix the creation on computer and then burn it to CD to play later, but you'll lose the spontaneous performance side of the live new mix, which is often what makes this so special and effective.
Cutting in
Cutting in beats from another tune gets its roots from beatjuggling (see Chapter 17). The idea is to beatmatch two tunes and move the cross-fader between them to temporarily cut in beats from one tune over the other. In the right hands, this method can be incredibly fast and complicated. Figure 16-10 shows a basic, slow pattern (underlined numbers are the beats you can hear).
You don't have to move the cross-fader all the way over when cutting in beats; you can go three-quarters of the way across so that you can still hear the original tune. I find placing a finger at the three-quarter point helps this, because you can just bounce the cross-fader off your finger – it stops the cross-fader getting any farther than three-quarters of the way across, no matter how fast or hard you cut in the other tune.
**Figure 16-10:** Various beats from Tune B are 'cut in' to Tune A to add power and a new feel to the tune.
A variation on cutting in beats is cutting out frequencies of the tune. Dropping the power out of the bass for the last bar of a phrase before it changes to a new element can be extremely effective, and doing this when the crowd is extremely excitable and energetic can blow the roof off the club – which is no mean feat if you're in the basement!
Effecting the transition
You don't just use effects in the main body of a tune to make it sound different; you can also use them to help the transition from one tune to the next. One example of this is if you're performing a long mix between two tunes but are having problems changing the balance of power to the new tune, and want this change to happen as the first verse of the new tune starts.
In this case, adding a flanger, filter, reverb, beatmasher or transform effect to the last bar of music before this change occurs can add a new sound to this mix, helping the power transfer between tunes:
Set flanger or filter effects to last for two bars, and instead of the music whooshing down and back up again when using it over just one bar of music, it will only whoosh down – taking the power out of the outgoing tune and helping you to finish the mix with the new tune playing louder.
Use the reverb set to maximum to effectively kill the power of the outgoing tune. The incoming tune needs to be quite high in the mix for this to work, and you need to sweep in the effect (gradually increase the strength) so it doesn't sound too sudden. The metallic sound it gives to the outgoing tune is a nice, quirky effect.
A fast transform over the last two beats of this bar (so it splits the sound into eight stutter sounds) can help this transition too.
Beatmasher effects create drum rolls out of thin air. By combining the sounds of the beats, you can change the last four single beats of a bar into a fast drum roll to get to the next tune.
Experiment with:
How long you use the effect
How strong or long the effect is set to last
Whether you sweep in and out the effect
How loud each of the tunes are in the mix
Whether you effect both tunes or just one of them
Whether you keep the outgoing tune in the mix after this balance of power shifts.
The ideas in this section are no means all the available effects or techniques. Experiment with all your effects; where, when, how and what to use is entirely up to you. If it sounds great, do it.
Mixing Different Styles of Music
Some genres of music don't rely on rules like beatmatching and perfect placement: in order to get from tune to tune, the music the DJ chooses to play is much more important than the mix itself. Making the transition from one tune to another without beatmatching takes a special skill and you still need these transition techniques as a beatmatching DJ – to change genres, take over from someone else or change the feel of the mix.
That's not to say you can't try beatmatching rock music or some party tunes. Some tunes work well together, but the problem lies in the fact that rock, for instance, isn't really designed to be mixed in the same way as electronic dance music. Drum machines, similar tempos and even the beat structure of dance music lends itself to beatmatching, but live drummers, vastly different tempos and sudden starts all mean that some other genres are a lot trickier, and you're best approaching their transitions in different ways.
The wedding/party/rock/pop mix
In many ways, the transition between tunes is a lot harder for the wedding/party/rock/pop DJ. A beatmatching DJ has the safety net of simply matching the beats and then fading between tunes, with no fade out, no sudden start, no change in tempo and no drastic genre change. The wedding/party DJ needs to work with all these issues.
The most important part of this mix is where in the new tune you start. Tunes like 'Brown Eyed Girl' by Van Morrison (a wedding favourite) that have a powerful, recognisable, instant start are great to work with.
You still need to think about beat structure when choosing when to start a tune like 'Brown Eyed Girl'. Starting it randomly won't sound good. As Tune A (the one you're mixing out of) fades out, or as you begin to fade it out, wait until the end of a bar (hopefully at the end of a phrase) and start 'Brown Eyed Girl' when Tune A plays beat one of a new bar, but fade it out completely before it does so.
If you want to mix a house tune with pounding bass beats into a track you can't beatmatch out of (still 'Brown Eyed Girl', for instance), the technique is the same. However, because house tracks tend to have long, beat-only intros, you may want to start them later, when the main tune kicks in.
Looking in more depth at the technique, you have to work out how much you need to fade out a tune before starting the next one, and when to start the next tune. Some tunes sound fine when you start them at the beginning of the outgoing tune's bar; some sound better on the third or fourth beat of the bar. Practice and experience listening to and playing your tunes lets you develop the skill and an instinct for how best to mix your tunes.
Of course, not all records have a powerful point in the tune that you'd like to start from. For instance, maybe you want to play a slow track so people can smooch and dance closer (and you can run to the bathroom or the bar). The mix out of the last track is the same as with mixing in 'Brown Eyed Girl', but instead of an immediate, full-volume start on the new track, it may sound better if you take a full bar (four beats) to go from quiet to full volume, and create a smooth, swelling fade-up of 'Wonderful Tonight', for example.
Another option is to talk during the mix. You can use tales of the buffet, drink promos and good-looking rock chicks and comments about the mother-of-the bride's inappropriate dancing to cover a mix.
The trick is to control the volume of the music as you speak into the microphone: keep the music low enough so that you can be heard, but loud enough so that it doesn't sound like your giving a monologue. Listen to how radio DJs talk over the beginning of songs that they play. They know when the tune changes from intro to the main song and time their chatter to coincide; get to know your tunes so you can do the same thing. Perform a simple cross-fade between the two tunes, speaking over the mix to hide the transition, and stop waffling just as the main tune starts.
The R&B mix
R&B doesn't tend to have the long, luxurious intros that house and trance music have, but the tunes often have a very good opening bar that you can use to mix over the last tune much like the party DJ mix. In addition, R&B tunes often kill bass beats for the last bar of a phrase, making this point perfect for mixing in the new tune because otherwise the complicated, bass-heavy drums could fight with each other.
R&B does have scope for beatmatching if you have tunes with similar beat patterns, but R&B works best when the beatmatch mix is as short as possible. Using the new tune, a short baby scratch (see Chapter 17) in time with the beats on the outgoing tune and then starting the new tune playing from a powerful point is an excellent way to mix when you can't match beats.
Drum and bass, and breakbeat
Drum and bass, and breakbeat are both genres that tend to follow the four-beats-to-a-bar structure that house/trance follows, so you're normally able to follow the basic principles of placement I mention in the earlier section 'Perfecting Placement'. However, the beats in the bars are a lot more complicated, so if you're struggling to beatmatch breakbeat or drum and bass, first see Chapter 14 for more information about beatmatching and then, instead of focusing on bass sounds, focus on the clearer snare sounds.
A huge phenomenon in drum and bass circles over the past few years has been the double drop, an extension of breakdown mixing. All genres can benefit from this technique. Beatmatch and start a mix so that two tunes are about to hit a breakdown (also called a drop) at the same time – the drop on either tune may be the main breakdown, or a shorter one earlier or later in the tune. The key is to mix the tunes together so they both come out of their drops at the same time, after which you keep both tunes audible, playing through the speakers. So if you're mixing an 8-bar drop into a 16-bar drop, be sure to start the 8-bar drop halfway through the longer one.
Tune selection is vital for creating a good sounding double drop. Don't perform it with just any two tunes – they need to have a complementary rhythm and key, and you need to pay special attention to volume and EQ control on both tunes to avoid a messy sound. Experiment with the tunes and the drops you use in the double drop. Performed well, this live re-mix of playing two tunes over each other sounds really powerful.
Beatmatching tunes with vastly different tempos
Beatmatching tunes with different tempos works across all genres – dance, rock, R&B and many more – but works best with tunes that have a strong but not overly complicated outro and intro. If you're DJing with rock, indie, party/wedding music and even drum and bass or jungle, mixing tunes of different tempos is a quirky way to mix between tunes that can be effective at various points in the night (as long as you don't overdo it).
When DJing in house/trance clubs, you want to keep the tempo high to keep the energy going when people are dancing, so a huge change in BPM might not go down well with the customers. However, if a tune actually slows right down during its outro, it's a good way to get back up to a faster tempo again, or it can be a creative way to change genres of music. This is a once-a-night mix for many house/trance sets rather than a technique you pepper throughout the night.
Beatmatching tunes with different tempos usually takes special equipment to perform well:
A deck with Master Tempo control on it, which keeps the pitch of the tune the same no matter how fast the playing speed
A large pitch range (you need a range of around +/–20 per cent at least)
In this case, a beat counter does help you get it right
If you have one rock tune that's banging out a good powerful outro at 125 BPM, and you want to mix in a tune at 100 BPM, spend two or four bars to reduce the pitch control right down so that it now plays at 100 BPM. When you're at the end of these bars, start the next tune and fade out the outgoing tune (refer to all the earlier sections in this chapter for guidance on EQ control).
How long you spend slowing down the tune is up to you – it'll most likely be dictated by the tunes you're trying to mix together. Think about times when you might want to do it the other way too – to add excitement and energy to your mix. It's certainly a technique that works best when slowing down a tune to match the new one, but with the right pair of songs it can work well the other way too, especially if you turn off Master Tempo to let the pitch go up as well as the speed.
Chapter 17
Scratching Lyrical
In This Chapter
Ensuring your gear is up to scratch
Marking your records properly
Scratching on vinyl, CD, MP3 and computer
Lending you a helping hand with basic scratching
Scratching is a specialised skill that takes a lot of practice and patience to master. When you've taken the time to develop the skill, half the people you know will drop their jaws in amazement at what you're doing, while the other half will open their mouths just as wide – and yawn.
Whether you go on to develop the crab, the flare or the twiddle is up to you, but if you can master the baby scratch, the forward scratch and the cut, even if you consider yourself only a beatmatching, mixing DJ, you'll be adding another weapon to your arsenal of knowledge.
Scratching skills help you develop a smooth, fast technique when using your equipment – especially vinyl. When you've grasped the basics, you develop a feel for how much pressure you need to apply (very little) to hold a record still while the deckplatter is turning, you're able to wind the record back and forth without the needle flying off and you develop solid, stable hands when holding the record stopped, ready to start it.
The website that accompanies this book has audio and video clips to support the information contained in this chapter, because most of the techniques are better shown rather than described. Be sure to log on to check that you're happy with what you're doing (see www.recess.co.uk).
Setting Up Equipment the Right Way
Anyone who has used equipment that was poorly configured or wasn't suitable for scratching will show the emotional scars as proof that you can't afford to get the setup wrong.
If you're using CDs to scratch with you don't need to set up much, apart from maybe the resistance of the platter (see Chapter 8) and switching the CD deck to vinyl mode in order to create the right scratch sounds.
For turntable scratch DJs, I mention a few of the basic but vital requirements that your turntables need to be suitable for DJing in Chapter 6. Turntables built for mixing share many of the same qualities as those you use for scratching: powerful, direct-drive motors are essential, and an adjustable tonearm, removable headshells and sturdy design are also crucial.
However, how you set up the needles, the orientation of the turntable and how you plug into your mixer are just as important as the make and model of turntable that you're using.
A big factor for scratch DJs is the positioning of the decks. Instead of setting them up as the manufacturer intended (tonearm and pitch fader on the right-hand side), scratch DJs rotate the entire turntable anticlockwise by 90 degrees, so that the tonearm and pitch control are farthest away from the DJ.
The traditional setup only gives the DJ around 100 degrees of the record's circumference to work with (shown in Figure 17-1, top), so the DJ can only pull the record back so far without hitting the needle out of the groove. Rotating the turntable by 90 degrees gives the DJ a lot more vinyl to work with (shown in Figure 17-1, bottom), making scratching much easier.
Weighing up needles
No matter what you use, how you set up the needle and the counterweight can drastically affect the stability of the needle. You don't want the needle jumping out of the groove when you're performing a tough scratch. Check out Chapter 7 for information on what makes a needle good for scratch use; the Shure M44-7 needle and cartridge (shown in Figure 17-2) has proved the most popular needle for scratching over the years.
The two ways to control the stability of your needle are through the downforce acting on the needle and the angle that it digs into the groove. Simply set the needle so that it angles into the groove by 10 degrees and it'll stick to the groove like glue. The downside, though, is that the needle wears out the groove like a hot knife through butter.
If you're adjusting the downforce on the needle to control stability, don't automatically add the heaviest counterweight available. Try to take the needle manufacturer's guidance first and then add weight gradually. Although you may only end up a couple of milligrams off maximum, those milligrams can add months to the lifespan of your needle and records.
**Figure 17-1:** Rotating the turntables gives you 250 degrees of vinyl.
**Figure 17-2:** The Shure M44-7 needle and cartridge.
If the worst comes to the worst, and the needle still flies when you're trying to scratch even with the counterweight set to maximum, you can try a couple of more drastic options:
Put the counterweight on backwards so the black ring (with numbers on it) points away from the tonearm. Because the other side of the counterweight isn't tapered, it has more bulk, which adds more weight.
Raise the height of the tonearm so the sharper angle makes the needle point down into the groove, creating more downforce. Don't put it too high, though, or the front of the cartridge may rub against the record.
The last and most destructive option is to create extra downforce by adding a weight, such as a coin or Blutack, stuck onto the headshell. Doing this may help keep the needle in the groove, but you'll wear out your records and needles quicker than your wallet can buy them!
Wearing out your records
Between the increased downforce into the groove and the repetition of the needle passing back and forth over the same part of the record when scratching, the record inevitably suffers wear and tear.
However, because audio fidelity isn't essential with scratching, record wear only becomes a problem if the record is damaged and starts to skip, or if the sample starts to sound too fuzzy. Keep your needles and records clean to reduce the possibility of dirt gouging holes in the record or making the needle less stable, and don't add more counterweight than you need to the needle, and your vinyl collection will still last a long time.
Giving slipmats the slip
As a vinyl scratch DJ your slipmats should be slippery enough so that they don't resist or drag when you're scratching, yet still have enough grip so they won't skid during a scratch, or when you let go of the record to play it. (Check out Chapter 7 for everything you need to know about slipmats.)
Touching up mixers
Chapter 10 covers the vital functions you need in a scratch mixer, but you can make a couple of further improvements yourself. Firstly, take a look at your cross-fader. Make sure that you keep it lubricated so that it moves smoothly, without unwanted resistance.
Secondly, secure the faders and cross-faders. The parts that you touch to move the faders do have a tendency to fly off if you're a bit rough with them. Pull the knob off and put a piece of paper over the metal protrusion that sticks out, making it thicker, and then put the knob back on. The knob is now wedged and harder to knock off, solving any flying knob problems!
Making the mixer a hamster
Many scratch DJs find it a lot more comfortable to scratch if they reverse the normal function of the cross-fader. This means that instead of moving the cross-fader to the left to hear Channel 1 and the right to hear Channel 2, you move to the right to hear Channel 1 and the left to hear Channel 2.
You can do this either with a hamster switch on certain mixers, or by connecting the turntables the wrong way round; you plug in the left deck, which you'd normally connect to Channel 1, into Channel 2, and the right deck connects to Channel 1 instead of Channel 2.
This is useful from a body mechanics point of view. You can perform some of the scratch moves (such as the crab and the twiddle that I describe later in this chapter) faster if you 'bounce' the cross-fader off the thumb (which is a quarter of the way along the cross-fader slot) and the end of the cross-fader slot to cut the music in and out very quickly. Some moves are quite uncomfortable for a lot of DJs because the standard mixer setup means twisting their wrists to do this, so the hamster switch sets the mixer to make these moves a lot easier and more comfortable to perform.
In case you're wondering, it's not called a hamster switch because a hamster chewed through the cables to reverse the control (which crossed my mind). It's named after The Bullet Proof Scratch Hamsters who used to connect the decks up to the mixer the wrong way round in order to reverse the normal channel and cross-fader setup.
Preparing for the Big Push
You can't scratch if you don't have anything to scratch with. You need to find a section of a tune (called a sample) that you'll use when scratching. For most scratches, this sample isn't very long – a few seconds at most – and often only about a second in duration. No rule dictates what to use as your sample, but vocal samples, drums, beeps and brass stabs can all sound great in the right hands.
There's no restriction on what record you can use to take your sample from either. Although you can use 7-inch singles and 12-inch LPs for scratching, they have grooves that are a bit too compact to scratch with properly, making it easier for the needle to jump out the groove, harder to mark the start of a sample and a lot harder to find a sample in a rush. This means DJs more commonly use 12-inch singles, but if you find a sample on an LP or 7-inch, can mark the record correctly and have the technique to scratch well with it, don't let anyone tell you that you're wrong.
You don't even need to pick dance records. Classical tunes, spoken word records, rock, folk and country – they all have the potential to have a sample that sounds great as a scratch. I had a 'Teach Yourself Spanish' record that I used a couple of times because of its strange vocal sounds.
The ultimate records for scratching, though, are specifically designed battle breaks with scratch-friendly samples. Although these records may only have ten short samples on an entire side, each sample repeats at the same point on the circumference of the vinyl. This design means that if the needle skips out of the groove into the groove next to it, you'll still be at the exact same point in the sample, and no one knows any different (unless the needle flies out of the groove by an inch into one of the other samples).
Marking samples
Scratch DJs need to locate the sample on a tune quickly, and be able to return to it accurately over and over again. CD scratch DJs can use cue points to instantly return to the start of a sample (see Chapter 8), but it's a little trickier for vinyl DJs. However, with a combination of markers on the vinyl locating the exact groove where the sample starts, and marks on the label to easily return to the beginning of that sample, it's made a little easier on vinyl.
The first thing you need to do is locate the specific point in a specific groove on a record that contains the sample you're going to scratch and mark it so you can return to it quickly.
One of the most popular ways to mark the start of the sample is to use a small sticker on the vinyl. I use numbered stickers that you used to get with video tapes, because they're small and the numbers help me remember what sample to use next (check out Figure 17-3). Every DJ has a different kind of sticker they like using, so find one that you like and . . . stick with it.
**Figure 17-3:**
A record with various numbered stickers marking samples.
Mark the groove to the left of the sample so that it's not in the way when you're performing the scratch. Here's how:
1. Find the sample on the record and press Stop on the turntable with the needle at the very beginning of the sample.
2. Place a sticker very lightly (so it's not stuck) directly in front of the needle. Then slowly turn the record with your hand so it plays in the forwards direction.
Turning the record pushes the sticker out of the way, into the groove to the left of the sample (if it goes to the right instead, try again, but when you place the sticker in front of the needle, offset it to the left slightly).
3. Check that you're in the right place by gently rocking the record back and forth, and if you got it right, press down on the sticker to make it stick to the groove next to the start of the sample.
The drawback to marking the record in this manner is that if you want to play the entire track, a great big sticker is in the way!
If you think that you'll want to play the record in full, try using a chinagraph pencil (a white, wax-based pencil) to lightly draw a line (or an arrow, whatever you want) directly onto the vinyl. Be sure not to press down too heavily, or the wax from the pencil gets in the grooves and is just as troublesome as the sticker. Marks made with ultraviolet pens (you need to remember a UV light so you can see them) are good alternatives, as are silver pens (but you still need to watch that the ink doesn't fill up the groove). Eventually, the pen marks do wear off, but as long as you catch the wear in time and reapply your marker, you shouldn't need to worry.
Following a line-up
Marking the start of a sample is a great way to find it initially, but a small pen mark is hard to return to when you're in the middle of a mad scratch move. To help you find the start of a sample quickly, draw a big fat line on the label of the record (see Figure 17-4).
Think of the record as a clock face. The idea is to draw a line on the label so that when it's pointing in a particular direction (12 o'clock and 9 o'clock are best) you know that you're at the beginning of the sample. Here's how:
1. Find the very beginning of the sample and stop the record.
2. Without moving the record (steady hands) use a CD case (or anything small and straight) to draw a line from the centre spindle to the outer edge of the record pointing to whatever clock number you'd like. (I strongly suggest 12 o'clock; straight up.)
3. Take the record off the deck to make the line more noticeable by using a thick marker.
Instead of drawing a line, you could stick a long, straight sticker on the record instead. If the sample is far enough into the record, add the sticker to the outer edge, pointing into the record. Or add the sticker on the inner part of the record so it protrudes over the blank grooves at the smooth, silent part, next to the label.
**Figure 17-4:** Drawing a line on a record label.
Fixing the hole in the middle
It's easy to blame a jumping needle on having too little counterweight, but sometimes the jump is due to the record having too large a hole in the middle. A wide hole can be so loose that the centre spindle bangs off the edges of the hole and bounces the needle out of the groove. The easiest way to fix this problem is to pass a 1-inch-long (2.5 centimetre) piece of tape through the hole, sticking equal halves of it to either side of the label. When you've stuck enough pieces of tape at different positions through the hole, the diameter reduces, solving the problem.
Sometimes the hole is too small so that the record won't fit over the centre spindle properly (either not at all, or it's way too tight, causing the turntable to slow down when you try to hold the record still). A simple fix is to get a small piece of sandpaper, roll it up into a cylinder, put it through the hole in the record and then, holding the sandpaper, spin the record round it. Do this action a couple of times and the hole opens up a bit.
If you spin the record too long, you may make the hole too big and have to tape it up. Or, if you're really unlucky and are a bit heavy-handed, you may cause small cracks in the record.
Scratching on CD, MP3 and Computer
CD decks which have large jog wheels (like the Pioneer CDJ1000) or decks which have motorised deckplatters (found on the Denon DNS3500), can let scratch DJs perform just as well (sometimes better) as they can with turntables. (See Chapter 8 for a more detailed description of jog wheels and deckplatters.)
Along with accurately emulating the sound of a record scratching, these decks have other attributes that allow them to compete with vinyl. Memory banks to store multiple cue points (start points – in this case, of samples), built-in effects, instant reverse play and more all make CD decks incredibly versatile for scratching compared to the more traditional vinyl.
These effects and controls have removed some of the art and skill from scratching that you associate with vinyl, but they've evolved the creative process of scratching to a completely new, technology driven level. Even though the fundamental basics of scratching are the same on a vinyl turntable or a CD deck, the skills are slightly different for either format (you can be rougher on CD decks for a start, because you don't need to worry about a needle jumping out of the groove), making direct comparison and competition between the two less and less relevant.
Marking CDs
Because you can't mark the CD itself, displays on the jog dial or a separate display on scratch CD decks have markers that you use to point to the start of the sample. It seems as if they've thought of everything . . .
Scratching on PC
Software like Serato Scratch Live and Traktor Scratch Pro have created the best of both worlds between CD and vinyl scratching. By still allowing DJs to use their turntables, the performance and skill of scratching remains, but with software adding creativity, stability and speed to the game, scratching has moved on to a new level.
Waveform displays on the computer monitor can reduce the need for sticky labels and marker pens. There's also a setting which makes any sample play as though it were on a battle breaks record (see the earlier section 'Preparing for the Big Push'). Computer scratching also avoids skipping problems, and effects, loops and multiple cue points explode the options for creating new sounds when scratching. Add to this the ability to quickly access a huge library of samples quicker than a traditional scratch DJ can change records, and it's no wonder that scratch DJs are falling in love with this way of scratching.
See Chapter 9 for more information about digital DJ setups: how turntables play music on a computer and how waveform displays let DJs see the music they're playing, and help scratch DJs always find the start of a sample.
Mastering the Technique
Technique is everything when scratching vinyl. If you can develop a smooth, flowing, yet still ultra-fast action, you're more likely to keep the needle glued into the groove. With CD decks, you still need a fluid motion to create a great scratch, but you don't need to worry about popping the needle out of the groove.
Practise with both hands. If you spend the time to develop the dexterity and the co-ordination needed to scratch with either hand on either of your decks and move the cross-fader independently, you're well on your way to becoming a world-class scratch DJ.
Getting hands on
Vinyl is really sensitive, and even with the extra counterweight pressure, the new needles, the proper hole size and the slippy mats, if you have a hand like a baby elephant, you're going to make that needle fly!
You need to develop the correct hand technique. Things to bear in mind are that although you're dealing with a lot of quick direction changes, try to be smooth; don't jerk the record back and forth. When performed in succession, too many rough jerky movements will pop the needle out the groove.
When you scratch the record, try to move it back and forth following the curve of the record. If you try to pull the record back and forth in a straight line, you're adding a lot of sideways pulling and pushing pressure, which when combined may be enough to jump the needle out of the groove.
Changing sample sounds
As you start to scratch you need to develop the knowledge of what changes the sound of the sample you're scratching. The five key ways to make a sample sound different when scratching are:
Location: You may have found a nice sample on a record, but you still have full control over what part of the sample you play. Just because the sample has someone saying scratch, doesn't mean that you have to play that full word. You may choose only to scratch with the sc part of the word, or maybe trying a scribble scratch on the tch part sounds unique and matches what you want to do perfectly.
Changing where in the sample you scratch by just a couple of millimetres (or a tenth of a second) can make the difference between a good sound and a great sound.
Direction: Nearly all samples sound incredibly different when you play them backwards as opposed to forwards, and if you're not too sure about the sound of your scratch, you may find that scratching the record in the other direction improves the sound immensely.
Speed: The speed at which any sample moves can alter your scratch from a low, rumbling, guttural sound to a high-pitched, shrill, chirpy sound. So don't fall into the trap of scratching at the same speed all the time. Change up mid-scratch from a fast-forward motion to a slow backwards move, mix up the speed during a move (see 'The tear' scratch section, later in this chapter) and listen out for how the speed at which you scratch the record can alter the power and sound of the scratch.
Audibility: How loud you hear the sample playing, or whether you can hear it at all, is very important. Although the cross-fader is the main control for whether you can hear the sample or not, don't forget about the channel-fader.
You can scratch using the channel-fader instead of the cross-fader, and you can use the channel-fader to set how loud you hear the scratch, which adds an extra dimension to the scratch. Gradually fading out the scratch using only the cross-fader is difficult, but when you use it on its own or in conjunction with the cross-fader, the channel-fader can give you an extra level of audio control.
EQ: Using the EQ (equaliser) to adjust the amount of bass, mid or treble present can change a shrill sounding scratch into a muddy, dark sounding one; in the middle of a scratch if you like.
Unless you have four hands, scratching using the cross-fader, the channel-fader and the EQ control all at the same time is hard, but with practice and patience you'll be amazed at how fast you can move from control to control.
Effects processors can also lend a hand. Effects like filters, flanger, distortion, echo, reverb and delay can all change the sound of the sample you're scratching. As with everything in DJing, experimentation is key. Consider the scratch technique you're performing and whether an effect will help it, hinder it or end up redundant. Give it a try, and weigh up whether the effect made the scratch better or worse.
Starting from Scratch and Back Again
All of the following scratch techniques work with any format, whether you're scratching on vinyl, CD or in software. Try the following scratches on their own first, without playing anything on the other deck. Then when you're happy choose a tune with a slow beat to play on the other deck, and scratch in time with that beat. You don't have to use a beat-only tune, but scratching over melodies and vocals may sound messy and confusing at first.
Check my website at www.recess.co.uk for audio files and movie clips of the scratch if you're unsure of what it should sound or look like. Or search the Internet for video tutorials, such as DJ QBert's.
For all these scratches I give guidance on what direction you should scratch in, and what cross-fader action you may need, but as you get used to each scratch adjust how quickly you do the scratch, what part of the sample you're scratching from and how much of it you play.
Scratching without the cross-fader
The three scratches I discuss in this section help you develop the hand control to work with the vinyl (or CD deckplatter or jog wheel) properly. Plus they're the building blocks of all the scratches that follow in the section 'Introducing cross-fader fever'. Even though they're simple moves, mastering them is very important. You don't need to use the cross-fader for these three scratches, so leave it in the middle position, with the channel-fader at full.
The baby scratch
The baby scratch is the first scratch for you to try, and it is by far the simplest, easiest scratch to attempt. This one is for anyone who comes to your house and asks, 'Can I have a go?' It may also be how you broke the needle on your dad's turntable when you were 9 years old . . .
The baby scratch is just a forward movement followed by a backward movement. Both directions are audible throughout the scratch (which is why you don't need to touch the cross-fader on this scratch). If the sample you're using is someone singing 'Hey!', then the sound would be like:
Hey (forwards) – yeH (backwards) – Hey . . . yeH . . . Hey . . . yeH . . .
When you're happy, and want to start scratching to the beat of a tune playing on your other deck, perform the forward motion on the first beat of the bar and the backward motion on the second beat:
Beats: 1 2 3 4 1 2 3 4
Scratch: Hey yeH Hey yeH Hey yeH Hey yeH
When you're comfortable matching the 1, 2, 3, 4 beats of the bar with 'Hey, yeH, Hey, yeH', (two full baby scratches), speed up the scratch so that you're going forwards and backwards on each beat (which makes four full baby scratches):
Beats: 1 2 3 4 1 2 3 4
Scratch: Hey-yeH Hey-yeH Hey-yeH Hey-yeH Hey-yeH Hey-yeH Hey-yeH Hey-yeH
The scribble scratch
The scribble scratch is similar to the baby scratch, except the amount that the record moves backwards and forwards is tiny (just the 'H' of hey, if that!), and you get a lot more scratches to the beat, let alone the bar!
By tensing the wrist and forearm while pressing down on the record with one finger, the muscles leading to your finger vibrate, causing the record to move backwards and forwards really quickly. If you think that you can generate enough speed without needing to tense your muscles, just move the record back and forth as fast as you can.
No matter what your technique is, you want to make the amount of vinyl passing under the needle as small as possible (less than 1 centimetre is best).
The tear
The tear is similar to the baby scratch, except that instead of two sounds, the scratch splits into three. You leave the cross-fader open (you can hear the sound) for the duration of the scratch, but introduce a change in the backward speed that creates the third part of the scratch.
The forward stroke (move) is the same as the baby scratch, but the first half of the backstroke is fast and the second half of the stroke is half that pace.
Practise changing the speed of just the backstroke first to help you get used to the change in tempo. When you're happy doing that, try adding in the forward stroke to the two-part backward stroke you've just mastered.
Introducing cross-fader fever
The scratches that I describe in this section involve using the cross-fader. Before you go any further, find out where the cut-in point on the cross-fader is. The cut-in point is where you have to move the cross-fader to in order to hear the appropriate channel. Depending on the cross-fader curve, this point can be a few millimetres of movement, or you may need to get the cross-fader into the middle before hearing the scratch at full volume. (Chapter 10 has more information on cross-fader curves and cut-in points.)
The forward scratch
The forward scratch gives you the perfect start to practising use of the cross-fader. Using exactly the same movement as in the baby scratch, start with the cross-fader past the cut-in point, so that you can hear the forward movement, and then before you move the record back close the cross-fader so that you can't hear the back stroke.
When you're happy cutting off the back stroke of the baby scratch, start to scratch to the beat. With the 'Hey!' example, you match the 1, 2, 3, 4 beat of the bar with Hey, Hey, Hey, Hey:
Beats: 1 2 3 4 1 2 3 4
Scratch: Hey Hey Hey Hey Hey Hey Hey Hey
If that's a little too fast for you at first, give yourself more time by slowing down the scratch so you only hear 'Hey' on odd beats:
Beats: 1 2 3 4 1 2 3 4
Scratch: Hey Hey Hey Hey
The backward scratch
As you may have guessed, the backward scratch is exactly the same as the forward scratch, except that this time you hear only the back stroke of the baby scratch. So, you hear 'yeH, yeH, yeH, yeH' as you scratch to the four beats of the bar:
Beats: 1 2 3 4 1 2 3 4
Scratch: yeH yeH yeH yeH yeH yeH yeH yeH
You may find it easier at first to use the backward scratch in the off-beat, which is where it would be naturally if you were performing a baby scratch:
Beats: 1 2 3 4 1 2 3 4
Scratch: yeH yeH yeH yeH yeH yeH yeH
The cut
The cut is when you play the sample at normal speed and direction, but only play parts of it. I used to love doing this scratch with the James Brown 'All Aboard' sample at the beginning of Kadoc's 'Nightrain'. It could sound something like 'All (pause) All All A All-Aboard':
Beats: 1 2 3 4 1 2 3 4
Scratch: All (rest) All All A All Aboard (rest) (rest)
After I'd scratched with it for a while over another tune, I'd just let the sample play, the tune would kick in and the mix was done, which shows that scratching and mixing aren't mutually exclusive; they can work together.
To perform this scratch, position the sample so that it's right behind the needle. On a particular point in the other tune (at the start of a bar in my Kadoc example), move the cross-fader in and let the record run. When you want the sample to stop, close the cross-fader, wind the record back to the beginning of the sample and let it run again.
The trick is to make sure that you wind the sample back to the correct place in time. This is the perfect time to mark a line on the record label, so that when the line is pointing at 12 o'clock you know that you're at the start of the sample (see the earlier section 'Marking samples').
The chop
The chop is very similar to the cut, except that instead of playing the record at normal pace, you control how fast the sample plays. By varying how fast you play parts of the sample, you can create some strange melodies to accompany what you're scratching over.
And of course, the reverse chop (and reverse cut) is when the fader is open for the back stroke rather than the forward stroke.
The chirp
The chirp is where hand co-ordination starts to become essential. Start the sample with the cross-fader open, but just as you hear the sample play, smoothly (though quickly) close off the cross-fader. For the back stroke, do the exact opposite; as you move the record backwards, open the cross-fader. It'll be easier to play the sample at normal speed at first, but you'll most likely find better results when you scratch the sample quickly back and forth.
With the right sample, speed of scratch and movement of the cross-fader, this technique creates a bird-like whistling, or chirp noise.
The transformer
The transformer is another simple scratch that helps with the timing of your cross-fader moves, and also develops co-ordination between your hands.
To get used to the transformer, play the sample forwards so that it lasts one bar's length (probably a couple of seconds, which means playing it very slowly) and then backwards for one bar. You can play for longer or shorter if you wish, but keeping the move to one bar gives you boundaries to work with for now that you can expand on when you get good at the transformer.
As you play the sample, open and close the cross-fader on each of the beats of the bar. As you do so, you hear the sample split into four parts playing forwards, and four parts of the sample playing backwards. When you're happy, double the speed that you cut the music in and out with. Then if you think that you can move the cross-fader fast enough, double it again, so that you're opening and closing the cross-fader 16 times for a bar.
Your thumb isn't only for hitch-hiking
Opening and closing the cross-fader becomes more difficult the faster you try to move it. When you feel limited, use your thumb as a spring to return the cross-fader to the closed position.
If you have a small distance to travel to the cut-in point on the cross-fader, rest your thumb at that point, but angle your thumb so that it leans toward the closed position. Using your middle (or ring) finger, tap the cross-fader so it bounces off your thumb and returns to the closed position, which is a lot quicker. This is easier to do if your mixer is set up hamster style (see the section 'Making the mixer a hamster').
Flares
The flare scratch takes the sample and cuts it into two by quickly closing and re-opening the cross-fader. The scratch starts with the cross-fader open, which closes halfway through the sample and then opens again. If the sample you're scratching is just someone saying the word scratch, then the flare means you'd hear scr tch.
When you close the cross-fader off quickly, it makes a clicking sound. In the preceding scr tch example, chopping the sample into two takes one movement, one click, and is called a one click forward flare.
Crab scratch
To get used to the cross-fader action for a crab scratch, click your fingers. Now instead of just your middle finger clicking off your thumb, click all four of your fingers across your thumb, starting off with the pinkie. This is the crab action: just place a cross-fader knob between your fingers and thumb.
Place your thumb as a spring to the cross-fader in the same way that you use it for the transformer scratch. As your fingers bounce the cross-fader off your thumb, you cut the sample into four, really quickly.
This is another scratch that can be easier to do if you set your mixer up in a hamster style, because you can bounce the fader off the side of the fader slot and your thumb.
Twiddle scratch
The twiddle scratch is the precursor to the crab scratch. Instead of using all four fingers to perform the crab scratch, you use only two to twiddle the cross-fader, which produces a slightly more constant rhythm to the scratch than the crab.
Combining scratches
When you're familiar with these fundamentals, start combining them to create strings of different scratches over the beat. Start off simply, by switching from one scratch to another, like changing a baby scratch to a forward scratch, or a forward scratch to a reverse scratch.
Here are a few more ideas:
Transforming with transformers: Adding transforms to any of your scratches is a great way to change up the sound of some of the basic moves. Add a transform to a forward scratch so that you transform the forward movement but still don't hear any of the back stroke. Or add a transform to a tear to really test your co-ordination!
Adding flare: Add a flare or a crab to my 'All Aboard' cut scratch example, which adds a stutter effect to part of it.
Add a speed bump: When scratching the record backwards, lightly tap the vinyl with your other hand, adding a 'hiccup' to the sound. Go even further by performing the hydroplane, where instead of tapping the record with your other hand you lightly rest your finger on the vinyl. The light touch should mean that friction caused when touching the record will lightly bounce/vibrate your finger when moving the record back, adding a rumble stutter to the scratch but without cutting it in and out.
Try drop-ons to make your own tune: This is where you hold the needle and quickly touch the record with the needle at different parts of the tune. Each time you touch the record, you hear a musical note. String these all together to make a tune (like, bizarrely, the 'Star Wars Death March', which I've just watched on YouTube . . .)
The fundamentals that I mention here are just building blocks to get you on your way towards a vast array of different scratches. Many combinations exist for how to move the record, how to move the cross-fader and the speed at which to do it all. Check out my website (www.recess.co.uk) and www.youtube.co.uk for a few more ideas on how to mix up the fundamentals.
Juggling the Beats
Beatjuggling is a great skill and one that, when mastered, earns you a lot of respect from your peers. Using two records (they don't have to be identical, but it helps at first) with just a drum beat, you create a new drum beat using a combination of all the scratch fundamentals.
Precision when returning the record (or CD) to the beginning of the sample is paramount, and a real test of your skills. Although the following guide explains the mechanics of how to do this with two records, you may find it a lot easier to do on CD or with software that has cue points saved to a memory that you can access instantly at the push of a button.
Properly marking your records is incredibly important here, because you won't have the time to listen in headphones to how you're cueing up the tune to start it again. You need to rely on spotting the marker line you may have set at 12 o'clock, and have faith that you're at the start of the sample.
Much as you would if you were juggling with balls, start off simply:
1. With two identical records, cue them so that they'll both play from the exact same point. Then start only one of them playing.
2. Play one bar of the drum beat on that record, and then start the other tune while moving the cross-fader over, to play another bar of beats.
3. While that second bar is playing, wind the first record back to the start of the bar. When the second record has finished its first bar, start the first record while moving the cross-fader over so you can hear it.
This method means that you play the same bar of drums over and over again, which may sound easy, but believe me, it isn't! You can get easily flustered, get the timing wrong for the start of the bar and make a pig's ear of something that sounds so simple. Or you might be a natural and get it first time! If you're finding it tricky at first, instead of repeating one bar, try four bars to give you lots more time to return the other tune to the beginning. Then, when you've got that, try three, then two and then one. Start easy and then make it harder and harder. Practise enough and you'll crack it.
If you're trying this on CD or DJing software, instead of winding back the sample to the beginning each time, just hit the Cue button to return to the beginning of the sample and hit Play again at the start of the bar. Your CD decks may differ as to how they return to the cue point and what you press to start the tune again, but as long as you can get back there in time to restart the tune, and start it at the right time, that's all that counts.
When you're happy repeating the whole bar, halve the time that one record plays before switching over (now two beats instead of four). Then when you're really confident, play the first beat from the first record and the second beat from the second record, and keep winding back the beats so you only hear the first two beats of the bar play over and over again.
Offsetting
By the time you can swap from beat to beat comfortably, you'll want to create more complicated drum beats. Offsetting one of the records is a great and simple way to start. Begin by starting one of the tunes half a beat later, so instead of a simple Bass Snare Bass Snare for the four beats of the bar, you hear BassBass SnareSnare BassBass SnareSnare in the exact same amount of time. The first bass is from the first tune, and the second one is from the second tune.
Leaving the cross-fader in the middle creates that run of beats, but closing the cross-fader off to some of the beats starts to chop it up a lot more.
Beats: 1 2 3 4 1 2 3 4
Sounds: B1 B2 S1 B1 S1 S2 B2 S1 S2 B1 B2 S1
(Where the B is Bass, S is Snare and the 1 or 2 means from Deck 1 or 2.)
If you have the Hot Cue function on your CD decks or software, you'll be in beatjuggling heaven because you can save individual beats to a Hot Cue trigger button. If using Pioneer CDJ1000s, instead of frantically spinning records back and forth you can save the bass drum from one tune to Hot Cue A on one deck, and the snare drum of another tune to Hot Cue A on the other deck. Leaving the cross-fader in the middle, just hit them in time to create your own new drum beat. And with three Hot Cues on each deck, you can save a selection of drum sounds for incredible creativity. You don't even need two decks! Just store the bass drum into Hot Cue A and the snare drum into Hot Cue B on the same CD deck, and create your own drum beat on one CD deck. For more on Hot Cues, see Chapter 8.
It's essential to have a great sense of rhythm if you're creating a full drum beat out of single beats. If you're not sure about creating drum beats, start off by checking out Drums For Dummies by Jeff Strong (Wiley).
These methods are only the tip of the iceberg for cutting up and creating drum beats. The faster you cut between tracks, how much you offset the beats and using beats from two different tunes can all come together to make a really complicated beat. And that's without even considering adding cymbals, hi-hats and drum rolls!
Practice, dedication and patience
Practice, dedication and patience should make up your personal mantra for beatjuggling (and scratching as a whole). Record knowledge and manual dexterity are extremely important, but you need to be fluent and tight with the beats. You need to keep your scratch moves fluid and in keeping with the rhythm of what you're scratching over, and if you're beatjuggling, the beat you make needs to flow as though a drummer were playing it – that way, you'll earn respect for your skills.
It's always good to take inspiration from others and set yourself a goal. Check out Kid Koala scratching 'Moon River' (on www.recess.co.uk) – when you can juggle and scratch like that, you'll be among the best.
Part IV
Getting Noticed and Playing Live
In this part . . .
One morning you'll wake up and realise that you're meant for more in this world than DJing in front of your cat (and annoying the neighbours). You may sound great when played through a home stereo or iPod, but the time when you play to a packed hall or a club filled with like-minded people is when you really spread your wings as a DJ.
This part of the book leads you through making the perfect demo mix, trying to secure work, and then what to do when you're standing in the DJ booth with a thousand people in front of you who want you to give them the best night of their lives.
This is DJing.
Chapter 18
Building a Foolproof Set
In This Chapter
Driving the rhythm
Selecting the right key for harmonic mixing
Developing a style all of your own
After you've taken a look at the different ways you can mix your tunes together (refer to Chapters 14, 16 and 17), you need to start examining the tunes you're using in the mix.
As well as looking a bit closer at why a tune can mix well with one tune but not another, this chapter covers developing your own style when DJing, rather than simply replicating all those who've come before you. No one's saying that following the same fundamentals as other DJs is wrong, but if you can think about what you're trying to do with the order of the tunes in your mix, you'll be a lot better DJ than the one who mixes Tune A with Tune B just because they sound good together.
Choosing Tunes to Mix Together
The tunes you select and the order in which you play them are just as important as the method you use to get from tune to tune. The best technical mix in the world can sound terrible if the tunes don't play well together, and boredom can set in if you stick to the same sound, genre and energy level (pace and the power of the music) all night.
In order to get a feel for what kind of tunes mix well with each other, you need to consider the core differences that make tunes different from one another (other than the melody, the vocals, the instruments used and so on). The main differences are the driving rhythm, the key in which the tunes are recorded and the tempo at which a tune was originally recorded.
Beatmatching – the next generation
Matching the pounding bass beats of your tunes is one thing, and after you get the knack, playing bass drums together is relatively simple and sounds good. However, the core driving rhythm is another rhythm that you need to consider and listen out for in the tunes, and it isn't just attached to dance music. All music is made up of combinations of core driving rhythms.
A track is made up of the backing track (the drums, bass line and any rhythmic, electronic sounds), and the main melody and/or vocals. The backing track is the driving force to the tune, and within it is a rhythm of its own that is separate, but works in harmony with, the pounding bass beats. A great example of this is the 'duggadugga duggadugga duggadugga duggadugga' driving rhythm in Donna Summer's 'I Feel Love'.
If what follows sounds a little childish, that's because it is. I remember it from school, so thanks to Mr Galbraith for making this concept stick!
When beatmatching bass drum beats you only have to consider the solid thump thump thump of the beats playing over each other. Now you need to start listening out for one of the four driving rhythms too: ta, ta-te, ta-te-ta and ta-fe-te-te. Most popular music has four beats to a bar, and each of the driving rhythm fundamentals occur on the beat so you get four of each to a bar:
Ta is just a single sound on each beat of the bar (sounds like baa from the nursery rhyme 'Baa, Baa, Black Sheep'):
Beat | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4
---|---|---|---|---|---|---|---|---
Rhythm | Ta | Ta | Ta | Ta | Ta | Ta | Ta | Ta
Word | Baa | Baa | Baa | Baa | Baa | Baa | Baa | Baa
Ta-te are two sounds of equal length on each beat, though often one's emphasised, making it more powerful than the other (sounds like Have you in the line 'Have you any wool' from 'Baa, Baa, Black Sheep'):
Beat | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4
---|---|---|---|---|---|---|---|---
Rhythm | Ta-te | Ta-te | Ta-te | Ta-te | Ta-te | Ta-te | Ta-te | Ta-te
Word | Have you | Have you | Have you | Have you | Have you | Have you | Have you | Have you
Sometimes you don't hear the ta (Have) part of the rhythm, and just hear the second, te (you) part; known as an offbeat. This simple offbeat is a favourite rhythm for producers who want a powerful, stripped-down sound to a tune.
Ta-te ta is like saying lemonade on each beat. It's very similar to ta-te, except that instead of two equal sounds you get two quick sounds (which take up the same time as ta in the ta-te rhythm) followed by one sound that lasts as long as the te half of ta-te. Splitting the ta-te ta rhythm into two, the halves are ta-te and ta (Lemon and ade). You say lemon very quickly, and it lasts the same duration as ade:
Beat | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4
---|---|---|---|---|---|---|---|---
Rhythm | Ta-te ta | Ta-te ta | Ta-te ta | Ta-te ta | Ta-te ta | Ta-te ta | Ta-te ta | Ta-te ta
Word | Lemonade | Lemonade | Lemonade | Lemonade | Lemonade | Lemonade | Lemonade | Lemonade
Ta-fe-te-te is like saying Mississippi on each beat of the bar; four equal sounds to each beat give a powerful, hypnotic rhythm to the tune. This sound is the duggadugga rhythm I mention earlier for 'I Feel Love'. It adds a lot of energy to a bass melody, and if you add a filter or a flanger effect to this rhythm (see Chapter 10), it leaves the dance floor in a trance.
Beat | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4
---|---|---|---|---|---|---|---|---
Rhythm | Ta-fe-te-te | Ta-fe-te-te | Ta-fe-te-te | Ta-fe-te-te | Ta-fe-te-te | Ta-fe-te-te | Ta-fe-te-te | Ta-fe-te-te
Word | Mississippi | Mississippi | Mississippi | Mississippi | Mississippi | Mississippi | Mississippi | Mississippi
Producers combine these base-driving rhythm fundamentals with each other to make more complicated rhythms when writing tunes. For instance, they might use three ta-te ta's followed by a ta-fe-te-te to make up one bar or get even more complicated and create bars with ta, ta-te, ta, ta-te-ta driving rhythms. The options are endless, but when considering what tunes to use in the mix, listen to how well these driving rhythms play over another.
Check out my website, www.recess.co.uk, where you can find various video and audio clips demonstrating different driving rhythms in tunes.
Mixing with care
Mixing between similar driving rhythms can be a bit tricky. In the right hands, ta-fe-te-te mixes in beautifully to another ta-fe-te-te and it's often this constant driving rhythm that adds a feeling of power and energy to the mix. But if you don't precisely beatmatch the tunes, the four sounds fall in between each other, giving eight very messy sounds. The same goes for ta-te ta: you need good beatmatching skills to mix two of these sounds together (or to mix ta-te ta into ta-fe-te-te).
Mixing simpler ta or ta-te rhythms (including the offbeat part of ta-te, where you only hear the second te sound) with each other, or into either of the more complicated rhythms (ta-te ta and ta-fe-te-te) is a solution to this problem. However, this method will eventually stifle your creativity (and often the energy of the mix). If you need to go from a complicated driving rhythm to a simple one and then back again to a complicated one in order to progress through a mix, you'll break up the flow of the set. That's why spending time to refine your beatmatching skills is important, so that you're happy mixing complicated driving rhythms.
Although ta and ta-te are simpler and easier to beatmatch, they tend to be strong bass lines, and because they're so strong they don't always mix well. If the rhythm of one tune is ta, and the other is the offbeat te, (you don't hear the ta from ta-te) unless the ta note from one tune and the offbeat te from the other tune are very similar, the mix can sound strange and out of tune. (See 'Getting in tune with harmonic mixing', later in this chapter, for some tips.)
The same driving rhythm principles apply to the hi-hat pattern (the tchsss-sounding cymbals). Though most tunes tend to use an open hi-hat sound played in between each bass drum beat (the same as the offbeat te), be careful when the patterns get more complicated. If you try to mix two ta-fe-te-te hi-hat patterns together, and get the beatmatching wrong, it'll sound dreadful.
Changing gear
Mixing from one driving rhythm to another is extremely important to the power of the set. Going from a ta rhythm to ta-te ta can make the mix sound faster and more intense, even if the beats per minute (BPMs) are still the same. Changing from ta-fe-te-te to the offbeat version of ta-te (only the te part) is an incredibly effective way of making the mix sound darker by simplifying and concentrating the sound from a frantic, four-sound rhythm to a single-sounding, simple, basic rhythm. When coupled with a key change (see 'Changing the key', later in this chapter), the effect can lift the roof off!
Getting in tune with harmonic mixing
Your beatmatching may be perfect (see Chapter 14), your volume control may be spot on (see Chapter 16) and you've chosen two tunes with complementary driving rhythms, but sometimes two tunes sound out of tune with each other. Harmonic mixing comes in at this point, and is the final step for creating truly seamless mixes. Harmonic mixing isn't an essential step of the mixing ladder by any means, and it may be something party and rock DJs never consider, but as an electronic dance music DJ, if you want to create long, flowing, seamless mixes, harmonic mixing certainly plays a very important part.
Every song with a melody has a musical key, and instruments and vocals play and sing their notes based around this musical key (that's why you may have heard people say 'I'll sing this in C Minor', for example). This kind of key may not unlock any real doors, but it does unlock vast chasms of creativity for you. DJs like Sasha, Oakenfold, John Digweed and many others have all harnessed harmonic mixing to create smooth, controlled mixes that add an extra level of depth and skill to their styles.
Most DJs first approach harmonic mixing by accident, and then try to improve through trial and error. Trial and error is extremely important. Blindly following the rules that follow in this section of what key mixes into what is a bad idea. Knowing how the key affects how well tunes mix together is important, but more important is developing an ear for what sounds good when mixed together, rather than referring to a piece of paper or rule that you read in an incredibly informative book.
However, you need somewhere to start and somewhere to turn to if you're unsure what to do next, which is where the principle of key notations comes in, and you have the choice of two systems to help you understand.
Brace yourself here. The terminology surrounding key notations may seem like a foreign language, but don't worry – it's not something to be too scared of.
Traditional key notation
In the Western world music has 24 different keys – 12 major and 12 minor. This is known as the traditional key notation system. Whether a key is major or minor depends on the notes you used to create that key. Each key mixes perfectly with four keys, and mixes to an acceptable level with two other keys, as shown in Table 18-1. Don't worry if Table 18-1 looks like nonsense; there's an explanation of what it means at the end of it!
Table 18-1 Harmonic Song Key Combinations
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Key of Song Playing | Tonic | Perfect Fourth (Sub-Dominant) | Perfect Fifth (Dominant) | Relative Minor
C Major | C Major | F Major | G Major | A Minor
Db Major | Db Major | Gb Major | Ab Major | Bb Minor
D Major | D Major | G Major | A Major | B Minor
Eb Major | Eb Major | Ab Major | Bb Major | C Minor
E Major | E Major | A Major | B Major | Db Minor
F Major | F Major | Bb Major | C Major | D Minor
Gb Major | Gb Major | B Major | Db Major | Eb Minor
G Major | G Major | C Major | D Major | E Minor
Ab Major | Ab Major | Db Major | Eb Major | F Minor
A Major | A Major | D Major | E Major | Gb Minor
Bb Major | Bb Major | Eb Major | F Major | G Minor
B Major | B Major | E Major | Gb Major | Ab Minor
C Minor | C Minor | F Minor | G Minor | Eb Major
Db Minor | Db Minor | Gb Minor | Ab Minor | E Major
D Minor | D Minor | G Minor | A Minor | F Major
Eb Minor | Eb Minor | Ab Minor | Bb Minor | Gb Major
E Minor | E Minor | A Minor | B Minor | G Major
F Minor | F Minor | Bb Minor | C Minor | Ab Major
Gb Minor | Gb Minor | B Minor | Db Minor | A Major
G Minor | G Minor | C Minor | D Minor | Bb Major
Ab Minor | Ab Minor | Db Minor | Eb Minor | B Major
A Minor | A Minor | D Minor | E Minor | C Major
Bb Minor | Bb Minor | Eb Minor | F Minor | Db Major
B Minor | B Minor | E Minor | Gb Minor | D Major
It's okay; no need to start worrying: calculating which keys combine best with each other is actually very simple. In Table 18-1, look at C Major and then look at the keys written next to it. It obviously mixes with a tune with the same key as its own (known as the tonic), but it also mixes beautifully with the three keys next to it: F Major, G Major and A Minor. However, because C Major works really well with A Minor, you can also incorporate the keys that A Minor works well with. These key combinations from A Minor are acceptable rather than perfect. You have to judge for yourself whether they match well enough for what you're trying to do (which is why it's important to use your ears).
This chart is kind of mind blowing though, and isn't easy to read. The minor/major thing is a bit confusing if you don't have any musical experience, and working out what mixes into what can take a while. Fortunately, Mark Davis at www.harmonic-mixing.com developed the Camelot Sound Easymix System, which takes the confusion out of working out what key mixes with what.
The Camelot Sound Easymix System
The Camelot Sound Easymix System is an alternative approach that addresses the confusing layout and label names of the traditional key notation system (see Table 18-1). With the Camelot system each key has a keycode: a number from 1 to 12 and a letter (A for Minor and B for Major). Then all the keys are arranged as a tidy clock face, as shown in Figure 18-1.
**Figure 18-1:** The Camelot Sound Easymix System.
(Copyright 2001, Camelot Sound/DJ Pulse, used with permission)
The keys that mix harmonically are identical to the traditional notation, but rather than looking at a confusing table you only need to look at the keycode for the key of the tune that you're playing, and then look to the left and right and directly above or below, depending on whether the key you're referring to is on the inner or outer ring of the diagram.
So if your tune is 12B (E Major), you can mix it with a tune with the same key, with 11B, 1B from the same major family, but you can also mix it perfectly with 12A from the minor ring and you can get a nice result mixing into 11A and 1A tunes.
This works perfectly if you calculate each of your tune's keys and play them all at zero pitch, never changing their speed. But when beatmatching, you need to alter the speed of your tunes, and on normal CD decks and turntables the pitch of the tune changes as you change the speed, and the original key starts to change into a new one. Therefore, when using the Camelot Sound Easymix System, for every 6 per cent you change the pitch, you need to change the keycode by 7 numbers according to their system.
For example, if you have a 3B tune and pitch it up to 6 per cent, it's no longer a 3B tune but is now a 10B tune. Or if you pitch down by 6 per cent, it becomes an 8B tune. Move round the circle by 7 segments to see for yourself. A 6 per cent pitch change means that the 3B tune is no longer suited to 4B, 2B, 3A, 4A and 2A. For a good harmonic mix, you need to choose tunes which, when you adjust their pitch so you can beatmatch them, play with a keycode of 11B, 9B, 10A, 11A or 9A.
If DJing with turntables this 6 per cent keycode adjustment can depend entirely on how accurate your turntables are. Use the calibration dots on the side of the turntable to see whether it truly is running at 6 per cent. (Refer to Chapter 6.)
Some CD decks, turntables and software titles have Master Tempo controls that keep the pitch of the music the same no matter how you change the speed at which it plays, or a separate control that lets you alter the pitch without changing the speed. This can help greatly when trying to match the keys of your tunes, but because not all decks and DJ booths have this function, don't grow to rely on it.
Harmonic mixing is a vast concept that you can bend, twist, break or ignore at will, and the extreme concepts could take up ten of these books. If you want to delve deeper into the theory of harmonic mixing, visit DJ Prince's website, which is dedicated to harmonic mixing. Visit www.djprince.no when the mood strikes, and say hi from me.
Keying tunes
Both the traditional and Camelot notation systems may sound helpful, and believe it or not they're very simple and easy to understand, but one thing is still missing: how do you determine the key of the tune you're currently playing?
The three different ways to work out the key of a tune are
Review online databases: DJ forums and websites across the Internet offer huge databases of song keys. The people who created the Camelot Sound Easymix System have a subscription-based database at www.harmonic-mixing.com, and forums like www.tranceaddict.com/forums have huge posts dedicated to the keys of tunes, old and new.
Use your ears: Figuring out the key by ear is by far the hardest amount of work, taking patience, a good ear for music and a fair bit of musical theory knowledge.
1. Play the tune at zero pitch on the turntable/CD player.
2. Use a piano/keyboard or a computer-generated tone to go through all 12 notes on the scale, as shown in Figure 18-2.
**Figure 18-2:** The 12 notes on a piano scale.
3. The note that sounds the best and melts into the music is the root key (the C in C Major, and so on).
Finding whether the key is minor or major takes the whole thing to another level of complication, and if you want to go into that in detail you need to start looking at musical theory books. Check out books like Guitar For Dummies, 2nd Edition, by Mark Phillips and John Chappell, and Piano For Dummies by Blake Neely (both published by Wiley), because they explain this theory in a way that's easy to understand.
I'm a drummer at heart and have zero musical theory knowledge so the way I was taught how to gauge minor/major by ear is that if the music sounds striking, bold and solid, it's likely to be a major key. If the music evokes emotion and tugs at your heart strings, it's likely (though not guaranteed) to be in a minor key.
If you don't want to delve too deeply into musical theory, you can work out the root of the key and be happy with that knowledge, and then simply use trial and error to find the best tunes to mix in. This isn't much better than trial and error without knowledge of the theory, but it's a step closer to harmonic mixing – and sometimes a step is all it takes.
Though it's hard work and takes a lot of musical knowledge, working out the key (or just the root key) yourself is useful because as you listen to the tunes and find out the key, you develop an appreciation for what to listen to and will eventually develop an ear to judge which tunes match together without the need to refer to a list of suitable tunes or a notation like the Camelot Easymix Sound System.
Software: Computer programs are available that work out the key for you. One of these programs, Mixed in Key, analyses each of your wave and MP3 files and calculates what key they're recorded in according to the Camelot system (see the earlier section 'The Camelot Sound Easymix System'). The program is surprisingly accurate, extremely effective and available from www.MixedInKey.com.
When you've worked out what key your tune is in, write a little note on the record sleeve or next to the track name on the CD case or digital library.
Knowing how much to pitch
Your decks may offer you an 8 per cent pitch range, or may let you go faster or slower by 100 per cent, but unless you have a special use for going really fast or slow, if you go much over 5 per cent pitch then the majority of music may start to sound strange to the ears of the people on the dance floor. If you have a Master Tempo control on your decks, you can play the music as fast or slow as you like and the pitch won't change, just the speed, but I don't suggest going much past the 10 per cent mark unless you're trying to be creative.
The brain can account for around 5 per cent pitch difference to the original and still consider the music as normal. But as you get farther past that guide number, you risk the listener thinking that something's not right.
How far you can push the pitch of a tune (without Master Tempo) depends entirely on the tune itself, and the genre of music you're playing. When playing rock sets it's rare that I go more than 3 per cent slower or faster – but I've got loads of instrumental house tunes that I happily pitch up to 12 per cent and no one notices. However, I'd never go past 5 per cent with most vocal tracks.
You can transform many genres into something new by cranking up the pitch. A DJ I know used to play a 33 RPM house record at 45 RPM because it changed it into a great sounding drum and bass tune (though I don't think that track had any vocals).
Like everything else in DJing no hard and fast rule exists, but if you find yourself straying too far past 5 per cent it's important to ask yourself whether the tune still sounds okay. The reason you need to increase (or decrease) the pitch by so much may be because you're crossing genres – trying to mix a smooth house track into a trance track, for example. Although the structure, the key, the driving rhythm and the pitch of the tune may all sound fine, from a genre point of view you need to decide whether these tunes really play well next to each other. Like the bully and the weird kid at school, just because two tunes fit together like jigsaw pieces in many ways, it doesn't mean that they're meant to stick together. They may be from different jigsaw puzzles!
Developing a Style
The tunes you pick to play and the way you mix them come together to define your DJ style. Your style can and should be pliable, depending on what club you're playing in and what kind of music is expected of you.
If, like me, you came to DJing because you were inspired by another DJ or a music genre as a whole, you'll already have a basic style before you even start to think about one. However, try not to simply be a copycat of your favourite DJ. Listen to as many DJs as you can for inspiration, then put everything you've picked up into a big pot, give it a stir, add in your own creative ideas that have grown from listening to these DJs and hopefully you have that little twist to your style that makes you different from other DJs.
Your style may also change from what you play in the bedroom and hand out on CD to what you play in a club. You may be a trance fiend in the bedroom, but the club you work at demands commercial dance music, so you have to tone down the music you play. This fact doesn't pigeonhole you as a commercial dance DJ; it's quite the opposite. You're actually a well-rounded DJ: you can play top trance in the biggest clubs in the land, or play commercial tunes and tailor your set list to a mainstream crowd.
The genre of music you play doesn't define how you put it together, though. Between key changes, tempo changes, energy and genre changes, you can put together your own unique style, but also one that's still aimed at the people you're playing for – the crowd in front of you.
Easing up on the energy
Whether it's rock music or dance music, if all you do is play music at full pace, full power all the time, the only thing you can do is slow down or reduce the energy. But if you're almost at full energy, waiting to give more when the time's right, you'll be a DJ in control of the crowd or listener.
If you're at 100 per cent where do you go?
I always think back to a guy called Martin Woods, my old squash coach. One thing I learnt from him was that if I hit everything as hard as possible all the time, I'd never have a way to change my game apart from slowing it down, which would make me predictable and boring. So he advised me to hit the ball at about 90 per cent of power for most of the rallies, so I could inject pace and energy when I knew it was time to add pressure, or slow it down and change my game to keep my opponent guessing. And this translates perfectly into power and tempo when DJing.
When playing live, try to take the crowd through different levels of emotions. Take them from cheering and smiling to a little more intense, eyes closed and hands in the air, and then back to cheering and bouncing up and down on the dance floor. If you can put together a musical experience instead of choosing 20 tunes just because they mix well with each other, you'll be more creative, be able to work the crowd and hopefully be regarded as a great DJ.
If you're DJing at parties or at rock nights, power and tempo can often come second fiddle to how well known a tune is. Consider the big tunes you play at parties – the energetic ones that get the most people onto the dance floor. If you play one after the other for two hours, everyone will be exhausted! In this instance, it's good to think about using slower tracks to give people a breather (and others the chance to fall in love).
You'll want to be at 100 per cent power often through your set, but don't stagnate at that level and become stale. At least look to undulate the power of your tunes from start to finish, if not the tempo. Changing the driving rhythm (see the section 'Beatmatching – the next generation', earlier in the chapter) is a great way to alter the power.
Changing the key
Harmonic mixing (see 'Getting in tune with harmonic mixing', earlier in this chapter) isn't just a way to let you mix in the next tune seamlessly – you can use key changes to step up the power of the night, or take the set into a more intense, dramatic level.
If you're trying to get a bit more moody and serious with the mix, lowering the key of the mix using a simple offbeat bass melody, or a rugged sounding ta-fe-te-te driving rhythm (see the earlier section 'Beatmatching – the next generation' for an explanation) can really take the mix into a deep, intense place that's like saying to the crowd, 'Come with me . . . I'm going to take you somewhere for the next 20 minutes.'
When you want to come up for air from a deep place, I find that changing up in key so that the notes are slightly higher in pitch makes the mix sound brighter, happier and full of renewed energy. If you've spent a long time in the set playing dark, complicated trance or hard house tunes, a simple offbeat driving rhythm that changes the mix up in key can be like a strong espresso in the morning – it gives the mix and the crowd a burst of energy, and leads you into a new part of your mix.
Increasing the tempo
For dance DJs, if the first tune you used in a mix was set to play at 130 BPM (beats per minute) and you beatmatched all the tunes that followed precisely, the entire set would play at 130 BPM and bore the pants off the dance floor.
The normal progression of a set is to have an upward trend in BPM from start to finish, with little speed bumps to slow the pace down by one or two BPM for a couple of tunes but then rev it all up again, which can work really well. Slowing down the set slightly can add energy, rather than kill it.
If you have a BPM counter on your mixer (refer to Chapter 10), play a premixed CD by one of your favourite DJs through it, and watch the counter gradually move up through the set, and look for these tempo speed bumps.
Getting a backhanded compliment
I once lost out on getting the big, main-set, Saturday night slot in a club because the owner said, 'You'd only try to take the crowd somewhere special. We just want a DJ who plays random tunes and lets the crowd decide how happy they are.' At the time I was annoyed to be missing out on the bigger slot, but looking back it was one hell of a compliment. It meant the club was noticing everything I was striving to do; even if they did lack the sense to act on it.
The easiest way to increase the pace is to gradually increase the pitch fader through a series of tunes. If you have the patience (and length of tune to allow it), at the end of every two bars move the pitch fader by a small amount (about 2 or 3 millimetres). Spread out through enough tunes, you can get to the perfect BPM at which you want to play with no one noticing.
Be careful when moving the pitch control because if you do it too quickly, the people on the floor will hear the music get higher in pitch (remember, it's not just a speed control – it also changes the pitch of the music). If you have equipment with Master Tempo activated, which keeps the pitch the same no matter what speed you set it to play at, you can be a bit faster about this tempo change (about 15 seconds per BPM).
Jumps
If you don't have the patience to stand over the tune and move the pitch control in small amounts, you can use the breakdowns and other changes in the tune to boost, or jump, the pitch by around half a per cent. Use the first beat of the bar on the new phrase to jump up the pitch control. How much you can increase it, and whether you can spread this move over a couple of bars rather than the entire track, depends on the tune you're playing.
Or if you're planning to instantly jump the pitch as the tune hits the breakdown, do it between the last beat of the phrase and the first beat of the breakdown. You're best doing this with tunes that don't have a strong melody to the breakdown, and it takes practice and experimentation to get it right.
Genre changes
Switching from house to R&B or from trance to breakbeat (and eventually back again) can be an extremely effective and unnoticeable way of speeding up the mix because the change in beat structure can hide the tempo changes.
Using your brain
A few years ago I heard a great breakbeat tune called 'Symmetry C' by Brainchild that Oakenfold used as a way to step up energy, if not tempo. So I wondered how well it would work as a tempo change tool too. One night I'd increased the BPM to about 133 by the gradual method, at which point the floor was packed and happy because I'd been playing lots of music they knew and liked. But I wanted to take the mix up a gear.
Instead of playing faster and heavier music from the same genre, which would eventually lead to boredom, I used 'Symmetry C' as a bridge. As it had a swelling, beatless intro, I didn't even need to beatmatch it in; I just faded up over the outro of the last tune. I didn't play it for long, but it meant that I was able to jump from 133 to about 138 in one step. Over the course of the next two or three tunes, everyone went nuts without knowing why!
Avoiding stagnation
When you think enough about the music you play and the order and style you play it in, you start to fall in love with a few mixes. I've fallen into this trap a few times, repeating the same series of mixes week after week, or night after night. (This is especially common in warm-up sets, when you can wrongly assume that people don't care about what or how you mix.)
The downsides to repeating mixes are:
A mix that works in one club to one set of people won't automatically work the next night to a different set of people.
Regulars to the club recognise the mix, and you appear uncreative.
You're going through the motions; the fun and excitement has gone.
Because of the amount of time you've spent practising, you should have a sixth sense about the options that are available to you when mixing in and out of tunes. For the sake of your development, the people on the dance floor and the tunes in your box that never get to see the light of day, don't stick to the same transitions.
Respecting the crowd
Developing your own style is extremely important, but you still need to respect the crowd you're playing to, especially when trying to get work. It's one of those catch-22 situations that you can't avoid: how do you get experience if you need experience to get a job that gives you the experience? If you're a famous DJ, your style can be anything you want. Almost like the emperor's new clothes, some folks will love what you're doing no matter what you do or what you play.
But when you're trying to build up your reputation or just starting off, you need to be careful about pushing the crowd past their comfort level. If you're playing in a rock club where they're used to loads of scratching, samples dropped in all the time and some pretty freaky choices of tunes, then you're okay, the crowd will like what you're doing and if you're any good someone will notice you and you'll get on the next rung of the ladder.
If you're working in a more commercial club, though, and you try to do exactly the same strange, odd-sounding moves from the DJ booth, you may look up and find 200 people staring blankly at you, only to pause to let the tumbleweed roll past them. In this instance, tone your style down to what the audience probably expects: some solid, rocking tunes with a smooth, constant beat for them to dance to, with not many challenging tunes or mix techniques.
This reaction may sound like selling out, but ask yourself whether you'd rather be a poor artist or a paid DJ who can afford the time and money to develop in the right places at the right time, and has the ambition to do so!
Demonstrating your style
When you make a demo mix CD to show off your skills, your style is entirely up to you (head to Chapter 19 to find out more about making a demo). Your demo is a reflection of who you are and what you want to do. Let it rip, show off how good you are at scratching, use your six turntables past their potential and create the most awe-inspiring mix anyone's ever heard.
Have a game plan when you show off this taster as your DJ style. If you're sending it to clubs and the feedback you get it that it's too full on, send another one back to them that you've toned down a bit. But carry on handing out demos to your friends that are mixed in the way you want to mix them. Adapt to get work, and then start to drip feed your own style into your sets if you get the chance, but never give up on what truly inspires you and makes you want to DJ in your own time. If you compromise too far in one direction, you may never come back!
Chapter 19
Creating a Great Demo
In This Chapter
Putting together a list of tunes to be proud of
Making sure that the mix has a point
Setting the levels and EQs for perfect sound
Staying focused and being a perfectionist
Recording to computer and burning CDs
Getting noticed
You've spent a long time developing your skills as a DJ. Now you have to let people out there know how good you are by making a demo of your best mix.
Your demo reflects you in every way. You won't have the benefit of standing next to the club owner to explain that at 15 minutes and 20 seconds into your mix the cat jumped onto the decks, which caused the needle to jump and threw your concentration, and that's why the mix sounds awful.
You can't send in a sloppy looking (and sounding) CD and expect a club owner to think that you're professional. You must let this taster be your best work. Your demo marks you as a good DJ or a bad DJ, so make it sound great.
Preparing to Record the Demo
The most important aspects of your demo are that the sound is well recorded, the music is mixed well and it doesn't seem as if you've just thrown together 20 tunes with no real thought. Your demo must show that you have a vision of how to entertain and progress a mix from start to finish.
You'll probably make your first demo in your bedroom, but in time you can become comfortable enough with your skills as a DJ to record a live set, and hand that out to people.
Programming your set
Which tunes to put on a demo and how to progress from start to finish is up to you and your DJing style. Some DJs like to make their demos emulate the pro-mixed CDs that they own; start off with a sample from a movie or some ambient sound effects, mix into the first tune that also has a quiet introduction and then build up the mix for the next 90 minutes. Others prefer just to put on the first tune with a pounding beat, hit Start and take it from there; no need for a gentle introduction for these DJs!
Progressive and trance DJs are more likely to be the ones who use the gradual introduction into a mix because it sets a mood for what's to come. House DJs are about the rhythm and the musicality of what they play, so starting off with the bass beat and bass melody or a strong vocal with the beats coming in 16 bars later (see Chapter 15) is a really powerful way to start for this style of DJ.
The quality and style of your demo is a reflection of you as a DJ. If you simply recreate a Zane Lowe set list from start to finish, what are you going to be like when you first stand in the DJ booth and have to create something from scratch? The club will soon realise that you can't mix without the benefit of plagiarism after the fifth week in a row of playing the same set!
The last thing to think about before rifling through your library of tunes is showing what sort of music you can play. If you plan to send in a demo to a rock club, adding some epic trance to the mix isn't very relevant. And if you want to send a mix to a house or commercial club with a view to being the DJ from start to finish, you'll probably want to create your set so that you start off with some relaxed house music, move up in tempo and energy, and finish off with tunes that you know will make the crowd go wild on the dance floor.
Picking and arranging the tunes
In the months (or weeks if you're a natural) you've spent getting to grips with DJing, you should have developed a few mixes from tune to tune that give you goose bumps when you perform them. (There's no shame in taking pride in what you do. If you do a mix that makes you smile, there's a fair chance everyone else will smile too!) If you have six or seven of these individual mixes between two tunes, that gives you 12 to 14 tunes to work with for your demo. Assuming that each track lasts about four minutes, you have just under an hour's worth of music to play.
Depending on the range of music in your DJ box, no doubt some of these tracks differ slightly in style, and won't mix into any of the others. However, you still have a library brimming with tunes that you love to play, so consider some of these as the glue tunes that hold your mix together.
From the 14 tunes you know you want to use in your demo, you can create a map of the mix by arranging them in order. If, for example, your current play-list contains two gentle house tracks, two light, chart dance tracks, four vocal house tracks, two uplifting American house tracks and four trance tracks, you may want to play them in the following order:
Gentle house
Vocal house
Uplifting American house
Chart (popular, mainstream) club tunes
Trance
The order gives the mix a progression of power from beginning to end. This playlist is very simple and basic in structure, and certainly isn't right for a lot of music styles, DJs and clubs you may apply for, but the idea of progressing through a mix, rather than throwing songs into the mix because you think that they may mix well, is crucial to showing your overall DJ skills, rather than just your mixing and beatmatching skills.
Chapter 18 has more information on creating an undulating set list, so before you make your first demo, try to develop a solid understanding of progressing the mix – then you can start experimenting with the order in which you play your tunes, varying the amount of energy in the mix just like a roller-coaster going up and down.
Bridging the gaps
Take a look through your library of music and hunt for the glue tunes that'll help you progress from one level of energy or genre to the next. Sometimes you find a glue tune that mixes perfectly, is the perfect genre and perfectly increases the energy enough to be a great transition into next track. Sometimes the two tunes you're trying to bridge between don't work because they have such a large divide in pace and style between them that you'd be unwise to keep forcing that mix (what I call crowbarring in a tune).
Don't simply include tunes to bridge the gap between your original tracks because they're musical glue. You want to use them because you really like playing them, and really want to include these tunes in the mix. Don't ever add a tune into the mix only with the purpose of bridging from one tune to another. Whether it's a vocal sample, a movie clip or just another tune from the box, you need to be happy that this tune reflects on you as a DJ – because you chose it and you put it in the mix.
Be careful if you plan to use mix techniques like spinbacks, dead stops or even fade outs (refer to Chapter 16) to get around any problems of tunes mixing together. You can use them incredibly effectively and can add a level of excitement (and energy) to the mix, but if performed poorly or at the wrong time (or too many times), they can sound as if you've used them because you couldn't mix from one tune to the other. Your skills as a DJ are on show in your demo, so these techniques may actually work against you.
These bridging tunes, when added to the ones you originally picked out, hopefully end up lasting no more than the 74 minutes you can fit on a CD (assuming that's what you're planning to send out). If the mix lasts more than 74 minutes, take another look at your tracklist and take out some of the weaker tunes.
Practising your set
After you've chosen all your tunes, and you've decided on the order in which you think they play best, the time has come for you to practise your set in stages before trying to perform it all in one go.
Record your practice sessions so you can listen back to them. It's funny how mixes can sound good when you do them, but when you listen back they sound really rushed and amateurish. Alternatively, they may even sound better than you thought.
Feel free to experiment at this stage with how you mix your tunes together. If you think that a mix between two particular tunes can be slightly better, trust your instincts and look at ways to improve what you're currently trying to do.
Ask yourself the following questions about your mix:
If you change the mix transition between tunes by 4, 8 or 16 bars, does that make a difference?
If you start the new tune 16 bars later, does everything fall into place?
Are you using the EQ (equaliser) controls and faders with enough subtlety to create the seamless mix you're looking for?
One last time, are you sure that your tunes are in the best order?
Address each possibility and create a mix that's the best you can do.
Practise makes more than perfect
If you take a long time to put together and play the mix in full, don't fret. When you started putting the mix together, you were unlikely to be able to play it perfectly in front of an audience. Therefore, a perfect mix probably wasn't an accurate reflection of your abilities at that point, and practising your set does have several major benefits:
When you practise your set to perfection, you put out your best work for people to listen to.
Playing the set over and over again and analysing how to make it better is the best way to develop the skills you need to spot a bad mix, and know how to improve or fix it. This skill carries over to all your future mixes.
Each time you practise the set, any beatmatching skills and knowledge of beat structure through repetition increase incredibly.
Creating a set you're excited about, that has a purpose other than general practice and that uses tunes you love listening to removes any boredom factor, and your skills develop without you realising it!
Practise your set until you're completely comfortable playing it. Reaching the stage where you know the mix points and starting cue points like the back of your hand is important, as is being happy with all the EQ settings and strange volume anomalies that may occur (see the later section 'Looking After Sound Processing').
Setting up to record
Before you can start to record your demo, you need to set up your equipment to ensure the best possible sound quality. Two factors can affect your sound quality:
You need a good quality recorder that you know how to work, which can faithfully record your mix without failing on you, crashing or cutting out halfway through.
You need to be familiar with your mixer and know how to control the sound output on it.
Avoiding poor-quality recordings
The only thing less appealing than a demo with train wreck mixing and a poor choice of music is one that's badly recorded. Always keep in mind that no matter who you send your demo to – whether it's your best friend, your mother or Paul Oakenfold – this mix demonstrates your skills as a DJ. If it's badly recorded, you instantly lose points and you'll be dubbed as unprofessional!
Tape versus CD for demos
From purely a functional point of view, these days you should really make a demo CD of your mix rather than a tape. Apart from the fact that tape is almost obsolete, the sound quality is far better on CD and the ability to skip tracks to the next mix instantly on CD, rather than messing around with the fast-forward button on a tape deck, makes CD the preferred format.
If you have the time (and the money for the increased cost), make both. It may be a waste of time making a tape, but why reduce the options of how someone can listen to your mix? When you send both formats, you show consideration and thought toward those you're trying to get work from, because they may not have a tape player or CD player where they'll be listening to the demo (a car, for instance).
If you're going to record to tape, it's vital that you record properly. Different makes of tapes have different tolerances to the amount of signal they can handle (how loud you play the music from the mixer to the tape recorder). The packaging on the tape tells you the perfect range (in decibels). If you play too loud, the sound distorts; too quiet a signal and you get a lot of tape hiss, which loses the clarity and brightness of the sound of the music.
Although a CD plays at a quiet volume on a stereo if under-recorded, you shouldn't have any problems with sound quality from low level recordings. Set the recording levels on the CD (or computer) too loud, though, and you'll suffer terribly from digital clipping, with the music cutting and popping in and out – a frankly hideous noise to avoid at all costs.
Don't hand out demo mixes you know are bad
When I first started DJing I had a stereo that would temporarily drop the high frequencies from the music when recording. I was so excited at being a DJ and I really wanted to make sure that all my friends had tapes of me DJing. Everybody would politely take these tapes from me, but one day I went to a friend's house and saw my 'Recession' mix tape sitting next to the stereo with tape over the record-prevent tabs. When I asked him about it, he said that although he liked the mix, after listening to it once he'd got fed up with the sound problems and figured that he'd rather have a recording of Pete Tong from the radio instead. That really hurt, but it taught me a valuable lesson.
Mastering MiniDisc and DAT for demos
You may have a MiniDisc recorder or a professional DAT (digital audio tape) recorder at home, and may be tempted to send out demos in these formats. However, bear in mind that very few people have equipment to play these formats back.
Your best option if you really want to use these for recording is to use them as a 'Master' of your mix, then use this master DAT or MiniDisc to make all the CD and tape copies you're planning to send out.
Correcting recording levels
In order to make sure that the mixes you record hit the balance between enough volume to prevent tape hiss with no risk of CD sound distortion, your recorder needs to have some kind of record level indicator.
This indicator is usually very similar to the output VU meter on your mixer; a set of two lines of LEDs that are different colours (green, yellow and then red) depending on how strong the signal is. The meter should be laid out so that any music you play over a certain level (sometimes when it hits +3 decibels) makes the red LEDs start to flash.
If your recorder can accept up to +8 decibels as an input strength before distortion occurs, and you set the record level to a normal maximum of +3 decibels, if the music spikes by 2 decibels because of an unexpected loud part of the tune, you're still within the recording limits of your equipment (because the signal is only +5 decibels, which is still 3 decibels under the recording limits). If you set the record level so that it's almost hitting the +8 decibel mark for the normal playback of your records, when this 2 decibel musical spike occurs, the level is now +10 decibels, and you'll distort the recording.
Limiters
You use limiters to clamp down on any peaks in level, helping to prevent distortion. If you do have a limiter on your home recorder, it will probably have a very harsh attack, so if the music does peak, the limiter immediately reduces the overall level of the music by 2 or 3 decibels. This dip can be very noticeable on the recording, and sounds as though you've crashed down on the output level on the mixer by accident.
Some professional limiters are really good, and you can use them as a great safety net for unexpected peaks in the music signal. But I still recommend that you concentrate on setting the record levels correctly in the first place, so you don't lose some quality and clarity when the limiter kicks in.
Matching the levels
The best way to control the audio levels being recorded is to make sure that when the music is playing at its loudest point, you set the mixer's output level meter to display the same as the recorder's input level meter. This way, you can look at the output LEDs on the mixer showing +3 decibels and be happy that the recorder is recording the music at +3 decibels too.
Lining up your equipment
Setting your equipment so that everything you look at shows the same value is known as lining up your equipment. You make this alignment by playing a reference tone through the mixer. A common reference tone is a constant sine wave playing at 1 kilohertz.
A constant tone is preferable because you can be sure you're measuring the precise signal level. When you play music as a line up, the LEDs are erratic and flash up and down to show the different changes in the signal level. A constant tone is just that; constant. The level (and the LEDs) change only if you move the faders on the mixer or the input control on the recorder.
The process of lining up equipment using tone is as follows:
1. If you haven't got your own reference tone, download one from www.recess.co.uk and transfer it to CD or MP3.
Even if you use turntables it's okay; find a CD or MP3 player to plug into your mixer and play this tone into one of the channels.
2. If you need to press a switch or button to see the input level coming into the mixer, do so now (see Chapter 10 for information on input level controls).
3. Adjust the gain on the mixer (using the gain controls) so that the mixer's input level LEDs show +3 decibels.
This adjustment may mean increasing or reducing the gain control. If you're playing the reference tone out of the headphones of an MP3 player, the signal may be weaker than normal; if so, turn the volume up on the MP3 player as well as the gain control to make sure that the input level is at +3 decibels.
4. Set the channel-fader for this channel to the maximum position you'd set it at when playing a tune normally.
For scratch DJs this is normally right up to the top. For beat-mixing DJs, party and rock DJs I always recommend setting your maximum point to three-quarters of the way up (the section 'Keeping an even volume', later in this chapter, explains why).
5. If you need to switch the display LEDs back to display the Master Output level, do so now.
6. Use the Master Level control-fader to make the LEDs for the output of the mixer display +3 decibels.
After you've made this adjustment, any changes you make to the gain control on the input channel are mirrored by the readout of the mixer. If you reduce the gain on the reference tone to only zero decibels, you notice that the Master Level output LEDs also drop down to zero decibels.
(If you've just tried setting the gain to zero decibels, return the gain, and therefore the Master Level, to +3 decibels before proceeding.)
7. Set the recording level on the tape recorder.
Setting this level is simply a case of increasing (or decreasing) the input control so the LEDs display +3 decibels on the recorder.
You use the +3 decibel level only to line up your equipment and make the LED displays show the same thing. If you want a +6 decibel output to the recording device, increase the gain control on the channel input to +6 decibels, and you'll see the Master Level Output display and the display on the recording equipment both now show +6 decibels.
Unfortunately, this precise guide on how to line up your equipment only works properly if your recording equipment has a record level control. If you send the music into a home-style hi-fi with a preset record level, you may have to spend a lot of time trying to find the proper output level from your mixer through trial and error in order to create good quality recordings.
Looking After Sound Processing
When you come to look after the sound of your mix, you have two major considerations: keeping an even volume between tunes, and the EQs.
Keeping an even volume
Keeping a smooth volume to your mix is almost as important as keeping the bass beats in time or a smooth fade between tunes. Quieter parts of tunes can still be quieter, but the aim is to keep the overall volume of the mix (when the tunes are at their loudest) the same. If you line up the equipment (see the preceding section) properly, volume control is a simple process. You need to use the gain controls and the input level meters on your mixer to match the input levels of your tunes.
If you don't have input level meters on your mixer, you'll find keeping the volume of your tunes in the mix the same is a lot harder. What you can do is put both ears of the headphones on and quickly switch from hearing each tune through them. If you hear a drop in volume from one tune to the next, use the gain controls to increase or decrease the level of the incoming tune (the tune you're about to mix in) until they both sound about the same.
If you don't have gain controls on your mixer, I recommend saving up to buy a new one, quickly! In Chapter 16, and the previous section, I mention the importance of setting the channel-faders to three-quarters of the way up rather than all the way up. This is of extreme benefit to the people without gain controls, because if a tune you've just mixed in doesn't sound as loud as the one you're mixing out of, you still have some headroom (the other quarter of the way up on the channel-fader) to increase how loud the new tune plays. With practice and patience, you'll eventually develop the knack to catch these changes before anyone else can hear them.
Digital DJs win out again here, because software titles often have an auto-gain setting, matching the input level of the tunes in the mix automatically.
Assuming that you don't have the luxury of auto-gain, but you do have a mixer with gain controls and input level meters, making sure that all your tunes play out at a similar volume through the duration of the mix is very simple. Here's how:
1. Before you press record, with the EQs for bass, mid and high frequencies set to the position for perfect sound to come out from the mixer (see the next section 'Setting your EQs'), start a tune and look at the input level LED display on the mixer (you may need to press a button or switch to do this).
2. Use the gain control to set the input level to your preferred point.
I usually suggest that the meter should light up the first red LEDs (sometimes at the +3 decibel point), and maybe make the next set light up from time to time, but not constantly. Your settings depend entirely on the mixer you use and what you're recording to, though.
3. Pick out the next tune and play it through the headphones with the EQs set to the optimum play-out position.
4. Use the gain control to set the input level LEDs on the new tune so that they're as close as possible to the input level setting you made on the current tune playing through the speakers (see Step 2).
When you set both the channel-faders to the same level, both tunes should play out of the mixer at the same volume. Unless:
You forget to set the EQs to the optimum play-out level before checking the input level LEDs, which gives an artificial reading. If you killed the bass (when mixing out of the last tune, for instance) and you don't reset it to neutral (which is hopefully zero), when you check the new tune's input level, the reduced bass will cause it to have a lot less signal strength than it should. So if, for example, you'd set the gain control to make the input LEDs match the +3 decibels of the other tune, when you finally realise you've cut the bass, and put it back in, the tune may now play with a +8 decibel signal strength. Get into the routine of resetting the EQs after every mix so you don't fall into this trap.
Your tunes have a bass beat and rhythm that, although sounding fine, over-powers the rest of the tune, showing a false 'high' reading. So although the LEDs show an input strength of +3 decibels, the tune actually sounds weak (reduced volume and power) compared to the other tunes in the mix.
The only way to get around this problem is to get to know your tunes. If this problem happens once in practice, take a note (or make a note on the record sleeve) to remind you to kill the bass level slightly to allow you to increase the gain to match the volume with the rest of the mix.
Cross-fader curves also have a part to play in the volume of a mix. Check out Chapter 10 for information about how the cross-fader curve affects the volume during a mix between two tunes, but if the curve allows both tunes to play at full volume at the same time, the overall output level increases and may cause the sound to distort (see Figure 19-1).
**Figure 19-1:** Two tunes playing at a similar level combine to make the output from the mixer a lot louder.
The two ways around this problem are to use a cross-fader curve that has a slight dip in the middle to compensate for the boost of two tunes playing together at full volume (see Figures 10-2 and 10-3 in Chapter 10 for more about cross-fader curves), or use the channel-faders to dip a tune's level through the mix and then return it to full when the mix is almost over. Chapter 16 has more information on using channel-faders to enhance the mix.
Setting your EQs
The best way of making sure that you select the best EQ settings for your recording is to start off with a blank sheet. The first thing to do is set all the EQs on the mixer to their neutral point. This point is normally marked with a zero, or is the halfway point on the control (for rotary knobs, this means setting the EQ so that it's pointing to the 12 o'clock position on a clock face.) In this way, the EQ controls aren't affecting the music that you're sending out of the mixer.
However, different mixers process sound slightly differently. With some cheap mixers you need to increase the bass and high frequencies slightly and reduce the mid-range in order to make the tune sound right. If you have a good pair of headphones, use them to gauge the audio quality from the mixer and use the EQs to set the sound of the music so it sounds good to you.
Obviously, different tunes need you to tweak their EQs in separate ways in order to make the bass or high frequencies stand out a little more in the mix. Different tunes also have different sounding bass drums, and you may want to use the mid and bass EQs to try to match the strength of the bass beat as you go through the mix.
Testing, testing
When recording to CD (or to a computer), perform a test recording to make sure no boost or cut in the amount of bass, mid-range or high frequencies occurs in the recording. This is more common when recording to tape, but some computer soundcards and CD recorders can be troublesome.
As well as any problems caused by your recording equipment, you also have to consider how you set up the EQs on your amplifier. If you have the bass set very high on your amp (or stereo), you probably have the bass EQs on the mixer set lower than normal. With this setting, the recordings you make sound a bit thin (a description of a sound that's lacking in bass).
Listen to the recording on equipment other than the one you've used to record it with. I find that car stereos play music back very faithfully. If the music sounds fine in the car (especially when compared to pre-recorded CDs that you normally play in the car) then you can be 95 per cent sure that you've set up the EQs and levels on your mixer (and recorder) to allow the mix to record properly.
If the recording doesn't sound right and you need to add a little more bass, look to the recording unit first before adjusting the mixer. If your recorder has EQs that you can adjust, increase the bass slightly and do another test recording. If your recorder doesn't have EQ controls, you need to adjust the EQs on the mixer in order to make the music sound as good as possible.
The reason you change the EQs on the recorder first is because as a DJ you use the EQs more as a mixing tool than as a sound processing tool. See Chapter 16 for more information on how to use the EQs to enhance your mixes, but the key here is that if you have to boost the bass by 6 decibels (most controls go to about 12 decibels) in order to make the music sound good when recorded, when you mix in another tune with elevated bass frequencies you risk the danger of your mixer not being able to process that combined, high-bass signal well enough, and the sound quality of your mix suffers.
Sound engineers take the time to EQ instruments and vocals precisely, but hardly move the EQs away from those settings after they set them. As a DJ you'll be constantly changing the EQs as you mix, so knowing that you just need to return each control to zero to make the tune sound normal greatly benefits the sound processing and speed of your mixes.
Setting EQs on the recorder or the mixer may take a little time to get right, but helps you record the best sounding mix possible.
Adjusting the amplifier
You change the EQ settings on your amplifier depending on your circumstances. You may be recording the music through your home hi-fi, which also acts as your amplifier, so the EQ settings you make to improve the recording also affect the sound from the hi-fi (amplifier).
If you're using a separate recorder from the amplifier, though, concentrating on the sound that goes from the mixer into the recorder is more important than adjusting the amp. After you've set up the sound to make the perfect recording, you can then go to your amplifier and tweak the frequencies to give you the best sound you'd like to hear from the speakers.
If you set the EQs for the amp first and then find that you have to increase the bass EQ on the mixer to get a perfect recording, the bass through the amp is now going to be too high and you have to re-adjust it, and probably the mid and high frequencies, too. You may also feel reluctant to alter the beautiful sound you've created through the amplifier and sacrifice the sound quality of your recording.
Only you know how you like to hear the music through the amp, but the basic guideline is for the sound to have a clear, solid bass beat (but not so much that the bass frequencies take over the rest of the tune, which may make it sound muddy), and the mid range shouldn't be so high that it dominates the bass frequencies. To still give crisp vocals, guitars and melodies, the high frequencies should be set so that you can hear the hi-hat cymbals playing crisply over the bass and mid frequencies.
Performing the Demo
You've chosen a good order for your tunes that make up the demo, you've set all the recording controls to get the best sound possible and you've practised the set so that you actually dream about how the tunes are put together. Now take the final step and record your demo.
Press the record button on the CD/tape/MiniDisc/DAT/computer (let tapes run for about five seconds to make sure that you're past the blank leader tape at the very beginning) and then take a deep breath – it's for real this time – and start the mix. An hour or so later you'll either have gold dust or fertiliser sitting in the recording device.
If it's the latter, get a glass of water (or similar), compose yourself and do it again, and again, and again – until you get it right. You don't need to get too annoyed with yourself if you mess the demo up (though admittedly messing up right at the end of your mix is especially frustrating). Remember that the professional DJs who actually mix on their CD releases (rather than using computer software to do it for them) have been doing this DJing lark a lot longer than you have, and are (for the time being) just plain better than you.
The pros also have the option to stop when they make an error and then start again from where they left off, and piece everything together in the recording studio. If you record directly to CD, you need to perform the entire set from start to finish without getting anything wrong. If you record your mix to a computer first, you can edit out the bad parts and repair your errors by stopping and starting.
When you're starting to learn how to DJ, you're cheating yourself out of an invaluable process of improving your DJing if you use a computer to tidy up your mixes. Each time you go through your set, whether you complete it or not, you're expanding your skills and getting one step closer to being as good as your idols. If you just stop and restart the mix between two tunes after an error when recording to computer, it amounts to nothing more than shortcutting.
But if you do like taking the easy route and cheating with shortcuts, head to the section 'Making a Demo CD on Computer', later in this chapter, to find out more about editing your mix on computer.
Staying focused
If you have to run through your set three or four times (or more) before you create a recording that you're happy with, maintain your composure, stay focused on what you're trying to do and try not to get frustrated and angry by any mistakes you make.
You can do a few simple things to help keep your head in the game:
Arrange your tunes in the order you plan to play them in, so you don't have to hunt through a record box, CD wallet or digital library to find the next tune, run out of time and mess up the mix.
Wipe off any dust from the records, check for any build-up of grime or fluff-balls on the needles, clean CDs and reboot your computer before you start the mix.
Have something to eat before you start recording. Low blood sugar is the number one cause of snapped records in my DJ room. I get grumpy and frustrated when I'm hungry, and (reluctantly) admit to throwing one or two records into a wall after a bad mix on an empty stomach.
Keep some water on hand. Hunger can sometimes be thirst in disguise. Keep yourself hydrated so you don't start to feel tired and worn out.
If you mess up a mix after getting one hour through it and feel frustration brewing, take a ten-minute break, go for a walk, clear your head and come back to the mix ready to have another go. This break not only takes out any boredom factor that may lead to impatience, but also gives your ears a rest from the music playing out from the amp.
Go to the toilet before you start. Needing to pee during a set not only makes you rush a mix so you can run off to the smallest room, but you may be in there a while and miss the next mix. Be sensible and go before you start the mix. Just remember to wash your hands, please.
DJing made me put on weight
I thought I'd be smart about not getting hungry when I recorded mixes. I used to keep a bag of Jelly Babies with me when DJing at home or in clubs, just in case I got a drop in my sugar levels and needed a quick jolt. A bag of Jelly Babies per night makes your waistline grow incredibly fast. Couple that with more time spent DJing than on the squash court and it's no wonder my waistline grew!
Becoming a perfectionist
No matter how long you take to get the mix right, get the mix right. Keep in mind that your demo can be passed to anybody. You never know who may hear your work and have an influence on your career.
The demo has got to be perfect in your eyes. Never, ever utter the words 'That'll do'. If you want to be a bedroom DJ for the rest of your life, then fine, it probably will do. But if you've even a pinch of ambition in you, start again. Even if you miss out one beat, or have a picky problem with the levels, re-do the mix. To make an error is acceptable; not to improve because of your errors, or fix them, is completely unacceptable. Get to a stage that when you hear demos by DJs who don't care as much as you do, you can take pride in being more of a professional than them.
If the demo is for submission to a competition or a job, remember that you're up against thousands of other budding DJs; your perfectionism may be the reason you're hired instead of someone else.
Listening with an open mind
When you listen back to your mix to gauge how your performance sounds, judge it with an open mind. Things to listen out for are:
Noticeable drops in volume through the tune transitions
Distortion on the tape
Galloping horse bass drum beats when beatmatching dance music
Noticeable pitch bends when you temporarily speed up (or slow down) a tune to get it back in time
Poor EQ control
Choosing the wrong time to mix from one tune to another
However, knowing exactly when a mix happens and exactly what to listen to can make you snow blind to the overall sound of the mix, and because you hear the transition you automatically assume that it's a bad mix. I actively encourage you to listen to the mix with a critic's ear, but also listen to it with a passive listener's ear.
If you performed the mix well and it sounds great, is it really bad or have you just fallen into a trap of over-criticism because you know the mix so well? Come back to that same mix in a couple of months' time, when you don't have every second of it fresh in your mind, and I'm sure that you'll like it more than you do now.
Don't use the chance that your opinion may change with the passage of time as an excuse to let poorly beatmatched or poorly conceived mixes stay in your demo. Be 100 per cent happy with your finished product.
Making a Demo CD on Computer
Recording to computer can make your demo a lot more versatile. You can add CD track markers precisely where you'd like them to be before burning to disc, and (although not encouraged) you can edit out your fluffs (mistakes) when recording to a computer first.
After you successfully connect your mixer to the computer (refer to Chapter 13) and set up the software to process the incoming music at the correct recording level (refer to the manual that comes with your software), you need to set the quality of your recording.
CD quality sound is 44.1 kilohertz (or 44,100 hertz), 16 bit (binary notation), stereo (multiple sound), and you should change the audio recording quality to this setting using your recording software (even when using the basic Windows Sound Recorder system). This recording setting takes up about 100 megabytes for every ten minutes you record, so make sure that your hard-drive has at least twice the space you require. Some software records to a virtual cache first, taking up space on the hard-drive, but you need the same amount of space again to save the file.
With the record levels set correctly (see the manual for your software) and sample rates all set, all you need to do is press Record on the software, start your mix, press Stop when you've finished it and save it to the hard-drive.
Editing your mix
To edit your mix you need software that's a bit more sophisticated than the Windows Sound Recorder. For PC, I use Adobe Audition, NGWave or Pro Tools. On the Mac, I use Apple Soundtrack, Pro Tools and Audacity to edit, effect and save the mixes to different formats. Hundreds of different software audio editors are available. You may even have one installed with your CD burner software. Have a look through your program folder on your PC/Mac before spending any money on some expensive software.
Here's how to fix a mix if you make errors while performing it:
1. When you record your mix to computer and make an error, press Stop on the software and save the file.
2. Call this file something recognisable like 'Mix Part 1' and save it to a new folder, keeping your work organised and tidy.
3. If it was a beatmatching error, work out whether this happened because you set the pitch of the incoming tune incorrectly, and if so, adjust the pitch on that tune.
Only change the pitch on the incoming tune. If you change the pitch on the tune you were mixing out of, the beats (and pitch of the tune) won't match the saved file where you left off.
4. Move the needle or skip the CD about 30 seconds before you're due to start the mix. Press Record on the PC, press Start on the CD/turntable and continue with the mix as though you'd never stopped.
If you make any more errors, save the file each time you stop as a sequential number (Mix Part 2, Mix Part 3 and so on). After you've completed the mix, albeit split into three or four different files, you need to start putting the mix back together again.
The software or even computer you use may be different from what I'm about to describe, but the principle remains the same:
1. Open up the Mix Part 1 file (the first file) and play it.
A visual representation of the music (a symmetrical group of peaks and troughs called the waveform – see Figure 19-2) appears on screen to help you navigate the file. Usually, there's a time indicator bar that moves along the waveform as the music plays to let you see what part of the music is currently playing.
2. Find an appropriate point on Mix Part 1 to stop.
This point is probably before you started mixing into the next tune and it's best to stop playback at the beginning of a phrase (see Chapter 15 if you're unsure what a phrase is). Zoom in to the waveform close enough to see the different peaks as each bass beat hits. When you've zoomed in close enough, you should easily be able to position the time indicator at the exact point the first bass beat of the first bar of a phrase hits.
**Figure 19-2:** The waveform displayed on NGWave.
3. Open up the Mix Part 2 file in another window.
4. Find an appropriate point on Mix Part 2 to stop.
Because you've started Mix Part 2 before the error in Mix Part 1, this overlap means you can find the identical point in Mix Part 2 at which you stopped Mix Part 1. If you know the tunes well, and stopped Mix Part 1 at the beginning of a phrase, this operation doesn't take too long. You need to zoom in to the waveform on Mix Part 2 to be able to get the time indicator to exactly the same position in the music that Mix Part 1 has been left at.
5. Select Mix Part 2's waveform from where you set the time indictor to the end of the waveform.
(In Adobe Audition, you just click and drag from the indicator all the way to the right-hand side of the waveform.)
6. Copy this selection of the waveform to the clipboard.
You normally just press Ctrl+C (or CMD+C on a Mac) or choose Edit then Copy from the menu bar.
7. Change the window back to the Mix Part 1 waveform and write down the time that the time indicator is currently sitting at, so you can easily check your edit point.
8. Without moving the time indicator on Mix Part 1, paste the file from the clipboard onto the waveform.
Choose Edit then Paste, or press Ctrl+V (or CMD+V for Mac users).
This stage may vary according to the software you're using, but the essence is that you're pasting Mix Part 2 over Mix Part 1 from the point where you left the time indicator, so you shouldn't have any noticeable repetition, or cut in music, and the music should continue as though nothing's happened.
9. Set the time indicator to the time you wrote down, and listen to the join between the two parts of the mix.
The join should sound completely normal. If it doesn't, undo the paste of Mix Part 2 (Ctrl Z, CMD+Z or Edit, Undo), check where you set your time indicators and have another go.
10. Repeat this process for all the mix parts you had to make in order to get the end of the mix without any errors, and save this file as Master Mix.
You now have one file made up of all your changes that sounds as though you've never done anything wrong.
When saving the file, save it as a Wave file (WAV) (or as an AIFF for Mac) and be sure to check that the save settings are the same as the record settings (44.1 kilohertz, 16 bit, stereo). You may also want to save the file as an MP3 or any other audio format you'd like. MP3s are perfect for uploading to the Internet for others to listen to. I prefer making MP3's at a date rate of 320 Kbps (kilobits per second) but 192 Kbps still sounds fantastic at a massively reduced file size compared to the CD quality WAV or AIFF files.
Burning a CD
After you save your final mix as a WAV or AIFF file, you can burn the mix to CD. Depending on your operating system, you can probably just insert a blank CD into your CD recorder, drag the WAV or AIFF file onto the CD icon on your computer and follow the prompts to burn an audio CD (rather than a data CD, which won't play in a normal CD player).
Or if you have designated software to control your CD burner (like Toast for a Mac or Nero for a PC) you can customise the information that's burnt with the CD. This includes being able to split the one large music file up so that instead of one long track burnt to CD you have a different track on the CD for each tune you used in your mix, without any audio gaps between them.
Creating a track-split CD
Not only does this method make your mix seem a lot more professional, but a demo that you split up into its component mixes means that the people you send the CD out to can easily scan through the CD to listen to just the transitions between tunes, rather than listening to the entire CD or trying to scan through one long, 74-minute track to find your mix points. This does mean they might skip through any mix trickery like scratching or effects you were doing during individual tunes, but unfortunately, some people don't have time to listen to the entire mix at first listen and just care about transitions. Don't worry – if they like what they hear, they'll listen to the whole thing.
You can split a CD in two ways:
The hardest way: You can create a CD with multiple tracks by using your audio editing software (see the section 'Editing your mix'). The software gives you a time code for the music, and this code is essential to doing this method properly. The time code is a precise measurement for working out where you are in the tune. The measurement is normally shown as hours, minutes, seconds and thousands of a second (HH:MM:SS:DDD). Here's how to do it the hard way:
1. If your first tune starts at 0:00:00:000 and you want the second track on the CD to start at 0:04:15:150, then save the mix from 00:00:00:000 to 00:04:15:150 as an individual file.
2. If track two ends at 0:09:35:223, save the mix from 0:04:15:151 (notice that it's one thousandth of a second ahead of the last cut point) to 0:09:35:223 as another separate file.
3. Go through this process for the whole mix so that you now have individual WAV files for each tune that makes up your mix. Give the files numbers when saving them, not titles, which makes life easier when you come to keeping them in the correct order.
4. With each file saved in sequence (1, 2, 3, 4, 5, 6, 7, 8, 9 and so on) use your CD burning software to add each of the files to the list of files to be burnt to the CD (in numerical order).
5. Set the gap between each track to zero seconds. You may have to refer to the manual for how to make this setting. If you don't set the gap to zero seconds, you may get a gap of silence between each of your tracks, which won't sound like a proper DJ mix and the club will no doubt file your demo – in the trash can!
6. After you've added all the tracks and set the gap between tracks to zero seconds, burn the disc to CD and play it back to make sure that you've split all the individual tracks up properly, with no blips in sound caused by getting the split time codes wrong.
The simplest way: Create a track split CD by using the built-in track splitting functions on software such as Nero Burning Rom or Sonic Foundry. Each piece of software has a way of marking where you'd like to add track split points, without having to split up the wave file itself.
The process is almost the same as splitting the file into separate files. The software normally shows a waveform of the music (see Figure 19-2), which you play through from start to finish, adding markers to the waveform as you review it. You don't need to play the track in real time from start to finish; you can skip ahead, back, play slowly and so on, all in aid of finding the exact point you'd like to add the track split marker.
As long as you remember to set the gap between each of the tracks to zero seconds, the finished CD is neatly split into your chosen tracks, with no danger of blips in the sound from the previous method.
Check the manual that came with your software for more detailed instructions on how to make CDs with individual split tracks.
Mix CDs you find in shops tend to put track splits at the end or halfway through a mix, but this way if the club owner hits Next on the CD player, he'll skip past your DJing skills. So for a demo, you may want to split the CD before each of the mixes start, so that the club owner can just skip forward to hear how you perform each of the transitions.
Sending Off the Mix
After you've created your demo, the final stage is to create a package that sells you properly and to make sure that whoever receives it knows where it came from, even if the demo gets separated from the rest of the items you send. (See Chapter 20 for more info on where to send your demo.)
To create a selling package you may wish to include a brief CV along with the demo, covering your experience as a DJ, the styles of music you mix, whether you drive, how old you are, where you live, whether you DJ with vinyl, CD or MP3s on a laptop and whether you're comfortable speaking through a microphone. Include a quick paragraph explaining why you've applied to the club for work, and why it would be mutually beneficial for you to be their DJ.
If you think you look good, popping a photograph into the package is a good idea too. If you can show how presentable you are, the club may be more likely to consider you, and if you're good looking, they may not even listen to the mix but just hire you based on how the ladies or guys will fawn over you!
Decide whether you want to send in multiple formats of the mix. Obviously, a tape, a CD and an iPod with just your mix on it covers most bases, but this can get costly when you're sending out loads of demos. If you can, send a CD and a tape. If not, just send a CD. (Sending an iPod counts as bribery . . .)
Include a track list of your mix, and indicate key moments in the demo if you haven't split it into separate tracks.
I can't stress enough the importance of following this piece of advice: clearly write your name, your phone number and your email address on every piece of paper or plastic – every cover, CD, tape, photograph and inlay sleeve – and the covering letter that you send out with your demo.
If you can print a label on your CD, make it a nice design, but make sure your details show up clearly. Add stickers to tapes, type up your CV and keep everything clear and neat.
And remember, the devil's in the detail; get your phone number and email address right!
Chapter 20
Getting Busy With It: Working as a DJ
In This Chapter
Marketing yourself the smart way
Dealing with DJ agencies
Schmoozing your way into the DJ booth
When you start off as a DJ, the hardest thing you do is master how to beatmatch. Now that you're a great DJ, the next hurdle to overcome is getting yourself that first DJing job.
You've put together a great demo; you love it, your cat loves it, your mum loves it, it's huge on the Internet and even your best friend can't pick any holes in it. So now's the time to put it to good use – selling yourself as a DJ.
This chapter provides you with advice and guidance on how to approach bars and clubs for work and gives you a pep talk about persistence. Though I can't guarantee that you'll get any work, this chapter should fill you up with ideas and enthusiasm for the task at hand.
You have three main ways to get ahead, and get work:
Market yourself
Join an agency
Network
Marketing Yourself
Self-promotion is the key to success. No one else does the work for you. Sure, when you make it as a big DJ, you can farm the hassle onto other people, but when you're starting off you need to promote yourself diligently and single-mindedly. The same unfaltering perseverance and determination that kept you going through any difficulties you had when developing your DJing skills are exactly what you need to effectively sell yourself.
Flooding the world with your demo
You should have a pile of CDs that are properly labelled with your name on them and a tracklist together with an accompanying CV (and photo) packaged up ready to deliver to the clubs and pubs you want to work at. If you've not got that far yet, check out Chapter 19 for advice on making a good demo.
Knowing where to send your demo
Do some research in the areas you're going to spread around your demo so you know all the best places to send it to. Don't just stick to the places you go to on a Friday night; have a look at the area in which you're looking for work and make a list of all the appropriate pubs and clubs that may be interested in your skills.
If you're in a vibrant city with a large variety of bars, no doubt they'll demand the same qualities in a DJ as a club would. But this is great news for you, because by now you're a professional sounding, club-ready DJ.
Include a covering note in each of your demo packages that's specifically tailored to the bar or club you're trying to get work from. Do your research; if it's a club that plays different genres of music each night, mention which night you think you'd be best for. Show them that you know their establishment and tell them what you can add to their success if they hire you, promoting the fact that you're a focused, professional DJ with a goal of working at their club.
If your taste and music collection are suitable for a range of their nights, let the club owners know that you're a versatile DJ who can play anything from dance, to rock or indie, R&B or bhangra. Be as specific as you can; nothing's worse than being on the receiving end of a vague letter that simply says 'I want to be DJ; here's my CD'.
If you don't play a wide variety of musical genres, it may be an idea to only consider establishments that play the music you want to play. This reduces your chances of getting work, but sending in a demo filled with the latest rock tunes to an R&B club is probably a waste of a CD, your time and the club's time.
Offering owners what they want to hear
If you've been to a club your applying to, for research or a night out, you should already have an idea of what rocks the night, and what kills the night.
In your cover letter that accompanies your demo, mention all the things that make the club strong, and give an indication of what you can do to make it even better. Stop short of criticising the club and telling them what they're bad at, though! Use positive language and make the club feel that choosing you is a good thing.
And tell them you'll make them lots of money. Club owners like that . . .
Handing over your demo
By far the best approach when submitting your demo is to hand it in personally. Bars are easy because they're open for most of the day and night, so ask to speak to the manager or bar manager and hand over your demo. Ask the manager if she'd mind listening to your demo, and tell her you'll be back in a few days to see whether she likes it. Be polite and friendly when speaking with the manager, no matter how long the conversation lasts and whether or not she's polite and friendly in return.
If no management is available, don't be tempted to just leave your demo with the bar staff; come back another day when you may have a chance of meeting someone who can help.
Getting hold of someone of responsibility in a club, however, can be a little harder. When the club is open, these people are dealing with all the nuances of running the club and it'll be hard to get them to stop and spend time talking to you. Even if you have to return to the club a few times, strike up conversations with the bar staff or stewards to find the best time to come back with your demo. As long as you're polite and don't take up too much of the staff's time, your demo shouldn't end up in the bin.
If you live in a small town with no bars or clubs that play your kind of music, you need to develop some wanderlust. Look to the city or large town nearest to where you live for clubs that play the music you want to play. Don't try to force your music on people who don't want to listen. But at the same time, don't give up. Don't feel that a brick wall is in front of you and you can't get around. You just need to go to neighbouring towns and cities and dedicate yourself to spending a lot of time there instead.
Geography of a club: How far is too far?
You may want to try for global or national domination, but if you can't get to the club, what's the point? If you live 500 miles from a club to which you're sending your demo, have a think about how you're going to get there and whether it's financially viable to travel that distance. If you're only going to get £100 for a night's work, consider how much you're willing to pay to play by catching a train/plane to get there and then staying overnight in a hotel if you can't get back the same night.
Maybe you've booked a two-week holiday to Ibiza in the hope that you can get a spot in a pub or club out there for one or two nights. Send out a whole load of demos to places you think might let you play a few weeks (or months) before you travel, and keep in contact with them via email. Then, when you leave, take some tunes with you and follow up your submission personally. If you're spending the money to go there anyway, why not give it a bash?
At this early stage in your career, the problem of getting a gig 500 miles away is unlikely to occur, but try to think about every eventuality now so that you're not surprised when it happens.
Following up
When you're sure that the bars and clubs have your demo, follow up with a phone call a few days after you sent it. If someone is kind enough to take your call, ask politely what she thought of it, and hang on every word she says as she criticises your performance. Thank her for her time and honesty, and if she doesn't want to hire you, ask whether you can send in another demo that reflects her comments.
If the club hasn't received your demo, send in another one by the next post (or drop one off personally). Amend your cover letter to include the name of the person you spoke to, and include a line about chatting to her on the phone.
If you suffer from phone phobia, get over it. Don't be scared of phoning clubs and bars. You've nothing to lose in a phone call, and everything to gain.
Handling rejection
You can't afford to have a fear of rejection. You need to put yourself out there, and hope people like you. Different club owners and promoters may respond in different ways: some take time to say no; some just don't get back in touch. The best ones say yes!
If clubs don't respond, keep sending demos until they do get back in touch – remember, persistence is key. If a club owner does respond, but doesn't want to hire you, then hopefully she told you the reason why she didn't like the demo. If she comments on something you didn't realise, and you agree with it, fix the problem and send off a new demo. She may say 'I was actually just being polite before', but perhaps the time you've taken to make another demo reflecting her comments may show her how serious you are about working for her.
The knack is to keep trying until the club owner either takes you on or tells you to stop sending in demos because she doesn't like you! You have to be very strong minded because the rejection letters can come flooding in, and a lot of them won't be polite, but if you have the skills you'll find someone, somewhere, sometime who'll give you a chance and hire you.
Every time you start to wonder if this way truly is an effective form of selling yourself, think of John Digweed. He got his big break when he sent a demo to Renaissance, and he's now one of the most well-known DJs in the world.
Playing for free
Play for free are three little words that can get you very far. Ask yourself this question: would you rather play for free, or not play at all? As you try to get work, getting your foot in the door can be more important than getting paid.
If you think a club or pub might be interested in using you, but the owner sounds a bit unsure, offer to play one or two free nights (most likely as the warm-up DJ) so she can hear how good you are in the club's environment. This 'taster set' is a great way to land your first job; the club will hear firsthand if you're a good DJ in a live situation who can play music suitable for a warm-up or main set. Chapter 21 has tips on choosing music for warm-up or main sets.
Joining an Agency
Joining a DJ agency can be a good way of spreading the word about your skills. What role they play depends largely on how good and how famous a DJ you are.
You have your choice of several different types of agencies:
Artist management: Catering for famous, established, pro DJs who are in high demand rather than newbies trying to get a break or regular DJs at a small club. These agencies are less about hand-holding and advice, and are more about making sure nights go smoothly, clubs pay money on time and that the high profile DJs on their books are well publicised and booked solidly. As managers, these agencies deal with the publicity, bookings, travel, accommodation and so on, meaning the only thing that the DJ needs to worry about is the music.
Any booking fees payable to the DJ are paid to the management, who take a percentage cut (usually between 10 and 15 per cent) before passing the rest onto the DJ. The less bookings the DJ has, the less money the agency makes, so making sure that the DJs on their roster are reliable, booked solidly and getting paid is in the agency's best interest.
Local agencies: Large towns and cities have DJ agencies that cater for the clubs, bars, function rooms, wedding parties and any reason someone may want a DJ. Although fame won't be as large an issue, a strong track record of playing a lot of gigs is a necessity for these agencies to sign you up.
Local agencies take a similar percentage cut of the booking fee as the artist management agencies. Because the pool of available DJs on their books don't have fame to sell themselves, these agencies work hard for their cut.
Internet agencies: Internet DJ agencies help you with promoting yourself, rather than finding work for you. In most instances, they don't actively seek out work on your behalf, but clubs and bars come to them requesting a DJ and the agency passes on your details to the club. Reputable Internet agencies have a large dossier of clubs who request DJs on their roster, and are able to prove a large hit-rate for their DJs working at clubs.
In many cases, you pay a yearly subscription to the Internet agency, rather than handing over a percentage of what you earn. This is an extremely controversial concept, and opinions are very strong on both sides as to whether you should pay upfront to try to find work.
Paying upfront: For and against
Whether you should pay upfront before an agency gets you work is cause for a lot of heated discussion. One side of the argument is that you should only need to pay if the agency gets you work, and the agency should take a cut from the booking. Most bricks and mortar agencies, which have a staff of representatives visiting clubs, use the percentage cut approach. The club promoter pays the agency directly, who then pass the money (minus a cut) onto you.
Because most Internet agencies are actually just middlemen that let you promote yourself to their contacts, they have no way of telling whether you've been hired or paid. Relying on you to declare all the nights you've worked through agency contacts becomes an unworkable proposition; hence the request to pay for their services upfront.
The obvious risk with paying upfront is that you pay the money to the agency but they don't get you any work. Until Internet agencies get a stronger track record, my suggestion is to exhaust every possibility under the sun to get work under your own steam before approaching an Internet agency. If you're still finding it hard to get work, and you're sure it's not your skills that are letting you down, do a lot of background research into various Internet agencies and what they offer, and tread very carefully before choosing one and parting with any money.
Researching an agency
Before joining any agency (Internet, or otherwise), take a look at any testimonials that may be on their website, and if you get the chance, get in touch with the DJs and clubs to check that the agency is genuine. Some unscrupulous people out there do make up information to try to seem more professional, so do as much research as you can and post some questions on DJ forums (communities where DJs go to chat about their work – Chapter 22 has a list of some forums).
Alarm bells should ring if the agency's website has no recent testimonials from DJs, if DJs mentioned don't respond to your emails, if the agency forces you into a contract longer than a year or if you discover any hidden charges.
Contact the people in charge of running the agency. Even though they may sound fierce in their literature when they mention trying to contact them, they have to show you due care and attention. You need to be sure that you'll get a service for the money that you're looking to invest in their help. If they aren't polite, helpful and professional at the beginning of your relationship, run like the wind!
If the agency you're considering takes a cut of your booking fee, remember that the amount may vary between agencies. If the cut is larger than 10–15 per cent, find out whether you get better services for that extra money. If you don't, think hard about whether you want to hand over money for nothing.
Finally, when you're happy to sign on the dotted line with an agency, show the contract to a lawyer first, just in case you missed something.
Meeting the criteria to join
Pro-agencies for the famous DJ tend to headhunt acts. When someone gains a reputation for drawing a crowd, and has become a well-known DJ, these agencies swoop in and offer to add the DJ to their roster.
But local DJ agencies have a reputation to uphold, and as such, they do have some strict criteria that you must meet before they sign you up. Many agencies won't add you to their DJ roster based purely on a demo CD. They can't take the risk that the DJ may have taken months to perfect that one mix, or that the DJ used a computer program to touch up a sloppy performance. But more importantly, the difference between playing in the bedroom without any pressure and playing in a club in front of a thousand clubbers in a room with a bad sound system is huge. Nerves and comfort aren't an issue in the bedroom, but the first time you play live in a club you'll be nervous and in alien surroundings as a DJ. If you make a mistake because you're wet behind the ears, it won't reflect well on you or the agency promoting you.
Agencies may have a list of restrictions, like age limits and where you live, but the one constant you find is that you need to have had experience before these agencies will take you onto their books. If you've gained experience under your own steam, made your own contacts and developed them to gain you work as a DJ, then you show the talent needed to secure work and the determination and mindset needed to be a professional in the DJing business.
Keeping agencies in your musical loop
The music you play as a DJ may change the kind of agencies that you approach. Some agencies only work with wedding/party DJs, and others only represent club DJs and won't accept a wedding DJ onto their books.
When you approach an agency that represents a vast range of DJ styles, let them know at the outset what kind of music you play best. Even if you have a wide range from R&B to hard house, you need to let the agency know whether you have the music (or desire) to spend an evening playing Frank Sinatra and Neil Diamond tracks at a retirement party.
If you do have the patience to be a workhorse DJ who plays anything just to get ahead, let the agency know that you'll play anything, anywhere; and in time, hope that you've earned their trust so they start putting you in clubs where you can play the music you really want to play. The downside to the workhorse approach is the amount of bowling alleys in which you may have to play Britney Spears' tunes.
Cutting your losses
It's hard work trying to get on an agency's roster. Be persistent, but also be aware of when you're making the wrong move. I spent a long time trying to get involved with an agency in my area. When I finally tracked down the guy who ran it, we just didn't click, and when he found out that I already had work and I wasn't willing to drop it to join his agency, it ended as a very short phone call.
Depending on the contacts you build up through networking (see the next section), and the kind of places and size of clubs in which you want to play, you may never need the services of an agency. I've never been on an agency roster. That's not because I don't want to (or from a lack of trying); it's simply because the contacts I've made through networking have been helpful in getting me work.
Networking Your Way to Success
Get used to the phrase 'It's not what you know, it's who you know'. Everyone you talk to about your quest to find work eventually says this.
Networking can range from a simple meet and greet with a club or bar owner when you hand over your demo, to meeting people who introduce you to more people, and eventually getting work from those connections.
Selling yourself
Attitude and presentation can go a long way in this industry. If you can convince a club or bar owner that you'd actually be good to have around, either because you seem like a reliable kind of person or because you're well dressed and attractive enough to be eye candy for the public, then you've already given yourself a step up the ladder. Some genres of music promote and thrive on the aloof 'too cool for you' style of DJ, but it's not something I'd recommend myself.
Making friends
Going straight to a club owner and asking for work is a ballsy move. If the owner says no, you may have blown your chances of working for the club. However, if you befriend the bar staff and the DJ, who may then recommend you for a small DJing spot, you might get a lot more luck.
How you develop your relationship with people is down to your personality. If you think you're the type who can strike up a friendship with a DJ in a pub, and use that friendship to get somewhere, by all means go for it. Just realise that the DJ will peg you for a DJ wannabe from the moment you even glance around his or her DJ booth. Don't pretend that's not why you're there, but unless you think it's worthwhile pushing it, play it cool and hold off the hard sell for a while.
Getting to know bar staff, particularly senior bar staff, can be another good avenue to get into the club, even as a warm-up DJ. Again, you need to take some time, become a regular, get to know the staff and the club well, and when you're happy that you can start to push your luck, hand over a demo and see what becomes of it.
Beginning my journey
My journey began when I was a barman in a pub in Glasgow called Café Cini. Before the DJs arrived, a tape would play at low level through the sound system. After a couple of months of working behind the bar, I slipped one of my tapes into the machine. Luckily Pauline, the manageress, liked the tape and asked who'd made the switch. When she found out it was me, she offered me a one-hour warm up before the DJ arrived (paid in Irn Bru). This spot led to an hour during the main part of the night (more Irn Bru) and then became a night of my own for money (which I spent on Irn Bru), and expanded on from there (as did my waistline due to all that Irn Bru!).
One of the other DJs who'd just opened up his own club offered me a warm-up spot, giving me my first piece of club experience. From there, I met another DJ who was giving up his Friday night residency at a club and suggested, with his recommendation, that I should get in touch with the owners to take over.
So from a basic bar job, my DJ career began. It can be that easy for you too.
Going undercover
Getting a foot in the door when you're already inside is easy! Insider knowledge is the best advantage you can have. A bar job in a club or pub you want to work in is an excellent way of selling yourself surreptitiously. You can subtly spread word of your skills and repeatedly let people hear your demo until they realise that they like you and want to put you in the booth. By the time they grasp your true agenda, it's too late: they're already happy to have hired you as the DJ!
Marketing Yourself on the Internet
Creating the best website in the world won't get you any work on its own, but a website that backs you up as a professional DJ goes a long way to impressing those who choose to check it out.
As well as hosting your latest mix and a DJ CV for future employers, your site can also promote the nights you work to other people. If you establish a good following that you can keep up to date through your website, and almost guarantee a club that a certain number of people will turn up, your case for working at the club is sweetened by the guaranteed door money they'll receive.
With the creation of social networking sites like Twitter and Facebook, you don't even need to have your own website any more, and can instantly get in touch with all your 'friends' to let them know where and when you're playing next.
Websites like MySpace and Bebo let you create a more tailored page for your visitors to see, and you don't need any web-design knowledge. WYSIWYG (what you see is what you get) layout editors let you create vibrant, well-laid-out profiles that sell you just as well as a personal website.
The only downside to using these kinds of sites compared to your own website is simply the professionalism of the web URL. I think that as a web URL www.recess.co.uk looks more professional than www.myspace.com/dj_recess.
For a more dedicated DJ approach to the websites your profile is viewed on, check out sites like www.djpassion.co.uk, www.djpromoter.com and www.mydjspace.net.
Some DJ profile sites link to venues that use the DJs who submit profiles. Others on the Internet are enhanced forums and Internet radio stations. But as long as they're free, sign up and promote yourself as much as you can through all possible avenues.
Internet forums are a great way to promote yourself and find out what's going on in the music world. Chapter 22 has a list of the best forums on the Internet. And the discussion forum for this book is located at www.djrecess.co.uk/php.
Chapter 21
Facing the Music: Playing Live
In This Chapter
Knowing what to expect from the venue
Being prepared for all eventualities
Reading a crowd, and reacting to their actions
Dealing with requests, with tact
Ending the night just right
You're ready. You've practised for months, your friends know how good you are, you've sent your demo to bars and clubs to let them know how good you are, and now's your chance to show hundreds of people on the dance floor just how good you are. Stepping out of the bedroom and into a club's DJ booth is a big leap, so you have a few things to consider.
I've always said that this leap is like driving a car. You spend ages with a driving instructor who teaches you how to pass your test, and then only when you're on your own in the real world, making decisions for yourself, do you really learn how to drive. As a new DJ you spend a year or more in your bedroom perfecting your technique and building knowledge about your music, and only when you get out into the real world and find work do you develop the skills to become a true DJ.
The difference between DJing in the bedroom and in a club is crowd control, knowing what people want to hear and being able to adapt to how they're reacting to the music you're playing. Knowing when to move up from one genre to another or when to increase the energy of the mix is something that comes with experience and practice, but the most important skill you develop is the ability to lose yourself and love what you're doing while simultaneously reading the crowd's reaction to the music you're playing.
Investigating the Venue
Nothing's scarier than the unknown. Investigate the club or hall you're booked to play well in advance. If you're putting on your own night in a club, you only have to worry about getting people to turn up. If you've been asked to play a party or wedding in the local town hall, you need to find out what you're expected to play and what equipment you need to take, and start memorising the bride and groom's names!
Scoping out a club
No matter whether this is your first ever set in a club, or if you're an established DJ, do your homework. Set up a meeting with the club owner, manager or promoter to discuss a few things. If you can't set up a meeting, try to go to the club on a similar night to the one you've been booked for (the same night a week before is perfect), listen to the music the DJ's playing and watch the crowd's reaction (see 'Reading a crowd', later in the chapter).
When you're doing some investigation at the club, try to strike up a conversation with the bar staff and the toilet attendants (if the club has them). Because they hear everything that's said and everything that's played through a night, staff can sometimes be a better font of knowledge than the club promoter for the music that works best, the kind of people who go there and the general mood and patterns of the people who frequent the club.
When you're the warm-up DJ
If you've been asked to do the warm-up set before the main DJ comes on, ask the promoter/manager if he has any limitations to what kind of music you can play. Whether it's a house/trance club or a rock/indie club, the promoter may want you to play lighter, well-known, musical tunes to help warm up the crowd, so the main DJ can take the mix from soft tunes to harder ones when he takes over the main set of the night.
The warm-up set is extremely important to the club, and your career. If you treat this gig as a throwaway hour and a half where what you mix doesn't matter, the customers at the club won't get warmed up, and the club won't ask you to return. Although the music may be softer than you normally play at home, suppress your musical snobbery and realise that playing whatever the club asks you to play is really important, so you can keep your foot in the door and hope that they'll eventually let you play the main set where you can show them what you're capable of.
When you're playing the main set
As the main set DJ you have fewer constraints, but you still need to find out whether the club has a music policy. They may have a limit as to how fast a tempo you can play and limit you to playing certain genres (perhaps they'd rather you didn't play hardcore stuff in trance clubs, or death metal in rock clubs).
You may think that you're there to play the latest, greatest underground tunes, but maybe the guy you've been hired to replace just played hard, loud music all the time and the club's looking for a change. So if you've been brought into a club that used to play hard dance music and they're now trying to move away from that, you may find that they'll ask you to throw in some lighter, commercial, popular, maybe even older tunes in the main part of the set.
Every set may be your big break. So swallow your pride and realise that for every five commercial tunes you play, you may be able to play one or two that people haven't heard yet but that you know will be massive. But don't push your luck! Research the music scene, read magazines, listen to other DJ mixes and listen to suitable radio shows, and you'll develop an ear to pick tunes that eventually become popular. You won't have to gamble with what you play; you'll know that you're playing the next big thing.
Provided this doesn't annoy the management, when you pick the right tunes that launch from underground to mainstream, the club owner and promoter will recognise that you know your stuff and will hopefully start to respect your musical knowledge and give you a little more musical wriggle room.
When you're replacing a DJ
If you're replacing a DJ, finding out whether and why the club asked him to leave is important, because you don't want to end up making the same kind of mistakes as the last guy. Ask the promoter what led to the DJ's dismissal and if he was doing something wrong.
I was lucky enough to be invited to watch a DJ that I was replacing play the week before he finished up, so I could hear for myself what was going wrong. I had to tell the promoter what I thought he was doing wrong, though, and how I'd do it better as a test of my DJ skills, but fortunately, I passed his test!
You may find that the DJ has been doing everything perfectly, but that a personality clash has led to his dismissal or resignation, in which case put on a smile and remember what the DJ was doing that worked.
A little reconnaissance
If you've managed to secure a meeting with the manager when the club is closed, try to get a sneaky peak inside the DJ booth and take a note of its equipment and where everything is located. The main things to check are:
Which mixer, turntables and CD decks they use
Whether a booth monitor is provided
Where you put your records/CDs
Where the amplifiers are
Whether they have a digital DJ installation
If the club doesn't supply a monitor, you can ask about getting one, but unless you're a famous DJ that'll make the club loads of money, they probably won't agree to your request. If you don't have a monitor, you need to work out the best way to get around the audio delay. (See Chapter 14 for different headphone monitoring options that'll help you. )
If you're unsure of how to use any of the controls in the club's DJ booth, do some research before you turn up on the night for your set. If the mixer has functions that you'd like to use, but don't know how, finding out how is very important. The first time I used a DJM-500 mixer I had no idea how to work the effects on it, and was banging the yellow button with no result. I didn't find out how to use the mixer properly until I got home and read about it. Most house/trance clubs still cater for vinyl DJs and tend to use the industry standard Technics 1210s, but if they're innovative and use turntables with extra features like the Vestax, Gemini and Numark range, a quick read over an online manual gives you all the knowledge you need to properly use them. If you're an indie/rock DJ who uses vinyl you might not be as lucky, because not as many of these clubs continue to provide for vinyl DJs. This makes it especially important to check out the DJ booth before you play.
If you use bottom-of-the-range twin CD decks at home, and you're faced with top-of-the-range single CD decks at the club, check online or ask someone who has those decks, to make sure that you're happy using them on the night.
As much as all DJs would love to use their own turntables, mixers and CD decks, not many clubs let you take your own kit. If you're lucky, in the right club, with a friendly manager, you may be able to take along your own mixer if you're working the entire night, but CD decks and turntables are normally off-limits to change.
Blowing speakers by proxy
I know from experience that you need to be very careful when swapping over equipment. I used to take my own mixer to a club because theirs was quite basic. Unfortunately, the cables weren't marked well, and when I plugged them back into their mixer at the end of the night I didn't do it right. The next night the unknowing DJ turned on all the amps and almost blew out most of the speakers due to the electrical pop my incorrect connections created.
Digital DJs enter a new realm of caution in the DJ booth. Not only do you need to make sure you can fit in your computer (which is a lot easier if you use a laptop style PC or Mac) but you also need to wrestle with how to connect to the club's sound system.
Chapter 9 has more information about different ways to connect a digital DJ setup to a DJ booth, but they're split into two different camps:
All mixing is performed in software on the laptop (sometimes with an external controller), with the mix output sent to an input on the mixer in the DJ booth, and played through the club's amplifiers and speakers.
Outputs of the turntables and/or CD decks in the DJ booth are re-directed to an audio in/out interface (a specially designed external soundcard) to control music playing in software on a computer. This music is then sent back to individual channels on the DJ mixer to be mixed like a normal CD/record and played through the club's sound system.
The first option is easier. It usually means connecting an audio output of the computer to a spare input on the mixer using a pair of phono (also known as RCA) cables and setting the controls on the mixer for that channel so the music plays out loud and clear (normally the channel-fader is between 75 per cent and maximum, and the EQ's at centre position, but this varies depending on the club's sound system setup).
The second option can be a lot more difficult. If a club isn't prepared for a digital DJ, it can mean unplugging CD decks and turntables from the mixer in order to reconnect them to the audio in/out interface. If you're DJing for the entire night you can do this when you arrive at the club and then disconnect at the end of the night, but if the club's brought you in to do just two hours in the middle of an eight-hour night, it'll be a lot harder to get in and out of the back of the mixer while someone's still using it!
As more DJs go digital, clubs buy audio in/out interfaces to permanently install into their DJ booth, taking care of all the connections themselves so all the DJ has to do is plug the computer into this hardware box with a USB cable. Check, however, that the software that a club's audio interface works with is the one you use. If a club has a Serato Scratch audio interface installed and you use Traktor then you still have some rewiring to do, because Traktor software and control records/CDs don't work with Serato Scratch hardware.
Money matters
The last thing to discuss with management before you come to play your set is money. Different clubs, nights and locations change how much you can charge. When you get your first gigs, you're DJing for the love of music and the opportunity, not the financial gain, but it doesn't hurt to get something in writing that states how much you'll get, and when the club's going to pay you!
Gearing up to party
Houses and town halls aren't designed to be makeshift clubs, so you need to do a little more investigation to make sure that you're well prepared for playing at these venues.
If you decide to have a party in your house so that you can impress your friends with your skills, the only things you have to worry about are the neighbours, keeping enough ice in the fridge and where to set up. But if you hire a hall to play at, you need to think about suitable amplification (refer to Chapter 12), lights and something to set up on that's more substantial than the kitchen table. If you've invited 200 people along, think about security; you may need a few big fellas there, just in case things get out of hand.
Whether the party you're running is at your house or in a hired hall, music policy isn't an issue because you decide what to play. You do need to react to how people at the party respond to what you're playing, though. Don't be bullheaded: don't persevere with music people aren't enjoying just because you want to play it.
If you're booked to play at someone else's party – be it a birthday party, leaving night or wedding – the client can give you an indication of what he expects you to play beforehand. If it's someone who knows that you're a DJ, but doesn't know that you specialise in drum and bass, you may want to let him know, so he doesn't expect Britney Spears and Beyoncé but actually get old Roni Size and Goldie tracks instead.
Unless you're told otherwise, don't expect the client to provide any equipment. You'll be lucky if you find a table for your equipment setup. So arranging suitable amplification and lighting is down to you, and you'll need to use your own DJ setup. Visit the venue you've been booked to play at well in advance. Someone who works there should be able to tell you the most popular place to set up your makeshift DJ booth, and when you see the hall you can work out how much amplification you need.
Preparing to Perform
Baden Powell wasn't wrong about the value of preparation. When your set looms only hours away, try to think of everything before you play so you're not faced with any big surprises.
Selecting the set
From your music policy discussions with the club owner or organiser of the party, you should know what music you're able to play during your set. With this in mind, you can flick through your collection or library and pick out the tunes you're most likely to play that night.
Now go back into your collection and pick out the same amount again. There's nothing wrong with taking loads of music with you. If you have the space, use it. Longing for a tune that you haven't put in your selection is a bad thing, but reaching for that tune – the one that you'd otherwise have left at home – and using it to win over a tough crowd can only be a good thing.
Predetermined set lists
Trying to work out the entire set from start to finish before you get to a club isn't a good idea. Even if the club owner has given you a music policy to stay within, you still need to tailor the music for the people on the dance floor.
If you decide before your set to play light house music for the first two hours but the club is packed after an hour, demanding more energetic music, you have the choice of playing the other hour of house music (which may bore the people out of the club) or skipping directly to the music that they want to hear – only to worry about the extra hour of music you have to fill at the end of the night.
You might want to put a lot of thought into your opening tunes if you're taking over from another DJ, though. Don't get tunnel vision and think of only one or two openers. Have enough tunes with you to cover many eventualities; one tune if it's a bit low key, another if the dance floor is going wild and another if it's in-between, in a bizarre transitional phase.
Checkpoint tunes
If you don't like the idea of a completely off-the-cuff set but don't want to create a start-to-finish set list, use key tunes for your set, like checkpoints that you pass as you increase the energy and the tempo of the night. If the checkpoints are tunes that people love to hear, you can use them as markers to help you map out your set from start to finish.
Provided you practise enough with your collection, you should be able to choose from a lot of tunes that you can mix in and out of the checkpoint tunes, all of which in turn mix into another large number of good tunes. Keep your eye on the dance floor, and try to estimate when you think you're going to change the pace or energy again, and work towards putting in the next key tune to move the mix to another level.
But remember, on every journey you sometimes need to take a detour. Even with a skeleton framework of tunes to link your mix, you still need to be flexible and react to the crowd (see the section 'Reading the crowd', later in this chapter).
Organising your box
You don't have to organise your tunes alphabetically or by genre if you don't want to, but by having an order to the chaos of your record box or CD wallet, you make it much easier to find that elusive track when you need it most. You have a couple of organisational options:
By genre: If you're doing a set that requires you to play multiple genres, or multiple subgenres of music, grouping each genre together in the record box or CD wallet makes good sense. Especially because most of these genres relate to a specific point in the night (for instance R&B at the beginning, then vocal house, then commercial dance, then trance and then progressive house), grouping these genres together makes navigating your way through the set more manageable.
Multiple boxes/bags: If you have a few boxes and bags that you take with you, have one for each genre or power level in the night, splitting your boxes so that all the beginning-of-the-night tunes are in one box, and all the main-set tunes are in another box. This way, you won't have to wade through two boxes crammed with 120 records (or CD wallets with thousands of tunes) to find a specific track.
Laziness has its value . . . at last!
I'm quite lazy as a DJ when it comes to arranging tunes. I pick them out from anywhere, but always replace them at the front of the box. But this method means that the tunes I play most often are always at the front of the box. Before I set off for a night, though, when I look through the tunes that I think I might play I put the ones I'm 90 per cent sure to include at the front of the box, the ones I'll play only if I think the crowd's the type to respond are next and then ones I'll only play in an emergency, or if the night's going so well that I can play anything, go right at the back.
DJ software (or even your iPod if you use that for DJing) takes a lot of effort out of organising your tunes. Not only do most software titles include a handy search box, so you can instantly call up a tune you want to play, but you can quickly and easily sort the library of tunes by artist, genre, BPM (beats per minute) or any other definition you may have given them.
I like giving power ratings to each of the tunes in my digital library. So, for example, I can find progressive house tunes that I think will hit the dance floor at full-power, or try to find a good trance tune that has a lesser effect on the dance floor for use as a 'breather' in the set.
Knowing What to Expect at the Club
Getting to a club early lets you plan your evening properly and gives you time to get used to the equipment, chat to the bar staff and promoter about what kind of night they think it's going to be and steady any nerves that may have snuck up on you.
Dealing with nerves
Unless you're a rock, you'll feel nervous on the first night you play. If you're lucky, your nerves will subside with time, to be replaced by magical, nervous excitement. I believe that the moment you stop getting that excited feeling in your stomach before playing a set, you should take stock and ask yourself whether you still love what you're doing or are just going through the motions.
You may be tempted, but try not to turn to alcohol as a way to get over your nerves, even if it's free. You want to be as clear-headed as possible when you're playing. Dutch courage isn't courage, it's a mask. Your nervousness reduces after a few good mixes anyway, but you should leave yourself aware of this feeling and use it as a reminder that what you're doing is important, and your fear of messing up is born of your desire to be a great DJ.
Getting used to your tools
Take the opportunity of turning up at the club early and throwing on a couple of tunes to get used to the equipment. You should already have investigated the club's setup (see the earlier section 'Scoping out a club'), but if you've only read how to use something in the booth you've not encountered before in a manual, this time is great for working through anything you're unsure of.
Setting the levels and EQ
As well as getting used to the equipment, you can figure out how the sound comes across in the club and hopefully change it to your liking. There's a long night ahead of you. If you don't like the sound, it'll be even longer!
Put on a tune you know really well, with all the EQs set to 12 o'clock (this is the flat position on your mixer, where you haven't added or cut any frequency by any amount). Turn the music up loud and stand at various parts of the dance floor. Don't only stand in front of the massive bass speakers, where you'll be shaken to pieces by the vibrations; move around, from the outskirts of the dance floor to the centre and in front of the booth.
During your journey around the dance floor, listen to the sound in each position. If the different areas of the club are covered by multiple amps and EQs, ask whether you can change them to suit the sound that you prefer. If only one amp and EQ is available for the entire dance floor, stand in the middle and set the best sound for that position.
Unfortunately, it's likely the club won't let you adjust the sound system, so you'll need to use the EQs on the mixer instead. This isn't the best option, but is still better than the music sounding shrill, with no bass in it. The tune that you use to check the sound should be a benchmark. Use this tune to set the EQs, and then match everything that follows to this benchmark.
Don't forget that people suck up sound vibrations. Clothes, skin and big gangly bones all absorb sound frequencies as the club gets busier and busier. This fact means you have to set the mixer to play louder as the club gets busier and you'll also find a lot of the bass frequencies disappear into the crowd's greedy bellies.
Every once in a while (probably when you need a pee), jump onto the dance floor and have a quick listen to how the music sounds. If you can hear too much conversation rather than music, of if your ears start shimmering with the amount of mid range, cross your legs and adjust the EQs or output level so the music sounds better – then go to the bathroom during the next track.
Setting the monitor
If you have a monitor in the DJ booth, take time to adjust it to create a virtual stereo image between the music in your headphones and the music playing from the monitor. (If you have no idea what I'm on about, see Chapter 14.)
Pop in an ear plug (honestly, I strongly recommend that you use an ear plug in your live ear – refer to Chapter 11) and set the level so that you can hear everything clearly but the music isn't so loud that you're eardrums are quivering. I've heard people talk about tiring the ear – which, to me, means if you play music too loud, for too long, you find that concentrating on the music blaring out at you is hard and you'll run the risk of ending up with permanent hearing damage.
If the club doesn't have a monitor, I hope you found that out when you went for a visit to the club and have either spent time learning how to mix with a split cue function (if the club's mixer has it; see Chapter 14) or you've been practising mixing with both tunes playing in both ears of the headphones.
Working in a loud environment
This job may be the first time that you play in a volume level louder than your home stereo, so use the opportunity of turning up early to get used to all the differences that a club's volume may throw at you.
Nothing prepares you for the feeling of the beat thumping through your body when DJing. When you're in a club as a customer on the dance floor, it's a cool feeling, but as a DJ if the beat is slightly delayed to what you're hearing through the monitor or the headphones, you can find the timing a little disconcerting at first.
It's not all bad live, though. A club's sound system can be very forgiving for small beatmatching errors. The heavy sub bass can be so thick sounding that a slight l'Boom or B'loom (see Chapter 14 if you've no idea what I mean) is easily hidden. With good headphones you can hear this small timing error before anyone can hear it on the dance floor.
The music sounds different too. The sound system in a club doesn't have the full fidelity of your headphones, with the sub-bass sometimes overpowering the bass and mid-range melodies, so you find that some mixes that don't work quite as well on CD work fine played live with the right EQ controls or by minimising any key or melody mismatches – see Chapter 16 for some examples.
Playing Your Music
You've investigated, discovered and prepared until you're blue in the face. You've been a polite DJ and turned up as early as possible (even if it is just to give you the chance to sit in the bathroom). Your night's about to begin.
Reading a crowd
If this night is your first time playing to a crowd of people you don't know, the main difference you notice is how much thought you need to put into your tunes in order to keep people on the dance floor.
In time, you'll become a body language expert, looking at the reactions of the people on the floor as they throw their hands in the air and dance like there's no tomorrow, or throw their hands up in the air in disgust . . .
First, think about how you react when you're at a club. When you're enjoying yourself, what do you do? If you're the type who grins from ear to ear and throws your hands in the air to dance music, or headbangs to rock music, and you're playing the kind of music that makes you want to do that, look for this kind of response from the people on the dance floor. When you're bored and listless, how do you react? Look into people's eyes. If they're staring into the distance or at the floor, or if they're dancing with no real thought or energy, they've gone to a happy place in their heads, waiting for something to change. It's up to you to make that change.
Don't base your readings on just the people in front of you. Look through the crowd. If you get a chance to go for a wander, walk around and look at how people are responding to the music. A glum face isn't a good thing to see. Fifteen glum faces are a kick up the backside that should make you play something better.
Just ask . . . if you dare
The relationship you've developed with the toilet attendant and bar staff can really help you out. They're a great source of information on how well you're doing, and how the night is going.
In one club that I worked at, the toilet attendant knew everything that was going on. If the people who came in to use the facilities were having a good night, he'd be quick to feed that info back to me, and if he heard tales that something wasn't quite right with the music, I'd know before it was too late. Never before or since has a visit to the bathroom been so enlightening.
If you want, you can just ask people how they're enjoying their night, either personally or collectively, over the microphone. If you get a collective groan, or even worse, silence, change the music quickly. If you get cheers, whoops and hands in the air, keep it going; you're doing well.
Progress the set
If DJs played the same style of music all night, things would get very dull. Dance DJs may start off with house music and end up playing pacey, chunky trance by the end of the night; rock DJs may start off with a mixture of older tunes and lighter rock to break people into the night and end up playing harder, newer music from heavier sounding groups.
DJing isn't a race. You won't win anything for playing all the newest, best and biggest tunes in the first 30 minutes; you'll lose everyone on the floor. You'll wear them out, they'll become bored with the same sound and because you won't have any big tunes left the people on the floor will get bored with the rest of the set. If you resort to repeating tunes, they've already heard them so they aren't as excited. Your light shone brightly, but not for long enough.
Use the checkpoint tunes (see the earlier section 'Checkpoint tunes') as a way to pepper the set with good tunes and to move the set on in energy and tempo. But don't just arbitrarily decide to change things. Always keep an eye on how the people on the dance floor are reacting to what you're playing. If the dance floor isn't busy enough, or if the alcohol level hasn't kicked in yet, playing slightly heavier music may empty the dance floor. Or maybe it's getting busy and you've played the same style for a while; if you don't change the pace soon, your set could start to sound dull and monotonous and people will start to haemorrhage off the dance floor.
Test the waters. If you can't tell what people want by the reaction on the dance floor, take things a little harder or faster, bit by bit, to see what the response is. Or maybe lessen the pace from time to time or throw in an older track to see what kind of stuff people are responding to, and then stick with that level until your crowd reading skills reveal that the time has come to move up (or down) a gear.
Handling requests
I deal with requests with the following considerations:
Was I going to play the tune they've asked for anyway? If so, I'm happy to say yes when someone asks, and say when it'll be on.
How polite was the person about the request? Manners go a long way. I'm not saying I'd play anything if someone was polite enough, but bad manners make me less likely to play something. Please and thank you don't take much time or effort to say, and they can get you so far in this world.
No matter what you consider when someone asks for a tune (this includes how good looking the person is), remember that he's paid money to get into the club and is expecting to be entertained, so at least let him down gently.
If you don't want to play the tune someone's asked for, either because you don't have it or it's not the right time to play that tune, say the following, depending on how hopeful you want to leave the person:
'I've left it at home . . . sorry.'
'I'll take a look, but I think I've left it at home . . . sorry.'
Requests as a warm-up DJ
The warm-up set can be difficult for requests. The owner/promoter's told you to play lighter tunes that everyone knows, not too hard and not the latest, biggest tracks. Halfway through the set a couple of people ask you to play the big tunes of the moment, or as someone once 'asked' me, 'Play some heavy stuff I can dance to – this stuff sucks.'
Herein lies a couple of problems. The place isn't near full and the promoter has strongly said no to playing those tunes, but this is the customer and he has paid to be entertained. This situation is why I stress the importance of talking to the owner/promoter when you get offered the job, to iron out these possible problems (see the earlier section 'When you're the warm-up DJ'). Maybe this is exactly why the club has a music policy; to weed out the kind of people who just want to dance or mosh at full speed on an empty dance floor.
Requests as the main DJ
Playing the main set in a club removes a lot of restrictions to what you can play. Requests become problems when someone asks for a tune that you don't like or don't have, or that isn't appropriate for that point in the night.
This situation can arise if someone doesn't realise the kind of club they've gone to. The amount of times I've been asked to play an R&B track in a trance club amazes me, but usually this request is prefaced by, 'I was dragged here by my friends and don't like this music, so . . . '
Friendly lighting jocks and bouncers can sometimes step in and take the role of a mediator in passing on requests. This option saves you from entering into a three-minute argument with someone over a tune that you're not willing to play and then end up missing the next mix.
Requests as a party DJ
As a club DJ you have some licence to say no to people when they ask for tunes – you got the job because you should have a superior knowledge about the music. But as a party DJ you have to appear at the mercy of the people you're playing for, whether you follow through with their requests or not.
However, a few occasions can crop up when you'd say no to a request, if you don't have that particular song or if it wouldn't go down well at all.
If you're working at a wedding, and the dance floor has all the grandparents on it, dropping the latest gangsta rap or nu metal tune may be a bit of a mistake. Or if you're a rock DJ and everyone's going nuts for the 1980s Bon Jovi/Van Halen set you're currently playing, agreeing to play one request for White Zombie may not prove to be the best decision you make all night.
Don't beat yourself up
You're in control of everybody's night as the DJ, and with that comes quite a lot of pressure. This pressure can make you flustered, and can lead to panic if things start to go wrong. In the bedroom if you make a mistake it doesn't matter, because you can start the mix again and no one will know any different. In a club if you make a mistake it means a lot more.
If your last mix was a disaster, be hard on yourself by all means because you're a perfectionist and should have done better, but don't let one mistake spoil the rest of your set. Not everyone hears errors, no matter how bad they are. A lot of people aren't as tuned in to the music as you are, or they're having too good a time to care. Watch for reactions: if the people on the floor start chanting 'Sack the DJ', you know that you've made a boo-boo, but if they're still smiling and dancing, don't beat yourself up over something that didn't matter in the end.
Taking over from someone else
The warm-up DJs have a hard life; they turn up, play for an hour and a half to get the crowd in the mood and then the next DJs push them out of the way and finish the job they started. When you're the person doing the pushing, pause and pay attention to what was happening before you entered the DJ booth.
Aim to get into the club at least 15 minutes before you start so that you can listen to the end of the warm-up DJs set. This time gives you a chance to gauge how the crowd is responding to the music, and also avoids you repeating a tune that's only just played. Ask the warm-up DJ questions about the crowd's reaction to the music already played and how he feels the night is going to continue based on his experience so far.
Checking the setup
Checking the setup is extremely important. Look at what the DJ is using. If he's only using CDs and you're about to use the turntables, quickly check the turntables and the settings on the mixer to make sure that the previous DJ hasn't disconnected, broken or switched off something that will end up causing you problems.
Look at how the DJ is mixing too. If he's only using the channel-faders, look at the cross-fader. If the mixer has assignable switches, the DJ may have switched off the cross-fader so it has no control over the mix.
A cacophony of sound
The very first time I played live, the warm-up guy before me had turned off the cross-fader and used the channel-faders on their own. The problem was, I forgot to turn the cross-fader back on, and as I needed to mix with the headphones on both ears because the DJ booth didn't have a monitor, it ended in disaster. I put on the headphones, set the input level for both channels, pressed the cue switches so both tunes played in my headphones and then raised the channel-fader to full and slowly moved the cross-fader from left to right.
Because the headphones were over both ears, I didn't hear that when I raised the channel-fader the new tune crashed in at full volume over the other tune, and when I moved the cross-fader from left to right nothing happened; both tunes continued to play over each other at full volume.
I took my headphones off and only after a brief moment of panic at the terrible noise coming from the speakers was it obvious what had happened. I slammed the channel-fader on the outgoing tune to zero and hung my head in shame. But the lesson here is that no one else noticed! I couldn't believe it.
Gauging the mood
Use your body language skills to judge what mood the crowd is in before deciding how to start your set. If the club is busy, with pent-up energy, and the warm-up DJ has been getting loads of requests for more upbeat tunes, use that to your advantage by instantly changing up from light, warm-up music to something a lot newer, faster and harder. That change gives an instant boost to the crowd. Bear in mind, though, not to blow your entire set trying to take the crowd even higher, only to run out of tunes to play.
If the people are still tentatively moving onto the dance floor, be a bit more gradual about the change in music. Do start to move on from what the previous DJ played, to add a feeling of impending energy and excitement, but do it gradually to keep the people on the dance floor.
Playing with momentum
If you're taking over from someone who's already playing fast, powerful tunes, you have a choice: you can mix out of the DJ's last tune in a smooth, seamless, unnoticeable mix, announce your arrival with a change in tempo/genre/key/volume or try something like a dead stop, spinback or power off if you really want to let people know that you're taking over. (Check out Chapters 16 and 17 for more on these techniques.)
Playing too much, too soon
Although not always a mistake, slamming in a really heavy tune when only 20 people are on the dance floor is a dangerous gamble. I heard a DJ make a terrible mistake when the warm-up was still playing light vocal house as the dance floor was only just beginning to fill up. Instead of gently coaxing more people onto the floor with a steady increase in pace and energy, the new DJ tried an instant, dramatic change using an older, classic tune: 'Born Slippy' by Underworld. It's a great tune at the right time, but straight on the back of light, musical house music, the change was way too much, and the 20 people who had made it to the dance floor quickly left, leaving an empty, desolate dance floor for the DJ to panic about.
My preference is to use a basic, simple sounding tune. Something that's just drums and a powerful, offbeat bass melody coming out of a quite frantic tune is a good way to change the power without changing the tempo (described in Chapter 16 as an offbeat only ta-te into a ta fe te te). I can then build the set back up to a fuller feel in my own time, rather than carrying on with the same sound as the other DJ, which the crowd will soon tire of.
You can also be a bit cheeky, and gradually for the last couple of minutes of the warm-up DJ's last track lower the volume it's playing out a little. Then when you play your powerful starter tune at the same volume the warm up was playing at, it'll actually sound like you've really cranked up the sound-system at the start of your set.
Changing the music
One of the most interesting things I've ever had to do was take over from a heavy metal DJ. Changing from Iron Maiden to David Morales isn't a natural thing to do! I used a simple fade out with an instant start of the next tune, which isn't a particularly hard mix, but choosing the right tune to start with is important. The tune I used, 'Needin' U' by David Morales, was a simple, recognisable tune with the offbeat simple bass line I mention in the previous section, and it worked very well.
Finishing the night
After a successful night in the DJ booth, putting on the last tune and letting it run out can be hard – you just want to keep playing all night long. Have a think about how you want to finish your set about an hour before you finish.
How busy the club is determines how you end the set. If the club is still packed, keep playing great tunes until the end, and then try to finish with the best tune you can think of. I used to love finishing with BT's 'Believer' because it's an energetic, musical track that finishes with a repeating vocal line 'I'm a believer . . .' echoing into silence. This is so much better than just fading out drums, or a tune that whimpers off into silence.
Some clubs request that you tone down the energy and pace of the music towards the end of the night or when the dance floor starts to get quieter, so people aren't hyperactive as they leave the club. I think that sells the club and the customers short a bit – you need to play the most suitable music for the people who are there from start to finish.
Respect the licensing laws for the club you're playing in; you don't want them to lose their licence just because you wanted to squeeze in one more track. Even if people are screaming for another, don't take the law into your own hands and play another tune. That's a sure route to the club not asking you back next week! The owner/promoter will probably hang over you towards the end of the night to make sure that you stop anyway, so don't push your luck.
The last things to do as you finish your night are to pack up all your tunes (and any equipment you brought), disconnect anything you've used to record your set, put it all in a safe place and then find the person who has your money!
If you're working through an agency, your payment gets sorted through them, so you only need to say your goodbyes and leave with the knowledge that you've had another successful night. Otherwise, you have to play what I call hunt the money-man. You may have to look in some strange places, but you'll eventually find the person who pays you. Unless you've something better to do, don't leave their sight until you get paid. In full.
While you're still in the club, have a last word with the bar staff and the toilet attendant to find out how they felt the night went. Always listen to feedback. If they say something you don't agree with, that's fine, but remember it and look out for it next time, in the unlikely event that they know better than you.
Part V
The Part of Tens
In this part . . .
The Part of Tens is a regular feature in all For Dummies books. Short and snappy, these chapters are the really fun ones!
From how to go to the toilet in the middle of a DJ set, to where to go to find out more information on DJing, the nuggets of information in the final chapters of this book aren't as much the icing on the cake – more the knife to cut the cake!
Chapter 22
Ten Resources for Expanding Your Skills and Fan Base
In This Chapter
Knowing where to go for more information
Discovering tuition that may be available to you
Exposing yourself (musically)
The skills you're developing are the strong foundations that lead you to become a good DJ. Unfortunately, you can't rest on your laurels. Your skills and reputation need constant bolstering, and the following ten resources keep you ahead of the scene and boost your reputation so that people know who you are when you're playing, and will seek you out.
Your thirst for knowledge should never end. The moment you think that you know it all, you start going backwards. Keep up with new equipment and technology, keep an eye on the scene so you can start to read drifting music tastes, and share as much information as you can with other DJs.
Staying Current with Media
TV, radio, DVD, magazines and the Internet are all incredible resources for your development as a DJ.
Magazines (and their supporting websites) dedicated to DJ culture, equipment and music always keep you up to date. Music reviews and DJ charts in magazines can be invaluable as long as you trust the DJ or reviewer's opinions and they keep you ahead of DJs who think that going to a club once a month is enough.
I'm on the mailing list for a magazine that's dedicated to news about new clubs opening, new sound installations and all the juicy information that you usually only hear about a couple of months later. If you can find out about a new club development in your area before the other DJs, you can get a head start and send off a demo to the developers before the other DJs know about it.
Radio shows are great ways of hearing new music. Most of them announce what tracks they're playing regularly (or have a website that updates with a track list). BBC Radio 1 is an unbelievable resource for new music. If you're outside the UK, check out (www.bbc.co.uk/radio1) – most evenings they play the best new music from various different genres.
TV programmes that interview DJs who play music you love, have features on equipment and culture, and reviews about the clubs that play your style of music can give you insight into how you need to develop in order to progress in an ultra-competitive market.
DVDs and videos that show you how to DJ can be a great help. Sometimes you need to see a technique to fully understand it (which is why my website, www.recess.co.uk, has video clips of most techniques). Inspirational footage or video clips of your favourite DJ hosted online (do a search through www.youtube.com) can light a fire under you to make you more determined to become a DJ as well as show you a whole host of new skills.
Visiting DJ Advice Websites
Ten years ago, the Internet had a dearth of information about DJing, with only a couple of websites trying to shed light on how to be a DJ.
Since then, many sites have sprung up with different ways of explaining how to DJ. Apart from my own website (www.recess.co.uk), the best websites on the Internet for club mixing are www.djmandrick.com (a great site about how to beatmatch), www.djprince.no for incredibly detailed information about harmonic mixing and www.i-dj.co.uk, the website for International DJ magazine, which keeps you up to date on the music scene and new equipment.
Getting Answers through DJ Forums
DJ forums are a great place to post any questions that are troubling you, and are also a fantastic way to get involved with a good community that listens to your mixes and gives you brutally honest feedback to help you with your development. Create a screen name (go for an anonymous one, so that you can post those embarrassing questions without fear of personal ridicule), and visit forums like:
www.djforums.com/forums A huge community with advice on technique, a classified section, mix submissions, advice for mobile DJs and a lot more.
www.i-dj.co.uk/discussion This is the forum for I-DJ magazine, which has loads of subsections and a lot of members on hand to help you out. Nearly all magazines have their own forum, so check out the homepage of your favourite magazine to see whether it has a community you'd like to join.
www.tranceaddict.com/forums A friendly, fun community, not just for trance fans, with a great thread for DJs to post pictures of their own DJ equipment setup. Humour, advice and guidance are all on hand here.
www.djchat.com/boards The previous forums are primarily for the club/electronic dance music DJ. DJChat.com has tens of thousands of members, but more importantly, deals with all different types of DJing, from country to Christian to karaoke to Latin music.
Most users on forums are polite and helpful, but to minimise any flaming (abuse), try to post into the correct section, check your spelling and be polite – also, do a quick search to check that someone hasn't already posted your question.
You'll find me on any of the preceding forums as Recess or DJ Recess or on the forum on my own website (www.djrecess.co.uk/php).
Reading Other Books
I'm hurt that you'd think of reading another DJing book after this one.
On a serious note, of the other books out there on the market on DJing, by far the best one to buy, in my opinion, is How to Be a DJ by Chuck Fresh (Premier Press). The book covers every aspect of becoming a DJ, and is aimed at every kind of DJ, from wedding to radio to club DJing. But the best thing is how it's written: Chuck's very friendly, he doesn't patronise you and he doesn't spend the whole time swearing and trying to be cool.
Beware of some of the e-books and guides available in the back of DJ magazines or online. Although many of them are genuine and very helpful, others are a complete waste of time and money or, as I've found, are rip-offs of my website! Post a request on a DJ forum (see the previous section for ideas on where to go) for a review of a particular guide, just to be sure.
Getting Hands-On Advice
If you have the money and want hands-on advice on all aspects of DJing, then academies like DJ Academy (www.djacademy.org.uk), SubBass DJ Academy (www.subbassdj.com) and Point Blank Music College (www.pointblanklondon.com) in the UK, or Norcal DJMPA (www.norcaldjmpa.com) and Scratch DJ (www.scratch.com) in the US are the most popular. Because courses cost money (out of your own pocket), do some research into a course before signing up for it, to ensure that any money you spend will be money well spent, rather than thrown away.
Universities and colleges have also realised that there's an avenue for teaching DJs, with the formation in the UK of the National Certificate in Music Technology, DJ & Mixing course. Covering beatmatching, scratching, studio production, computer technology, sound creation and more, these courses, like the private DJ academies, can teach you a lot about DJing and related industries, but have the added advantage of keeping your mum off your back because you can tell her you're at college, learning a skill.
The benefit of formal training is that you have the continuity of someone who's there to correct you when you're doing something wrong, who makes you practise (rather than you drifting off to play your Xbox) and, most importantly, someone who you can ask questions when you're unsure what to do.
Check locally in your area too. A local experienced DJ may like to share knowledge with other people. This is something I like to do on occasion, because it's always great to meet and help new DJs.
Courses can show you the mechanics of how to mix, and they provide information on the other aspects of DJing (sound production, accountancy, promotion and so on) but what they can't teach you is how to be a DJ in a more esoteric sense. What do I mean by esoteric? That partly you develop and absorb DJing into your knowledge not by the process of someone telling you what to do, but through spending time practising; through experience, confidence, failure, trial and error; and simply by listening to your tunes. If you do a course, you still need the same amount of time practising and developing to grow into your talent and truly become a great DJ.
Listening to Other People's Mixes
When you listen to different genres and different DJs on the radio, the Internet or in a club, you open your eyes to different techniques. No matter how good or bad the performance, you always gain something from listening to any kind of mix, including music you haven't heard before.
Listening to a bad mix is just as helpful as hearing a good one. If you can recognise what makes a bad mix bad, you can listen out for those same things in your own mixes (such as bad tune selection, poor beat-matching and sloppy volume or EQ (equaliser) control) and keep those problems out of your mixes.
Participating in Competitions
You can hand out as many demos as you like, but sometimes you need a few more strings to your bow so that you can spread the word about your DJ prowess. Take a look at magazines, the Internet and what's on in your local area to see whether any DJ battles or competitions are on the horizon that provide the perfect opportunity for you to show off your skills.
Due to its very nature, club DJing is quite hard to put into a proper competition format without becoming a competition for how many tunes you can play in your 15-minute slot. However, Bedroom DJ competitions invite unknown DJs to send in a full-length mix and are a strong avenue to propel DJs' careers.
For scratch DJs, you don't get a better opportunity than the DMC Scratching Championships to show off your mad skillz. You'll be up against really tough competition, but hopefully the experience and the chance to meet top level DJs will improve your career prospects.
If you can't face any competitions or the rejection of not making the final of a magazine competition, look for clubs and bars that have an open booth night, where DJs take half-hour slots to play music and impress the people on the floor. If you're good, you'll be noticed.
Hosting Your Own Night
If you can't find anyone to let you work on a Friday night in their club, the solution's simple. Put on your own night. You may have to settle for a town hall somewhere, or a Tuesday night in a dingy club, but if you can get enough people to turn up to a night you run, if you organise it well and if you make it a complete success (which means loads of people come and no one gets hurt!), word will spread and you may get headhunted (in the good way). Even if the night doesn't generate any direct interest from a club owner or promoter, you'll have a very strong section on your DJing CV to show people you're driven and serious about becoming a DJ.
Promotion is the key. Get as many friends and friends of friends along as you can. If you can run the night with another DJ, all the better; that's two sets of friends you can get into the club. Hand out flyers (without littering or getting arrested), wander around a few pubs to get more people to come along, run an Internet site promoting the event and do everything you can to try to get as many people to come as possible.
Make sure that everyone knows what music to expect, try to get a group of ringers (people specifically invited for the task) who'll dance on the floor no matter what you play and don't forget to read the crowd and play music that they want to hear. If you only play your set all night, and don't try to entertain the people who've come to see and hear you, you'll find a dramatic drop in numbers the next time you play.
Under-18 discos and running a night in Scout halls and town halls are a good idea, but can be fraught with logistical problems. Most often, the problems involve alcohol and security, so be careful if you're trying to run a night without professional help – be sure that you're on the right side of the law.
Uploading Podcasts or Hosted Mixes
As disc space and bandwidth gets cheaper and cheaper, more websites (such as www.djpassion.co.uk, www.djmixtape.net and www.mydjspace.net to mention only three of the hundreds available) give you the choice to upload and promote your set for anyone across the world to download (and sometimes cast judgement on).
You find many different podcasting directories out there, from iTunes to www.podcast.com. Each one has a slightly different requirement on how to upload and set up the podcast, so I recommend that you visit the website of the directory you wish to use, and follow their tutorials to get your podcast . . . cast.
Immerse Yourself in What You Love
The most obvious resource for your development is visiting the clubs that you love. In the same way that listening to as many mixes as possible can help your development, so can going to as many clubs as possible. Clubs with music other than the genre you play can teach you a lot, but your best development comes from going to clubs that play the music you love.
Split yourself in two. Be the DJ who absorbs what's happening, recognising how the DJ is working (or alienating) the crowd, and take everything you can from a good DJ and absorb the good things into your own skills. But also, spend time on the dance floor as a normal clubber. Dance like a mad person, feel the music, let the bass flood through your body and don't stop smiling the whole time.
This is what you want to make other people do – experience and recognise a good night when you're on the dance floor, and then look for yourself in the crowd next time you play live.
Chapter 23
Ten Answers to DJ Questions You're Too Afraid to Ask
In This Chapter
Leaving your post and keeping your cool
Modifying the mood by customising the music and lighting
Making a good impression – picking your DJ name, and dressing for success
This chapter covers miscellaneous FAQs. The following ten questions are the most popular sheepish questions I've been asked over the past decade, and although I answer many questions in this book, these two handfuls don't really fit in anywhere else, and are perfect as a Part of Tens chapter.
What kind of DJ you are, and where you're playing at, can generate a different answer to a lot of the following questions. Where applicable, I split the answer into club DJ and party DJ (which covers weddings, parties, bowling alleys, anywhere that's all about fun and entertainment).
Do I Need to Talk?
Whether you need to address your audience when you're DJing is a really good question. A lot of people become DJs because they love the music and love mixing it together, but many of them don't figure that they'll ever have to use a microphone and speak to the audience. In short, yes, you need to talk.
The mechanics of using a microphone are simple enough. Put the microphone very close to your mouth, and as you speak reduce the channel-fader of the music that's currently playing, so you can be heard over it. When you're not talking, move the microphone away from your mouth (so the audience doesn't hear you breathing at 100 decibels) and raise the channel-fader back to normal. You could be raising and lowering the fader many times in one sentence, but as long as you do it quickly, and with confidence, it's okay.
You may have a talk-over button on your mixer that does the same thing. The drop in volume of the music can be a bit sudden though, so if the sound isn't right, forget about it and use the channel-faders instead.
If you want to run a party or wedding night well, you need to get used to talking to people on the dance floor. You may be asked to introduce the bride and groom or announce that the buffet is open, so you need to be comfortable, clear and confident when you speak through the microphone. If you're a shy type, just become an actor and put on your DJ voice. If you think that your voice is a bit dull, add a little radio DJ inflection to your voice while you're talking to the partygoers. This may sound a bit forced to you, but they won't know any better (and, let's be honest, probably won't be listening). No one wants to hear you announce the buffet with nerves in your voice; they may wonder what you did to the potato salad!
What Should I Wear?
If you're a club DJ, the question of what to wear is easily answered by taking your lead from the dress code of the club you're playing and picking a comfortable version of that. I tend to wear a black T-shirt, fawn coloured jeans and Timberlands when I'm DJing. The T-shirt keeps me cool and comfortable in a hot DJ booth, and the colour of the jeans tends to fit in with most clubs' dress code. If you're doing the whole set on your feet for six hours, choose comfortable shoes.
Famous DJs can wear what they want. As they become icons though, their fashion sense can be held to scrutiny, so expect their black T-shirts to be made by a top fashion label.
If you're a wedding DJ, remember that everyone else at the wedding has made an effort. I'm not saying to turn up in a frock, tux or kilt (though it would probably be appreciated), but turn up smart, with a pressed shirt and trousers.
You're probably charging a lot of money for your service, and the reason you can charge this amount is because you're a professional DJ. Be professional and turn up smart and smiling.
How Do I Go to the Toilet?
Quickly.
If you can, try to go before you go. If you're nervous, you may be hopping on and off of the lavatory anyway, but try to make sure that any visits to the toilet are quick, and won't involve a long time sitting down (if you get what I mean).
If you're a club DJ and have an urge to purge, put on a long record, ask a trusted friend or a bouncer to stand by the decks, then get in and out as fast as you can. By trusted, I mean someone who won't think that he or she can take over while you're gone.
As a wedding DJ, however, you may be on your own. If the pressure mounts so to speak, first try to hold it in until the buffet break (if you get one). If you can't, quickly make friends with a waiter or girl/guy who you think that you can trust to look after your decks, or just make a break for it – and get back as quick as you can.
Just remember, you always have enough time to wash your hands!
No matter what type of DJ you are, the tune you put on to cover your comfort break is quite important. It has to be long enough to cover your absence, have little chance of skipping or jumping while you're gone and not be too repetitive (so the crowd doesn't get bored with it).
Worst case scenario for blokes involves peeing into a beer bottle. Not nice.
Can I Invite My Friends into the DJ Booth?
Whether you invite your friends into the DJ booth very much depends on what kind of place you're working at. If you take your girlfriend/boyfriend with you to a party as your DJ assistant to make your life easier by getting drinks and taking requests, it's probably welcomed. If you're in a club and your other half sits grumpily behind you in the DJ booth, takes up space and gets in everybody's way, the club manager may eventually ask her or him to leave the booth.
Your friends will just want to have a laugh in the DJ booth and will probably end up ripping the needle off the record, or pressing Stop on the CD decks for a lark. If you got your friends into the club for free, make them pay their way by spending most of their time on the dance floor, having the time of their lives, keeping the night looking like a huge success.
How Do I Remove the Beat, or Vocals?
How you go about completely removing the beat or vocals from a track is a tricky one. For an entire tune, currently, you can't. Sometimes, you can remove enough of the frequencies from a sample (a small section) of music so that it sounds clean enough for you to play over something else.
A friend of mine, in a band called Pacifica, did this with the 'Ooo ooo – aa aa' vocal hook from Blondie's 'Heart of Glass'. Unfortunately, even the cleanest sounding part of 'Heart of Glass' still has drums and a bass melody over it. Eventually, with patience and a good engineer using compressors, expanders, filters, EQs (equalisers) and a little voodoo magic, my friend cleaned up the sample for use in the song.
Another method is to use computer software to embrace the stereo properties of music to isolate the vocals, and only then remove unnecessary frequencies to 'tidy up' the sound. It's not a perfect science yet, but it's getting better.
When you record music, the standard procedure is that the instruments are panned left and right into a stereo signal, but the vocals remain centered in the middle. Computer software works out what's what and can remove everything that's in the centre pan (the vocals), leaving only the stereo music information, or vice-versa.
Some tunes work better than others with this method, and like everything else in DJing, it takes a lot of time and practice to get right.
The danger with both of these methods is that stereo and mono sounds and audio frequencies are mixed together through all parts of the tune. For example, some of the frequencies that make up the drum sounds and music also make up the vocal sample. So when you cut the high frequencies to remove the high-hats cymbals, you also remove all the sibilance (the ssssss sounds) from the vocal. The same applies to the bass and mid frequencies, with the end result sounding poor.
Also, the stereo image is never as clean cut as 'all music left and right – vocals in the middle'. Although the vocal will predominantly be centred, sound engineers cleverly mix the vocal into the stereo field to create better soundscapes, meaning you'll still be able to hear some of the vocal playing even after removing the centred sound.
If you do ever hear a clean vocal-only version of a tune, it's probably an a capella (vocals with no accompanying music) released by the artist, or maybe someone has recorded a very good imitation of the vocals and used that, hoping no one could tell the difference.
How Do I Choose My DJ Name?
You may decide that your own name isn't powerful enough to be displayed on a billboard (here's hoping), or perhaps you're looking for anonymity and crave a DJ name. In which case you can create a full name pseudonym (such as Bob Sinclar – real name Christophe LeFriant) or come up with a DJ name, in DJ 'Something' format, or just one name. That's why I came up with Recess, because John Steventon wouldn't look that good on the back of a bus.
When trying to pick a name think of what you do, who you are, what you play, how you play, what your other interests are, what your real name is – and see how you can mutate that to a good DJ name.
Or, if you're lazy or looking for inspiration, check out the website called Quiz Meme (www.quizmeme.com) where you type your name and it spits out a DJ name for you. I typed in John Steventon, and got DJ Flowing Cranny. I typed in Recess – and got DJ Vinyl Artist; so it must be right!
Another way to come up with a name is to mutate words. Think of ten words that you'd use to describe yourself or your music, and consider whether they (or any derivations of them) would be good. For example, if you're a deep house DJ who likes to fish you might come up with DJ Deep Lure, which you could then mutate into DJ D'Allure. Or not . . .
However, how you're commonly known is still one of the most personal ways to create your DJ name. Nicknames are a great start, but if, like in my case, you were called something stupid like 'Butter' at school, you may want to explore other avenues. Alexander Coe had the easiest name change in the world, and is now one of the most famous DJs on the planet – he could've chosen Xander, Zander, Alex Coe or anything else as his DJ name, but instead he chose Sasha (which is the Russian derivation of the similar Aleksandr), and that worked out very well for him!
In my case, Recess is bit of both. My initials are J.R.C.S. and I dropped the J to leave RCS, which mutated to Recess. (JRCS reads too much like jerks . . .)
Do I Get Free Drinks? (And How Do I Get Drinks from the Bar?)
If you're a club DJ, try to negotiate whether you get free drinks when you first speak to the owner/promoter about working at the club. The worst the promoter can say is no, and it saves any future embarrassment.
If you're well enough known as a DJ, you can submit a rider (a condition of the job) before you get to the club, demanding a case of Bud, a bottle of Jack and a bag of green Jelly Babies to be in the booth for when you start. But for local clubs and lesser known DJs, you probably find that you only get a free drink when the bar manager comes into the booth for a chat.
If you're a party DJ and you're lucky, the father of the bride, or birthday girl or boy, may offer you drinks through the night when they're having a really good time and at their happiest point – but don't count on it.
At clubs, leaving the DJ booth to head to the bar for a drink is usually a big no-no. If you don't get free drinks at a club, and no one's available to go to the bar for you, you'll probably have to go thirsty until a glass collector or a member of bar staff comes along and you can ask him or her to get a drink for you. But take a bottle of water (or whatever you think is better for you) just in case no one's kind enough to offer.
At pubs, parties and weddings, popping to the bar to buy a drink is normally okay, and if the staff know that you're the DJ (believe me, some don't) you'll probably get served really quickly.
Who Does the Lighting for the Night?
Regarding the question of who does the lighting for the night, wedding and party DJs tend to bring their own lights, as well as amps and DJing equipment, and they control the lights. When choosing lights, you may want to go for ones that have sensors in them to make them move and flash based on the sound of music (no, not the film starring Julie Andrews and some mountains). With these, all you need to do is set everything up and the lights take care of themselves. The other option is to get a compact control unit with different preset patterns to make the lights move and flash in different orders (though usually still in time with the music).
As far as clubs are concerned, I've worked in a few that had a similar pre-set lighting arrangement, except that they tend to have more lights than the wedding or party setup. However, most of the places I've worked in (and been to as a clubber) had a separate lighting jock to control the lights.
The difference that a good or bad lighting jock can make is almost as important as the music you play. Creative use of strobe lights, gobos (the rotating flashing lights) and intricate laser shows along with VJs (video jockeys), who use machines like the Pioneer DVJ-1000 to create incredible displays with video images, can really enhance the clubbing experience for the crowd.
If you strike up a good relationship with the lighting jock, and explain anything peculiar about the tunes you're playing that may help him or her work in harmony with your mix, the two of you can eventually build an incredible show together that feels like an orchestrated event. Or you can just ask him or her to get your drinks for you . . . it's your choice.
Should I Reset the Pitch to Zero After Beatmatching?
Do you reset the pitch to 0 after beatmatching one tune with another? No.
The two main reasons why you beatmatch tunes when mixing are:
To keep a constant, pounding bass beat for the clubbers to dance to
To play the music at a pace that matches the speed of the clubbers' beating hearts
If you decide that 135 BPM (beats per minute) is the perfect pace at which to play your music, and you put on a tune that plays at 130 BPM when set at 0 pitch, you need to raise the pitch control to about 4 per cent in order to get it to play at 135 BPM, and then leave it there to keep the music at 135 BPM.
Setting the pitch control back to 0 after you've beatmatched and mixed the two tunes together sounds terrible as the pitch of the music lowers (unless you're using decks with master tempo, which keeps the pitch the same no matter how fast you play the tune). And now the tune's playing at a speed that's way below the pace of the clubbers' heartbeats, so they have to dance slower and you kill the energy of the night.
The result is even worse the other way round. Imagine that you've had to reduce the tempo of a 140 BPM tune to –4 per cent. When you speed the track up by resetting the pitch to 0, you tire everyone out by the end of the tune because it's now playing at 140 BPM to a dance floor that's used to grooving at only 135 BPM!
Fluctuations in BPM as you progress through a two-hour set can be useful (refer to Chapter 18), but when you're beatmatching, you'll find you'll rarely play any of your tunes at 0 pitch.
What Do I Do If the Record or CD Skips or the Software Crashes?
You're a professional DJ. Be professional about getting around what to do if the record or CD skips or jumps. A jump on a record isn't too bad, as at least it's just a repeat of one or two seconds of music that plays through the PA, but if a CD skips it's a nasty sound, and you need to do something, instantly.
If you can't just skip to the next track on the CD, hit the Search button on the CD deck to advance five or ten seconds past the part that's skipping (lower the channel-fader at the same time to hide what you're doing).
With a record, the best thing to do is quickly lower the channel-fader to about 25 per cent of normal playout volume and knock the needle forward through the record by half a centimetre or so. Yes, this method won't sound too good, and yes, you may damage your record, but your record's already damaged if it's skipping, and it already doesn't sound good because it's repeating itself!
Prevent this sort of occurrence happening by cleaning your records or CDs before playing them (head to Chapters 4 and 7 for more on caring for your music collection).
I like to cue up the next track almost instantly after mixing into a track for this very reason, because then I have the next tune sitting there, ready to mix in quickly if something goes wrong. Sure, an emergency mix won't sound great, but how does that compare to how the music currently sounds?
If you're a digital DJ and the software crashes, it may feel as though your whole world has collapsed around you. In many cases, if you don't have any other CDs, or the CD/turntables aren't able to play without the software, the only thing you can do is reboot – quickly – and get back into the mix.
If you do have access to a CD and a CD deck that plays without needing to be fed through the computer, quickly put in the CD and press Play. You may even want to keep a CD deck with a 'safety CD' inside it, or an iPod/MP3 player hooked up to your mixer for this kind of occasion, just to give you time to reboot your system and get back up and running again.
Succeeding in anything you do, DJing or otherwise, involves skill and knowledge, but also how you cope under pressure. If you can fix a catastrophe like a skipping, damaged CD with composure and professionalism, you show all those around you that you're in control and meant to be where you are – in the DJ booth as a professional DJ.
Chapter 24
Ten Great Influences on Me
In This Chapter
Recognising what's influenced me over the years
Accepting what's made me stronger as a DJ
Losing faith, and gaining it back again
Your influences are very personal: look at the music you listen to, the people you meet and the places you go as key points in your career. With these influences, you should be able to make a map of how you developed as a DJ. This chapter describes my journey.
Renaissance: Disc 1
Renaissance – Disc 1 was my first introduction to real dance music. Until I heard this mix by Sasha and Digweed, I thought that dance music was the acid scene and pop acts such as Snap releasing repetitive, obvious music. Up until I heard this disc, all I listened to were rock bands like Van Halen and Mr Big.
Individually, the tunes on the mix are powerful, well-made pieces of work, but the way Sasha and Digweed mixed them to create a 74-minute journey has always affected me. I think that the skill it involves is the reason I've always strived to create a seamless mix that has a start, a middle and an end – rather than just 20 tunes thrown together because they sound nice.
I've always had a copy of this mix to hand since the day I first heard it. I had it on tape on my Walkman while mowing lawns, on a CD in the car when driving to college, on a MiniDisc in my pocket looking for a job and now on an iPod strapped to my arm as I go to the gym before work.
Tonsillitis
An odd choice as an influence, I agree, but as I lay in bed, ill, for a week, falling in and out of consciousness, with only Radio 1 to keep me from a fevered delirium, I was able to hear music that I'd never heard.
I'd never heard of a guy called Pete Tong, and at six o'clock on a Friday night his show started, and my eyes were opened to so many different genres of dance music. From trance to drum and bass, to American house, I lay in bed, struggling to stay awake. I'd never listened to Radio 1 during weekends, so the Essential Selection, Trevor Nelson, Dave Pearce and the Essential Mix all opened my eyes to more than just the same Renaissance CD I'd been listening to over and over again.
What started off as an accident because I was too ill to stand up and change the station (or turn on the TV) ended up as a Friday night ritual; me, Pete Tong, a piece of paper and a tape recorder to take note of the best tunes.
La Luna: 'To the Beat of the Drum'
I couldn't dance, I had long hair and I wasn't dressed very well. I spent most of the night a bit lost, standing on the stairs while everyone had fun, but what I do remember is that the very first piece of music I heard as I walked into my first dance club was La Luna's 'To the Beat of the Drum'.
The piece of music was really simple, but seeing the reaction of the people in the club, feeling the bass drum vibrating through my body and hearing dance music at this volume, in this atmosphere, for the first time unlocked something in me that left the Van Halen and Mr Big CDs unplayed for the next seven or eight years!
(A haircut and better clothes followed almost immediately.)
Ibiza 1996, Radio 1 Weekend
BBC Radio 1 has developed a tradition of broadcasting from Ibiza since 1995. This event became a solid part of Radio 1's programming, but for me, they've never done better than the 2 to 4 a.m. slot at Amnesia in July 1996. I can honestly say that the reason I became a DJ was because of the 90 minutes I could fit on tape of Sasha in the mix. So if you want anyone to blame, give him a call!
As far as a DJ set is concerned, Sasha's set was a step forward from the Renaissance mix I'd heard over and over again. Because it was in a live situation, there was an obvious gearing of the set list to working the crowd rather than appealing to a home listener on CD, and it showed me the magic of DJing – that DJing was about more than just playing other people's records.
What sold this mix to me, and still gives me goose bumps when I listen to it (which I am right now in case you're wondering) was at around the halfway point – after playing some really strong, energetic, pounding tunes, he played 'Inner City Life' by Goldie. While still keeping the energy and the tempo of the mix at a similar level, Sasha was able to completely change the dynamic of the mix with just this one tune. It was like having a rest – without having a rest!
Bringing the power back into the mix using the snare beats of a tune called 'Yummy' by Agh was the turning point for the real power of the mix. The crowd went wild, and I can't say I've heard a mix since that's affected me as much.
The Tunnel Club, Glasgow
The Tunnel Club in Glasgow was like my home for six or seven years. It still exists now, in a slightly tamer version of its past, but it still holds incredible memories for me.
The three things I'll take away from that club are the smell of dry ice and Red Bull that blasted into your face as you entered the club, the constant quality level of DJs and music that they played every weekend, but most importantly, that I met my wife Julie there – dancing with friends on the other side of the floor.
Julie's support, advice and ability to smile politely when I'm boring her with new music and new ways to mix from tune to tune has kept me striving to improve myself since the mid '90s. Because it was due to the Tunnel that we met, I can hold the club responsible for my current happiness, and position to write this book.
Jamiroquai: 'Space Cowboy'
Jamiroquai's 'Space Cowboy' was the first time I'd ever heard an original tune remixed to be something better in my eyes than the original.
I didn't know much about Jamiroquai, but did know 'Space Cowboy' when they released it as a single. I thought it was okay, but nothing special. Then David Morales gave the tune an overhaul. His remix of 'Space Cowboy' is always in my record box (mostly unplayed, unfortunately), and is always in my top ten favourite tune list.
Listening to this track was the first time I'd been able to compare the original to a remix and understand the elements needed to change a song from a good original recording to a dance remix, and have the structure and sounds that work perfectly on the dance floor.
Digital DJing
After CD DJing really took hold of the DJ market, like thousands of other DJs I moved toward this format and started leaving the dust covers on the turntables more and more often. For me, this was always with a sad reluctance. I loved what CD decks could do, and I loved the fact that it was so easy to find and remix new music and burn it to CD ready to play that night, but not using turntables to play the music left a real hole in my heart.
This all changed when I first used my turntables to control DJ software. Now I had the best of both worlds: the flexibility of any music available at the click of a mouse, but the tactile sense and the showmanship of using turntables to control the music instead of button clicks and CD trays.
I felt like a real DJ again. Each time I stepped into a DJ booth, instead of feeling apologetic for using CDs, I felt empowered and at one with the music I was playing. The combination of the strong historical foundation of turntables alongside the versatility, stability and creativity of using DJ software made me feel like I was coming home – no matter where the DJ booth was.
Alice Deejay: 'Better Off Alone'
Not all my influences have been positive ones.
I found this tune when it was just an instrumental by DJ Jurgen. It has a lovely little hook in it, and sounds great. I played it a lot, and got a good response in the pubs and clubs whenever I played it.
The problem was, someone got hold of the tune and put a vocal over it, changing the dynamic sound of the track from something that was an interesting musical piece to commercial cheese. Because I preferred the original tune I automatically disliked this vocal version, because it managed to turn a good track that I liked to play into a bad track I hated playing.
Unfortunately, everyone else loved it, so I still had to play it. The places I worked at demanded a high amount of commercial tracks on the playlist to offset any unknown, more underground sounding tracks (ironically, the track was classed as underground before getting the vocal).
This track, and several others to come, taught me that sometimes you have to play what the club and the clubbers want. Until you become a DJ with the renown and power of Tiesto, Sasha or Oakenfold, you have to follow the club's guidelines. At the beginning, DJing is all about keeping people happy, and making enough money to eat. If I'd refused to play that track, I wouldn't have been asked to return as the DJ, and I knew that the right thing to do was just keep playing the tune until the appeal wore off.
Delirium: 'Silence'
In Chapter 4, I write about falling in love with the tune 'Silence' by Delirium, playing it as often as I could, and how it still means a lot to me to listen to. But I see this tune as a double-edged sword. I see this tune as the turning point in my DJing career, when it went a bit sour. This tune wasn't directly responsible, but after 'Silence' was such a success, the market was flooded with records that were very simple, obvious, bland melodies with some woman singing over them.
Obviously, people had released records of this sort for years before 'Silence', but the success of 'Silence' opened the gates for money-grabbers who figured they could release a weak record with vocals and make some money. Which they did. Not all of them were bad; some really good vocal tracks came out of this wave. But many producers missed the point that 'Silence' was such a big success because the music was really good and stood well on its own, but more importantly, Sarah McLachlan's voice was haunting, unique and perfectly matched to the music and a club atmosphere.
Ultimately, this crossover commercialisation of the dance scene drove the good music away. The people who were buying these records started to go to the clubs that would normally play less commercial music, and they started to demand to hear what they knew. Club owners, reacting to a new voice, seeing the rise in profits with the new batch of clubbers, happily agreed. This move drove the music I loved playing deeper and deeper underground to a point that it was hard to get work playing it.
The problem with commercial trends is that by their very nature they move from fad to fad. Eventually, as each new track sounded more like the old one, the novelty of this music wore off and the clubbers moved away to R&B and nu metal. This meant that the clubs that had abandoned their old music policy needed to readjust.
Some clubs started to play heavier and heavier music, to let people into the clubs that they wouldn't have in the past or to change their music scene completely. This left music (and the club scene as a whole as I saw it) in a state of flux, leaving me a bit concerned for my future as a DJ and for the music I loved to play.
Sasha and Digweed, Miami 2002
My last key influential music moment in this chapter is the Radio 1 Essential Mix that Sasha and Digweed did in April 2002 at the Winter Music Conference in Miami, USA.
By the time I heard this mix in late 2003, I was spending more time teaching DJing than performing, because I wasn't as in love with the music as I used to be. But I did still have a soft spot in my heart for Sasha and Digweed – I still thanked them for the reason I'd started to listen to dance music in the first place. A friend had this mix on his iPod, and I asked if I could have a copy, just to hear what was going on.
Two hours later, I realised that my assumptions and prejudices about music and how the dance scene had ended up after its hyper-commercialisation were wrong in a more global view. I felt as if I was being musically reborn.
The mix was incredibly well thought out and some of the tunes were amazing (the mix from Adam Dived 'Headfirst' to Solid Session 'Janeiro' almost blew the speakers in my car I played it so loud!). This mix was the key that marked my return to this music, and to DJing – and is the reason why I'm here, writing this book.
Chapter 25
Ten DJing Mistakes to Avoid
In This Chapter
Avoiding mistakes that make you look and sound unprofessional
Leaving for the night with all your equipment and tunes, and all your money received
The ten common mistakes I describe in this chapter are exactly that: common. A couple of them may never happen to you, but, unfortunately, some may happen too often. I haven't made all the mistakes in this chapter. Most of them, yes. But not all.
What's important about the mistakes you make (in DJing or just life in general) is that you learn from them. Make sure that you don't do them again, or at the very least, make sure that you know how to cope with the consequences . . . such as the sound of silence in a club.
Forgetting Slipmats/Headphones
Forgetting your slipmats (which is an easy thing to do) isn't too much of a big deal because most clubs have their own set, but if you fail to bring your headphones, the club is unlikely to have a spare pair of quality headphones lying around for forgetful DJs to use.
Check out Chapter 26 for a checklist of ten things that you need to take with you when DJing.
Taking the Needle off the Wrong Record
Taking the needle off the wrong record is exactly the same as pressing Stop or Eject on the wrong CD player. I guarantee that at some stage in your DJ career, you'll make this mistake. Hopefully, you'll be in the sanctuary of your own bedroom, where only the cat can judge you on your error.
If you're unfortunate enough to make this mistake when DJing live in a club, put the needle back on (carefully, don't throw it back on the record in a mad panic), or quickly press Play on the CD deck. If you ejected the CD, press Play on the other deck and quickly move the cross-fader over to that channel.
Next, deflect blame like a true pro. It's probably easier to blame the sound system. You never know, someone in the crowd may be gullible enough to believe you! Then squat down to hide in the DJ booth for a couple of minutes and wait for the abuse to die down.
Banishing Mixer Setting Problems
Mixers are now available with an increasing number of functions, which unfortunately means that the chance of you forgetting to change these settings increases too.
Leaving assign controls set to the wrong channel is easily done, so when you move the cross-fader, you're fading into silence (or the wrong tune). Or you may unwittingly leave bass kills on during a mix, and it only dawns on you halfway through the tune that the bass is missing. And you can easily leave on effects like flanger or echo because you're focusing your attention on the next tune (or the girl/bloke on the dance floor). A lapse of concentration is all it takes to ruin a good mix (and sometimes your night) – so concentrate!
Getting Drunk when Playing
You need to be fully in control of your equipment but you won't be able to do that if you've had too many beers or Jack's back there in the DJ booth. Having a couple of alcoholic drinks for Dutch courage is all very well, but no one's going to think you're professional if you're so plied with booze that you can't even see the mixer in front of you and can't mix properly.
I've heard tales of DJs guzzling a case of Bud before going behind the decks, but unless you have a liver the size of a small house, if you must drink just make it a couple and then stick to water.
Surfing while Mixing
A new mistake for the digital DJ: you have a computer in front of you and you're connected to the club's wi-fi – surely it can't hurt to check a couple of emails, or update your Facebook status? Take it from me, you'll spend too long away from the mix, and either have to rush the next transition or miss the next mix altogether, leaving silence and tumbleweed on the dance floor.
Copy-cat rip
I saw a great photo in DJ magazine a few years ago of Sasha leaning across the decks so that someone from the dance floor could light his cigarette. (I actually have it as a poster above my home setup). Back in the days when I did smoke (it's not big, it's not clever and it will kill you) I thought this look was so cool, I'd try to do the same.
Not only did I receive some friendly abuse from the lighting guy while I waited for someone to oblige with a match, but when I did lean over the decks my T-shirt got caught on the needle on the record, ripping it right off. (The needle, that is, not the T-shirt.) Fortunately, it was the cued record rather than the one playing to the dance floor, but it was further compounded by me dropping the lit cigarette onto the turntable because I was so flustered by what I'd just done.
Leaning Over the Decks
As the DJ, you're the host of the evening, and you're allowed to show or receive some appreciation (handshakes and kisses on the cheeks being the best way). Just make sure you're appreciated a little to the left of the decks so that you don't bump into them or hit something on the mixer.
Avoiding Wardrobe Malfunctions
Avoiding a wardrobe malfunction is harder than you think. From jeans that are cut too low (so when you bend over to pick up a record, everyone can see your butt-cleavage) to ladies wearing a white bra under a black top so the UV lights show off their glowing chests, you'd be surprised what can go wrong.
Hats, scarves, ponchos and false beards will all eventually get tangled up in your equipment, or fall onto the decks. Wearing costumes (think Elvis costumes, gorilla outfits or Tarzan wraps) seem like a good idea in principle, but try to have a quick practice wearing them before you start mixing; your furry paws or rhinestone cuffs may turn your mixing into a nightmare.
Spending Too Long Talking to Someone
Stay professional: don't spend so long talking to a friend, potential employer or member of the opposite sex that you don't have enough time to properly cue up and mix in the next track. Even if you do have enough time to cue up the tune, don't rush the mix just so that you can go back to talking to them. And whatever you do, don't spend so long talking to someone that the record runs out completely; unless of course you want to get fired.
Leaving Your Last Tune Behind
If you're just doing part of the night and someone's taking over from you, chances are you finished your set on a really good tune, so you don't want to leave it behind. Wait until the next DJ has mixed out of your last tune, then pick up your record/CD, pack your bags and leave the booth. If you're pulled away by someone, ask the DJ to put your tune to one side and say that you'll pick it up later – at least that way he or she won't walk off with it by accident.
And digital DJs – remember to leave with your laptop . . .
Not Getting Paid Before You Leave
After a night rocking the crowd, don't leave the club before you've been paid in full. Don't fall for excuses such as 'I don't have my cheque book' or 'I don't have it all here; can I give you half now and the rest next time?'. I've fallen for this in the past (both times with club promoters whom I thought I could trust; the irony of being stung like this in a club called Pravda – Russian for truth – is still very much with me).
Every case is different, and you should know how much you can push and stand your ground with the club promoter or owner or bride and groom to demand payment. The safest thing to do is to agree on an amount before you set foot in the DJ booth (preferably on paper, signed by both you and the client). That way, you can be very persistent about making sure that you get all the money you're due.
If you don't agree on an amount before playing, though, good luck with that . . .
Chapter 26
Ten Items to Take with You When DJing
In This Chapter
Tooling up for a night of DJing
Remembering things to keep you going through the night
Getting home with your head out of the clouds
From the obvious items like your CDs, records and headphones, to the less obvious matter of taking a drink and something you can use to record your mix, the ten items I describe in this chapter are everything you need for a successful night on the decks.
Keep this list taped to the back of your door, or next to your car keys, so that you can check it over before you leave the house. (And take the list with you, so you know to bring everything back with you!)
All the Right Tunes
You may have thousands of records or CDs in your collection. Make sure that you're taking the right ones with you. Checking for one last time that you've picked up the right box or CD wallet won't hurt! Also take a carbon brush to clean your records, and a soft cloth for CDs.
If you're a digital DJ you need your computer (normally a laptop), or an external drive that contains all your music if you're using a club's installation (remember to check that they use the same software as you, though!).
If you're taking your laptop, boot it up before you leave and make sure it still works and that all the music is stored on it (not left on an external drive). Remember power cables, audio interfaces and controllers/control vinyl if you use them too.
Making It Personal with Headphones and Slipmats
Have a last check to make sure that your headphones still work and that you take any adaptors you need to make them work. If you use headphones that you can repair with spare parts (like the Sennheiser HD25s), take your bag of tools and spares.
Put your slipmats between some records in the record box so they stay flat and undamaged. Just remember to take them back at the end of the night!
Using your own slipmats prevents any problems with fluffy, thick, dirty slipmats that a club may use. You'll have become accustomed to how slippy your own slipmats are on a set of Technics 1210s. Basic slipmats on a club's set of decks may create a lot of drag, and even worse, may damage your records due to dirt and crusted beer spillages.
You're a Star! Taking a Digital Recorder/Blank CD
Make the most of every opportunity by recording yourself in the mix, which is especially helpful at the start of your career. You'll benefit dramatically because you can study your performance and improve on it. If a club doesn't have any means to record the mix (check beforehand), take along something you can use to record your mix so you can take away evidence that you rocked the crowd!
Packing Your Tools and Saving the Day
Any homeowner knows that the only tools you need are WD-40 and duct tape. But if you want to get fancy, throw some differing sized and shaped screwdrivers into a bag too, because you never know when you may need a Phillips-head screwdriver to save the day.
Always Being Prepared: Pen and Paper
Not just for taking phone numbers of good-looking clientele, you need a pen and paper for taking requests, sending drinks orders to the bar and swapping phone numbers with people who want to book you.
Keeping Fuelled with Food and Drink
Unfortunately, you're not there to have a picnic; you've got a job to do. But take some sustenance to keep you going in case your body needs fuel.
Contrary to popular belief, you don't have to put vodka into your Red Bull or Irn-Bru 32. Keep one or two cans of your chosen energy drink with you, and if you start to flag halfway through the night, drink one for the caffeine fix.
Be warned, though, that some people don't react well to the sudden hit of caffeine. So trying an energy drink in the middle of a set in front of 1,000 people isn't the best time to find out whether your body likes caffeine and guarana!
In addition to an energy drink, you also need to take something to eat in case you get hungry. Hunger leads to bad moods, which can make you lose your concentration, and you won't be as attentive to the crowd's needs. Wine gums and jelly babies give you a quick sugar fix, and they contain almost no fat. Eating an energy bar gives you a better range of nutrients and fills you up for longer, but it has a larger fat content and does run the risk of tasting like cardboard.
Spreading the Music with Demos
Nothing beats someone asking for a copy of your work after hearing you play in a club. Nothing's worse than not having one with you. Take a few CDs of your most recent mix (check out Chapter 19 for tips on how to create the best-sounding and best-looking CD) and hand them out with a big smile on your face.
A few examples of your best work are also really handy if someone wants to book you for a night somewhere. If you give people a great mix to take away, they won't forget about you – just remember to include your phone number!
Keeping Moving with Car Keys
You're not going to get far without your car keys. I've spent many an evening standing at the boot of the car, head in hands in disbelief that I left my keys behind again! Okay if you're just leaving your house, but not okay if they're in your jacket pocket, in the locked-up club in which you've just played.
Have Wallet, Will Travel
You never know when you'll need a little cash, either for taxis home (because you left your car keys behind) or just to go grab some chow after your set.
If you have a few business cards, keep them in your wallet or purse, on hand to give out when you need to do some self-promotion.
Just Chilling: Chill Mix for the Ride Home
Sometimes, I finish my set at four o'clock in the morning, and am in no mood to keep the buzz going by listening to more pumping tunes on the way home. So I keep a copy of the soundtrack to the film The Big Blue in my car for such occasions. It contains some of the most fantastic pieces of music I've heard in a long time. My wife Julie worries about the music sending me to sleep on the drive home, but all it does is take the edge off the natural high I've got from an evening of energy and musical rapture (but it doesn't do much about the caffeine rush I have due to one too many of those energy drinks!).
I recommend the film too . . .
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\section{Introduction \label{sec:Introduction}}
The determination of collinear parton distribution functions (PDFs)
of the nucleon is becoming an increasingly precise discipline with
the advent of high-luminosity experiments at both colliders and fixed-target
facilities. Several research groups are involved in the rich research
domain of the modern PDF analysis \cite{Dulat:2015mca,Harland-Lang:2014zoa,Ball:2017nwa,Alekhin:2017kpj,Accardi:2016qay,Abramowicz:2015mha,Alekhin:2014irh}.
By quantifying the distribution of a parent hadron's longitudinal
momentum among its constituent quarks and gluons, PDFs offer both
a description of the hadronic structure and an essential ingredient
of perturbative QCD computations. PDFs enjoy a symbiotic relationship
with high-energy experimental data, in the sense that they are crucial
for understanding hadronic collisions in the Standard Model (SM) and
beyond, while reciprocally benefiting from a wealth of high-energy
data that constrain the PDFs. In fact, since the start of the Large
Hadron Collider Run II (LHC Run II), the volume of experimental data
pertinent to the PDFs is growing with such speed that keeping pace
with the rapidly expanding datasets and isolating measurements of
greatest impact presents a significant challenge for PDF fitters.
This paper intends to meet this challenge by presenting a method for
identifying high-value experiments which constrain the PDFs and the
resulting SM predictions that depend on them.
That such expansive datasets can constrain the PDFs is a consequence
of the latter's universality \textemdash{} a feature which relies
upon QCD factorization theorems to separate the inherently nonperturbative
PDFs (at long distances) from process-dependent, short-distance matrix
elements. For instance, the cross section for inclusive single-particle
hadroproduction (of, \textit{e.g.}, a weak gauge boson $W/Z$) in
proton-proton collisions at the LHC is directly sensitive to the nucleon
PDFs via an expression of the form
\begin{align}
& \sigma(AB\rightarrow W/Z\!+\!X)\ =\ \sum_{n}\,\alpha_{s}^{n}(\mu_{R}^{2})\,\sum_{a,b}\int dx_{a}dx_{b}\,\label{eq:fact}\\
& \times\,f_{a/A}(x_{a},\mu^{2})\,\hat{\sigma}_{ab\rightarrow W/Z+X}^{(n)}\big(\hat{s},\,\mu^{2},\mu_{R}^{2}\big)\,f_{b/B}(x_{b},\mu^{2})\ ,\nonumber
\end{align}
in which $f_{a/A}(x_{a},\mu^{2})$ represents the PDF for a parton
of flavor $f_{a}$ carrying a fraction $x_{a}$ of the 4-momentum
of proton $p_{A}$ at a factorization scale $\mu$; the $n^{\mathit{th}}$-order
hard matrix element is denoted by $\hat{\sigma}_{ab\rightarrow W/Z+X}^{(n)}\big(\hat{s},\,\mu^{2},\mu_{R}^{2}\big)$
and is dependent upon the partonic center-of-mass energy $\hat{s}=x_{a}x_{b}s$,
in which $s$ in the center-of-mass energy of the initial hadronic
system; and $\mu_{R}$ is the renormalization scale in the QCD coupling
strength $\alpha_{s}(\mu_{R})$. In Eq.~(\ref{eq:fact}), subleading
corrections $\sim\!\!\Lambda^{2}/M_{W/Z}^{4}$ have been omitted,
and we emphasize that factorization theorems like Eq.~(\ref{eq:fact})
have been proved to arbitrary order in $\alpha_{s}$ for essential
observables in the global PDF analysis, such as the inclusive cross
sections in DIS and Drell-Yan processes. For compactness and generality,
we shall refer henceforth to a PDF for the parton of flavor $f$ simply
as $f(x,\mu)$.
Given this formalism, one is confronted with the problem of finding
those experiments that provide reliable new information about the
PDF behavior. With the proliferation of potentially informative new
data, incorporating them all into a global QCD fit inevitably incurs
significant cost both in terms of computational resources and required
fitting time. Indeed, tremendous progress in the precision of PDFs
and robustness of SM predictions is driven by the technology for performing
global analysis that has vastly grown in complexity and sophistication.
Nowadays, the state-of-the-art in perturbative QCD (pQCD) treatments
are done at NNLO (and increasingly even N$^{3}$LO), and advanced
statistical techniques are commonly employed in PDF error estimation.
The magnitude of this subject is vast, and we refer the interested
reader to Refs.~\cite{Gao:2017yyd,Butterworth:2015oua} for comprehensive
reviews. The tradeoff of this progress is that the impact of an experiment
on the ultimate PDF uncertainty is often hard to foresee without doing
a complicated fit. Various publications claim sensitivity of
new experiments to the PDFs. In this paper, we look into these claims
using statistical techniques that bypass doing the fits,
and with an eye on theoretical, experimental, and methodological components
relevant at the NNLO precision.
The potential cost is steepened by the large size of the global datasets
usually involved. This point can be seen in Fig.~\ref{fig:data},
which plots the default dataset considered in the present analysis
in a space of partonic momentum fraction $x$ and factorization scale
$\mu$. We label these data as the ``CTEQ-TEA set,'' given that
it is an extension of the 3287 raw data points (given by the sum over
$N_{\mathit{pt}}$ in Tables~\ref{tab:EXP_1} and \ref{tab:EXP_2}) treated
in the NNLO CT14HERA2 analysis of Ref.~\cite{Hou:2016nqm}, now augmented
by the inclusion of 734 raw data points (given by the sum over $N_{\mathit{pt}}$
in Table~\ref{tab:EXP_3}) from more recent LHC data. These raw measurements
can ultimately be mapped to 5227 typical $\{x,\mu\}$ values
in Fig.~\ref{fig:data}, such that each symbol corresponds to a data point from
an experiment shown in the legend, at the approximate $x$ and $\mu$
values characterizing the data point as described in Appendix~\ref{sec:supp}.
The experiments are labeled by a short-hand name which includes the
year of final publication ({\it e.g.}, ``HERAI+II'15'' --- corresponding to the
2015 combined HERA Run I and Run II data),
following the translation key also given in Tables~\ref{tab:EXP_1}\textendash \ref{tab:EXP_3}
of App. \ref{sec:Tables}. The experiments included in the CT14HERA2
analysis are listed in the left column and upper part of the right column of the legend, while
the newer LHC data considered for the upcoming CTEQ-TEA analysis are the last 14
entries of the right column.
\begin{figure*}
\includegraphics[width=1\textwidth]{figs/xQbyexpt_xQ_replot.pdf}
\caption{A graphical representation of the space of $\{x,\mu\}$ points probed
by the full dataset treated in the present analysis, designated as
``CTEQ-TEA''. It represents an expansion to include newer LHC data of the CT14HERA2 dataset
\cite{Hou:2016nqm} fitted in the most recent CT14 framework \cite{Dulat:2015mca},
which involved measurements from Run II of HERA \cite{Abramowicz:2015mha}.
Details of the datasets corresponding to the short-hand names given in the legend
may be found in Tables~\ref{tab:EXP_1}--\ref{tab:EXP_3}.
}
\label{fig:data}
\end{figure*}
The growing complexity of PDF fitting stimulates development of
less computationally involved approaches to estimate the
impact of new experimental data on full global fits, such as Hessian
profiling techniques \cite{Camarda:2015zba} and Bayesian reweighting
\cite{Ball:2010gb,Ball:2011gg} of PDFs. Although these approaches
do simulate the expansion of a particular global fit
by including theretofore absent dataset(s), they are also limited in
that the interpretation of their outcomes is married to the specific
PDF parametrization and definition of PDF errors. For example, conclusions
obtained by PDF reweighting regarding the importance of a given data
set strongly depend on the assumed statistical tolerance or the choice
of reweighting factors \cite{Sato:2013ika,Paukkunen:2014zia}.
Parallel to these efforts, the notion of using correlations between
the PDF uncertainties of two physical observables was proposed in
Refs.~\cite{Pumplin:2001ct,Nadolsky:2001yg} as a means of quantifying
the degree to which these quantities were related based upon their
underlying PDFs. The PDF-mediated correlation $C_{f}$ in this case,
which we define in Sec.~\ref{sec:Correlations}, embodies
the Pearson correlation coefficient computed by a generalization of
the ``master formula'' \cite{Pumplin:2002vw} for the Hessian PDF
uncertainty. The Hessian correlation was deployed extensively in Ref.~\cite{Nadolsky:2008zw}
to explore implications of the CTEQ6.6 PDFs for envisioned LHC observables.
It proved to be instrumental for identifying the specific PDF flavors
and $x$ ranges most correlated with the PDF uncertainties for $W,$
$Z,$ $H$, and $t\bar{t}$ production cross sections as well as other
processes. The Pearson correlation coefficient has also
proven to be informative in the approach based on Monte-Carlo PDF replicas,
see, e.g., Refs.~\cite{Ball:2008by,Carrazza:2016htc}.
However, the PDF-mediated correlation with a theoretical
cross section is only partly indicative of the sensitivity of the
experiment. The constraining power of the experiment also depends
on the size of experimental errors that were not normally considered
in correlation studies, as well as on correlated systematic effects
that are increasingly important.
As a remedy to these limitations, we introduce a new format for the
output of CTEQ-TEA fits and a natural extension of the correlation
technique to quantify the sensitivity of any given experimental data
point to a PDF-dependent observable of the user's choice. In this
approach, we work with \emph{statistical residuals} quantifying the
goodness-of-fit to individual data points. We demonstrate that the
complete set of residuals computed for Hessian PDF sets characterizes
the CTEQ-TEA fit well enough to permit a means of gauging the influence
of empirical information on PDFs in a fashion that does not require
complete refits.
A generalization of the PDF-mediated correlations called
the \textit{sensitivity $S_{f}$} \textemdash{} to be characterized
in detail in Sec.~\ref{sec:Sensitivities} \textemdash{}
better identifies those experimental data points that tightly
constrain PDFs both by merit of their inherent precision and their
ability to discriminate among PDF error fluctuations. Such an approach
aids in identifying regions of $\{x,\mu\}$ for which PDFs are
particularly constrained by physical observables.
\begin{figure*}
\includegraphics[width=0.47\textwidth]{figs/corr_xQ+1_f8_samept_replot.pdf}\ \ \
\includegraphics[width=0.47\textwidth]{figs/corrdr_xQ+1_f8_samept_replot.pdf}
\caption{
For the full CTEQ-TEA dataset of Fig.~\ref{fig:data}, we show the
absolute correlation $|C_{f}|$ and sensitivity $|S_{f}|$ associated
with the 14 TeV Higgs production cross section $\sigma_{H^{0}}(14\,\mathrm{TeV})$.
310 input data points with most significant magnitudes of $|C_{f}|$
and $|S_{f}|$ are highlighted with color.
When only the $|C_{f}|$ plot is considered, only a very small
subpopulation of jet production data (diagonal open circles and closed squares
with $\mu\gtrsim100$ GeV) exhibits significant correlations with
$|C_f|>0.7$ (orange and red colors),
as well as some HERA DIS, high-$p_T$ $Z$ boson, and $t\bar{t}$ production data points.
Our novel definition for the sensitivity in the right panel, on the other
hand, reveals more points that have comparable potency for constraining
the Higgs cross section. In this case, a larger fraction of the jet production
points is important (especially CMS measurements of CMS8jets'17 and CMS7jets'14),
as well as a number of other processes at smaller $\mu$, particularly
DIS data from HERA, BCDMS, NMC, CDHSW, and CCFR (experiments HERAI+II'15, BCDMSd'90,
NMCrat'97, CDHSW-F2'91, CCFR-F2'01, CCFR-F3'97). Although its cumulative impact
is comparatively modest, ATLAS $t\bar{t}$
production data (ATL8ttb-pt'16, ATL8ttb-y\_ave'16, ATL8ttb-mtt'16, ATL8ttb-y\_ttb'16)
register significant per-point sensitivities, as do E866 $pp$ Drell-Yan pair production
(E866pp'03), LHCb $W, $Z production (LHCb7ZWrap'15, LHCb8WZ'16), and charge lepton
asymmetries at D0 and CMS (D02Masy'08, CMS7Masy2'14, CMS7Easy'12). Similarly,
some of the high-$p_T$ $Z$ production information (ATL7ZpT'14, ATL8ZpT'16)
from ATLAS provide modest constraints.
\label{fig:CorrSensH14}}
\end{figure*}
In fact, in the numerical approach presented in the forthcoming sections,
the user can quantify the sensitivity of data not only to individual
PDF flavors, but even to specific physical observables, including
the modifications due to correlated systematic uncertainties in every
experiment of the CT14HERA2 analysis. For example, for Higgs boson
production via gluon fusion ($gg\rightarrow H$) at the LHC 14 TeV, the short-distance
cross sections are known up to N$^{3}$LO with a scale uncertainty
of about 3\% \cite{Anastasiou:2016cez}. It has been suggested that
$t\bar{t}$ production and high-$p_{T}$ $Z$ boson production on their own
constrain the gluon PDF in the $x$ region
sensitive to the LHC Higgs production, and that these are comparable to the
constraints from LHC and Tevatron data \cite{Czakon:2016olj,Boughezal:2017nla}.
Verifying the degree to which this hypothesis is true has been difficult
without actually including all these data in a fit.
As an alternative to doing a full global fit, we can critically assess
this supposition in the context of the entire global dataset
of Fig.~\ref{fig:data} using the Hessian correlations and sensitivities,
$|C_{f}|$ and $|S_{f}|$.
The detailed procedure is explained in Secs.~\ref{sec:Correlations} and \ref{sec:Sensitivities}.
In the example at hand, we could rely on the established wisdom that
the theoretical cross sections that have an especially large correlation
with $\sigma_{H^{0}}$ may constrain the PDF dependence of
$\sigma_{H^{0}}$; say, when $|C_f|\gtrsim 0.7$ \cite{Nadolsky:2008zw}.
Along this reasoning, the left frame in Fig.~\ref{fig:CorrSensH14}
illustrates 310 experimental data points in $\{x,\mu\}$ space
that have the highest absolute correlation, $|C_{f}|$, between the point's
statistical residual defined in
Sec.~\ref{sec:Correlations} and the cross section
$\sigma_{H^{0}}$ at 14 TeV via the CT14HERA2 NNLO PDFs.
To locate such points in the figure,
we highlighted them with color according to
the convention shown on the color scale to the right.
The respective $|C_f|$ for the highlighted data points ranges between
0.42 and 1. The rest of the data points have smaller correlations and are
shown in gray.
We find that the 310 data points with the highest correlation
for $\sigma_{H^{0}}$ belong to 20 experiments. Nearly all of them
are contributed by HERA Neutral Current (NC) DIS,
LHC and Tevatron jet production, and HERA charm production.
Some of the data points with highest $|C_f|$ come from high-$p_T$ $Z$ boson
and even $t\bar t$ production.
The correlations $C_f$, however, do not reflect the experimental
uncertainties, which vary widely across the experiments.
In the left panel of Fig.~\ref{fig:CorrSensH14},
fewer than 30 points have a strong correlation of $0.7$ or more; but
more data points impose relevant constraints in the global fit.
To
include the information about the uncorrelated and correlated
experimental errors, in the right panel
of Fig.~\ref{fig:CorrSensH14}, we plot the distributions of 310 data
points with the highest sensitivity parameter $S_f$, which more faithfully
reproduces the actual constraints during the fitting.
In general, we find substantial differences between the
$C_f$ and $S_f$ distributions. Even the most significant correlations,
of order $|C_{f}| \sim 0.7$ and above, do not guarantee a significant
contribution of the experimental point to the log-likelihood
$\chi^2$ if the errors are large. On the other hand,
we argue that $|S_f|$ is closely related to a
contribution of the data point to $\chi^2$. According to the
distribution in the right figure, the 310 data points with the highest
sensitivity $|S_f|$ to $\sigma_{H^0}(\mbox{14 TeV})$ arise from 27
experiments. Among these data points, only some have
a large correlation $|C_f|$ with
$\sigma_{H^0}(\mbox{14 TeV})$. Nonetheless, they have medium-to-large
sensitivity, $|S_f| > 0.21$, according to the criterion developed
in Sec.~\ref{sec:Sensitivities}.
We stress that, while one might suggests plausible dynamical reasons why
certain experiments might be particularly sensitive to Higgs production via
the gluon PDF, ({\it e.g.}, via the leading-order $qg$ and $gg$
hard cross sections in jet production and DGLAP scaling violations in
inclusive DIS), this reasoning alone does not predict the actual
sensitivity revealed by $S_f$ in the presence of multiple experimental
constraints.
As one noticeable difference from the $|C_f|$ figure,
while inclusive DIS at HERA continues to
contribute a large number of data points (about 80) with a high
$|S_f|$, also the fixed-target DIS experiments (BCDMS, NMC, CDHSW,
CCFR) contribute about the same number of sensitive points in the
right panel that were not identified by large correlations. Other sensitive
points belong to the jet production
data sets from ATLAS and CMS and some vector boson production
experiments (muon charge asymmetries at D0, CMS;
E866 low-energy Drell-Yan production; LHCb 7 TeV $W$ and $Z$ cross
sections).
On the other
hand, HERA charm production, ATLAS 7/8 TeV high-$p_T$ $Z$ production,
have suppressed sensitivities despite their large correlations,
reflecting the larger experimental uncertainties in these measurements.
While the LHC $t\bar t$ production experiments have large per-point
sensitivities, they contribute relatively little to $\chi^2$ because
of their small total number of data points. From this comparison,
one finds, perhaps somewhat unexpectedly, that fixed-target DIS
experiments impose important constraints on $\sigma_{H^0}(\mbox{14
TeV})$, thus complementing the HERA inclusive DIS data.
One would conclude that efforts to constrain PDF-based SM predictions
for Higgs production by relying only on a few points of $t\overline{t}$
data, but to the neglect of high-energy jet production points, would
be significantly handicapped by the absence of the latter. We will
return to this example in Sec.~\ref{sec:CaseCTEQ-TEA}.
The discriminating power of a sensitivity-based analysis
therefore forms the primary motivation
for this work, and we present the attendant details below. To assess
information about the PDFs encapsulated in the residuals for large
collections of hadronic data implemented in the CTEQ-TEA global analysis,
we make available a new statistical package \textsc{PDFSense} to map
the regions of partonic momentum fractions $x$ and QCD factorization
scales $\mu$ where the experiments impose strong constraints on the
PDFs. In companion studies,
we have applied \textsc{PDFSense} to select new data sets
for the next generation of the
CTEQ-TEA global analysis, to quantitatively explore the physics
potential for constraining the PDFs at a future
Electron-Ion Collider (EIC) \cite{Accardi:2012qut,Boer:2011fh,Abeyratne:2012ah,Aschenauer:2014cki}
and Large Hadron-Electron Collider (LHeC) \cite{AbelleiraFernandez:2012cc}, and to investigate the
potential of high-energy data to inform lattice-calculable
quantities \cite{Lin:2017snn} like the Mellin moments of structure functions \cite{Gockeler:1995wg} and quark quasi-distributions \cite{Ji:2013dva}.
We reserve many instructive results for follow-up publications currently in preparation,
while presenting select calculations in this article to demonstrate the power of the method. We find that the
sensitivity technique generally agrees with the preliminary
CTEQ-TEA fits and Hessian reweighting realized in the \textsc{ePump} program
\cite{Schmidt:2018hvu}. However, assessing the sensitivity is much
simpler than doing the global fit. It does not require access to a fitting
program or the application of (potentially subtle) PDF reweighting techniques.
The remainder of the article proceeds as follows. Pertinent aspects
of the PDFs and their standard determination via QCD global analyses
are summarized in Sec.~\ref{sec:PDF-preliminaries}. Then,
we introduce {\it normalized residual variations} to extract,
visualize, and quantify statistical information about the global QCD
fit. In Sec.~\ref{sec:QuantifyingDistributionsOfResiduals}, we
construct a number of statistical quantities that
characterize the PDF constraints in the global analysis using the
residual variations. In Sec.\ \ref{sec:CaseCTEQ-TEA}, we apply
the thus constructed sensitivity parameter
to examine the impact of various CTEQ-TEA datasets
on extractions of the gluon PDF $g(x,\mu)$. In this section and
in the conclusion contained
in Sec.\ref{sec:Conclusions}, we emphasize a number of {\it physics insights}
that we obtained by applying our sensitivity analysis techniques. Additional
aspects of the technique and supplementary tables are reserved for
Apps.~\ref{sec:supp}, \ref{sec:Tables}, and \ref{sec:SM}.
\section{PDF preliminaries \label{sec:PDF-preliminaries}}
\subsection{Data residuals in a global QCD analysis \label{sec:Data-residuals}}
While various theoretical models exist for computing nucleon PDFs
\cite{Farrar:1975yb,Hobbs:2014lea,Hobbs:2013bia},
unambiguous evaluation of the PDFs entirely in terms of
QCD theory is not yet possible due to the fact that the PDFs can in
general receive substantial nonperturbative contributions at infrared
momenta. For this reason, precise PDF determination has proceeded
mainly through the technique of the QCD global analysis \textemdash{}
a method enabled by QCD factorization and PDF universality.
In this approach, a highly flexible parametric form is ascribed for
the various flavors in a given analysis at a relatively low scale
$Q_{0}^{2}$. For example, one might take the input PDF for a given
quark flavor $f$ to be a parametric form
\begin{equation}
f(x,\mu^{2}=Q_{0}^{2})=A_{f,0}\,x^{A_{f,1}}(1-x)^{A_{f,2}}\,F(x;\,A_{f,3},\dots)\ ,\label{eq:fitform}
\end{equation}
in which $F(x;\:A_{f,3},\dots)$ can be a suitable polynomial function,
\textit{e.g.}, a Chebyshev or Bernstein polynomial, or replaced with
a feed-forward neural network $\mathrm{NN}_{f}(x)$ as in the NNPDF
approach. While the full statistical theory for PDF determination
and error quantification is beyond the intended range of this analysis,
roughly speaking, a best fit is found for a vector $\vec{A}$ of $N$
PDF parameters $A_{l}$ by minimizing a goodness-of-fit function $\chi^{2}$
describing agreement of the QCD data and physical observables computed
in terms of the PDFs. Based on the behavior of $\chi^{2}$ in the
neighborhood of the global minimum, it is then possible to construct
an ensemble of error PDFs to quantify uncertainties of PDFs at a predetermined
probability level.
There are various ways to evaluate uncertainties on PDFs,
\emph{e.g.}, the Hessian \cite{Pumplin:2001ct,Pumplin:2002vw},
the Monte Carlo \cite{Giele:1998gw,Giele:2001mr}, and the
Lagrange Multiplier approaches \cite{Stump:2001gu}. In this analysis
our default PDF input set is CT14HERA2, which uses the Hessian method
to estimate uncertainties and is therefore based on the quadratic
assumption for $\chi^{2}(\vec{A}$) in the vicinity of the global
minimum. In the Hessian method, an orthonormal basis of PDF parameters
$\vec{a}$ is derived from the input PDF parameters $\vec{A}$ by
the diagonalization of a Hessian matrix $H$, which encodes the second-order
derivatives of $\chi^{2}$ with respect to $A_{l}$. The eigenvector
PDF combinations $\vec{a}_{l}^{\pm}$ are found for two extreme variations
from the best-fit vector $\vec{a}_{0}$ along the direction of the
$l^{th}$ eigenvector of $H$ allowed at a given probability level.
The uncertainty on a QCD observable $X$ can then be estimated with
one of the available ``master formulas'' \cite{Pumplin:2002vw,Nadolsky:2001yg},
the ``symmetric'' variety of which is
\begin{align}
\Delta X & =\frac{1}{2}\sqrt{\sum_{l=1}^{N}(X_{l}^{+}-X_{l}^{-})^{2}}\ .\label{DelX}
\end{align}
In the CTEQ-TEA global analysis, the $\chi^{2}$ function accounts
for multiple sources of experimental uncertainties, as well as for
some prior theoretical constraints on the $a_{l}$ parameters. Consequently,
the global $\chi^{2}$ function takes the form
\begin{equation}
\text{\ensuremath{\chi}}_{global}^{2}=\sum_{E}\chi_{E}^{2}+\chi_{th}^{2}\ ,
\label{eq:chi2glob}
\end{equation}
where the sum runs over all experimental datasets $(E);$ and $\chi_{th}^{2}$
imposes theoretical constraints. The complete formulas for $\chi_{E}^{2}$
and $\chi_{th}^{2}$ can be found in Ref.~\cite{Gao:2013xoa}. For
the purposes of this paper, we express $\chi_{E}^{2}$ for each experiment
$E$ in a compact form as a sum of squared\emph{ shifted residuals}
$r_{i}^{2}(\vec{a})$, which are summed over $N_{\mathit{pt}}$ individual
data points $i$ in this experiment, as well as the contributions
of $N_{\lambda}$ best-fit nuisance parameters $\overline{\lambda}_{\alpha}$
associated with correlated systematic errors:
\begin{align}
\chi_{E}^{2}(\vec{a}) & =\sum_{i=1}^{N_{\mathit{pt}}}\,r_{i}^{2}(\vec{a})+\sum_{\alpha=1}^{N_{\lambda}}\overline{\lambda}_{\alpha}^{2}(\vec{a})\ .\label{eq:chi2}
\end{align}
In turn, $r_{i}(\vec{a})$ for the $i^{th}$ data point is constructed
from the theoretical prediction $T_{i}(\vec{a})$ evaluated in terms
of PDFs, total uncorrelated uncertainty $s_{i}$, and the shifted
central data value $D_{i,sh}(\vec{a})$:
\begin{align}
r_{i}(\vec{a}) & =\frac{1}{s_{i}}\,\big(T_{i}(\vec{a})-D_{i,\mathit{sh}}(\vec{a})\big)\ .\label{eq:residual}
\end{align}
This representation arises in the Hessian formalism due to the presence
of correlated systematic errors in many experimental datasets, which
require $\chi_{E}^{2}$ to depend on nuisance parameters $\lambda_{\alpha}$.
This is in addition to the dependence of $\chi_{E}^{2}$ on the PDF
parameters $\vec{a}$ and theoretical parameters such as $\alpha_{s}(M_{Z})$
and particle masses. The $\lambda_{\alpha}$ parameters are optimized
for each $\vec{a}$ according to the analytic solution derived in
Appendix B of Ref.~\cite{Pumplin:2002vw}. Optimization effectively
shifts the central value $D_{i}$ of the data point by an amount determined
by the optimal nuisance parameters $\overline{\lambda}_{\alpha}(\vec{a})$
and the correlated systematic errors $\beta_{i\alpha}:$
\begin{equation}
D_{i}\rightarrow D_{i,\mathit{sh}}(\vec{a})=D_{i}-\sum_{\alpha=1}^{N_{\lambda}}\beta_{i\alpha}\overline{\lambda}_{\alpha}(\vec{a})\ .
\end{equation}
It should be noted that the contribution of the squared best-fit nuisance
parameters to $\chi_{E}^{2}$ in Eq.~(\ref{eq:chi2}) is dominated
in general by the first term involving the shifted residuals, which
tends to be much larger \textemdash{} especially for more sizable
datasets.
We point out also that some alternative representations for $\chi^{2}$
include the correlated systematic errors via a covariance matrix $\left(\mbox{cov}\right)_{ij}$,
rather than the above mentioned CTEQ-preferred form that explicitly
operates with $\lambda_{\alpha}$. Various $\chi^{2}$ definitions
in use are reviewed in \cite{Ball:2012wy}, as well as in \cite{Alekhin:2014irh}.
Crucially, however, the representations based upon operating with
$\lambda_{\alpha}$ and $\left(\mbox{cov}\right)_{ij}$ are derivable
from each other \cite{Gao:2013xoa}. From an extension of the derivation
in Ref.~\cite{Pumplin:2002vw}, we may relate the shifted residual
to the covariance matrix at an $i^{th}$ point and optimal nuisance
parameters as
\begin{align}
r_{i}(\vec{a})\ & =\ s_{i}\sum_{j=1}^{N_{\mathit{pt}}}(\mathrm{cov}^{-1})_{ij}\,\left(T_{j}(\vec{a})-D_{j}\right),\label{eq:res-cov}\\
\overline{\lambda}_{\alpha}(\vec{a}) & =\sum_{i,j=1}^{N_{\mathit{pt}}}(\mathrm{cov}^{-1})_{ij}\frac{\beta_{i\alpha}}{s_{i}}\frac{\left(T_{j}(\vec{a})-D_{j}\right)}{s_{j}},
\end{align}
where
\begin{equation}
(\mathrm{cov}^{-1})_{ij}\ =\ \left[\frac{\delta_{ij}}{s_{i}^{2}}\,-\,\sum_{\alpha,\beta=1}^{N_{\lambda}}\frac{\beta_{i\alpha}}{s_{i}^{2}}A_{\alpha\beta}^{-1}\frac{\beta_{j\beta}}{s_{j}^{2}}\right]\ ,\label{eq:covmat}
\end{equation}
and
\begin{equation}
A_{\alpha\beta}\ =\ \delta_{\alpha\beta}\,+\,\sum_{k=1}^{N_{\mathit{pt}}}\frac{\beta_{k\alpha}\beta_{k\beta}}{s_{k}^{2}}\ .
\end{equation}
Thus, even for those PDF analyses which operate with the covariance
matrix one is still able to determine the shifted residuals $r_{i}$
from $\left(\mbox{cov}^{-1}\right)_{ij}$ using Eq.~(\ref{eq:res-cov}).
In this article, we conveniently follow the CTEQ methodology and obtain
$r_{i}(\vec{a})$ directly from the CTEQ-TEA fitting program, together
with the optimal nuisance parameters $\overline{\lambda}_{\alpha}(\vec{a})$
and shifted central data values $D_{i,sh}(\vec{a}).$
\subsection{Visualization of the global fit with the help of residuals}
The shifted residuals $r_{i}$ draw our interest because, in consequence
of the definitions in Eqs.~(\ref{eq:chi2})-(\ref{eq:residual}),
they contain substantial low-level information about the agreement
of PDFs with every data point in the global QCD fit in the presence
of systematic shifts. The response of $r_{i}(\vec{a})$ to the variations
in PDFs depends on the experiment type and kinematic range associated
with the $i^{th}$ data point, and the totality of these responses
can be examined with modern data-analytical methods. The sum of squared
residuals over all points of the global dataset renders the bulk
of the log-likelihood, or experimental, component $\chi_{E}^{2}$
of the global $\chi^{2}$. In turn, the root-mean-squared residual
$\langle r_{0}\rangle_{E}$ for experiment $E$ and the central PDF
set $\vec{a}_{0}$ is tied to $\chi_{E}^{2}(\vec{a}_{0})/N_{\mathit{pt}},$
the standard measure of agreement with experiment $E$ at the best
fit:
\begin{equation}
\langle r_{0}\rangle_{E}\equiv\sqrt{\frac{1}{N_{\mathit{pt}}}\sum_{i=1}^{N_{\mathit{pt}}}r_{i}^{2}(\vec{a}_{0})}=\sqrt{\frac{1}{N_{\mathit{pt}}}\left(\chi_{E}^{2}(\vec{a}_{0})-\sum_{\alpha=1}^{N_{\lambda}}\overline{\lambda}_{\alpha}^{2}(\vec{a_{0}})\right)}\approx\sqrt{\frac{\chi_{E}^{2}(\vec{a}_{0})}{N_{\mathit{pt}}}}.\label{r0E}
\end{equation}
Notice that $\langle r_0 \rangle_E \approx 1$ when the fit to the experimental data set $E$ is good.
We will now invoke the Hessian formalism to first organize the analysis
of the PDF dependence of individual residuals, and then introduce
a framework to evaluate sensitivity of individual data points to PDF-dependent
physical observables. To test the effectiveness of the proposed method,
we study constraints using CT14HERA2 parton distributions \cite{Hou:2016nqm}
fitted to datasets from DIS processes, $Z\rightarrow l^{+}l^{-}$,
$d\sigma/dy_{l}$, $W\rightarrow l\nu$, and jet production ($p_{1}p_{2}\rightarrow jjX)$.
We include both the experiments that were used to construct the CT14HERA2
dataset, as well as a number of LHC experiments that may be fitted
in the future. The experimental data sets are summarized in
Tables~\ref{tab:EXP_1}-\ref{tab:EXP_3}.
Given the urgency in improving
constraints on the gluon PDF for investigations of the Higgs sector,
we focus attention on several candidate experiments that may probe
$g(x,\mu)$: high-$p_T$ $Z$-boson
production (ATL8ZpT'16, ATL7ZpT'14), $t\bar{t}$ production (ATL8ttb-pt'16, ATL8ttb-y\_ave'16, ATL8ttb-mtt'16, ATL8ttb-y\_ttb'16),
as well as high-luminosity or alternative data sets for jet production, such as
the high-luminosity ATLAS 7 TeV jet data (ATLAS7jets'15) that is to replace the
counterpart low-luminosity set ATL7jets'12, or the CMS 7 TeV jet data set (CMS7jets'14)
that extends to lower jet $p_T$ and higher rapidity,
$2.5<|y_{j}|<3$, than the previously fitted CMS 7 TeV
jet data set (CMS7jets'13).\footnote{As a result, a small number of data points
that contributes to both the data sets CMS7jets'14 and CMS7jets'13 is double-counted
in the histograms, without affecting the conclusions.
}
The dependence of such experiments on $g(x,\mu)$ is scrutinized in a
number of ways. We examine their statistical properties using both the
PDFs from the CT14HERA2 NNLO analysis, which already impose
significant constraints on the large-$x$ gluon using
the Tevatron inclusive jet data sets, CDF2jets'09 and D02jets'08; and in some comparisons using
a special version of the NNLO PDFs that are fitted to the same CT14HERA2
data set, except without including the above jet data sets. As yet
another aspect, we investigate a range of measurements of Drell-Yan
pair production cross sections and charge lepton asymmetries with the
goal to understand their sensitivity predominantly to the (anti)quark sector.
To parametrize the response of a residual $\vec{r}_{i}$, we evaluate
it for every eigenvector PDF $\vec{a}_{l}^{\pm}$ of the CT14HERA2
PDF set with $N=28$ PDF parameters. Then, given the
{\it normalized residual variations}
\begin{equation}
\delta_{i,l}^{\pm}\equiv\left(r_{i}(\vec{a}_{l}^{\pm})-r_{i}(\vec{a}_{0})\right)/\langle r_{0}\rangle_{E}\label{deltapmil}
\end{equation}
between the residuals for the PDF eigenvectors $\vec{a}_{l}^{\pm}$
and for the CT14HERA2 central PDF $\vec{a}_{0}$, we construct a $2N$-dimensional
vector
\begin{equation}
\vec{\delta}_{i}=\left\{ \delta_{i,1}^{+},\,\delta_{i,1}^{-},\,...,\delta_{i,N}^{+},\,\delta_{i,N}^{-}\right\} \label{deltail}
\end{equation}
for each data point of the global dataset.
The components of $\vec{\delta}_{i}$ parametrize responses of $r_{i}$
to PDF variations along the independent directions given by $\vec{a}_{l}^{\pm}$.
The differences are normalized to the central root-mean-square (r.m.s.)
residual $\langle r_{0}\rangle_{E}$ of experiment $E$ {[}see Eq.~(\ref{r0E}){]}
so that the normalized residual variations do not significantly depend on $\chi^{2}(\vec{a}_{0})/N_{\mathit{pt}},$
the quality of fit to experiment $E$. Recall that a substantial spread
over the fitted experiments is generally obtained for $\chi_{E}^{2}/N_{\mathit{pt}}$.
Moreover, it is reasonable to expect significantly larger values for
$\chi_{E}^{2}/N_{\mathit{pt}}$ for the experiments that have not been
yet fitted, but are included in the analysis of the residuals, \textit{e.g.},
the new LHC experiments shown in Fig.~\ref{fig:data}. With the definitions
in Eqs. (\ref{deltapmil}) and (\ref{deltail}), however, $\vec{\delta_{i}}$
is only weakly sensitive to $\chi_{E}^{2}/N_{\mathit{pt}}$.
Thus, we represent the PDF-driven variations of the residuals of a
global dataset by a bundle of vectors $\vec{\delta}_{i}$ in a $2N$-dimensional
space.\footnote{In this section, we consider separate variations along $\vec{a}_{l}$
in the positive and negative directions. Alternatively, it is possible
to work with a vector of $N$ symmetric differences $\delta_{i,l}\equiv\left(r_{i}(\vec{a}_{l}^{+})-r(\vec{a}_{l}^{-})\right)/\left(2\langle r_{0}\rangle_{E}\right)$
and arrive at similar conclusions. Symmetric differences will be employed
to construct correlations and sensitivities in Sec.~\ref{sec:QuantifyingDistributionsOfResiduals}.
\label{fn:sym-deltail}} This mapping opens the door to applying various data-analytical methods
for classification of the data points and identifying the data points
of the utmost utility for PDF fits. As the length of $\vec{\delta}_{i}$
is equal to the PDF-induced fractional error on $r_{i}$ as compared
to the average residual at the best fit, it can be argued that important
PDF constraints arise
from new data points that either have a large $|\vec{\delta}_{i}|$
or are otherwise distinct from the existing data points. Conversely,
new data points with a small $|\vec{\delta}_{i}|$, or the ones that
are embedded in the preexisting clusters of points, are not likely to
improve constraints on the PDFs.
\subsection{Manifold learning and dimensionality reduction \label{subsec:Manifold-learning}}
\subsubsection{\emph{PCA and t-SNE visualizations} \label{sec:embedding}}
We illustrate a possible analysis technique carried out with the help
of the TensorFlow Embedding Projector software for the visualization
of high-dimensional data \cite{EmbeddingProjector}. A table of 4021
vectors $\vec{\delta}_{i}$ for the CTEQ-TEA dataset (corresponding
to our total number of raw data points) is generated by our package
\textsc{PDFSense} and uploaded to the Embedding Projector website.
As variations along many eigenvector directions result only in small
changes to the PDFs, the 56-dimensional $\vec{\delta}_{i}$ vectors
can in fact be projected onto an effective manifold spanned by fewer
dimensions. Specifically, the Embedding Projector approximates the
56-dimensional manifold by a 10-dimensional manifold using principal
component analysis (PCA). In practice, this 10-dimensional manifold
is constructed out of the 10 components of greatest variance in the
effective space, such that the most variable combinations of $\delta_{i,l}$
are retained, while the remaining 46 components needed to fully reconstruct
the original 56-dimensional $\vec{\delta}_{i}$ are discarded. However,
because the 10 PCA-selected components describe the bulk of the variance
of $\delta_{i,l}$, the loss of these 46 components results in only
a minimal relinquishment of information, and in fact provides a more
efficient basis to study $\delta_{i,l}$ variations.
We encourage the reader to download the table of the normalized
residual variations $\vec\delta_i$ for
CT14HERA2 NNLO from the \textsc{PDFSense}
website \cite{PDFSenseWebsite} and explore it for themselves using the Embedding
Projector \cite{EmbeddingProjector} or another program for multidimensional data visualization
such as a tour \cite{Cook:2018mvr}. These tools help to understand
the detailed PDF dependence of individual data sets
{\it without doing the global fit}.
Performing such task has been challenging for non-experts,
if not for the PDF fitters themselves. With the proposed method, we
can visually examine the PDF dependence of the residuals from the diverse data
sets before quantitatively characterizing these distributions using
the estimators developed in the next sections.
In the future, a computer algorithm
can be written to select the experimental data for PDF fits,
based on the residual variations, and with minimal involvement from humans.
To offer an illustration, while grasping the full PDF dependence of the
data points in the original 56-parameter space is daunting,
in the 10-dimensional representation obtained via PCA,
some directions result in efficient separation of the data points
of different types according to their residual variations.
The left panel of Fig.~\ref{fig:PCA-TSNE} shows one such 3-dimensional
projection of $\vec{\delta}_{i}$ that separates clusters of residual
variations arising from data for DIS,
vector boson production, and jet/$t\bar{t}$ production.
In this example, the jet/$t\bar{t}$ cluster, shown in red, is roughly
orthogonal to the blue DIS cluster and intersects it. This separation
is quite remarkable, as it is based only on numerical properties of the
$\vec{\delta}_{i}$ vectors, and not on the meta-data about the types
of experiments that is entered only after the PCA is completed; in other
projections, the data types are not separated. The underlying
reasons for this separation, namely, dependence on independent PDF
combinations, will be quantified by the sensitivities in the next section.
As an alternative, the Embedding Projector can organize the $\vec{\delta}_{i}$
vectors into clusters according to their similarity using $t$-distributed
stochastic neighbor embedding (t-SNE) \cite{vanderMarten:2008}. A
representative 3-dimensional distribution of the vectors obtained
by t-SNE is displayed in the right panel of Fig.~\ref{fig:PCA-TSNE}.
In the figure, we show that the t-SNE method is able to identify and
separate the clusters of
data according to the experimental process (DIS, vector production, or
jet production). In fact, the reader can perform the t-SNE analysis
on the Embedding Projector website themselves and verify that it actually
sorts the $\vec\delta_i$ vectors into the clusters
according to their values of $x$ and
$\mu$, and even the experiment itself. This exercise demonstrates,
yet again, that the statistical residuals provided in \textsc{PDFSense}
reflect the key properties of the global fit.
Information can be extracted from them and examined in a number of ways.
The breakdown of the vectors over experiments in the PCA representation
is illustrated by Fig.~\ref{fig:PCA-CTExperiments}. Here, we see
that the bulk of the DIS cluster from the left Fig.~\ref{fig:PCA-TSNE}
originates with the combined HERA1+2 DIS data [HERAI+II'15].
The jet cluster in Fig.~\ref{fig:PCA-TSNE} will be dominated by
ATLAS and CMS inclusive jet datasets [CMS7jets'14, ATLAS7jets'15, and CMS8jets'17],
which add dramatically more points across a wider kinematical range
on top of the CDF Run-2 and D0 Run-2 jet production datasets (CDF2jets'09)
and (D02jets'08).
In contrast, although the $t\bar{t}$ production experiments (ATL8ttb-pt'16, ATL8ttb-y\_ave'16, ATL8ttb-mtt'16, ATL8ttb-y\_ttb'16)
are generally characterized by large $\vec{\delta}_{i}$
vectors, they contribute only a few data points lying within the jet
cluster of Fig.~\ref{fig:PCA-CTExperiments} and, by themselves, will not make much difference in a global
fit. The same conclusion applies to data from high-$p_{T}$ $Z$ production,
which has too few points to stand out in a fit with significant inclusive
jet data samples. We return to this point in the discussion of reciprocated
distances below.
It is also interesting to note that semi-inclusive charm production
at HERA [HERAc'13]
lies between, and partly overlaps with, the DIS and jet clusters. Finally,
CCFR/NuTeV dimuon semi-inclusive DIS [SIDIS] (CCFR-F2'01, CCFR-F3'97, NuTeV-nu'06, NuTeV-nub'06)
extends in an orthogonal direction, not well separated from the other datasets in the
selected three-dimensional projection.
\begin{figure*}
\centering{}\includegraphics[width=0.48\textwidth]{figs/pca.pdf}\ \ \includegraphics[width=0.48\textwidth]{figs/tsne.pdf}
\caption{Distributions of residual variations $\vec{\delta_{i}}$ from the
CTEQ-TEA analysis obtained by dimensionality reduction methods. Left:
a 3-dimensional projection of a 10-dimensional manifold constructed
by principal component analysis (PCA). Right: a distribution from
the 3-dimensional t-SNE clustering method. Blue, orange, and red colors
indicate data points from DIS, vector boson production, and jet/$t\bar{t}$
production processes. \label{fig:PCA-TSNE}}
\end{figure*}
\begin{figure*}[p]
\centering{}\includegraphics[width=0.9\textwidth,height=0.85\textheight]{figs/CTexperiments.pdf}
\caption{The PCA distribution from Fig.~\ref{fig:PCA-TSNE}, indicating distributions
of points from classes of experiments. In the numbering scheme used here, points labeled
1XX correspond to fixed-target measurements and 5XX to jet and $t\bar{t}$ production as given in Tables~\ref{tab:EXP_1}--\ref{tab:EXP_3}.
The specific experiments are noted in the plots.
}
\label{fig:PCA-CTExperiments}
\end{figure*}
\subsubsection{\emph{Reciprocated distances} \label{sec:Reciprocated-distances}}
As a complement to the visualization methods based on PCA and t-SNE
just presented, it is also possible to evaluate another similarity
measure based on the distances between the vectors of the
residual variations. For example,
rather than applying the PCA
to an ensemble of $\vec{\delta}_{i}$ vectors to perform dimensionality reduction,
we might instead compute over the vector space a pair-wise
\textit{reciprocated distance} measure, which we define as
\begin{equation}
\mathcal{D}_{i}\ \equiv\ \left(\sum_{j\neq i}^{N_{\mathit{all}}}\frac{1}{|\vec{\delta}_{j}-\vec{\delta}_{i}|}\right)^{-1}\ ,\label{eq:recip}
\end{equation}
and evaluate for the $i$ points in each experimental dataset. We
allow the sum over $j$ in Eq.~(\ref{eq:recip}) to run over all
the data points in the CTEQ-TEA set regardless of experiment
(denoted by $N_{\mathit{all}}$). The distances can be computed either
in the 56-dimensional space or in the reduced dimensionality space.\footnote{Alternative definitions for the reciprocated distance can be also
used, with qualitatively similar conclusions. For example, we could
sum over all experimental data, but excluding those points belonging
to the same experiment as point $i$, and normalizing $\mathcal{D}_{i}$
by $(N_{\mathit{pt}}-N_{\mathit{all}})/N_{\mathit{pt}}$ to compensate for different numbers of
points in the experiment. } We plot the result of applying Eq.~(\ref{eq:recip}) to the 56-dimensional
residual variations of the full CTEQ-TEA dataset computed using two PDF ensembles:
CT14HERA2 fitted to all data in the left panel, and CT14HERA2 fitted
only to the DIS and vector boson production data (excluding jet production
data) in the right panel. Fig. \ref{fig:recip} represents the distribution
of the reciprocated distances over individual experiments of the CTEQ-TEA
dataset. The CT Experiment ID \# is shown on the abscissa, and the $\mathcal{D}_{i}$
values for every point of the experiment are indicated by the scatter
points.
The advantage of the definition in Eq. (\ref{eq:recip}) is that it
enables a quantitative measure of the degree to which separate experiments
broadly differ in terms of their residual variations, and therefore
provides information analogous to that found in Figs. \ref{fig:PCA-TSNE}\textendash \ref{fig:PCA-CTExperiments}.
For example, by inspection of Eq. (\ref{eq:recip}) it can be seen
that those experimental measurements which are widely separated from
the rest of the CTEQ-TEA dataset in space of $\vec{\delta}_{i}$ vectors
will correspond to comparatively large values of $\mathcal{D}_{i}$,
and experiments that systematically differ from the rest of the total
dataset are thus expected to have especially tall distributions in
the panels of Fig. \ref{fig:recip}. On this basis, it can be seen
that information yielded by W asymmetry measurements (D02Masy'08, CMS7Masy2'14,
D02Easy2'15) are particularly distinct, as well as the combined HERA DIS data
(HERAI+II'15) and fixed-target Drell-Yan measurements, such as E605
(E605'91) and E866 data (E866rat'01 and E866pp'03). Similarly,
direct comparison of the $\mathcal{D}_{i}$ distributions in the panels
of Fig. \ref{fig:recip} allows one to compare constraints with and
without the jet data. We note that the 7 and 8 TeV ATLAS high-$p_{T}$
$Z$ production (ATL7ZpT'14 and ATL8ZpT'16) and $t\bar{t}$ production (ATL8ttb-pt'16)
provide a number of ``remote'' points and hence are potentially
useful in the fits sensitive to the gluon. On the other hand, new
jet production experiments (CMS7jets'14, ATLAS7jets'15, CMS8jets'17) all include large numbers
of points characterized by significant reciprocated distances.
\begin{figure*}
\centering{}\includegraphics[width=0.47\textwidth]{figs/rd54_CT14HERA2_new2.pdf}
\ \ \ \centering{}\includegraphics[width=0.47\textwidth]{figs/rd54_CT14HERA2_nojets_new2.pdf}
\caption{ A plot of the reciprocated distances $\mathcal{D}_{i}$ obtained
from the PDFs fitted to the full CT14HERA2 dataset {[}left{]} and
to the CT14HERA2 dataset without jet production experiments {[}right{]}.
The horizontal axis displays numerical experimental CT IDs of the constituent
CTEQ-TEA datasets, for each of which is shown a column of values of
the reciprocated distance. We highlight columns corresponding to Expt.~IDs
ATL7ZpT'14 [247], ATL8ZpT'16 [253], and ATL8ttb-pt'16 [565] as discussed in text. \label{fig:recip}}
\end{figure*}
\section{Quantifying distributions of residual variations\label{sec:QuantifyingDistributionsOfResiduals}}
We have demonstrated that the multi-dimensional distribution of
the $\vec{\delta}_i$ vectors reflects the PDF dependence of individual data points. In this section,
we will focus on numerical metrics to assess the emerging geometrical
picture associated with the $\vec{\delta}_i$ distribution, and to visualize the regions of partonic momentum fractions
$x$ and QCD factorization scales $\mu$ where the experiments impose
strong constraints on a given PDF-dependent observable $X$.
Gradients of $r_{i}$ in a space of Hessian eigenvector PDF parameters
$\vec{a}$ are naturally related to the PDF uncertainty. Recall that
in the Hessian method the PDF uncertainty on $X(\vec{a})$ is found
as
\begin{equation}
\Delta X(\vec{a})=X(\vec{a})-X(\vec{a}_{0})=\vec{\nabla}X|_{\vec{a}_{0}}\cdot\Delta\vec{a},
\end{equation}
where $\vec{a}_{0}$ is the best-fit combination of PDF parameters,
and $\Delta\vec{a}$ is the maximal displacement along the gradient
that is allowed within the tolerance hypersphere of radius $T$ centered
on the best fit \cite{Pumplin:2001ct,Pumplin:2002vw}. The standard
master formula
\begin{equation}
\Delta X=\left\vert \vec{\nabla}X\right\vert =\frac{1}{2}\sqrt{\sum_{l=1}^{N}\left(X_{l}^{+}-X_{i}^{-}\right)^{2}}\label{masterDX-1}
\end{equation}
is obtained by representing the components of $\vec{\nabla}X$ by
a finite-difference formula
\begin{equation}
\frac{\partial X}{\partial a_{i}}=\frac{1}{2}(X_{i}^{+}-X_{i}^{-}),\label{dXdzi-1-1}
\end{equation}
in terms of the values $X_{l}^{\pm}$ for extreme displacements of
$\vec{a}$ within the tolerance hypersphere along the $l$-th direction.
In this setup, a dot product between the gradients provides a convenient
measure of the degree of similarity between PDF dependence of two
quantities \cite{Nadolsky:2008zw}. A dot product $\vec{\nabla}r_{i}\cdot\vec{\nabla f}$
between the gradients of a shifted residual $r_{i}$ and another QCD
variable $f$, such as the PDF at some $\{x,\mu\}$ or a cross section,
can be cast in a number of useful forms.
\subsection{Correlation cosine }
\label{sec:Correlations}
The correlation for the $i^{th}$ $\{x,\mu\}$ point, which we define
following Refs.~\cite{Pumplin:2001ct,Nadolsky:2001yg,Nadolsky:2008zw,Gao:2017yyd}
as
\begin{equation}
C_{f}\,\equiv\,\mbox{Corr}[f,r_{i}]=\frac{\vec{\nabla} f\cdot\vec{\nabla} r_{i}}{\Delta f\,\Delta r_{i}},\label{eq:corr}
\end{equation}
can determine whether there \emph{may} exist a predictive relationship
between $f$ and goodness of fit to the $i^{th}$ point. The correlation
function $\mathrm{\mbox{Corr}}[X,Y]$ for the quantities $X,\,Y$
in Eq.~(\ref{eq:corr}) represents the realization in the Hessian
formalism of Pearson's correlation coefficient, which we express as
\begin{align}
\mathrm{\mbox{Corr}}[X,Y] & =\frac{1}{4\Delta X\Delta Y}\sum_{j=1}^{N}(X_{j}^{+}-X_{j}^{-})(Y_{j}^{+}-Y_{j}^{-})\ ,\label{eq:corr-def}
\end{align}
with the sum in these expressions being over the $j$ parameters of
the full PDF model space. Geometrically, $\mbox{Corr}[X,Y]$ represents
the cosine of the angle that determines the eccentricity of an ellipse
satisfying $\chi^{2}(\vec{a})<\chi^{2}(\vec{a}_{0})+T^{2}$ in the
$\{X,Y\}$ plane. This latter point follows from the fact that the
mapping of the tolerance hypersphere onto the $\{X,Y\}$ plane is
an ellipse with an eccentricity that depends on the correlation of
$X$ and $Y,$ which is given in turn by Eq.~(\ref{eq:corr-def})
above.
$\mbox{Corr}[f,r_{i}]$ does not indicate how constraining the residual
is, but it may indicate a predictive relation between $r_{i}$ and
$f$. On the basis of previous work \cite{Nadolsky:2008zw}, we say
that the (anti-)correlation between $X$ and $Y$ is significant roughly
if $\left|\mbox{Corr}[X,Y]\right|\gtrsim0.7$, while smaller (anti-)correlation
values are less robust or predictive. Following this rule-of-thumb,
correlations have been used successfully to identify PDF combinations
that dominate PDF uncertainties of complicated observables, for instance
to show that the gluon uncertainty dominates the total uncertainty
on LHC $W$ and $Z$ production, or that the uncertainty on the ratio
$\sigma_{W}/\sigma_{Z}$ of $W^{\pm}$ and $Z^{0}$ boson cross sections
at the LHC is dominated by the strangeness PDF, rather than $u$ and
$d$ (anti-)quark PDFs \cite{Nadolsky:2008zw}.
\subsection{Sensitivity in the Hessian method}
\label{sec:Sensitivities}
The correlation $C_{f}$ alone does not fully encode the potential
impact of separate or new measurements on improving PDF determinations
in terms of the uncertainty reduction. Rather, we employ $\vec{\nabla} f\cdot\vec{\nabla} r_{i}$
again to define the \textit{sensitivity} $S_{f}$ to $f$ of the $i^{th}$
point in experiment $E$:
\begin{equation}
S_{f}\equiv\frac{\vec{\nabla} f\cdot\vec{\nabla} r_{i}}{\Delta f\,\langle r_{0}\rangle_{E}}=\frac{\Delta r_{i}}{\langle r_{0}\rangle_{E}}\,C_{f}\ ,\label{eq:sens}
\end{equation}
where $\Delta r_{i}$ and $\langle r_{0}\rangle_{E}$ are computed
according to Eqs.~(\ref{DelX}) and (\ref{r0E}), respectively. In
other words, $\Delta r_{i}$ again represents the variation of the
residuals across the set of Hessian error PDFs, and we normalize it
to the r.m.s.\ residual for the whole dataset $E$ to reduce the impact
of random fluctuations in the data values $D_{i,\mathit{sh}}$. This definition
has the benefit of encoding not only the correlated relationship of
$f$ with $r_{i}$, but also the comparative size of the experimental
uncertainty with respect to the PDF uncertainty. In consequence, for
example, if new experimental data have reported uncertainties that
are much tighter than the present PDF errors, these data would then
register as high-sensitivity points by the definition in Eq.~(\ref{eq:sens}).
\begin{figure*}
\includegraphics[clip,width=0.48\textwidth]{figs/sf_projection1.pdf}
\quad\quad \includegraphics[clip,width=0.4\textwidth]{figs/sf_projection2.pdf}
\caption{Left: A PDF-dependent quantity $f$ defines a direction in
space of $(2)N$ PDF parameters. The direction is specified by the
gradient $\vec\nabla f$ in the symmetric convention.
Here, the Embedding
Projector \cite{EmbeddingProjector} visualizes the
vectors $\vec \delta_{907}$ and $\vec \delta_{914}$ for
NNLO cross sections for Higgs boson production at 7 and 14 TeV, and
vectors $\vec\delta_i$ for CT14HERA2 NNLO data points from
\cite{PDFSenseWebsite} (brown circles), showing only $\vec\delta_i$
with the smallest angular distances to $\vec\delta_{914}$. These
points impose the strongest constraints on the PDF dependence of the
Higgs cross sections in the CT14HERA2 analysis, if they have large enough
$|\vec \delta_i|$. Again, in the numbering scheme used here, points labeled
1XX correspond to fixed-target measurements, 2XX to Drell-Yan processes and boson production, and
5XX to jet and $t\bar{t}$ production as given in Tables~\ref{tab:EXP_1}--\ref{tab:EXP_3}. Right: the sensitivity $S_f$ of the $i$-th data
residual can be interpreted as the projection of $\vec \delta_i
\equiv \vec \nabla r_i/\langle r_0\rangle_E$ onto the direction of $\vec\nabla f$.}
\label{fig:sfprojection}
\end{figure*}
Geometrically, $S_{f}$ represents a projection onto the direction of
the gradient $\vec{\nabla}f$ of the residual variation $\vec{\delta_{i}}$, defined in Sec.~\ref{sec:QuantifyingDistributionsOfResiduals}
using the symmetrized formula for $\delta_{i,l}$ noted in footnote~\ref{fn:sym-deltail}, namely,
\begin{equation}
\delta_{i,l}\equiv\left(r_{i}(\vec{a}_{l}^{+})-r(\vec{a}_{l}^{-})\right)/\left(2\langle r_{0}\rangle_{E}\right)\ .
\end{equation}
Figure~\ref{fig:sfprojection} shows a pictorial illustration of this interpretation. This interpretation
suggests that the total strength of constraints along the direction
of $\vec{\nabla}f$ can be quantified by summing projections $S_{f}$
onto this direction of all individual vectors $\vec{\delta}_{i}$.
As with correlations, only a sufficiently large absolute magnitude
of $\left|S_{f}\right|$ is indicative of a predictive constraint
of the $i^{th}$ point on $f$. Recall that $r_{i}^{2}$ is the contribution
of the $i^{th}$ point to $\chi^{2},$ and that only residuals with
a large enough $\Delta r_{i}$ as compared to the r.m.s.\ residual
$\langle r_{0}\rangle_{E}$ are sensitive to PDF variations. The $S_{f}$
magnitude is of order $\Delta r_{i}/\langle r_{0}\rangle_{E},$ which
suggests an estimate of a minimal value of $S_{f}$ that would be
deemed sensitive according to the respective $\chi^{2}$ contribution.
For the numerical comparisons in this study, we assume that $\left|S_{f}\right|$
must be no less than 0.25 to indicate a predictive constraint, as
the PDF uncertainty of the $i^{th}$ residual contributes no less
than $r_{i}^{2}=$0.0625 to the variation in the global $\chi^{2}$.
The reader can choose a different minimal value in the
\textsc{PDFSense} figures depending
on the desired accuracy. The cumulative sensitivities that we obtain
in later sections are independent of this choice.
Yet another possible definition, which we list for completeness, is
to further normalize the sensitivity as
\begin{equation}
S_{f}^{\prime}\equiv\frac{\vec{\nabla} f\cdot\vec{\nabla} r_{i}}{f_{0}\,\langle r_{0}\rangle_{E}}=\frac{\Delta f}{f_{0}}\,S_{f}\ .\label{eq:sens-prime}
\end{equation}
For instance, if $f$ is the PDF $f(x_{i},\mu_{i})$ or parton luminosity
evaluated at the $\{x_{i},\mu_{i}\}$ points extracted according to
the data, the definition of $S_{f}^{\prime}$ in Eq. (\ref{eq:sens-prime})
de-emphasizes those points where the PDF uncertainty $\Delta f(x_{i},\mu_{i})$
is small compared to the best-fit PDF value $f_{0}(x_{i},\mu_{i})$
\textemdash{} analogously to how $S_{f}$ de-emphasizes (relative
to the correlation $C_{f}$) those data points whose normalized
residual variations $\Delta r_{i}/\langle r_{0}\rangle_{E}$
have already been more tightly constrained.
\subsection{Sensitivity in the Monte-Carlo method}
The above statistical measures are general enough and can be extended
to other representations for the PDF uncertainties, such as the
representation based on Monte-Carlo replica PDFs \cite{Giele:1998gw,Giele:2001mr,Ball:2008by}
of the kind employed, e.g., in the NNPDF framework.
A family of Monte-Carlo PDFs consists of $N_{\rm rep}$ member PDF sets
$q_a^{(k)}(x,\mu)\equiv \{ q^{(k)} \}$, with $k=1,\ ...,\ N_{\rm rep}$, and
those are used to determine an expectation value
$\langle X\rangle$ for a PDF-dependent quantity $X[\{ q \}]$ such as a
high-energy cross section:
\begin{equation}
\langle X \rangle = \frac{1}{N_{\rm rep}} \sum_{k=1}^{N_{\rm rep}}
X [ \{ q^{(k)} \}]\ .
\label{eq:NNPDF_masterave}
\end{equation}
The resulting Monte-Carlo uncertainty on $X$ can be extracted from the ensemble as
\begin{equation}
\Delta_{\rm MC} X\ =\ \left( \frac{1}{N_{\rm rep}-1}
\sum_{k=1}^{N_{\rm rep}}
\left( X [ \{ q^{(k)} \}]
- \langle X \rangle\right)^2
\right)^{1/2}\ .
\label{eq:NNPDF_error}
\end{equation}
In consequence of these definitions, the central value of a particular
PDF itself in the NNPDF framework is specified as
\begin{equation}
q_{(0)} \equiv \langle q \rangle = \frac{1}{N_{\rm rep}}
\sum_{k=1}^{N_{\rm rep}} q^{(k)} \ .
\label{eq:NNPDF_mcav}
\end{equation}
Akin to the Pearson correlation defined in Eq.~(\ref{eq:corr}) of
Sec.~\ref{sec:Correlations}, statistical correlations between two PDF-dependent
quantities $X[\{ q \}]$ and $Y[\{ q \}]$ can be constructed from the PDF
replica language above in terms of ensemble averages \cite{Ball:2008by}:
\begin{equation}
\mbox{Corr}_{\rm MC} \left[ X, Y \right]
=\frac{\langle X Y \rangle
- \langle X \rangle \langle Y \rangle}{\Delta_{\rm MC} X \Delta_{\rm MC} Y}\ .
\label{eq:NNPDF_corrPDF}
\end{equation}
Then, using our definitions in Eqs.~(\ref{eq:corr}) and
(\ref{eq:sens}), we immediately construct the realizations of the
correlation and sensitivity for a PDF-dependent quantity $f$
in the Monte-Carlo method:
\begin{eqnarray}
C_{f,\ {\rm MC}} &=& \mbox{Corr}_{\rm MC}[f,r_{i}]\ , \label{eq:corrMC}\\
S_{f,\ {\rm MC}} &=& \frac{\Delta_{\rm MC} r_{i}}{\langle
r_{0}\rangle_{E}}\,\mbox{Corr}_{\rm MC}\left[f, r_i \right].\label{eq:sensMC}
\end{eqnarray}
\section{Case study: CTEQ-TEA global data \label{sec:CaseCTEQ-TEA}}
\subsection{Maps of correlations and sensitivities}
\begin{figure*}
\includegraphics[clip,width=0.38\textwidth]{figs/ghist_C_fix_y.pdf}
\includegraphics[clip,width=0.60\textwidth]{figs/corr_xQ+1_f0_samept_nohigh.pdf}
\\
\includegraphics[clip,width=0.60\textwidth]{figs/corr_xQ+1_f0_samept_replot.pdf}
\caption{Representations of the correlation $|C_{g}|(x_{i},\mu_{i})$ of
the gluon PDF $g(x,\mu)$ with the point-wise residual $r_{i}$ of
the augmented CT14HERA2 analysis. In the first panel, we plot a histogram
showing the distribution of correlations for 4021 physical measurements.
In the second panel we show the 5227-point $\{x_{i},\mu_{i}\}$ map corresponding
to these data within the full dataset, generated as in Appendix~\ref{sec:supp}.
To adjust for the fact that some measurements of rapidity dependent quantities
match to two distinct points in $\{x_{i},\mu_{i}\}$ space using the rules of
Appendix~\ref{sec:supp}, we assign weights of $0.5$ to these complementary
$\{x_{i},\mu_{i}\}$ points in computing the $N_{\mathit{pt}}=4021$-count histogram
at left. The third figure is the same as the second one, but only the
data points satisfying $|C_f|>0.7$ are highlighted.
}
\label{fig:corr-main}
\end{figure*}
We will now discuss a number of practical examples of using $C_{f}$
or $S_{f}$ to quickly evaluate the impact of various hadronic data
sets upon the knowledge of the PDFs in a fashion that does not require
a full QCD analysis of the type described in Sec.~\ref{sec:PDF-preliminaries}.
For this demonstration, we will continue to study the dataset shown
in Fig.~\ref{fig:data} of the CT14HERA2 analysis~\cite{Hou:2016nqm}
augmented by the candidate LHC data.
We have already noted the extent of this dataset in the $\{x,\mu\}$
plane in Fig.~\ref{fig:data}, where it is decomposed into constituent
experiments labeled according to the conventions in Tables~\ref{tab:EXP_1}-\ref{tab:EXP_3}.
It is instructive to create similar maps in the $\{x,\mu\}$ plane
showing the $C_{f}$ or $S_{f}$ values for each data point.
Such maps are readily produced by the
\textsc{PDFSense} program for a variety of PDF flavors and for user-defined
observables, such as the Higgs cross section. For demonstration we
have collected a large number of these maps at the companion website
\cite{PDFSenseWebsite}. We invite the reader to review these additional
figures while reading the paper
to validate the conclusions that will be summarized below.
Thus, we obtain scatter plots of $C_{f}(x_{i},\mu_{i})$ or $S_{f}(x_{i},\mu_{i})$
for a given QCD observable $f=\sigma$, such as the LHC Higgs production
cross section shown in Fig.~\ref{fig:CorrSensH14}, or with a PDF
$f$ evaluated at the same $\{x_{i},\mu_{i}\}$ determined by the
data points, with examples shown for $g(x_{i},\mu_{i})$ in Figs.~\ref{fig:corr-main}
and \ref{fig:sens-main}. The typical $\{x_{i},\mu_{i}\}$ values
characterizing the data points are found according to Born-level approximations
appropriate for each scattering process included in the CTEQ-TEA dataset,
with the formulas to compute these kinematic matchings summarized
in App.~\ref{sec:supp}. Here and in general, we find it preferable to
consider the absolute
values $|C_f|$ and $|S_f|$ on the grounds that the
signs of $C_f$ and $S_f$ flip when the data points randomly overshoot
or undershoot their theory predictions.
Together with the map in the $\{x,\mu\}$ plane, \textsc{PDFSense
}also returns a histogram of the values for each quantity it plots.
An example is shown for $\left|C_{g}\right|(x_{i},\mu_{i})$ in the
first panel of Fig.~\ref{fig:corr-main}. One would judge that stronger
constraints are in general provided to those PDFs for which the $|C_{f}|$
histogram has many entries comparatively closely to $|C_{f}|\sim1$.
In the first panel of Fig.~\ref{fig:corr-main}, we can see that,
while the distribution peaks at low correlations,
$|C_{g}|\sim0$, the distribution has an extended
tail in the region $0.7\lesssim|C_{g}|\lesssim1$.
This feature shows that, of the 4021 experimental data
points within the augmented CT14HERA2 set in Fig.~\ref{fig:data},
nearly two-hundred --- specifically, 192 --- have especially strong
($|C_{f}|\ge0.7$) correlations (or anti-correlations) with the gluon
PDF. This region of such strong correlations within the histogram
is indicated by the horizontal blue bar that runs along the abscissa.
\begin{figure*}
\includegraphics[clip,width=0.38\textwidth]{figs/ghist_S_fix_y.pdf}
\includegraphics[clip,width=0.60\textwidth]{figs/corrdr_xQ+1_f0_samept_nohigh.pdf}\\
\includegraphics[clip,width=0.60\textwidth]{figs/corrdr_xQ+1_f0_samept_replot.pdf}
\caption{Like Fig.~\ref{fig:corr-main}, but for the gluon sensitivity $|S_{g}|(x_{i},\mu_{i})$
as defined in Eq.~(\ref{eq:sens}). In the third figure, only the
data points satisfying $|S_f|>0.25$ are highlighted.}
\label{fig:sens-main}
\end{figure*}
To identify these points, we plot complementary information in the
second panel of the same figure \textendash{} specifically, a map in
$\{x,\mu\}$ space of each of the data points shown in
Fig.~\ref{fig:data}.
As before, they are colorized according to the magnitude of $|C_{g}|$
following the color palette in the ``rainbow strip'' on the right.
``Cooler'' colors (green/yellow) correspond to weaker correlation
strengths, while ``hotter'' colors (orange/red) represent comparatively
stronger correlations, as indicated. To reveal the data points with
the highest correlations, we reproduce the same figure in the third
panel, but showing in color only the data points satisfying $|C_f|>0.7$.
Thus, we obtain two maps in the
$\{ x,\mu \}$ plane that look similar to the $|C_f|$ map in the left
panel of Fig.~\ref{fig:CorrSensH14}, apart from the differences that
(a) Fig.~\ref{fig:corr-main} shows the correlation $|C_g|$ for
$g(x_i,\mu_i)$ at the same typical values $\{x_i,\mu_i\}$ as in the
data, rather than $|C_{\sigma_{H^0}}|$ for Higgs production cross
section in Fig.~\ref{fig:CorrSensH14}; and (b)
Fig.~\ref{fig:CorrSensH14} highlights 310 points with the highest $|C_{\sigma_{H^0}}|$.
The correlations for the LHC Higgs production cross section trace those for
$g(x_i,\mu_i)$, but not entirely, as we will see in a moment.
Large magnitudes of $|C_{g}|$ in Fig.~\ref{fig:corr-main}
are found for inclusive jet production measurements, especially those
recently obtained by CMS at 8 TeV \cite{Khachatryan:2016mlc} (Expt.~CMS8jets'17,
inverted triangles) with $|C_{g}|(x_{i},\mu_{i})$ as high as
0.85, including at the highest values of $x$ and $\mu$. Beyond these,
a sizable cluster of HERA (HERAI+II'15) data points at the lowest values of
$x$ are also seen to have large correlations with the gluon PDF,
consistent with the common wisdom that HERA DIS constrains the gluon
PDF at small $x$ via DGLAP scaling violations. Under the jet production
cluster, high-$p_{T}$ $Z$ production (ATL7ZpT'14, ATL8ZpT'16) and $t\bar{t}$
production (ATL8ttb-pt'16, ATL8ttb-y\_ave'16, ATL8ttb-mtt'16,
ATL8ttb-y\_ttb'16) at the LHC show a high $|C_{g}|(x_{i},\mu_{i})$
correlation. At the same time, many other measurements, including
fixed-target data at large $x$ and $W$ asymmetry data near $\mu\!\sim\!100$
GeV, have feeble correlations with $g(x_i,\mu_i)$ and would therefore be less
emphasized by an analysis based solely upon the PDF-residual correlations.
We can also consider the analogous plots for the sensitivity
$\left|S_{g}\right|(x_{i},\mu_{i})$ as defined in Eq.~(\ref{eq:sens}), which we plot in Fig.~\ref{fig:sens-main}. In the first panel, we again consider
the histogram, here for the magnitudes of the gluon sensitivity $|S_{g}|(x_{i},\mu_{i})$,
in which the correlations $|C_{g}|$ are now weighted by the relative
size of the PDF uncertainty $\Delta r_{i}$ in the residual. As discussed
in Sec.~\ref{sec:Sensitivities}, this additional weighting
emphasizes those data points for which the PDF-driven fluctuations
in the residuals are comparatively large relatively to experimental
uncertainties. This leads to a redistribution of the data points
shown in the $|C_{g}|$ histogram of Fig.~\ref{fig:corr-main}, with
the result being a considerably longer-tailed histogram for $|S_{g}|$
such that, in this instance, there are 546 raw data points
with larger sensitivities,
$|S_{f}|\ge0.25$, indicated by the horizontal blue bar. Unlike the correlation, $|S_{g}|$ can be arbitrarily large,
depending on the $\Delta r_{i}$ value. It is suppressed at the data points with
large uncertainties or smeared over the regions of data points with correlated systematic
uncertainties.
In the second and third panels, we show the respective $\{x,\mu\}$
maps for $\left|S_{g}\right|$, with color highlighting given either for all points or only
those with high sensitivities $|S_f|>0.25$, respectively. $\left|S_{g}\right|$ places additional
emphasis on the combined HERA dataset (HERAI+II'15) constraining $g(x_{i},\mu_{i})$
at lowest $x$. In contrast to the $|C_{g}|$ plot, we observe increased
sensitivity in the precise fixed-target DIS data from BCDMS (BCDMSp'89, BCDMSd'90) and CCFR
(CCFR-F2'01, CCFR-F3'97), which are sensitive to the gluon via scaling violations
despite only moderate correlation values.
Similarly, we observe heightened sensitivities at
highest $x$ for the LHC (CMS7jets'14, ATLAS7jets'15, CMS8jets'17) and Tevatron (D02jets'08) jet production
data, which have both large correlations with $g(x_{i},\mu_{i})$
and small experimental uncertainties. Sensitivity $\left|S_{g}\right|$
of LHC jet experiments, CMS7jets'14, ATLAS7jets'15, CMS8jets'17, varies in a large range, and
can significantly improve, depending on the implementation of
experimental systematic uncertainties in the analysis, cf.\ the
discussion of the jet data in the next section.
We also observe enhanced
sensitivity for \emph{individual points} in a large number of experiments,
including CDHSW DIS (CDHSW-F2'91); HERA $F_{L}$ (HERA-FL'11); the Drell-Yan process
(E605'91, E866pp'03); CDF 8 TeV $W$ charge asymmetry (CMS7Masy2'14); HERA charm SIDIS
(HERAc'13); ATLAS high-$p_{T}$ $Z$ production (ATL7ZpT'14, ATL8ZpT'16); and especially
strongly sensitive points in $t\bar{t}$ production (ATL8ttb-pt'16, ATL8ttb-y\_ave'16,
ATL8ttb-mtt'16, ATL8ttb-y\_ttb'16). However, since the latter category includes fewer
points per each experiment, it constrains the gluon less than the high-statistics DIS
and jet production data.
These findings comport with the idea that the gluon PDF remains dominated
by substantial uncertainties at both $x\!\sim\!0$ and in the elastic
limit $x\!\rightarrow\!1$, a fact which has driven an intense focus upon production
of hadronic jets, $t\bar{t}$ pairs, and high-$p_{T}$ $Z$ bosons,
which themselves are measured at large center-of-mass energies $\sqrt{s}$
and are expected to be sensitive to the gluon PDF across a wide interval
of $x,$ including $x\!\sim\!0.01$ typical for Higgs boson production
via gluon fusion at the LHC. Turning back to the distributions
of $\left|C_{\sigma_{H}}\right|(x_{i},\mu_{i})$ and $\left|S_{\sigma_{H}}\right|(x_{i},\mu_{i})$
for the Higgs cross section $\sigma_{H}$ at $\sqrt{s}=14$ TeV in
Fig.~\ref{fig:CorrSensH14}, we notice that they largely reflect
the distributions
of $\left|C_{g}\right|(x_{i},\mu_{i})$ and $\left|S_{g}\right|(x_{i},\mu_{i})$
around $x \sim M_H/\sqrt{s}=125/14000=0.009$ and $\mu= M_H=125$ GeV.
We also see some differences: although the average $x$ and $\mu$
are fixed in $\sigma_{H}$, it is nonetheless sensitive to some constraints
at much lower $x$ values as a result of the momentum sum rule.
The reader is welcome to examine the plots of sensitivities and
correlations available on the \textsc{PDFSense} website for a large
collection of PDF flavors and PDF ratios, such as
$d/u$, $\overline{d}/\overline{u}$, and
$\left( s +
\overline{s}\right)\!/\!\left(\overline{u}+\overline{d}\right)$. Sensitivities
for other PDF combinations and hadronic cross sections can be
computed and plotted in a matter of minutes
using the \textsc{PDFSense} program. We will
now turn to another aspect of this analysis: summarizing the abundant
information contained in the sensitivity plots. For this purpose, we
will introduce
numerical indicators and propose a practical procedure to
rank the experimental data sets according to their
sensitivities to the PDFs or PDF-dependent observables of interest.
\subsection{Experiment rankings according to cumulative sensitivities \label{sec:Experiment-rankings-according}}
Being one-dimensional projections of normalized residual variations
$\vec\delta_i$ on a given direction in the PDF parameter space,
sensitivities can be linearly added to construct a number of useful
estimators. By summing absolute sensitivities $|S_f^{(i)}|$ over the
data points $i$ of a given data set $E$, we find the maximal cumulative
sensitivity of $E$ to the PDF dependence of a QCD observable $f$.
Alternatively, from the examination of multiple $\{x,\mu\}$ maps for $\left|S_{f}\right|$
of various PDF flavors collected on the website \cite{PDFSenseWebsite},
we find that the most precise experiments constrain several flavors
at the same time; most notably, the combined HERA
data. For the purpose of identifying such experiments, we can compute an
overall sensitivity statistic for each experiment $E$ to the parton
distributions $f_a(x_i,\mu_i)$ evaluated at the same kinematic parameters
$\{x_i, \mu_i\}$ as the data.
Furthermore, to obtain one overall ranking, we can add
up sensitivity measures as an unweighted sum over the ``basis PDF'' flavors,
such as the six light flavors ($\overline{d},\,\overline{u},\,g,\,u,\,d,\,s$).
To obtain these measures, we say that an experiment $E$ consisting of
$N_{\mathit{pt}}$ physical measurements can be characterized by its mean sensitivity per raw data point\footnote{
For those circumstances in which an individual measurement, {\it e.g.}, obtained
via the Drell-Yan process, maps to two sensitivity values in $\{x,\mu\}$ space, we
compute the average of these and assign the result to that specific measurement.
}
to a PDF of given flavor $f_a(x,\mu)$:
$\langle|S^E_f|\rangle \equiv (N_{\mathit{pt}})^{-1} \sum_{i=1}^{N_{\mathit{pt}}}\left|S_{f}\right|(x_{i},\mu_{i})$,
from which we derive several additional statistical measures of experimental sensitivity.
For each experiment and flavor we then determine a cumulative sensitivity measure, numerically adjusted to the size of each experimental dataset $E$,
according to $|S^E_{f}| \equiv N_{\mathit{pt}}\, \langle|S^E_f|\rangle$.
In addition, we also track cumulative, flavor-summed sensitivity
measures $\sum_{f}|S^E_{f}|$ and
$\langle\sum_{f}|S^E_f|\rangle$, with $f$ running
over $\overline{d},\,\overline{u},\,g,\,u,\,d,\,s$.
We list the corresponding values of these four types of sensitivities
for each experiment of the CTEQ-TEA dataset in summary tables
in App.~\ref{sec:Tables}
as well as extensive Supplementary Material in App.~\ref{sec:SM}. This is also
detailed for categories of experiments from the CTEQ-TEA dataset.
With the above estimators, we {\it quantify}
and {\it compare} the cumulative sensitivities of each experiment to the basis 6
parton flavors. In fact, based on the various trials that we
performed, we find that the cumulative
sensitivity to the 6 basic flavors is a good measure of the overall
sensitivity to a large range of PDF combinations.
Recall that the $N_f=5$ CT14HERA2 PDFs (with up to 11 independent
parton species) are obtained by DGLAP evolution of the 6
basic parton flavors from the initial scale of order 1 GeV.
There exist alternative approaches for measuring the importance of a given
experiment in a global fit, for example, by counting the numbers of eigenvector
parameters \cite{Pumplin:2009sc} or eigenvector directions
\cite{Harland-Lang:2014zoa} that the experiment constrains. Those
other methods, however, require access to the full machinery of the global fit,
while the sensitivities allow the reader to rank the experiments
according to much the same information, for a variety of PDF-dependent
observables, with the help of
\textsc{PDFSense}, and at a fraction of computational cost.
In fact, in a companion study we use the above sensitivity estimators to select the new LHC
experiments for the inclusion in the next generation of the CTEQ-TEA
PDF analysis. Full tables given in App.~\ref{sec:Tables} and in the Supplementary Material of App.~\ref{sec:SM}
provide detailed information about the PDF sensitivities of every
experiment of the CTEQ-TEA data set.
For a non-expert reader, along the full tables, we provide
their simplified versions in Tables~\ref{tab5}-\ref{tab6},
where we rank the experimental sensitivities
according to a reward system described in the caption of Table~\ref{tab5}.
In each table, experiments are listed in descending order according
to the cumulative sensitivity measure $\sum_{f}|S^E_{f}|$ to the
six light-parton flavors. For each PDF flavor, the experiments with
especially high overall flavor-specific sensitivities receive an ``\textbf{A}''
rating (shown in bold), per the convention in the caption of
Table~\ref{tab5}. Successively
weaker overall sensitivities receive marks of ``B'' and ``C,'' while
those falling below a lower limit $|S^E_{f}|=20$ are left unscored.
We similarly evaluate each experimental dataset based on its point-averaged
sensitivity, in this case scoring according to a complementary scheme
in which the highest score is ``\textbf{1}''. The short-hand names of
the candidate experiments that were {\it not} included in the
CT14HERA2 NNLO fit, that is, the new LHC experiments, are also shown
in bold to facilitate their recognition in the tables.
Not only do the sensitivity rankings confirm findings known
by applying other methods, they also provide new insights.
According to this ranking system in
Tables~\ref{tab5}-\ref{tab6}, we find that the expanded HERA dataset
(HERAI+II'15) tallies the highest overall sensitivity to the PDFs,
with enhanced sensitivity to the distributions of the $u$- and $\bar{u}$-quarks,
as well as that of the gluon.
On similar footing, but with slightly weaker overall sensitivities, are
a number of other fixed-target measurements, including structure
function measurements from BCDMS for $F^{p,d}_2$ (BCDMSp'89, BCDMSd'90) and CCFR extractions
of $xF^p_3$ (CCFR-F3'97) --- as well as several other DIS datasets.
Among the LHC experiments, the inclusive jet measurements have the
highest cumulative sensitivities, with CMS jets at 8 TeV (CMS8jets'17),
7 TeV (CMS7jets'13, CMS7jets'14), and ATLAS 7 TeV (ATLAS7jets'15)
occupying positions 10, 12/13, and 16 in the total sensitivity
rankings. They demonstrate the strongest sensitivities among the candidate LHC
experiments, and at the same time are not precise enough and fall behind the top
fixed-target DIS and Drell-Yan experiments: BCDMS, CCFR, E605, E866,
and NMC. The two versions CMS7jets'13 and CMS7jets'14 of the CMS 7 TeV jet
data that largely overlap have very
close sensitivities and rankings in
Tables~\ref{tab5}-\ref{tab6}. The set CMS7jets'13 that extends to higher $p_{Tj}$ has a
slightly better overall sensitivity, surpassing the larger data set
CMS7jets'14 that includes the extra data points at $p_{Tj}<100$ GeV or
$|y_{j}|>2.5$, yet cannot beat CMS7jets'13 except for in
the overall sensitivity to the Higgs cross section at 7 TeV.
Going beyond the rankings based upon overall sensitivities, which are
more closely tied to the impact of an entire experimental dataset
in aggregate, it is useful to consider the point-averaged sensitivity
as well, which quantifies how sensitive each individual point
is. [Some experiments with very high point-averaged sensitivity have a
small cumulative sensitivity because of a small number of points.]
Based on their high point-averaged sensitivity, CMS $\mu$ asymmetry
measurements at 8 and 7 TeV (CMS8Wasy'16 and CMS7Masy2'14) especially stand
out, despite their small number of individual points, $N_{\mathit{pt}}=11$);
this is especially true again for the gluon, $\overline{d}$-, and
$u$-quark PDFs, for which this set of measurements is particularly
highly rated in Table~\ref{tab5}. Another ``small-size'' data set with
the exceptional point-average sensitivity is the
$\sigma_{pd}/(2\sigma_{pp})$ ratio from the E866 lepton pair
production experiment (E866rat'01). The average sensitivity of this data set to
$\overline u$ and $\overline d$ PDFs is 0.8, making it extremely valuable
for constraining the ratio $\overline{d}/\overline{u}$ at $x\sim 0.1$,
in spite of its small size (15 data points).
Aside from the quark- and gluon-specific rankings of specific measurements,
we can also assess experiments based upon the constraints they impose
on various interesting flavor combinations and observables as presented
in Table~\ref{tab6}. As was the case with Table~\ref{tab5}, a
considerable amount of information resides in Table~\ref{tab6} of
which we only highlight several notable features here. Among these
features are the sharp sensitivities to the Higgs cross section (\textit{e.g.}, $|S|_{H7}$, $\langle|S_{H7}|\rangle$, \textit{etc.}) found for
Run I$+$II HERA data, as well as the tier-C overall sensitivities
of the BCDMS $F^{p,d}_2$ and CMS jet
production measurements, corresponding to Exps.~BCDMSd'90, BCDMSp'89, CMS8jets'17 and CMS7jets'14.
While their
overall sensitivity is small, the corresponding ATLAS $t\overline{t}$
data also possesses significant point-averaged sensitivity. On the other
hand, measurements of $p_{T}$-dependent $Z$ production (ATL7ZpT'14, ATL8ZpT'16)
appear to have somewhat less pronounced sensitivity to the gluon and other PDF flavor
combinations. The total and mean sensitivities of high-$p_T$ $Z$ boson
production experiment ATL8ZpT'16 at 8 TeV is on par with HERA
charm SIDIS data (HERAc'13) and provides comparable constraints to charm
DIS production, albeit in a different $\{x,\mu\}$ region.
For the light-quark PDF combinations like $u_{v},\,d_{v},\,d/u,$
and $\overline{d}/\overline{u}$, the various DIS datasets \textemdash{}
led by Run II of HERA and CCFR measurements of the proton structure
function \textemdash{} demonstrate the greatest sensitivity. At the
same time, however, Run-2 Tevatron data from D0 on the $\mu$ asymmetry (D02Easy2'15)
and Run-1 CDF measurements for the corresponding $A_e(\eta^e)$ asymmetry (CDF1Wasy'96)
also exhibit substantial point-wise sensitivity as well. We collect
a number of other observations in the conclusion below,
Sec.~\ref{sec:Conclusions}.
\subsection{Estimating the impact of LHC datasets on CTEQ-TEA fits}
\label{sec:CTEQfit}
The presented rankings suggest that including the candidate LHC data
sets will produce mild improvements in the uncertainties of
the CT14 HERA2 PDFs. This projection may appear underwhelming, but
keep in mind that the CT14HERA2 NNLO analysis
already includes significant experimental constraints, for example,
imposed on the gluon PDF at $x>0.01$ by the Tevatron and LHC jet
experiments, CDF2jets'09, D02jets'08, ATL7jets'12, CMS7jets'13. If all jet experiments are eliminated
from the PDF fit, as illustrated in the Supplementary Material tables of App.~\ref{sec:SM}, the candidate LHC
experiments will be promoted to higher rankings, with the CMS 8 and 7 TeV jet experiments
(CMS8jets'17 and CMS7jets'13/CMS7jets'14) elevated to positions 4 and 7/8 in the overall sensitivity rankings,
respectively.
Our investigations also find that the sensitivities of
CMS jet experiments may improve considerably if
the current correlated systematic effects are moderately reduced
compared to the published values.
For instance, by
requiring a full correlation of the JEC2 correlation error over all
rapidity bins in the CMS 7 TeV jet data set CMS7jets'14, instead of its
partial decorrelation implemented according to the CMS recommendation
\cite{Khachatryan:2014waa}, we obtain a very strong sensitivity of the
data set CMS7jets'14 to $g$ over the full $\{x,\mu\}$ region; but also strong
sensitivities to $\overline u, \overline d$, and even $\overline s$
PDFs.\footnote{With the fully correlated jet energy correction JEC2 source, the data set CMS7jets'14
would provide a strong overall constraint on $s(x,\mu)$ comparable to
one of the NuTeV or neutrino CCFR experimental data sets.}
The overall sensitivity of the data set CMS7jets'14 in this case is
elevated to the 4th position from the 13th position in the CT14HERA2
NNLO analysis in Tables~\ref{tab5} and \ref{tab6}. Similarly, for the CMS
8 TeV jet data set CMS8jets'17, the sensitivity to the above flavors can
increase under moderate reduction of systematic uncertainties, easily
surpassing the sensitivity of CMS7jets'14 because of the larger number of
points in CMS8jets'17.
\subsection{Comparing {\sc PDFSense} predictions to post-fit constraints from Lagrange Multiplier scans}
\label{sec:Validation}
\begin{figure}[p]
\hspace*{-0.2cm}\includegraphics[clip,width=0.46\textwidth]{figs/sens_LM_du_refit.pdf} \ \
\includegraphics[clip,width=0.53\textwidth]{figs/LM_du_scan2T2.pdf}
\caption{
Left: the \textsc{PDFSense} map for the sensitivity of the
fitted dataset of the CT18pre NNLO analysis to the $d/u$ PDF ratio,
$d/u(x\!=\!0.1,\mu\!=\!1.3\, \mbox{ GeV})$. Right:
Dependence of $\chi^2$ for the individual and all experiments
of the CT18pre dataset on the value of $d/u(x\!=\!0.1,\mu\!=\!1.3\, \mbox{ GeV})$
obtained with the LM scan technique. The curves show the deviations
$\Delta \chi^2_\mathrm{expt.}\equiv\chi^2_\mathrm{expt.}(\vec a)-\chi^2_\mathrm{expt.}(\vec a_0)$
from the best-fit values in $\chi^2$ for the indicated experiments, as well as for the totality of
all experiments.
}
\label{fig:valid_du}
\end{figure}
\begin{figure}[p]
\hspace*{-0.2cm}\includegraphics[clip,width=0.46\textwidth]{figs/sens_LM_gMH_refit.pdf} \ \
\includegraphics[clip,width=0.53\textwidth]{figs/LM_gMHT_scan2T.pdf}
\caption{
Like Fig.~\ref{fig:valid_du}, but comparing the \textsc{PDFSense} map (left)
and LM scan (right) for the gluon PDF $g(x\!=\!0.01,\mu\!=\!m_H)$ in the Higgs boson production region.
}
\label{fig:valid_higgs}
\end{figure}
How do the surveys based on \textsc{PDFSense} compare against the actual
fits? As we noted, the \textsc{PDFSense} method is designed to provide a
fast large-scope estimation of the impact of the existing and future
data sets in conjunction with other tools, such as the \textsc{ePump} \cite{Schmidt:2018hvu}
program for PDF reweighting. It works the best in the quadratic
(Hessian) approximation near the best fit, and when the new experiments
are compatible with the old ones. When detailed understanding of the
experimental constraints is necessary, the \textsc{PDFSense} approach
must be supplemented by other techniques, such as Lagrange
multiplier (LM) scans \cite{Stump:2001gu,Pumplin:2000vx,Brock:2000ud}.
As an illustration of the scope of the differences between the
\textsc{PDFSense} predictions before and after the fit,
the left panels in Figs.~\ref{fig:valid_du} and \ref{fig:valid_higgs}
show the \textsc{PDFSense} maps for
$d/u(x\!=\!0.1,\mu\!=\!1.3\,\mbox{ GeV})$ and
$g(x\!=\!0.01,\mu\!=\!125 \mbox{ GeV})$ evaluated using a
preliminary CT18 NNLO fit (designated as ``CT18pre'') that includes 11 new
LHC experimental data sets, namely CMS8jets'17, CMS7jets'14,
ATLAS7jets'15, LHCb8WZ'16, CMS8Wasy'16, LHCb8Zee'15, LHCb7ZWrap'15, ATL8ZpT'16, ATL8ttb-pt'16, ATL8ttb-mtt'16,
and 8 TeV $t\bar{t}$ production at CMS (`CMS8 ttb pTtyt') \cite{Sirunyan:2017azo} in
addition to the experiments included in the CT14HERA2 fit. The full
details of the CT18 fit will be presented in an upcoming
publication \cite{CT18}. Some modifications were made in the
methodology adopted in CT18, as compared to CT14HERA2; notably the PDF
parametrization forms and treatment of NNLO radiative contributions
have been changed, while some shown curves are also subject to a
theoretical uncertainty associated with the QCD scale
choices. In accord with the
\textsc{PDFSense} predictions based on the CT14HERA2 NNLO PDFs, we find
that including the above LHC experiments into the fit
produces only mild differences between the CT18pre and
CT14HERA2 NNLO PDFs. Consequently the \textsc{PDFSense} $\{x,\mu\}$ maps based on
CT18pre NNLO PDFs are similar to the CT14HERA2 ones
\cite{PDFSenseWebsite}. One noticeable difference is that the
sensitivity of the new experiments decreases after they are included
in the CT18pre fit, because the new information from the newly
added experiments suppresses PDF uncertainties of data residuals.
In the right panels of Figs.~\ref{fig:valid_du}
and \ref{fig:valid_higgs}, we illustrate the constraints on the same
quantities, $d/u(0.1,1.3\mbox{ GeV})$ and $g(0.01,125\mbox{ GeV})$
in the candidate CT18pre NNLO fit, now obtained with the help of
LM scans. A LM scan \cite{Stump:2001gu,Pumplin:2000vx,Brock:2000ud}
is a powerful technique that elicits detailed information about a
PDF-dependent quantity $X(\vec a)$, such as a PDF or cross section,
from a constrained global fit in which the value of $X(\vec a)$ is fixed by
an imposed condition. By minimizing a modified goodness-of-fit function
$\chi^2_{LM}(\lambda,\vec{a})$ that includes a `generalized-force'
term equal to $X(\vec{a})$ with weight $\lambda$, in addition to the
global $\chi_{global}^2$ in Eq.~(\ref{eq:chi2glob}), a LM scan reveals
the parametric relationship between $X(\vec a)$ and
$\chi^2_\mathrm{global}$ or $\chi^2_\mathrm{expt.}$ contributions from
individual experiments, including any non-Gaussian dependence.
In the LM scans at hand, the modified fitted function takes the form
\begin{equation}
\chi^2_{LM}(\lambda,\vec{a}) = \chi^2_\mathrm{global}(\vec{a}) + \lambda X(\vec{a}),\
\end{equation}
and $X(\vec a)$ are $d/u(x,\mu)$ or $g(x,\mu)$ at a specific location in
$\{x,\mu\}$ space. For the optimal parameter combination
$\vec{a} \equiv \vec{a}_0$ at which $\chi^2_\mathrm{global}(\vec{a})$ is minimized,
we find in Fig.~\ref{fig:valid_du} that $d/u(0.1,1.3\mbox{ GeV}) \approx 0.7$. The LM scan for the
$d/u$ then consists of a series of refits of the parameters
$\vec{a}_k$, as the multiplier parameter $\lambda$ is dialed along a set
of discrete values $\lambda_k$, effectively
pulling $d/u$ away from the value $\sim\! 0.7$ at $\vec{a} = \vec{a}_0$
preferred by the global fit. The right panel of Fig.~\ref{fig:valid_du}
shows the relationship between
$d/u(0.1,1.3\mbox{ GeV})$ and $\chi^2_\mathrm{global}$ that is quantified
this way; and similarly for $g(0.01,125\mbox{ GeV})$.
We can also examine how the $\chi^2$ changes for the individual
experiments. Figs.~\ref{fig:valid_du} and \ref{fig:valid_higgs} show
the curves for 11 experiments with the largest variations
$\mathrm{max}(\chi^2)-\mathrm{min}(\chi^2)$ in the shown ranges of $d/u$
and $g$, i.e., the most constraining experiments.
We notice that, while the $\Delta\chi^2$ dependence is
nearly Gaussian for the total $\chi^2$, it is sometimes less so for
the individual experiments. Some experiments may be inconsistent
when they have a large best-fit $\chi^2(\vec a_0)$ or
prefer an incompatible $X$ value. Figure~\ref{fig:valid_du} is an
example of a good agreement between the experiments, when the individual
$\Delta\chi^2_{expt.}$ curves are approximately quadratic and
minimized at about the same location. Figure~\ref{fig:valid_higgs}
shows more pronounced inconsistencies, notably in the case of the E866pp
and ATL8ZpT curves that prefer a significantly larger
$g(0.01, 125\mbox{ GeV})$ than in the rest of the
experiments.
The LM procedure thus allows a systematic exploration
of the exact constraints from the experiments on $X$
without relying on the Gaussian assumption
that is inherent to the \textsc{PDFSense} method.
Both \textsc{PDFSense} and LM scans successfully identify the experiments with the strongest sensitivity
to $X$, while their specific rankings of such experiments are not
strictly identical and reflect the chosen
ranking prescription and settings of the global fit.
We emphasize that, though informative, the LM scans are computationally intensive, with a typical
30-point scan at NNLO requiring $\sim\!\! 6500$ CPU core-hours on a
high-performance cluster. This is in contrast to the \textsc{PDFSense}
analysis, which can be run for our entire 4021-point dataset on a single CPU core
of a modern workstation in $\sim\!\! 5$ minutes, representing
a $\sim\! 0.8 \times 10^5$ savings in computational cost.
\begin{table}
\begin{tabular}{|c c| c || c c| c|}
\hline
\multicolumn{3}{|c||}{$d/u(x\!=\!0.1,\mu\!=\!1.3\,\mbox{ GeV})$}
&\multicolumn{3}{c|}{$g(x\!=\!0.01,\mu\!=\!125 \mbox{ GeV})$} \tabularnewline
\multicolumn{2}{|c|}{\textsc{PDFSense}} & LM scan & \multicolumn{2}{c|}{\textsc{PDFSense}} & LM scan \tabularnewline
\hspace{0.5cm} CT14HERA2 \ \ & \ \ CT18pre \ \ & \ \ CT18pre \ \ & \ \ CT14HERA2 \ \ & \ \ CT18pre \ \ & \ \ CT18pre \hspace{0.3cm} \tabularnewline
\hline
\hspace{0.5cm} HERAI+II'15 & NMCrat'97 & NMCrat'97 & HERAI+II'15 & HERAI+II'15 & HERAI+II'15 \hspace{0.3cm} \tabularnewline
\hspace{0.5cm} BCDMSp'89 & HERAI+II'15 & CCFR-F3'97 & CMS8jets'17 & CMS8jets'17 & CMS8jets'17 \hspace{0.3cm} \tabularnewline
\hspace{0.5cm} NMCrat'97 & BCDMSp'89 & HERAI+II'15 & CMS7jets'14 & CMS7jets'14 & ATL8ZpT'16 \hspace{0.3cm} \tabularnewline
\hspace{0.5cm} CCFR-F3'97 & CCFR-F3'97 & BCDMSd'90 & ATLAS7jets'15 & E866pp'03 & E866pp'03 \hspace{0.3cm} \tabularnewline
\hspace{0.5cm} E866pp'03 & BCDMSd'90 & BCDMSp'89 & E866pp'03 & ATLAS7jets'15 & ATLAS7jets'15 \hspace{0.3cm} \tabularnewline
\hspace{0.5cm} BCDMSd'90 & E605'91 & CDHSW-F3'91 & BCDMSd'90 & BCDMSd'90 & CCFR-F2'01 \hspace{0.3cm} \tabularnewline
\hspace{0.5cm} CDHSW-F3'91 & E866pp'03 & E866rat'01 & CCFR-F3'97 & BCDMSp'89 & D02jets'08 \hspace{0.3cm} \tabularnewline
\hspace{0.5cm} CMS8jets'17 & E866rat'01 & CMS7Masy2'14 & D02jets'08 & D02jets'08 & HERAc'13 \hspace{0.3cm} \tabularnewline
\hspace{0.5cm} E866rat'01 & CMS8jets'17 & NuTeV-nu'06 & NMCrat'97 & NMCrat'97 & NuTeV-nub'06 \hspace{0.3cm} \tabularnewline
\hspace{0.5cm} LHCb8WZ'16 & CDHSW-F3'91 & CMS8jets'17 & BCDMSp'89 & CDHSW-F2'91 & CCFR-F3'97 \hspace{0.3cm} \tabularnewline
\hline
\end{tabular}
\caption{
We list the top 10 experiments predicted to drive knowledge of the
$d/u$ PDF ratio and of the gluon distribution in the Higgs region
according to \textsc{PDFSense} and LM scans.
For both, we list the \textsc{PDFSense} evaluations based both
on the CT14HERA2 fit and on a preliminary CT18pre fit
in the first and second columns on either side of the
double-line partition.
}
\label{tab:valid}
\end{table}
Let us further illustrate these observations by referring again to
Figs.~\ref{fig:valid_du} and \ref{fig:valid_higgs}, as well as to
Table~\ref{tab:valid} that displays the top 10 experiments with the
largest cumulative sensitivity to $d/u(0.1,1.3 \mbox{ GeV})$ and
$g(0.01,\ 125 \mbox{ GeV})$ according to \textsc{ PDFSense} and LM
scans, with either CT14HERA2 or CT18pre PDFs used to
construct the \textsc{PDFSense} rankings.
In the \textsc{PDFSense} columns, the experiments are ranked in order
of descending cumulative sensitivities $\sum_{i=1}^{N_{pt}} |S_{f}|(x_i,\mu_i)$ according to the
same prescription as in Sec.~\ref{sec:Experiment-rankings-according}.
For the LM scans, the table shows the experiments that have the
largest variations $\mathrm{max}(\chi^2)-\mathrm{min}(\chi^2)$ in the
range of $X$ corresponding to $\Delta \chi^2_{global}\leq 100$, that
is, within approximately the 90\% probability level interval of the CT18pre NNLO
PDFs. As the residual uncertainties $\Delta r_i$ in the sensitivities $S_f$ are normalized to
the root-mean-squared residuals $\langle r_0\rangle_E$ at the best fit,
cf. Eq.~(\ref{eq:sens}), we similarly divide
$\mathrm{max}(\chi^2)-\mathrm{min}(\chi^2)$ by the best-fit
$\chi^2(\vec{a}_{0})/N_\mathit{pt}$ of the experiment in the rankings for the LM scans in Table~\ref{tab:valid}.
From the side-by-side examination of the figures and the table, we can draw a broad conclusion
that both the pre-fit \textsc{PDFSense} and post-fit LM scan
approaches agree in identifying the most constraining
experiments, even though they may result in different orderings of these
experiments. This agreement is especially impressive
in the instance of $d/u(x\!=\!0.1,\mu\!=\!1.3\,\mbox{ GeV})$, when
the rankings agree on 8 out of 10 leading experiments, confirming the
dominance of the NMC $p/d$ ratio, HERAI+II, CCFR $F_3$, and
BCDMS $p$ and $d$ measurements. For $g(x\!=\!0.01,\mu\!=\!m_H)$,
for which we see more tension and non-Gaussian behavior in Fig.~\ref{fig:valid_higgs},
both \textsc{PDFSense} and LM scans concur on the crucial role played by the top 5-6 experiments, namely,
HERAI+II, E866pp, and inclusive jet production data from CMS, ATLAS, and
D0 Run-2. The upward pull on $g$ from the incompatible ATL8ZpT data set seen
in Fig.~\ref{fig:valid_higgs} modifies the rankings of the trailing
experiments, such as CMS7 jets or BCDMS. Based upon an extended
battery of LM scans we have performed, including the two examples
presented here, we conclude that the \texttt{PDFSense} surveys perform
as intended.
Lastly, we reiterate that a number of subtleties exists in comparing
the results of LM scans and \textsc{PDFSense} sensitivity plots. Most importantly,
\textsc{PDFSense} is intended by conception as a tool to quantify the
anticipated {\it average} impact of potentially unfitted data
based upon their precision in comparison to the PDF
uncertainties. We discussed simplifying assumptions made in
\textsc{PDFSense} in order to bypass certain complexities of the full
fit and obtain quick estimates.
LM scans, on the other hand, provide post-fit assessments of the contributions of specific
data to the global $\chi^2$ function, as specific quantities predicted
by the QCD analysis are dialed away from
their optimal values. In the comparisons we made,
the detailed pictures produced by both \textsc{PDFSense} and the LM
scans depend on a variety of theoretical settings like pQCD scale
choices, as well as upon the specific implementation of correlated
experimental uncertainties [from up to $\sim\!\! 100$ different sources in
some experiments] and the parametric forms chosen for the nonperturbative
parametrizations at the starting scale $\mu = Q_0$. The inclusion of additional theory uncertainties
and decorrelation of some experimental correlated errors are
necessitated in a few experiments
by the relatively large $\chi^2$ values that would otherwise be obtained.
All these have some peripheral effect on the specific orderings of experiments shown in Table~\ref{tab:valid}.
Thus, rather than anticipating an exact point-to-point matching
between the \textsc{PDFSense} and LM methods, we instead expect, and
indeed find, the general congruity between the most important
experiments identified by the two approaches illustrated in this section.
\section{Conclusions }
\label{sec:Conclusions}
In the foregoing analysis, we have confronted the modern challenge
of a rapidly growing set of global QCD data with new statistical methodologies
for quantifying and exploring the impact of this information. These
novel methodologies are realized in a new analysis tool \textsc{PDFSense
\cite{PDFSenseWebsite},} which allows the rapid exploration of the
impact of both existing and potential data on PDF determinations,
thus providing a means of weighing the impact of measurements of QCD
processes in a way that allows meaningful conclusions to be drawn
without the cost of a full global analysis. We expect this approach
to guide future PDF fitting efforts by allowing fitters to examine
the world's data \textit{a priori,} so as to concentrate analyses on
the highest impact datasets. In particular, this work builds upon
the existing CT framework with its reliance on the Hessian formalism
and assumed quasi-Gaussianity, but these features do not impact the validity
of our analysis and conclusions.
Our approach provides a means to carry out a detailed study of
data residuals, for which we explored novel visualizations in several
ways, including the PCA, t-SNE, and reciprocated distance approaches
discussed in Sec. \ref{subsec:Manifold-learning}. These techniques
show promise for moving forward by providing useful insights into the
numerical relationships among datasets and experimental processes.
Crucial to this analysis is the leveraging of both the existing and
proposed statistical measures laid out in Secs.~\ref{sec:Correlations} and \ref{sec:Sensitivities}.
Of these, the flavor-specific sensitivity $S_{f}$ of Eq.~(\ref{eq:sens})
for a data point to the PDF serves as a particularly powerful discriminator,
and we deployed it and the correlation $C_{f}$ of Eq.~(\ref{eq:corr})
to map PDF constraints provided by data over a wide range in $\{x,\mu\}$.
This was facilitated by the fact that the sensitivity and correlation
are readily computable over the extent of the global dataset. The
companion website collects a large number of figures illustrating
the sensitivities to various flavors as a function of $x$ and $\mu$.
To quantify the abundant information contained in the maps of sensitivities,
in Sec.~\ref{sec:Experiment-rankings-according}
we presented statistical estimators to systematically rank and assess subsidiary
datasets within the world's data according to their potential to be influential
in constraining PDFs. We note that one
is allowed some freedom in choosing a specific ranking prescription, but we find our
conclusions to be stable against variations among these possible choices. In this context,
we reaffirmed the unique advantage of DIS and jet production for determination of the PDFs.
Many intriguing physics results can be established using our
sensitivity methods, and the specific results in the previous sections
are only illustrative examples. We stress that these results take
the complementary form of sensitivity tables (for example, Table \ref{tab5})
and $\{x,\mu\}$ plots (such as Fig. \ref{fig:CorrSensH14}), which
respectively offer global categorizations of the experimental landscape and
detailed mappings of the placements of PDF constraints in
$\{x,\mu\}$ space. In totality, the full range of physics insights from this method
is beyond the scope of the present article, but the interested user
can explore them using our \textsc{PDFSense} package at \cite{PDFSenseWebsite}.
We mention only a representative sample of these to motivate the reader:
\begin{itemize}
\item A wide range of experimental processes possess sensitivity to the
nucleon's quark sea distributions; for example, for the distribution
$\overline{d}(x,\mu)$, the $\sigma_{pd}$ DY measurements of E866
(E866rat'01) exhibit strong sensitivity, but so do DY data from E605 (E605'91)
as well as (at larger $\mu$) information on the $\mu$-production
asymmetry $A_{\mu}(\eta)$ from CMS at 7 TeV (CMS7Masy2'14); at high $x$ and
$\mu$, CMS inclusive jet data (CMS8jets'17, CMS7jets'14) also acquire some sensitivity
to $\bar u$ and $\bar d$.
Still, however, the recent HERA data (HERAI+II'15) registers the greatest
overall sensitivity.
\item Were they taken cumulatively together as a single dataset, CMS jet
production at 7 and 8 TeV (CMS7jets'14 and CMS8jets'17) would provide a total sensitivity
$|S^E_s| = 11.9 + 8.11$ to $s(x,\mu)$ that is comparable to
one of the NuTeV (NuTeV-nu'06) or CCFR (CCFR SI nu'01, CCFR SI nub'01) dimuon SIDIS experiments,
which have very strong average sensitivity to the strange
distribution. Still, the strongest constraint is contributed by
a mix of the DIS measurements, including $\nu\mu\mu$ data from NuTeV
(NuTeV-nu'06), data on $\nu(\overline{\nu})\mu\mu$ processes from SIDIS
at CCFR (CCFR SI nu'01 and CCFR SI nub'01), as well as the inclusive DIS data at lower $x$ from
HERA1+2 (HERAI+II'15) that actually has the strongest cumulative sensitivity.
Similarly, various vector boson production data sets have a rank-3
point-averaged sensitivity to the strangeness, including
the $A_{\mu}(\eta^\mu)$ data from D0 (D02Masy'08) and CMS (CMS8Wasy'16, CMS7Masy2'14), as well
ATLAS $W/Z$ production (ATL8DY2D'16, ATL7WZ'12) and high-$p_T$ $Z$ production (ATL8ZpT'16)
cross sections. Although each of the
individual vector boson production data set has a weak cumulative sensitivity
to $s(x,\mu)$ because of a small number of data points,
in totality a group of {\it mutually consistent} LHC experiments on
vector boson production can
provide a competing constraint on $s(x,\mu)$ that confronts the
low-energy CCFR/NuTeV constraints.
\item Knowledge of the charm distribution $c(x,\mu)$ is most influenced
by a number of datasets, with HERA (HERAI+II'15) at low $x$ especially important.
Fixed target measurements, particularly those of CDHSW on the proton's
$F_{2}^{p}$ structure function (CDHSW-F2'91) have strong sensitivity at slightly
higher $x\!\sim\!10^{-1}$, while a wide range of jet measurements, including
7 TeV data from ATLAS (ATLAS7jets'15) and CMS (CMS7jets'14), and 8 TeV CMS (CMS8jets'17) points
are also sensitive. This pattern of sensitive
measurements broadly follows the corresponding plot for $|S_{g}|(x_{i},\mu_{i})$
{[}as well as $|S_{b}|(x_{i},\mu_{i})${]} due to the dominance of
boson fusion graphs in heavy quark production. The datasets of
importance we identify are broadly consistent with the conclusions
of the recent CT14 analysis \cite{Hou:2017khm} of the nucleon's
intrinsic charm \cite{Hobbs:2013bia}.
\item One can also study the correlations and sensitivities for various
derived PDF combinations. For instance, for the $\overline{d}/\overline{u}$
ratio representing deviations from flavor symmetry in the nucleon
sea, the E866 experiment (E866rat'01) shows exceptional point-averaged
sensitivity, $\langle|S_{\bar{d}/\bar{u}}|\rangle=1.67$ such that
its ``C'' ranking for its overall sensitivity to $\bar{d}/\bar{u}$
places it in the company of only a few other DIS and DY experiments, despite
their much larger number of measurements, $N_{\mathit{pt}}=15$. At somewhat lower $x\gtrsim0.01$,
NMC data on the structure function ratio $F_{2}^{d}/F_{2}^{p}$ (NMCrat'97)
show sensitivity in the range $0.8<|S_{\overline{d}/\overline{u}}|<2$.
At still lower $x$, the CMS 8 and 7 TeV $A_{\mu}$ points (CMS8Wasy'16, CMS7Masy2'14) and
$W/Z$ data from LHCb (LHCb8WZ'16) show strong pull, corresponding to
point-averaged rankings of ``2,'' ``{\bf 1},'' and ``2,'' respectively.
\item We also consider the PDF ratio $d/u(x,\mu)$, which often serves as
a discriminant among various nucleon structure models, especially at
high $x$. For $x>0.1$ an amalgam of fixed-target experiments, including
the NMC $F_{2}^{d}/F_{2}^{p}$ data (NMCrat'97) particularly, but also $F_{2}^{p}$
measurements from BCDMS (BCDMSp'89) and CCFR (CCFR-F2'01) as well as $xF_{3}^{p}$ data
from CCFR drive the current status.
At higher $\mu$, however, the LHCb $W/Z$ data (LHCb8WZ'16) and $A_{e}(\eta)$
measurements from Run-2 of D0 (D02Easy2'15) also constrain the high $x$
behavior of $d/u$ together with $A_{\mu}(\eta)$ points
from CMS at 7 TeV (CMS7Masy2'14).
\item
More generally, we note that, among the new LHC experiments to be considered for future
global fits, the datasets for inclusive jet production are expected to have the greatest
impact, followed by a group of vector boson production experiments at ATLAS, CMS, and LHCb.
We find that the constraints from jet production at the LHC depend significantly on
the treatment of experimental systematic uncertainties --- especially the correlated systematic errors.
It is conceivable that, with the full implementation of NNLO theoretical cross sections and
modest reduction in the experimental systematic uncertainties, the constraints from the LHC jet
production will catch up in strength to the effect of adding a large fixed-target DIS dataset, such as
BCDMS $F^p_2$ (BCDMSp'89). Meanwhile, the magnitude of the constraint on the gluon PDF from high-$p_T$ $Z$
production (ATL8ZpT'16) is comparable to those from the combined HERA SIDIS charm dataset (HERAc'13) or
inclusive jet production from CDF Run-2 (CDF2jets'09); that is, the high-$p_T$ $Z$ data are significant
in the event that the jet datasets are not included, in overall consistency with the findings in
Ref.~\cite{Boughezal:2017nla}. The smaller ATLAS $t\overline{t}$ production data sets (ATL8ttb-pt'16,
ATL8ttb-y\_ave'16, ATL8ttb-mtt'16, ATL8ttb-y\_ttb'16) have strong point-by-point sensitivity to the gluon,
but will have a more diminished role when combined with other, larger data sets. HERA DIS (HERAI+II'15),
BCDMS $F_2^d$ (BCDMSd'90), and CMS inclusive jets at 8 TeV (CMS8jets'17) render the strongest overall
constraints on the Higgs production cross section at the LHC according to the rankings in Table~\ref{tab6}.
\end{itemize}
Quantifying correlations and sensitivities thus provides a comprehensive means of
evaluating the ability of a global dataset to constrain our knowledge
of nucleon structure. It must be emphasized,
however, that this analysis is not a substitute for actually performing
a QCD global analysis, which remains the single most robust means
of determining the nucleon PDFs themselves. Rather, the method presented
in the paper is a guiding tool to both supplement and direct fits
by gauging the potential for improving PDFs with the incorporation of new
datasets.
The essential ingredients of this study are the PDF-residual correlation
and sensitivity $|C_{f}|$ and $|S_{f}|$, with the latter representing
an extension of the correlation used elsewhere in the modern PDF literature.
These definitions are robust enough that we can exhaustively score
the data points in an arbitrary global dataset to construct and map
the resulting distributions, as shown in Figs.~\ref{fig:corr-main}
and \ref{fig:sens-main}. Accordingly, we found it possible to impose
cuts on these distributions to identify points of especially strong
correlation ($|C_{f}|>0.7$) or sensitivity ($|S_{f}|>0.25$); we
stress that these cuts are chosen as approximate indicators, and any
user can adjust them freely. On the other hand, the distributions
themselves, as shown in the second panels of Figs.~\ref{fig:corr-main} and \ref{fig:sens-main},
are not subject to such cut choices.
Although the conclusions of this analysis are resistant to alterations
in the basic approach, it is worth noting that other formats are possible
for evaluating experimental sensitivities and performing the rankings of
measurements. For example, one might use somewhat different matchings than
those outlined in App.~\ref{sec:supp} to extract $\{x,\mu\}$ points from the
experimental data, but we expect the resulting impact on
the overall picture to be minor. Similarly, while the ordering inside
ranking tables like Table~\ref{tab5} was decided according to the total
sensitivity to serve our specific goal of identifying the most valuable experiments
for the CTEQ-TEA fit, for other purposes one might produce alternative tables ranked
according to point-averaged sensitivities, or sensitivities to
specific flavors. Such alternate conventions would also yield important
information, and \textsc{PDFSense} allows the user to do this. It should
be stressed that these elections for the form of our presentation
can always be recovered from the more fundamental information ---
the numerical values of the sensitivities detailed in the Supplementary
Material of App.~\ref{sec:SM}.
While we have demonstrated these techniques in the context of the
CT14 family of global fits, they are of sufficient generality that
one could readily repeat our analysis using alternative PDF sets.
For the sake of testing this point and validating our predictions
for the most decisive experiments in the CTEQ-TEA dataset, we performed
a preliminary fit including the CT14HERA2 and the candidate LHC experiments
(`CT18pre'), and directly compared \textsc{PDFSense} predictions against
Lagrange multiplier scans quantifying the constraints these fitted measurements
imposed on select quantities. This provided a demonstration of the robustness
of our sensitivity-based analysis, which identified the same sets of high-impact
measurements {\it before fitting}.
The results of this study can be expected to vary somewhat depending
on the specifics of the PDF sets used to compute $|C_{f}|$ and $|S_{f}|$,
but we see this as an advantage of \textsc{PDFSense}. One
could imagine exploiting them to undertake a systematic analysis of the impact of various theoretical
assumptions implemented in competing global fits (\textit{e.g.}, the
choice of input PDF parametrization or the status of the perturbative
QCD treatment implemented in various processes). The sensitivity $S_f$
can be constructed either from the Hessian or Monte-Carlo PDF uncertainties,
as prescribed by Eqs.~(\ref{eq:sens}) and (\ref{eq:sensMC}), while the shifted
residuals that are crucial to our analysis can be recovered from any type of
covariance matrix, as argued in relation to Eq.~(\ref{eq:res-cov}).
In the same spirit but on
the side of the data, \textsc{PDFSense} empowers the user to evaluate
the combined impact of multiple experimental datasets \textemdash{}
for example, to evaluate the extent to which the impact of a proposed
experiment might be diminished by the constraints already imposed
by existing measurements. These various functions collectively suggest
a number of possible avenues to use the presented approach and the \textsc{PDFSense}
tool to advance PDF knowledge in the coming
years.
\subsection*{Acknowledgments}
We thank our CTEQ-TEA colleagues, Davison Soper, and Madeline Hamilton
for support and insightful discussions, and
appreciate helpful clarifications concerning the LHC
experimental data sets from Alexander Glazov, Uta Klein,
Bogdan Malescu, and Klaus Rabbertz. We also thank German Valencia,
Ursula Laa, and Dianne Cook for helpful discussions related to data visualizations based
on the PCA and t-SNE methods. This work was supported in part by the
U.S.~Department of Energy under Grant No.~DE-SC0010129 and by the
National Natural Science Foundation of China under the Grant No.~11465018.
T.J.~Hobbs acknowledges support from an EIC Center Fellowship.
The work of J.G. is sponsored by Shanghai Pujiang Program.
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"redpajama_set_name": "RedPajamaArXiv"
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Re-reading the Three Musketeers
16 February 2020 by Davide Mana 9 Comments
Yesterday a friend informed me that the most recent Italian translation of Dumas' The Three Musketeers was selling for 99 cents on Amazon in digital format. Now I have my old copy here somewhere in some box, but I did the math and realized it's been something like thirty-six years since I last read the mother of all swashbuckler novels, and so I sacrificed one buck and got me the ebook.
Now Dumas' novel is one of those books that, for some reason, some have decided are kid's books. The consequence is these books are pushed on the unwary teenagers, usually with massive cuts and rewrites to excise the bits that are most obviously unfit for a younger audience.
Which is something that drives me crazy – cutting an adult novel to make it kid-friendly because you have decided it's for kids in the first place.
The new Italian translation is very elegant and yet it goes like a freight train – I sat with it after dinner and read the first five chapters in about two hours.
Dumas manages to build a classical intrigue, while providing a tongue-in-cheek commentary on issues like power and politics. It is a historical novel, a spy story, a swashbuckling adventure, a distinctively cynical romantic melodrama and, given the fact that it was written 176 years ago and never went out of print, it's Literature.
And French Literature, to boot.
Because of all of its different levels of reading, The Three Musketeers, like many classics, deserves to be read and re-read, as different ages and experiences bring the reader a different appreciation of some issues.
And I'm having a lot of fun, re-reading it.
Should you be interested, you can find a free ebook version, in English and in various formats, on the pages of Project Gutenberg.
Categories: Books, Other People's Pulp | Tags: Alexandre Dumas, The Three Musketeers | Permalink.
9 thoughts on "Re-reading the Three Musketeers"
Yes to all that! THE THREE MUSKETEERS is one of the great swashbucklers, and the old movie with Gene Kelly as d'Artagnan and Van Heflin, Gig Young and Robert Coote as his musketeer amigos — and memorably, Lana Turner as the ice-blooded and aptly named Lady Winter. She is about the most memorable villainess in literature.
The sequels, like THE MAN IN THE IRON MASK, increased the dark and cynical decay in the political world. The Hollywood versions (of course) turned it into the old evil king with an identical double who replaces him and sets everything right schtick, again and again, in many a remake. Okay, often it's the reverse, the good king with an evil double who wants to replace him and establish a tyranny, but still a cliché.
In the Dumas novel, Aramis has fulfilled part of his ambition, risen in the church and become a bishop, but further ambition drives him to try to replace the king with his secretly imprisoned twin brother and rule behind the scenes. Aramis has become what he once fought against with his friends, in the person of Richelieu, and he involves the trusting Porthos and eventually gets him killed. Nor is one twin evil and the other good. Philippe, quite naturally, wants to get out of prison instead of rotting there, and Louis, equally naturally, doesn't want civil war which knowledge of his brother's existence might provoke — or at least plots of a palace revolution. Which is just what Aramis is scheming to engineer.
It's dark but it's realistic. D'Artagnan, now the captain of musketeers, picks the impostor because Philippe, after years in prison, is paler than the real king, and Philippe ends his life in the iron mask, saying bitterly, "Call me not monsieur or monseigneur, call me accursed."
Indeed, 20 Years After is the Dumas book that gets most mistreated in movie adaptations and "for kids" editing.
And I agree the Gene Kelly adaptation was great fun – and Lana Turner was never more beautiful.
And yet I have a soft spot for Richard Lester's 1970s adaptations (I mean… Oliver Reed, Christopher Lee, Charlton Heston and Faye Dunaway…)
There are a lot of good moments in the old "Three Musketeers" with Gene Kelly. As when he gets into duels with all three at once, and Athos says to him, "You're impatient!" D'Artagnan explains that he has another duel in an hour, and doesn't want to keep that gentleman waiting for his fight — then adds diffidently, "If I survive this one." Athos says kindly, "Just as you like, but don't worry about it! You won't survive."
Then, when the cardinal's guard shows up to arrest them, the four fight the curs in red tabards, and the musketeers get a load of the youngster's swordsmanship, one of Athos's friends asks him derisively, "Is that the peasant you were going to fight with your left hand?" and Athos shows a classic offended scowl.
They don't do it like that no more.
Yes, the old Musketeers movie is full of quotable bits, and it does have a great cast.
And I always found the scene of Milady's execution frightfuly atmospheric and visually impressive.
Stian Slethei
Love that book! I first read it in a cut and abridged version from the norwegian "GGG" series ( Gyldendahls Gode Guttebøker, wich translates to "Gyldendahls good books for boys") I think it used to belong to my father, and was one I inherited. I later read a three volume abridged version when visiting my grandmom , years later, and then bought and read a thick and heavy version while at the university. I felt personally slighted when I became adult enough to understand that they cut and edit books, to market them for kids. i now own a four volume unabridged version in norwegia, wich I am currently reading. It is still great stuff. Wonderful literature, and partly to blame for why I became a soldier, and absolutely the whole reason for why I became , and still am, a rapier fencer
It is certainly what I would call "a lifetime book" – one we bring with us as we grow.
And I was also shocked and offended when Ilearned all thebooks I read as a kid were cut.
Because they always cut thebest parts!
Al-bloody-ways!
Hi Davide
which edition did you buy?
I found several on the kindle store, and some have bad reviews for typos, bad formatting, etc…. Thanks!!
I have the Feltrinelli edition, the one with the red cover.
It's the best around, or so I'm told. I actually liked the modern style and the light tone.
Leave a Reply to Davide Mana Cancel reply
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}
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Q: How to use grep in an if statement? I have the following command which gives me the correct result:
grep --include='*.java' -Ri 'System.loadLibrary' *
However, if I put it in an if condition, it always returns the same 0 result, no matter if the string exists or not:
if [ "grep --include='*.java' -Ri 'System.loadLibrary' *" = 0 ] then ...
What am I doing wrong?
A: Use grep -q option:
if grep -q --include='*.java' -Ri 'System.loadLibrary' .; then
echo "found a matching file"
fi
A: You can use -q as for a quiet output and directly say:
if grep -q ....; then
# things
Or even a short circuit operator if there will just be one action to perform:
grep -q ... && echo "yes"
Test
$ echo "23" > a
$ grep -q 23 a && echo "yes" || echo "no"
yes
$ grep -q 45 a && echo "yes" || echo "no"
no
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,607
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This highly unique, no flake formula gives a long lasting and flexible, medium – strong hold you'd expect from a traditional styling gel with a uniquely modern, textured flat matte finish once dry. Flat Matte contains a unique blend of proteins which continue to infuse into each hair strand after application building strength and volume from root to tip with continued use.
Certified Cruelty-free. Suitable for Vegans.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,190
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{"url":"http:\/\/www.newtonproject.ox.ac.uk\/view\/texts\/diplomatic\/MINT00886","text":"<132r>\n\nThe \\two\/ standard Piles of \\English Troy\/ Weights \\kept\/ in the{illeg} Excheqr & Mint were both made in the year 1588, & are of the same weight, excepting that the Mint Pile is about a grain heavier then the Excheqr Pile. The Scotch Pile mak|d|e in ye year 1607 \\has been kept without wearing &\/ is lighter then the English Pile by 9oz. 6dwt. 16gr, as it ought to be. The new \\Pile\/ made 1707 & stamped wth the rose & thistle crowned is about 3$\\frac{1}{2}$ grains heavier then ye excheqr Pile & 3gr heavier then the Old Mint Pile. {In} \\In\/ Th{is}|e| new\\Mint\/ Piles the small weights are in exact proportion wth the great ones. \\+\/ The old Mint Pile {ought}\\is to\/ be kept \\used kept\/ as a standard \\only\/ to try the new +|&| the new used as a standard to {mak} ty the Bell weights.\n\n+ In the Exchequer Pile the outmost weight is too light by 12 grains the outweight but one t{illeg}|o||o| heaving by 9 grains\n\n+ The outmost weight of the Exchequer Pile is 12 grains lighter then the outmost weight of the mint Piles & the outmost weight but one \\of ye Excheqr Pile\/ is 9 grains heavier th{a}|e|n then the outmost weight but one of the Mint Pile. The ounce weight & half ounce weight of the Excheqr Pile are each of them $\\frac{1}{4}$ grain lighter then ye like Mint weight. |{illeg}| The rest of ye Excheqr weights equal the correspondent Mint weights wthout any sensible difference. {illeg} \\Where the weights differ\/ The error|s| is|are| in ye Exchequer weights. For the {illeg} greater {& smaller mint} weights are in proportion to the samller, {illeg} in the Mint Pile, but not in the Excheqr Pile. For in the Excheqr {illeg}|P|ile the outward weight is a penny weight lighter then then ye rest \\remainder\/ of the weights within it, & the outward weight of this remainder is 9gr heavier them \\all\/ remainder {illeg}of the weights within it. \\But in ye Mint Pile the outward weight equals the summ of the inward {weights} in the ends within a grain or 2\/ The new Pile made \\this year\/ 1707 & stamped wth the rose & thistle crowned is \\about 3$\\frac{1}{2}$gr\/ heavier then the Excheqr Pile & 3gr {&} heavier then the Old Mint Pile. \\In the Mint Piles the small weights are in Proportion to the great {illeg}\/ This old \\Mint\/ Pile is now to be kept as a standard \\only\/ to try the new \\Mint Pile\/ & the new {illeg} is to be used as a standard to try the Bell weights. The weights in the new Mint Pile are in exact proportion to one another.\n\n<133v>\n\nThese are to will & require you forthwith {illeg}|u|pon receipt hereof to summons & warne all & every the persons hereunder written","date":"2019-10-20 15:01:52","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 3, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6605439782142639, \"perplexity\": 14678.732971145468}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570986710773.68\/warc\/CC-MAIN-20191020132840-20191020160340-00546.warc.gz\"}"}
| null | null |
{"url":"https:\/\/eprint.iacr.org\/2013\/833","text":"### Verifier-Based Password-Authenticated Key Exchange: New Models and Constructions\n\nFabrice Benhamouda and David Pointcheval\n\n##### Abstract\n\nWhile password-authenticated key exchange (or PAKE) protocols have been deeply studied, a server corruption remains the main threat, with many concrete cases nowadays. Verifier-based PAKE (or VPAKE) protocols, initially called Augmented-PAKE, have been proposed to limit the impact of any leakage. However, no satisfactory security model has ever been proposed to quantify the actual security of a protocol in the standard model. The unique model proposed so far is an ideal functionality in the universal composability (\\UC) framework, but is only meaningful in idealized models. In this paper, we first formally define some properties for the transform (password hashing) applied to the password for the storage on the server-side, for an efficient VPAKE use. A tight one-wayness is required to prevent improved password searches. We then enhance the Bellare-Pointcheval-Rogaway game-based model for PAKE to VPAKE protocols, in such a way that it allows a VPAKE protocol to be secure in the standard model. In addition, we show how to further extend this model to handle non-uniform and related passwords, both in case of PAKE and VPAKE. Finally, we propose very efficient constructions of password hashing and \\VPAKE protocols, which are nearly as efficient as the best PAKE protocols to date.\n\nAvailable format(s)\nCategory\nCryptographic protocols\nPublication info\nPreprint. MINOR revision.\nKeywords\nMulti-linear mapssmooth projective hash functionsauthenticationkey exchange\nContact author(s)\nfabrice ben hamouda @ ens fr\nHistory\n2014-10-14: revised\nSee all versions\nShort URL\nhttps:\/\/ia.cr\/2013\/833\n\nCC BY\n\nBibTeX\n\n@misc{cryptoeprint:2013\/833,\nauthor = {Fabrice Benhamouda and David Pointcheval},\ntitle = {Verifier-Based Password-Authenticated Key Exchange: New Models and Constructions},\nhowpublished = {Cryptology ePrint Archive, Paper 2013\/833},\nyear = {2013},\nnote = {\\url{https:\/\/eprint.iacr.org\/2013\/833}},\nurl = {https:\/\/eprint.iacr.org\/2013\/833}\n}\n\nNote: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.","date":"2022-07-03 12:36:17","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.21864497661590576, \"perplexity\": 5548.114787441597}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656104240553.67\/warc\/CC-MAIN-20220703104037-20220703134037-00261.warc.gz\"}"}
| null | null |
Essentials is a compilation album released by hip-hop artist Nate Dogg. All 16 tracks are taken from Nate Dogg's debut album G-Funk Classics, Vol. 1 & 2.
Track listing
"Nobody Does It Better" (Featuring Warren G)
"Who's Playin' Games?"
"I Don't Wanna Hurt No More" (Featuring Danny "Butch" Means)
"Me and My Homies" (Featuring 2Pac)
"Because I Got a Girl"
"Scared of Love" (Featuring Danny "Butch" Means)
"Just Another Day"
"Dogg Pound Gangstaville" (Featuring Snoop Dogg and Kurupt)
"No Matter Where I Go"
"Friends" (Featuring Snoop Dogg and Warren G)
"She's Strange" (Featuring Barbara Wilson)
"Never Leave Me Alone" (Featuring Snoop Dogg)
"My Money"
"Puppy Love" (Featuring Snoop Dogg, Daz Dillinger and Kurupt)
"Never Too Late"
"Hardest Man in Town"
References
Nate Dogg albums
2002 compilation albums
|
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\section{Introduction}
Self-interactions for massless spinning particles are severely constrained; with minimal assumptions, the only possibilities are Yang--Mills theory for spin-1 particles and general relativity for spin-2 particles~\cite{Weinberg:1965nx,Benincasa:2007xk,Schuster:2008nh,McGady:2013sga}. However, without additional assumptions such broad statements cannot be made for scalar field theories, where Lorentz symmetry is less constraining.
One powerful additional assumption is that a theory has a nonlinearly realized symmetry. This leads to certain exceptional effective field theories, where nonlinearly realized symmetries fix interaction terms with special properties. The on-shell avatar of a nonlinearly realized symmetry is a soft theorem for amplitudes. In the simplest case, this implies that an amplitude has a zero in the soft limit, i.e., the amplitude scales with a positive power of an external momentum as this momentum is sent to zero.
Examples of exceptional theories include nonlinear sigma models and the Dirac--Born--Infeld (DBI) scalar field theory. A nonlinear sigma model has a nonlinearly realized internal symmetry and amplitudes that scale linearly with the soft momentum, i.e., an Adler zero \cite{Adler:1964um} (see Ref.~\cite{Cheung:2021yog} for a recent geometric interpretation of soft theorems), while the DBI theory has a nonlinearly realized higher-dimensional Poincar\'e symmetry and a quadratic scaling of amplitudes in the soft limit.
Beyond these two examples, there is a single possibility for a single scalar field with a larger nonlinear spacetime symmetry and a cubic scaling of amplitudes in the soft limit, which is called the special galileon.\footnote{The flat space special galileon is a particular example of the more general scalar galileon theories \cite{Nicolis:2008in}, which have shift symmetries that are constant or linear in the spacetime coordinates. The special galileon has an additional shift symmetry that is quadratic in the coordinates \cite{Hinterbichler:2015pqa}.} No larger spacetime symmetries can be nonlinearly realized and no non-trivial higher scaling can be obtained in the soft limit \cite{ Cheung:2014dqa, Bogers:2018zeg, Roest:2019oiw}, given certain assumptions.
In addition to these theories with vanishing soft limits, there is a scalar theory where the soft limit obeys a nontrivial soft theorem, namely the dilaton, which spontaneously breaks conformal symmetry down to Poincar\'e symmetry
\cite{Callan:1970yg,Boels:2015pta,Huang:2015sla,DiVecchia:2015jaq,DiVecchia:2017uqn}. This dilaton theory can also be realized as the DBI theory of a brane embedded into an AdS space of one dimension higher \cite{Goon:2011qf,Goon:2011uw}.
The two formulations are related by a complicated field redefinition involving all powers of the field \cite{Bellucci:2002ji, Creminelli:2013fxa}.
Aside from their improved soft behavior, these exceptional scalar theories display other interesting structures. For example, they possess an intricate web of relationships---including relations to theories of massless particles~\cite{Cachazo:2014xea,Cheung:2017ems,Cheung:2017yef}---and interesting double copy structures~\cite{Bern:2019prr}. Additionally, these scalar theories can be thought of as analogues of gravity in a precise sense~\cite{Sundrum:2003yt,Klein:2015iud,Bonifacio:2019rpv}. The rich interconnections are indicative of recurring structural motifs in quantum field theory that the study of these theories can help to uncover.
The above paradigm is well-established for flat space. There are good reasons to investigate possible generalizations for the other maximally symmetric spaces. Chief amongst these are cosmology and holography: in the former, the inflationary period is usually modeled as close to de Sitter (dS) space while, in the latter, one considers gravity duals that asymptote to anti-de Sitter (AdS) space.
In this paper, we will for definiteness write things in the language of dS space in Lorentzian signature, though everything we consider can be straightforwardly extended to AdS spaces and to any signature.
The possible shift symmetries of a scalar field in dS space can be conveniently classified using flat ambient space. For $D$-dimensional dS space with coordinates $x^{\mu}$, $\mu=0, \dots, D-1$, we specify its embedding into the ambient space $\mathbb{R}^{D,1}$ through the ambient space coordinates $X^A(x)$, $A=1, \dots, D+1$, that satisfy $X^2(x)\equiv \eta_{AB} X^A(x) X^B(x)= H^{-2}$, where the ambient space metric is $\eta_{AB}={\rm diag}(-1, 1, \dots, 1)$.
A dS scalar field $\phi(x)$ can be represented by an ambient space field $\Phi(X)$ satisfying $\Phi(X(x))=\phi(x) $ and $\Phi(\lambda X) = \lambda^w \Phi(X)$ for $\lambda>0$, where the weight $w$ specifies how to continue $\Phi$ away from the dS surface (see Ref.~\cite{Bonifacio:2018zex} for more details of the ambient space formalism in our conventions). The possible shift symmetries of $\Phi$ can then be written as
\begin{equation} \label{eq:general-shift}
\delta \Phi = S_{A_1 \dots A_k} X^{A_1} \dots X^{A_k} (X^2 H^2)^{(w-k)/2} + \dots ,
\end{equation}
where $\dots$ denotes possible field-dependent terms, $S_{A_1 \dots A_k}$ is a constant, symmetric, traceless tensor in ambient space, and $k$ is an integer that denotes the order of the shift symmetry. Restricting the transformation \eqref{eq:general-shift} to the dS surface gives the shift symmetry of $\phi$, which is independent of $w$. For a given $k$, the mass of $\phi$ consistent with the shift symmetry is given by
\begin{equation}
m^2_k = -k(k+D-1)H^2.
\end{equation}
Although these squared masses are negative in dS space, the shift-symmetric scalars correspond to unitary exceptional series representations of the dS group \cite{Basile:2016aen,Sun:2021thf}. Their Euclidean sphere partition functions were calculated in Ref.~\cite{Law:2020cpj} using techniques developed in Ref.~\cite{Anninos:2020hfj}.
It is a non-trivial problem to deform these shift symmetries to non-commuting symmetries and find interactions that are invariant under the resulting symmetry algebras they form with the dS isometries.
In Ref.~\cite{Bonifacio:2018zex}, a manifestly $\mathbb{Z}_2$-invariant interacting Lagrangian for the case $k=2$ was found. This theory is the dS version of the special galileon. The full nonlinearly realized symmetry algebra is $\mathfrak{sl}(D+1, \mathbb{R})$, which is spontaneously broken to the dS isometries. The expression for this Lagrangian in general dimensions takes a rather complicated form involving hypergeometric functions. In this paper, we employ a kind of duality transformation---a field redefinition that reduces to galileon duality in the flat limit---to find another presentation of the theory. This new presentation is far simpler and has an interpretation in terms of broken diffeomorphisms, at the expense of obscuring the $\mathbb{Z}_2$ symmetry.
For $k=1$, there naively appears to be two interacting theories on dS space that realize an algebra with non-commuting shift symmetries. One is the dS DBI theory, constructed by embedding a dS brane into an AdS space of one dimension higher \cite{Goon:2011qf,Goon:2011uw}. Another is the dS conformal dilaton \cite{Hinterbichler:2012mv}, which nonlinearly realizes conformal symmetry on dS space.
These are the dS versions of the brane and dilaton realizations of conformal symmetry in flat space. In both cases, the full algebra is $\frak{so}(D+1,1)$, which is broken to the dS isometries. We will argue that these two theories are equivalent, by finding a perturbative field redefinition that relates the two theories up to very high order in the fields. This is the dS version of the transformation of Ref.~\cite{Bellucci:2002ji} and is consistent with our expectation that the symmetry breaking pattern alone determines the nonlinear theory governing the interactions of the Goldstones (this has been proven for internal symmetries \cite{Coleman:1969sm}, but not for spacetime symmetries).
Finally, we will see that the transformations for all of these nonlinear shift-symmetric theories on dS space can be given a geometric interpretation. They can be seen as arising from a subset of the infinitesimal diffeomorphisms of dS space. The diffeomorphisms of dS space include the Killing vectors which leave dS invariant, as well as certain ``exact diffeomorphisms" whose infinitesimal vector fields can be written as the gradients of scalars. Subsets of these exact diffeomorphisms can be identified with the nonlinearly realized symmetries realized by the scalar fields, which are the Goldstone modes for the spontaneous breaking down to the Killing symmetries.
\paragraph{Conventions:}
We denote the spacetime dimension by $D$. We use the mostly plus metric signature convention and the curvature conventions of Ref.~\cite{Carroll:2004st}. We denote the dS space Hubble scale as $H$, so that the Ricci scalar is $R=D(D-1)H^2>0$. Tensors are symmetrized and antisymmetrized with unit weight, e.g., $T_{(\mu\nu)}={1\over 2} \left(T_{\mu\nu}+T_{\nu\mu}\right)$ and $T_{[\mu\nu]}={1\over 2} \left(T_{\mu\nu}-T_{\nu\mu}\right)$. We define $\epsilon_{01\cdots D} = 1$.
\section{Special galileon in dS space}
We start with the $k=2$ theory, which is the special galileon in dS space. A rather complicated Lagrangian for this theory was written in Ref.~\cite{Bonifacio:2018zex}, with the advantage that the ${\mathbb Z}_2$ symmetry $\phi\rightarrow-\phi$ of the model is manifest. Here we find a much simpler Lagrangian that is not manifestly ${\mathbb Z}_2$ symmetric. We then show how these two Lagrangians are mapped into one another by a field redefinition that is like a dS version of galileon duality for the highest-derivative terms.
Galileon duality in flat space \cite{deRham:2013hsa} is a type of invertible field redefinition that preserves the galileon-like structure of the Lagrangian---it is local order-by-order in powers of the field, but it involves an infinite series of terms.
\subsection{Symmetry algebra}
In the ambient space $\mathbb{R}^{D,1}$, the generators of the dS isometries are packaged into an antisymmetric tensor, $J_{AB}$, that satisfies the $\mathfrak{so}(D,1)$ commutation relations,
\begin{equation} \left[ J_{A_1 A_2},J_{B_1 B_2}\right]= \eta_{A_1 B_1}J_{A_2 B_2}-\eta_{A_2 B_1}J_{A_1 B_2}+\eta_{A_2 B_2}J_{A_1 B_1}-\eta_{A_1 B_2}J_{A_2 B_1} \,.
\label{eq:Jcomm}
\end{equation}
These isometries are realized on an ambient space scalar field as
\begin{equation}
\delta_{J_{AB}}\Phi \equiv J_{AB}\Phi=X_A\partial_B\Phi-X_B\partial_A\Phi \,.
\end{equation}
The generators of the shift symmetries for a $k=2$ scalar are packaged into a symmetric, traceless tensor, $S_{AB}$, which transforms as a tensor under the isometries,
\begin{equation}
[J_{A_1 A_2}, S_{B_1 B_2}] = \eta_{A_1 B_1} S_{A_2 B_2} - \eta_{A_2 B_1} S_{A_1 B_2}+ \eta_{A_1 B_2} S_{A_2 B_1} -\eta_{A_2 B_2} S_{A_1 B_1}.
\label{k2commutatoralge}
\end{equation}
The unique possibility for the remaining commutators can be written as \cite{Bonifacio:2018zex}
\begin{equation}
[S_{A_1 A_2}, S_{B_1 B_2}] = -\frac{\alpha^2}{\Lambda^{D+2}} \left( \eta_{A_1 B_1} J_{A_2 B_2} + \eta_{A_2 B_1} J_{A_1 B_2}+ \eta_{A_1 B_2} J_{A_2 B_1} + \eta_{A_2 B_2} J_{A_1 B_1} \right),
\label{k2commutatoralge}
\end{equation}
where $\alpha$ is a dimensionless constant and $\Lambda>0$ is an energy scale.
For $\alpha^2>0$, these commutation relations correspond to the algebra $\mathfrak{sl}(D+1, \mathbb{R})$; this is true for any spacetime signature or sign of the curvature. For $\alpha^2<0$, the commutation relations correspond to a real form of $\mathfrak{sl}(D+1, \mathbb{C})$ that depends on the spacetime signature and the sign of the curvature. When $\alpha^2 = 0$, we get the undeformed algebra of a free theory.
\subsection{Manifestly $\mathbb{Z}_2$-invariant Lagrangian}
We start by reviewing the formulation of the dS galileon given in Ref.~\cite{Bonifacio:2018zex}. We nonlinearly realize the algebra $\mathfrak{sl}(D+1, \mathbb{R})$ on a scalar field through the following ambient space transformation:
\begin{equation}
\label{eq:delta-sgal-Z2}
\delta \Phi = S_{AB} \left(X^{A} X^B-\frac{\alpha^2}{\Lambda^{D+2}} \partial^{A}\Phi\partial^{B}\Phi \right),
\end{equation}
where the ambient space field has weight two,\footnote{We can always change the weight by rescaling the field by powers of $X^2H^2$. This will modify the ambient space form of the symmetry transformation but does not affect its form in the physical dS space.}
\begin{equation}
X^A \partial_A \Phi = 2\Phi.
\end{equation}
The ambient space transformation induces a transformation on the dS space field $\phi(x) = \Phi(X(x))$ that we can write as\footnote{To find this, we replace $S_{AB}={1\over 2}\partial_A\partial_B(S_{CD}X^CX^D)$ and then use the embedding space reduction rules discussed in Ref.~\cite{Bekaert:2010hk}.}
\begin{equation}
\delta \phi=\sigma-\frac{\alpha^2}{\Lambda^{D+2}} \left( {1\over 2} \nabla_{\mu}\nabla_{\nu}\sigma \nabla^\mu\phi\nabla^\nu\phi +H^2 \sigma(\nabla\phi)^2+2H^2\phi \nabla_\mu\phi\nabla^\mu \sigma+4H^4 \sigma\phi^2 \right),
\end{equation}
where $\sigma \equiv S_{AB} X^{A}(x)X^{B}(x)$.
A Lagrangian invariant under the above transformation was found in Ref.~\cite{Bonifacio:2018zex} and describes the unique ghost-free interacting theory of a $k=2$ scalar, which is the dS space version of the special galileon. In terms of the dimensionless field $\hat{\phi} \equiv - 2\alpha H^2 \phi/ \Lambda^{(D+2)/2}$, this Lagrangian is
\begin{align}
\label{eq:dS-sgal-Z2}
\frac{{\cal L}}{\sqrt{-g}}=& \frac{\Lambda^{D+2}}{4H^2 \alpha^2 } \Bigg[
\sum_{j=0}^{D-1}{(1+\hat{\phi})^{D-j}+ (-1)^{j}(1-\hat{\phi})^{D-j} \over (2H^2)^{(j+1)}(1-\hat{\phi}^2)^{\frac{D+3}{2}}\,\Gamma(j+3)} \left[(j+1)f_{j+1}(\hat{\phi})-(j+2) f_j(\hat{\phi}) \right] \partial^\mu\hat{\phi}\partial^\nu \hat{\phi} X^{(j)}_{\mu\nu}(\hat{\Pi}) \nonumber \\
& -\frac{2}{ (D+1)}\left(1-{(1+\hat{\phi})^{D+1}+(1-\hat{\phi})^{D+1}\over 2 (1-\hat{\phi}^2)^{(D+1)/2}}\right) \Bigg],
\end{align}
where we have defined
\begin{equation}
f_j (\hat{\phi})\equiv {}_2F_1\left({D+3\over 2},{j+1\over 2};{j+3\over 2};{(\partial \hat{\phi})^2\over 4H^2(1-\hat{\phi}^2)} \right)\,,
\end{equation}
and where $X_{\mu \nu}^{(j)}$ are defined recursively by
\begin{equation}
X^{(0)}_{\mu\nu}(\hat{\Pi}) \equiv g_{\mu \nu}, \qquad\quad X^{(n)}_{\mu \nu}(\hat{\Pi}) \equiv -n \hat{\Pi}_{\mu}{}^{\alpha} X_{\alpha \nu}^{(n-1)}(\hat{\Pi})+g_{\mu \nu}\hat{\Pi}^{\alpha \beta} X^{(n-1)}_{\alpha \beta}(\hat{\Pi}),
\end{equation}
with $\hat{\Pi}_{\mu \nu} \equiv \nabla_{\mu} \nabla_{\nu} \hat{\phi}$.
When expanded out, this Lagrangian contains only terms with even powers of the field, so it is manifestly invariant under the $\mathbb{Z}_2$ symmetry that acts as $\phi \rightarrow - \phi$.
\subsection{A simplified special galileon Lagrangian}
There are other ways to nonlinearly realize the algebra $\mathfrak{sl}(D+1, \mathbb{R})$ on a scalar field. Motivated by the reasoning described in Section \ref{sec:broken-diffs}, we consider the following ambient space transformation:
\begin{equation} \label{eq:sgal-new-ambient}
\delta \Phi = S_{AB} \left( \frac{1}{H^2X^2}X^{A} X^{B}+\frac{2\alpha}{\Lambda^{(D+2)/2}} X^{A }\partial^{B} \Phi \right) ,
\end{equation}
where the ambient space field has weight zero,
\begin{equation}
X^A \partial_A \Phi = 0.
\end{equation}
In terms of the dS field $\phi(x) = \Phi(X(x))$, this transformation is
\begin{equation} \label{eq:sgal-new-dS}
\delta \phi=\sigma+\frac{\alpha}{\Lambda^{(D+2)/2}}\nabla_\mu\phi\nabla^\mu \sigma,
\end{equation}
where $\sigma \equiv S_{AB} X^{A}(x)X^{B}(x)$.
This transformation satisfies the same commutation relations and symmetry breaking pattern as the transformation \eqref{eq:delta-sgal-Z2} and, as we will see, leads to a much simpler formulation of the dS space special galileon.
We now search for a ghost-free action invariant under the transformation \eqref{eq:sgal-new-dS}. By imposing invariance under the symmetry order by order in the field and then resumming, we get the following result:
\begin{equation}
\label{eq:Lsgal-new}
\frac{\mathcal{L}}{\sqrt{-g}} = \frac{\Lambda^{D+2}}{4\alpha^2 H^2} \left[ \frac{2}{D+1} \left( \cosh (D+1) \hat{\phi} -1 \right)- e^{-(D+1) \hat{\phi}} \sum_{j=0}^{D-1} (-1)^j\frac{\partial^{\mu} \hat{\phi} \partial^{\nu} \hat{\phi} X^{(j)}_{\mu \nu}(\hat{\Pi})}{(j+2)!H^{2j+2}}\right].
\end{equation}
This is much simpler than the manifestly $\mathbb{Z}_2$-invariant Lagrangian \eqref{eq:dS-sgal-Z2}, although the $\mathbb{Z}_2$ symmetry is no longer manifest.\footnote{Note also that with this Lagrangian we cannot realize other real forms of $\mathfrak{sl}(D+1, \mathbb{C})$ on real fields.}
The equations of motion also take a relatively simple form,
\begin{equation}
\label{eq:sgalEOM}
\frac{2\alpha}{\Lambda^{(D+2)/2} } \frac{\delta \mathcal{L}}{\delta \phi} =-e^{(D+1) \hat{\phi}}-\frac{e^{-(D+1)\hat{\phi}}}{D!} \epsilon^{\mu_1 \dots \mu_D} \epsilon^{\nu_1\dots \nu_D} G_{\mu_1 \nu_1} \dots G_{\mu_D \nu_D} =0\,,
\end{equation}
where
\begin{equation}
G_{\mu \nu} \equiv g_{\mu \nu}-\frac{1}{H^2} \nabla_{\mu} \nabla_{\nu} \hat{\phi}+\frac{1}{H^2} \partial_{\mu} \hat{\phi} \partial_{\nu} \hat{\phi}.
\label{eq:k2metric}
\end{equation}
This tensor $G_{\mu \nu}$ transforms covariantly, like a metric, under the shift symmetry \eqref{eq:sgal-new-dS}. We can use it to build higher-order invariants and to couple to other matter fields, as in Ref.~\cite{Bonifacio:2019rpv}.
\subsection{Mapping between Lagrangians}
We now have two formulations of the special galileon Lagrangian in dS space: the manifestly $\mathbb{Z}_2$-invariant Lagrangian \eqref{eq:dS-sgal-Z2} from Ref.~\cite{Bonifacio:2018zex} and the new simplified Lagrangian \eqref{eq:sgal-new-dS}, which is invariant under a shift symmetry that is linear in the field. Since these realize the same symmetry breaking pattern and are both ghost-free theories of the same derivative order, we expect that these two Lagrangians are related to each other by a field redefinition. We now show that this is indeed the case and that the field redefinition can be thought of as a dS uplift of the flat space galileon duality transformations described in Refs.~\cite{Fasiello:2013woa,deRham:2013hsa}.
We start from the ambient space transformation in Eq.~\eqref{eq:delta-sgal-Z2},
\begin{equation} \label{eq:delta-sgal-Z2-2}
\delta \Phi^{(0)} = S_{AB} \left( X^{A} X^{B}-\frac{\alpha^2}{\Lambda^{D+2}} \partial^{A}\Phi^{(0)} \partial^{B}\Phi^{(0)} \right),
\end{equation}
where $\Phi^{(0)}$ has weight two. This describes the shift symmetry of the manifestly $\mathbb{Z}_2$-invariant Lagrangian in Eq.~\eqref{eq:dS-sgal-Z2}.
Next we make a galileon duality transformation in its active form \cite{Kampf:2014rka} on the ambient space field,
\begin{equation} \label{eq:duality-ambient}
{\Phi}^{(1)}= e^{-\theta \bar{\delta}}\Phi^{(0)}, \quad {\rm with}\quad \bar{\delta} \Phi^{(0)} \equiv- \frac{\alpha}{2\Lambda^{(D+2)/2}}\partial_{A} \Phi^{(0)} \partial^{A} \Phi^{(0)},
\end{equation}
where $\theta$ is a dimensionless real parameter.
Under this field redefinition, the ambient transformation in Eq.~\eqref{eq:delta-sgal-Z2-2} becomes \cite{Hinterbichler:2015pqa}
\begin{equation} \label{eq:delta-sgal-mixed}
\delta \Phi^{(1)} = S_{AB} \left(X^A X^B+ \frac{ 2\alpha\theta }{\Lambda^{(D+2)/2}} X^A \partial^B \Phi^{(1)}+ \frac{\alpha^2(\theta^2-1 )}{\Lambda^{D+2}} \partial^A \Phi^{(1)} \partial^B \Phi^{(1)} \right).
\end{equation}
We now set $\theta = 1$, so we get
\begin{equation}
\delta \Phi^{(1)} = S_{AB} \left(X^A X^B+\frac{2\alpha}{\Lambda^{(D+2)/2}} X^A \partial^B \Phi^{(1)} \right),
\end{equation}
with only a linear term in $\Phi$.
Now define the weight zero field $\Phi^{(2)} \equiv \Phi^{(1)}/H^2 X^2$, so that
\begin{equation}
\delta \Phi^{(2)} = S_{AB} \left(\frac{X^A X^B}{H^2 X^2}\left(1+ \frac{4 \alpha H^2 \Phi^{(2)}}{\Lambda^{(D+2)/2}} \right)+\frac{2\alpha}{\Lambda^{(D+2)/2}} X^A \partial^B \Phi^{(2)} \right).
\end{equation}
Finally, we define the weight zero field
\begin{equation}
\Phi^{(3)} \equiv \frac{\Lambda^{(D+2)/2}}{4 \alpha H^2} \log \left(1+ \frac{4 \alpha H^2 \Phi^{(2)}}{\Lambda^{(D+2)/2}} \right),
\end{equation}
so that we get
\begin{equation}
\delta \Phi^{(3)} = S_{AB} \left(\frac{X^A X^B}{H^2 X^2}+\frac{2\alpha}{\Lambda^{(D+2)/2}} X^A \partial^B \Phi^{(3)} \right),
\end{equation}
which is the form of the shift symmetry of the new simplified Lagrangian \eqref{eq:sgal-new-dS}.
In summary, we have a redefinition defined by
\begin{equation}
\hat{\Phi}^{(3)} = -\frac{1}{2 } \log \left(1- \frac{2 }{X^2 H^2 } e^{-\theta \bar{\delta}} \hat{\Phi}^{(0)}\right), \quad\qquad \bar{\delta} \hat{\Phi}^{(0)} = \frac{1}{4H^2} (\partial \hat{\Phi}^{(0)})^2,
\end{equation}
where $\theta =1$ and $\hat{\Phi}^{(i)} \equiv -2\alpha H^2 \Phi^{(i)}/\Lambda^{(D+2)/2}$. In terms of physical dS fields, this is
\begin{equation} \label{eq:final-redef-ambient}
\hat{\phi}^{(3)} = -\frac{1}{2 } \log \left(1- 2 e^{-\theta \bar{\delta}}\hat{\phi}^{(0)}\right), \quad \bar{\delta} \hat{\phi}^{(0)} = {1\over 4 H^2} \left( (\partial \hat{\phi}^{(0)} )^2+4 H^2 (\hat{\phi}^{(0)})^2 \right),
\end{equation}
where $\theta =1$ and $\hat{\phi}^{(i)} \equiv -2\alpha H^2 \phi^{(i)}/\Lambda^{(D+2)/2}$.
As a check of this result, if we just consider the zero-derivative part of the transformation, then the field redefinition is\footnote{Defining $\bar{\delta}_0 \hat{\phi}=\hat{\phi}^2$ gives $\bar{\delta}_0^m \hat{\phi}^n=\frac{(n+m-1)!}{(n-1)!} \hat{\phi}^{n+m}$, so then we get
\begin{equation}
-\frac{1}{2} \log\left(1-2 e^{-\bar{\delta}_0}\hat{\phi}\right) = \sum_{n=1}^{\infty} \sum_{m=0}^{\infty} \frac{2^{n-1}}{n}\frac{(-1)^m}{m!} \frac{(n+m-1)!}{(n-1)!} \hat{\phi}^{n+m} = \tanh^{-1} \hat{\phi}.
\end{equation}}
\begin{equation}
\hat{\phi}^{(3)} = \tanh^{-1}\hat{\phi}^{(0)},
\end{equation}
under which we can check that the potential terms of the two Lagrangians get mapped into each other,
\begin{equation}
\cosh \left( (D+1) \hat{\phi}^{(3)} \right) = {\left(1+\hat{\phi}^{(0)}\right)^{D+1}+\left(1-\hat{\phi}^{(0)}\right)^{D+1}\over 2 \left(1-(\hat{\phi}^{(0)})^2\right)^{\frac{D+1}{2}}} .
\end{equation}
For general $\theta$, the transformation \eqref{eq:final-redef-ambient} leads to a one-parameter family of Lagrangians related by the ambient space duality. In the flat space limit $H\rightarrow 0$, this becomes the flat space galileon duality transformation \cite{Fasiello:2013woa,deRham:2013hsa} in its active form \cite{Kampf:2014rka} acting on the special galileon.
\section{DBI and conformal dilaton in dS space}
In this section, we discuss two formulations of the nonlinear $k=1$ theory in dS space, corresponding to the brane and dilaton realizations of conformal symmetry. Given that they both describe the same symmetry breaking pattern, we expect them to be related by a field redefinition. We show up to some high order in the fields that this is indeed the case.
\subsection{Symmetry algebra}
The shift symmetries for a $k=1$ scalar are packaged into a $(D+1)$-dimensional ambient space vector $S_{A}$. Since they transform as a vector under the isometries, we have the commutator
\begin{equation}
[J_{A B}, S_{C}] = \eta_{AC} S_{B } - \eta_{BC} S_{A} .
\label{k2commutatoralge}
\end{equation}
The unique commutator which completes the algebra can be written as
\begin{equation}
[S_{A}, S_{B}] = - \frac{\alpha^2H^2}{ \Lambda^{D+2}} J_{AB}.
\label{k2commutatoralge}
\end{equation}
For $\alpha^2>0$, these commutation relations correspond to the conformal algebra algebra $\mathfrak{so}(D,2)$. For $\alpha^2< 0$ the algebra is $\mathfrak{so}(D+1,1)$, while for AdS$_D$ it is $\mathfrak{so}(D-1,3)$ if $\alpha^2>0$ or $\mathfrak{so}(D,2)$ if $\alpha^2<0$.
\subsection{DBI Lagrangian}
One way to nonlinearly realize the conformal algebra $\mathfrak{so}(D,2)$ on a scalar field in dS space is through the ambient space transformation
\begin{equation}
\delta \Phi = S_A \left( X^A - \frac{\alpha^2H^2}{ \Lambda^{D+2}} \Phi \partial^A \Phi \right),\label{confdbiinsfle}
\end{equation}
where $\Phi$ has weight $w=1$.
A set of interactions invariant under this symmetry were given in general dimensions in Ref.~\cite{Bonifacio:2018zex}, but they were quite complicated since the interaction ansatz used there did not allow for their simplest form. If instead we look for a Lagrangian in the $P(\phi,(\partial\phi)^2)$
form, then there is a simple invariant interaction without a tadpole,
\begin{equation} \label{eq:DBI-sqrt}
\frac{\mathcal{L}}{\sqrt{-g}} = \frac{ \Lambda^{D+2}}{\alpha^2 H^2}\frac{1}{(1- \hat{\phi}^2)^{D/2}} \sqrt{1- \frac{ (\partial \hat{\phi})^2/H^2}{1- \hat{\phi}^2}}\,,
\end{equation}
where now $\hat{\phi} \equiv - \alpha H^2 \phi/ \Lambda^{(D+2)/2}$. Defining $ \hat{\pi} \equiv \tanh^{-1}\hat{\phi}$, this Lagrangian can be written as
\begin{equation} \label{eq:dbi-cosh}
\frac{\mathcal{L}}{\sqrt{-g}} = \frac{ \Lambda^{D+2}}{\alpha^2 H^2}\cosh^D \hat{\pi}\sqrt{1- \frac{ (\partial \hat{\pi})^2}{H^2 \cosh^2 \hat{\pi}}}.
\end{equation}
The tadpole interaction can be written as
\begin{equation}
\frac{\mathcal{L}'}{\sqrt{-g}} =- \frac{\Lambda^{D+2}\hat{\phi} }{\alpha^2 H^2} \, _2F_1\left(\frac{1}{2},\frac{D+2}{2} ;\frac{3}{2}; \hat{\phi}^2 \right).
\end{equation}
These Lagrangians realize the symmetry breaking pattern $\mathfrak{so}(D,2) \rightarrow \mathfrak{so}(D,1)$ and can be realized physically as the DBI theory of a dS$_D$ brane probing an AdS$_{D+1}$ bulk.\footnote{Defining instead $ \hat{\pi} \equiv \tanh^{-1}(1/\hat{\phi})$, the Lagrangian can be written as
\begin{equation} \label{eq:dbi-sinh}
\frac{\mathcal{L}}{\sqrt{-g}} = -\frac{ \Lambda^{D+2}}{\alpha^2 H^2}i^D \sinh^D \hat{\pi}\sqrt{1+ \frac{ (\partial \hat{\pi})^2}{H^2 \sinh^2 \hat{\pi}}}\,,
\end{equation}
which for $D=4$ takes the same form as the DBI theory of a dS$_4$ brane in an AdS$_5$ bulk of Refs.~\cite{Goon:2011qf,Goon:2011uw} (see also Ref.~\cite{Grall:2019qof}).
In the case of AdS, i.e., replacing $H \rightarrow i/L$ in Eq.~\eqref{eq:dbi-cosh}, we get the theory of an AdS$_D$ brane in an AdS$_{D+1}$ bulk from Ref.~\cite{Clark:2005ht}, which realizes the symmetry breaking pattern $\mathfrak{so}(D,2) \rightarrow \mathfrak{so}(D-1,2)$.}
From the dS DBI Lagrangian \eqref{eq:DBI-sqrt}, we can take various limits to recover other known theories.
For example, taking the flat limit $H\rightarrow 0$ and $\Lambda \rightarrow 0$ with $\Lambda_{\rm flat} \equiv (\Lambda^{D+2}/H^2)^{1/D}$ and $\phi$ held fixed, we recover the theory of a flat brane in a two-time Minkowski bulk spacetime,
\begin{equation}
\lim_{H \rightarrow 0}\frac{\mathcal{L}}{\sqrt{-g}} =\frac{\Lambda_{\rm flat} ^{D}}{\alpha^2} \sqrt{1- \frac{\alpha^2 (\partial \phi)^2}{ \Lambda_{\rm flat} ^{D}}}\,,
\end{equation}
i.e., flat space DBI with the sign of the quartic interaction that violates positivity constraints \cite{Adams:2006sv}.\footnote{Starting instead from AdS$_D$ with $\Lambda_{\rm flat} \equiv (\Lambda^{D+2} L^2)^{1/D}$ fixed gives the standard DBI theory,
\begin{equation}
\lim_{L \rightarrow \infty}\frac{\mathcal{L}}{\sqrt{-g}} =-\frac{\Lambda_{\rm flat} ^{D}}{\alpha^2} \sqrt{1+ \frac{\alpha^2 (\partial \phi)^2}{ \Lambda_{\rm flat} ^{D}}}\,,
\end{equation}
corresponding to $\mathfrak{iso}(D,1) \rightarrow \mathfrak{iso}(D-1,1)$.} This corresponds to the symmetry breaking pattern $\mathfrak{iso}(D-1,2) \rightarrow \mathfrak{iso}(D-1,1)$. If we instead take the limit $\Lambda\rightarrow0$ with $H$ fixed, then Eq.~\eqref{eq:DBI-sqrt} reduces after rescaling to the theory of a dS brane probing a flat background \cite{Goon:2011qf,Goon:2011uw},
\begin{equation}
\lim_{\Lambda \rightarrow 0}\frac{H^{(D+2)^2/2}}{\Lambda^{(D+2)^2/2}} \frac{\mathcal{L}}{\sqrt{-g}} =\frac{H^{D^2/2}}{i^D\alpha^{D+2} } {1\over \phi^D} \sqrt{1+ { (\partial \phi)^2\over H^2 \phi^2} },
\end{equation}
corresponding to $\mathfrak{iso}(D,1) \rightarrow \mathfrak{so}(D,1)$.\footnote{The same symmetry breaking pattern is realized by the dS galileon \cite{Goon:2011qf,Goon:2011uw,Burrage:2011bt}.} The final limit we consider is more subtle since we must give the field a vacuum expectation value that we send to $- \infty$. We replace $\hat{\pi} \rightarrow \ln(H/ 2\Lambda)+ \hat{\pi} $ in Eq.~\eqref{eq:dbi-cosh} and then take the limit $H \rightarrow 0$ with $\Lambda$ and $\hat{\pi}$ held fixed. Adding the tadpole interaction and rescaling the Lagrangian, this gives the theory describing a flat brane in a two-time dS bulk spacetime,
\begin{equation} \label{eq:2-time-dS}
\lim_{H \rightarrow 0} \frac{H^{D+2}}{\Lambda^{D+2}} \frac{1}{\sqrt{-g}}\left( \mathcal{L} -D \mathcal{L}' \right)= \frac{\Lambda^{D}}{\alpha^2 }e^{-D \hat{\pi} } \left(\sqrt{1- e^{2 \hat{\pi} }\frac{(\partial \hat{\pi})^2 }{\Lambda^2}}-1\right).
\end{equation}
This corresponds to the symmetry breaking pattern $\mathfrak{so}(D,2) \rightarrow \mathfrak{iso}(D-1,1)$.\footnote{If we instead start in AdS$_D$ and replace $\hat{\pi} \rightarrow -\ln( 2\Lambda L)+ \hat{\pi} $, then we get
\begin{equation} \label{eq:conformal-dbi}
\lim_{L \rightarrow \infty} \frac{1}{(\Lambda L)^{D+2}}\frac{1}{\sqrt{-g}} \left( \mathcal{L} -D \mathcal{L}' \right) = -\frac{\Lambda^{D}}{\alpha^2 }e^{-D \hat{\pi} } \left(\sqrt{1+ e^{2 \hat{\pi} }\frac{(\partial \hat{\pi})^2 }{\Lambda^2}}-1\right).
\end{equation}
This is the conformal DBI theory, which describes a flat brane in an AdS bulk spacetime \cite{deRham:2010eu}. This realizes the same symmetry breaking pattern $\mathfrak{so}(D,2) \rightarrow \mathfrak{iso}(D-1,1)$ as the Lagrangian in Eq.~\eqref{eq:2-time-dS}. While these two Lagrangians are inequivalent, as can be seen by calculating their $2\rightarrow 2$ scattering amplitudes, we expect there to be a field redefinition between them once we include the other invariant interactions. }
\subsection{Conformal dilaton Lagrangian}
An alternative way to nonlinearly realize the algebra $\mathfrak{so}(D,2)$ on a scalar field in dS space is through the following ambient space transformation:
\begin{equation} \label{eq:delta-dS-conf-dilaton}
\delta \Phi = S_A \left( \frac{1}{\sqrt{H^2 X^2}} X^A +\frac{\alpha}{\Lambda^{(D+2)/2}} \sqrt{H^2 X^2}\partial^A \Phi \right),
\end{equation}
where $\Phi$ has weight $w=0$. This is the form of the shift symmetry suggested by the discussion of Section~\ref{sec:broken-diffs}. It satisfies the same commutation relations as the transformation in Eq.~\eqref{confdbiinsfle} and realizes the same symmetry breaking pattern $\mathfrak{so}(D,2) \rightarrow \mathfrak{so}(D,1)$.
If we look for invariant interactions of the $P(\phi,(\partial\phi)^2)$ form, then for the interaction without a tadpole we get
\begin{equation} \label{eq:k=1-dilaton}
\frac{\mathcal{L}}{\sqrt{-g}} = \frac{\Lambda^{D+2}}{2\alpha^2H^2} \left[ -\frac{1}{H^2}e^{(D-2) \hat{\phi}} (\partial \hat{\phi})^2 +e^{D \hat{\phi}}-\frac{De^{(D-2) \hat{\phi}} -2 }{(D-2)}\right],
\end{equation}
where again $\hat{\phi} \equiv - H^2 \alpha \phi/ \Lambda^{(D+2)/2}$. This agrees with the interaction in Ref.~\cite{Hinterbichler:2012mv} when $D=4$. For $D=2$, the last term in square brackets should be understood as the $D \rightarrow 2$ limit. When $D=1$, the conformal dilaton Lagrangian \eqref{eq:k=1-dilaton} coincides with the special galileon Lagrangian \eqref{eq:Lsgal-new} in a space with half the Hubble constant, $ H_{k=2}= H_{k=1}/2$. This is possible due to the Lie algebra isomorphism $\mathfrak{so}(2,1) = \mathfrak{sl}(2, \mathbb{R})$.
There are additional independent invariant Lagrangians. For example, in every dimension there is the invariant tadpole term $e^{D \hat{\phi} }$.
In any even dimension, there is also a special interaction from the point of view of cohomology, the Wess--Zumino term, which in dS$_4$ is \cite{Hinterbichler:2012mv}
\begin{align}
\frac{\mathcal{L}'}{\sqrt{-g}} &= -\frac{ \Lambda^6}{\alpha^2 H^2} \left[ \hat{\phi} -\frac{1}{4 }e^{4 \hat{\phi}} +\frac{1}{2 H^2} (\partial \hat{\phi})^2-\frac{1}{6H^4 } (\partial \hat{\phi})^2 \Box \hat{\phi} -\frac{1}{12 H^4 }(\partial \hat{\phi})^4 \right].
\end{align}
There is also an interaction with the potential $\cosh^D( \hat{\phi} )$, which maps to the square root DBI action \eqref{eq:DBI-sqrt} under the field redefinition discussed below. In dS$_4$, this Lagrangian is
\begin{equation}
\begin{aligned}
\frac{\mathcal{L}}{\sqrt{-g}} =\,& -\frac{ \Lambda^6}{\alpha^2 H^2} \bigg[\frac{1}{2H^2}
(\partial \hat{\phi})^2 e^{- \hat{\phi} } \cosh ^2( \hat{\phi}) (\cosh \hat{\phi} -3 \sinh \hat{\phi} )-\cosh ^4( \hat{\phi} ) \\
&+\frac{11}{48H^8} (\partial \hat{\phi})^8 e^{-4 \hat{\phi} }+\frac{1}{24H^6} (\partial \hat{\phi})^6 e^{-4 \hat{\phi}} \left(e^{2 \hat{\phi} }-4\right)-\frac{1}{24H^4} (\partial \hat{\phi})^4 e^{-4 \hat{\phi}} \left(2 e^{2 \hat{\phi}}+1\right) \\
& -\frac{1}{H^2} \mathcal{L}^{\rm TD}_1(\hat{\Pi}) \left(\frac{5}{12H^6} (\partial \hat{\phi})^6 e^{-4 \hat{\phi} }+\frac{1}{24H^4} (\partial \hat{\phi})^4 e^{-4 \hat{\phi} } \left(e^{2 \hat{\phi} }+1\right)+\frac{1}{2H^2} (\partial \hat{\phi})^2 e^{-3 \hat{\phi} } \cosh \hat{\phi} \right) \\
&+ \frac{1}{H^4} \mathcal{L}^{\rm TD}_2(\hat{\Pi}) \left(\frac{1}{4H^4} (\partial \hat{\phi})^4 e^{-4 \hat{\phi} }+\frac{1}{12H^2} (\partial \hat{\phi})^2 e^{-4 \hat{\phi}
} \left(e^{2 \hat{\phi} }+2\right)\right) \\
&-\frac{1}{12 H^8} \mathcal{L}^{\rm TD}_3(\hat{\Pi}) (\partial \hat{\phi})^2 e^{-4 \hat{\phi} } \bigg],
\end{aligned}
\end{equation}
where $\mathcal{L}^{\rm TD}_n$ are terms that are total derivatives in the flat space limit and are defined recursively by
\begin{equation}
\mathcal{L}^{\rm TD}_n( \hat{\Pi}) = \sum_{j=1}^n (-i)^{j+1} \frac{(n-1)!}{(n-j)!} [ \hat{\Pi}^j] \mathcal{L}^{\rm TD}_{n-j}( \hat{\Pi}),
\end{equation}
with $[ \hat{\Pi}^j] \equiv \Pi_{\mu_1}{}^{\mu_2} \Pi_{\mu_2}{}^{\mu_3} \dots \Pi_{\mu_j}{}^{\mu_1}$ and $\mathcal{L}^{\rm TD}_0( \hat{\Pi}) =1$.
As with the DBI Lagrangian \eqref{eq:DBI-sqrt}, we can take limits of the dilaton Lagrangian \eqref{eq:k=1-dilaton} to recover other theories. Taking $H, \Lambda \rightarrow 0$ with $H^2/\Lambda^{(D+2)/2}$ fixed gives the kinetic term of the conformal galileon,
\begin{equation}
\lim_{H, \Lambda \rightarrow 0} \frac{\mathcal{L}}{\sqrt{-g}} = -\frac{1}{2} e^{(D-2) \hat{\phi}} (\partial \phi)^2,
\end{equation}
which corresponds to the symmetry breaking pattern $\mathfrak{so}(D,2) \rightarrow \mathfrak{iso}(D-1,1)$. This corresponds to the same symmetry breaking pattern as the theory of a flat brane in two-time dS space in Eq.~\eqref{eq:2-time-dS} and conformal DBI in Eq.~\eqref{eq:conformal-dbi}. A field redefinition that maps linear combinations of the conformal galileons into linear combinations of the conformal DBI interactions was worked out in Refs.~\cite{Bellucci:2002ji, Creminelli:2013fxa}, which shows the equivalence of these flat space theories.
\subsection{Mapping between Lagrangians}
We can demonstrate the equivalence of the dS DBI and conformal dilaton Lagrangians by finding a field redefinition that maps between them, as with the two formulations of the dS special galileon. The transformation maps each dS conformal dilaton Lagrangian into a certain linear combination of the dS DBI Lagrangians, as with the flat space versions of these theories \cite{Bellucci:2002ji,Creminelli:2013fxa}. For example, as mentioned above, the combination of conformal dilaton Lagrangians with potential $\cosh^D( \hat{\phi} )$ maps to the square root DBI action \eqref{eq:DBI-sqrt}.
We start with the DBI transformation
\begin{equation}
\delta \Phi^{(0)} = S_A \left( X^A - \frac{\alpha^2H^2}{ \Lambda^{D+2}} \Phi^{(0)} \partial^A \Phi^{(0)} \right),
\label{eq:k1deltaP0}
\end{equation}
where $\Phi^{(0)} $ has weight one. Now set $\Phi^{(1)} = e^{- \theta \bar{\delta}} \Phi^{(0)}$, where $\bar{\delta}$ is defined such that for $\theta=1$ we have
\begin{equation} \label{eq:k=1-delta-Phi1}
\delta \Phi^{(1)} =S_A \left( X^A + \frac{\alpha}{ \Lambda^{(D+2)/2}} \sqrt{H^2 X^2} \partial^A \Phi^{(1)} \right).
\end{equation}
Defining $\hat{\Phi}^{(0)} \equiv - H^2 \alpha \Phi^{(0)}/ \Lambda^{(D+2)/2}$, we find by a brute force calculation that, at least up to high orders, we can write the action of $\bar{\delta}$ perturbatively in ambient space as
\begin{align}
\bar{\delta} \hat{\Phi}^{(0)} &\equiv \sqrt{X^2H^2} \frac{(\partial \hat{\Phi}^{(0)})^{2}}{H^{2}} \left(\frac{1}{2}-\frac{1}{4} \frac{\hat{\Phi}^{(0)}}{\sqrt{X^2H^2}}-\frac{1}{8}\frac{(\hat{\Phi}^{(0)})^2}{X^2H^2}+\dots \right) +\sqrt{X^2H^2}\frac{(\partial \hat{\Phi}^{(0)})^{4}}{H^{4}} \left( \frac{1}{16}+\dots \right)+\dots \nonumber \\
& = -\sqrt{X^2H^2}\sum_{j=1}^{\infty} \frac{(\partial \hat{\Phi}^{(0)})^{2j}}{H^{2j}} f_j\left( \frac{\hat{\Phi}^{(0)}}{\sqrt{X^2H^2}} \right), \label{eq:k=1-derivation}
\end{align}
where $f_j$ is a power series. We do not know a closed-form expression for the $f_j$, but we have computed the terms contributing to $\bar{\delta}$ up to 17th order in the fields, which are listed in Table~\ref{tab:functions}.
\bgroup
\def\arraystretch{1.25
\begin{table}[!h]
\centering
{\scriptsize
\begin{tabular}{ l }
\hspace{6cm}
Expansions of $f_j(x)$\\ \hline\rule{0pt}{7ex}
$
\begin{aligned}
f_1(x)=&-\frac{1}{2}+\frac{x}{4}+\frac{x^2}{8}+\frac{x^3}{24}+\frac{x^4}{96}+\frac{x^5}{80}+\frac{7 x^6}{480}+\frac{19
x^7}{6720}-\frac{37 x^8}{17920}+\frac{197 x^9}{13440}+\frac{113
x^{10}}{8960}-\frac{41323 x^{11}}{1182720}-\frac{53429 x^{12}}{14192640} \nonumber \\
&+\frac{14633519 x^{13}}{92252160}-\frac{1095239 {x
}^{14}}{12300288}-\frac{285950669 x^{15}}{369008640} + \dots ,
\end{aligned}$\\
\rule{0pt}{7ex}
$
\begin{aligned}
f_2(x)=&-\frac{1}{16}+\frac{x^2}{32}+\frac{x^3}{64}-\frac{x^4}{120}+\frac{13 x^5}{3840}+\frac{101
x^6}{4480}-\frac{281 x^7}{17920}-\frac{1093 x^8}{26880}+\frac{40387 x^9}{430080}+\frac{206869
x^{10}}{2365440}-\frac{4802311 x^{11}}{9461760} \nonumber \\
&-\frac{222421 x^{12}}{20500480}+\frac{923059867
x^{13}}{295206912}+ \dots,
\end{aligned}$\\
\rule{0pt}{7ex}
$
\begin{aligned}
f_3(x) =& -\frac{1}{64}-\frac{x}{96}+\frac{11 x^2}{960}+\frac{23 x^3}{1920}-\frac{209
x^4}{13440}+\frac{59 x^5}{53760}+\frac{1523 x^6}{26880}-\frac{979 x^7}{15360}-\frac{7505
x^8}{39424}+\frac{773923 x^9}{1351680} \nonumber \\
& +\frac{104962307 x^{10}}{184504320}-\frac{317494109
x^{11}}{67092480}+\dots ,
\end{aligned}$\\
\rule{0pt}{7ex}
$
\begin{aligned}
f_4(x) =&-\frac{17}{3840}-\frac{61 x}{7680}+\frac{149 x^2}{35840}+\frac{411 x^3}{35840}-\frac{10481
x^4}{430080}-\frac{17 x^5}{86016}+\frac{286673 x^6}{1892352}-\frac{2239247
x^7}{9461760}-\frac{809516299 x^8}{984023040}\nonumber \\
&+\frac{1380091937 x^9}{421724160} + \dots,\end{aligned}$\\
\rule{0pt}{5ex}
$
\begin{aligned}
f_5(x) =& -\frac{19}{17920}-\frac{179 x}{35840}+\frac{137 x^2}{107520}+\frac{2677
x^3}{215040}-\frac{99019 x^4}{2365440}+\frac{24859 x^5}{9461760}+\frac{54077893
x^6}{123002880}-\frac{28892971 x^7}{30750720} + \dots, \end{aligned}$\\
\rule{0pt}{5ex}
$
\begin{aligned}
f_6(x) =&-\frac{13}{430080}-\frac{417 x}{143360}+\frac{677 x^2}{946176}+\frac{58859
x^3}{3784704}-\frac{6993213 x^4}{82001920}+\frac{27430969 x^5}{984023040} + \dots,\end{aligned}$\\
\rule{0pt}{5ex}
$
\begin{aligned}
f_7(x) = &\frac{189}{901120}-\frac{32833 x}{18923520}+\frac{205627 x^2}{98402304}+\frac{34589413
x^3}{1476034560}+ \dots,\end{aligned}$\\
\rule{0pt}{5ex}
$
\begin{aligned}
f_8(x) =&\frac{52727}{281149440}-\frac{558697 x}{393609216}+ \dots\end{aligned}$
\end{tabular}
}
\caption{\small Power series expansion of the first few $f_j$s appearing in Eqs.~\eqref{eq:k=1-derivation} and~\eqref{eq:eqwithfjs}. These are the contributions to~\eqref{eq:k=1-derivation} up to 17th order in fields. These expressions can be extended to higher orders with additional effort, though we have not been able to find closed-form formulas for them.
} \label{tab:functions}
\end{table}
\egroup
For general values of $\theta$, the first few terms in the shift transformation of $\Phi^{(1)} = e^{- \theta \bar{\delta}} \Phi^{(0)}$ are
\begin{equation}
\begin{aligned}
\delta \Phi^{(1)} =S_A &\bigg(X^A + \frac{ \theta \alpha}{ \Lambda^{(D+2)/2}} \sqrt{H^2 X^2} \partial^A \Phi^{(1)} + \frac{H^2\alpha^2(\theta-1)}{4\Lambda^{D+2}} \left[ 2(\theta+2) \Phi^{(1)} \partial^A \Phi^{(1)} - \theta X^A \left(\partial \Phi^{(1)}\right)^2 \right] \\
& + \frac{H^4\alpha^3 \theta (\theta-1)}{4\Lambda^{3(D+2)/2} \sqrt{H^2 X^2}} \left[ \left( X^2 \partial^A \Phi^{(1)} -X^A \Phi^{(1)}\right) \left(\partial \Phi^{(1)}\right)^2+ \partial^A \Phi^{(1)} \left(\Phi^{(1)}\right)^2 \right] + \dots \bigg), \label{eq:k=1-delta-Phi1-theta}
\end{aligned}
\end{equation}
so the shift transformation truncates to linear or quadratic order in the fields only for $\theta \in \{0, 1\}$. Note that we use the homogeneity condition $X^A \partial_A \Phi^{(1)} =\Phi^{(1)}$ to get Eq.~\eqref{eq:k=1-delta-Phi1-theta}.
Setting $\theta=1$, we now define the weight zero field $\Phi^{(2)} \equiv \Phi^{(1)}/\sqrt{H^2 X^2}$, so that
\begin{equation}
\delta \Phi^{(2)} = S_{A} \left(\frac{X^A}{\sqrt{H^2 X^2}}\left(1+ \frac{ \alpha H^2 \Phi^{(2)}}{\Lambda^{(D+2)/2}} \right)+\frac{\alpha \sqrt{H^2 X^2}}{\Lambda^{(D+2)/2}} \partial^A \Phi^{(2)} \right).
\end{equation}
Finally, we define the weight zero field
\begin{equation}
\Phi^{(3)} \equiv \frac{\Lambda^{(D+2)/2}}{ \alpha H^2} \log \left(1+ \frac{ \alpha H^2 \Phi^{(2)}}{\Lambda^{(D+2)/2}} \right),
\end{equation}
so that we get
\begin{equation}
\delta \Phi^{(3)} = S_A \left( \frac{1}{\sqrt{H^2 X^2}} X^A +\frac{\alpha}{\Lambda^{(D+2)/2}} \sqrt{H^2 X^2}\partial^A \Phi^{(3)} \right),
\end{equation}
which is the dS conformal dilaton transformation \eqref{eq:delta-dS-conf-dilaton}.
To summarize, the fields in the brane and dilaton presentations of the symmetry breaking pattern $\mathfrak{so}(D,2) \rightarrow \mathfrak{so}(D,1)$ are related by the ambient space field redefinition
\begin{equation}
\hat{\Phi}^{(3)} = - \log \left(1- \frac{e^{- \bar{\delta}} \hat{\Phi}^{(0)}}{\sqrt{H^2 X^2}}\right),
\end{equation}
where $\hat{\Phi}^{(i)} \equiv -\alpha H^2 \Phi^{(i)}/\Lambda^{(D+2)/2}$ and the derivation $\bar{\delta}$ is defined in Eq.~\eqref{eq:k=1-derivation}. In terms of dS fields, this is
\begin{equation}
\hat{\phi}^{(3)} = - \log \left(1-e^{- \bar{\delta}} \hat{\phi}^{(0)}\right), \quad \bar{\delta} \hat{\phi}^{(0)} = -\sum_{j=1}^{\infty} \frac{\left( (\partial \hat{\phi}^{(0)} )^2+H^2 (\hat{\phi}^{(0)})^2 \right)^{j}}{H^{2j}} f_j\left( \hat{\phi}^{(0)} \right),
\label{eq:eqwithfjs}
\end{equation}
where $\hat{\phi}^{(i)} \equiv -\alpha H^2 \phi^{(i)}/\Lambda^{(D+2)/2}$. The first terms of the power series $f_j$ are given in Table~\ref{tab:functions}.
\section{Broken diffeomorphisms and Goldstone modes}
\label{sec:broken-diffs}
In this section, we outline a geometric interpretation of all the dS scalar field theories with nonlinear symmetries---there is a unified description of them in terms of spontaneously broken diffeomorphisms. This discussion parallels that of Ref.~\cite{Roest:2020vny} for the special galileon in flat space.
\subsection{Nonlinearly realized extensions of the isometry algebra}
Under a general infinitesimal coordinate transformation $\delta x^\mu = - \xi^\mu(x)$, the metric transforms as
\begin{equation}
\delta {g}_{\mu\nu} = -2 {\nabla}_{(\mu} \xi_{\nu)} \,. \label{diff-transf}
\end{equation}
A special class of diffeomorphisms are those that leave the metric invariant. These correspond to Killing vectors, which generate the isometries of the space. For example,
in stereographic coordinates, $X^{\mu}(x)=\frac{x^{\mu}}{1+H^2 x^2/4}$ and $X^{D+1}(x)=\frac{1}{H}\frac{1-H^2 x^2/4}{1+H^2 x^2/4}$, the dS metric is
\begin{align}
{\rm d} s^2 = \frac{1}{\left(1 + \frac{H^2 }{4}x^2 \right)^2} \eta_{\mu \nu} {\rm d} x^\mu {\rm d} x^\nu \,,
\end{align}
where $\eta= {\rm diag} (-1, 1, \dots, 1)$ and $x^2 \equiv \eta_{\mu\nu} x^\mu x^\nu$, and the Killing vectors are given by
\begin{equation}
\xi^\mu = \omega^\mu{}_\nu x^\nu + \epsilon^\nu\left[\delta_\nu^\mu\left(1 - \frac{H^2}{4}x^2\right) + \frac{H^2}{2} x^\mu x_\nu\right] \,,
\end{equation}
for constants $\epsilon^\mu$, $\omega^\mu{}_\nu$, where
indices are raised and lowered with $\eta_{\mu\nu}$
and $\eta_{\mu \lambda} \omega^\lambda{}_\nu=-\eta_{\nu \lambda} \omega^\lambda{}_\mu$.
Any two vector fields commute into a third via the Lie bracket,
\begin{align}
\xi_3^\mu = \xi_1^\nu \nabla_\nu \xi_2^\mu - \xi_2^\nu \nabla_\nu \xi_1^\mu \,.
\end{align}
The total set of vector fields forms an infinite-dimensional Lie algebra with the Lie bracket as the commutator.
The commutator of two Killing vectors gives another Killing vector, so the isometries form a finite-dimensional Lie subalgebra of the algebra of all vector fields.
Our goal is to find an intermediate-sized algebra containing the subalgebra of isometries by including additional diffeomorphisms, which will now be nonlinearly realized on a scalar Goldstone mode instead of being isometries of the space. Importantly, we still wish the algebra to be finite dimensional.
Since we want the Goldstone mode to be a scalar field, we consider diffeomorphisms whose generators are exact as one forms, i.e., $\xi_\mu = \nabla_\mu \sigma$. The dS Killing vectors are not exact, as can be verified by showing that they are not closed.
Taking the commutator of an exact diffeomorphism $\nabla_\mu\sigma$ and a Killing vector $\xi^{\mu}$ gives another exact diffeomorphism $\nabla_\mu\sigma'$ with $\sigma' \equiv \xi^\mu \nabla_\mu \sigma$, so the exact diffeomorphisms form a linear representation of the isometry group.
Commuting two exact diffeomorphisms formed from $\sigma_a$ and $\sigma_b$ gives a diffeomorphism generated by the vector
\begin{equation}
\xi_{ab}^{\mu} \equiv \nabla^{\nu} \sigma_a \nabla_{\nu} \nabla^{\mu} \sigma_b-\nabla^{\nu} \sigma_b \nabla_{\nu} \nabla^{\mu} \sigma_a.
\end{equation}
One way to close the algebra is to require that $\xi_{ab}^{\mu}$ is itself a Killing vector, which gives the condition
\begin{align}
\nabla_{(\mu} \xi^{ab}_{\nu)} = \nabla^\rho \sigma_a \nabla_{(\mu} \nabla_{\nu} \nabla_{\rho)} \sigma_b - \nabla^\rho \sigma_b \nabla_{(\mu} \nabla_{\nu} \nabla_{\rho)} \sigma_a \, = 0.
\end{align}
We do not attempt to solve this equation in general, but rather restrict to the following simpler sufficient condition that will be enough to encompass the exceptional scalar theories of interest:
\begin{align}
\nabla_{(\mu} \nabla_\nu \nabla_{\rho)} \sigma_a =\lambda \, g_{(\mu \nu} \nabla_{\rho)} \sigma_a \,, \quad\qquad \nabla_{(\mu} \nabla_\nu \nabla_{\rho)} \sigma_b=\lambda\, g_{(\mu \nu} \nabla_{\rho)} \sigma_b\,, \label{condition}
\end{align}
where $\lambda$ is some constant.
Before discussing the possible solutions to Eq.~\eqref{condition}, let us see the relevance for the nonlinear scalar symmetries. The algebra including exact diffeomorphisms can be realized nonlinearly on a Goldstone mode $\phi$, provided the Goldstone mode transforms in the usual linear way under the Killing vectors and nonlinearly under the exact diffeomorphisms according to
\begin{align}
\delta_{\sigma_a} \phi = \sigma_a + \frac{\alpha}{\Lambda^{(D+2)/2}} \nabla^\mu \sigma_a \nabla_\mu \phi \,.\label{phitransphie}
\end{align}
For example, the commutator of two of these transformations is
\begin{equation}
[\delta_{\sigma_a}, \delta_{\sigma_b}] \phi = -\frac{\alpha^2}{\Lambda^{D+2}} \xi^{\mu}_{ab} \nabla_{\mu} \phi.
\end{equation}
From $\phi$ and the dS metric $g_{\mu\nu}$, we can then build a metric that transforms covariantly under the extended algebra, which can then be used to construct invariant interactions.
Returning to the condition \eqref{condition}, we can identify the following three sets of solutions that separately form irreducible representations of the isometry group:
\begin{itemize}
\item
$\boldsymbol{k=0}$: This case corresponds to the trivial solution with $\nabla_\mu \sigma = 0$, i.e., $\sigma$ is constant. This is a degenerate case because the parameter $\sigma$ corresponding to an exact diffeomorphism $\nabla_\mu\sigma$ is only defined up to a constant, though the transformation \eqref{phitransphie} depends on this constant. This constant represents a simple shift symmetry of the scalar. From this point of view, the shift symmetry is not really an extension of the spacetime isometries, but instead a kind of central extension realized by passing to the nonlinear realization \eqref{phitransphie}.
\item
$\boldsymbol{ k=1}$: This case consists of the solutions with $\nabla_{(\mu} \nabla_{\nu)} \sigma_a = -H^2 g_{\mu \nu} \sigma_a$. This implies that the exact diffeomorphisms are conformal Killing vectors. There are $D+1$ conformal Killing vectors, corresponding to dilations and special conformal transformations. In stereographic coordinates, the solutions read
\begin{align}
\sigma = \frac{1 - x^2 H^2/4 }{1+x^2H^2/4} ( c+c_\mu y^\mu) \,, \qquad y^\mu \equiv x^\mu / (1 - x^2 H^2/ 4) \,.\label{k1solepe}
\end{align}
These can be written as the restrictions of the ambient space objects $S_A X^A$.
The Killing and conformal Killing vectors together generate the algebra $\mathfrak{so}(D,2)$. The associated Goldstone mode is the dilaton. The following metric transforms covariantly under the nonlinearly realized symmetries
\begin{equation}
G^{(1)}_{\mu\nu} \equiv e^{2\hat{\phi}}g_{\mu\nu}, \quad \hat{\phi} \equiv -\frac{\alpha H^2}{\Lambda^{(D+2)/2}}\phi ,
\end{equation}
and can be used to construct invariant Lagrangians as diffeomorphism invariants (aside from a single Wess--Zumino term)~\cite{Hinterbichler:2012mv}.
\item
$\boldsymbol{k=2}$: Lastly, we have the solutions with $ \nabla_{(\mu} \nabla_\nu \nabla_{\rho)} \sigma_a =-4 H^2 g_{(\mu \nu} \nabla_{\rho)} \sigma_a $. These read in stereographic coordinates
\begin{align}
\sigma = \left( \frac{1 - x^2H^2 / 4}{1+x^2 H^2/4} \right)^2 ( c + c_\mu y^\mu + c_{\mu \nu} y^\mu y^\nu) \,. \label{quadratic}
\end{align}
These can be written as the restrictions of the ambient space objects $S_{AB} X^AX^B$.
The associated Goldstone mode will be the special galileon with the nonlinearly realized algebra $\mathfrak{sl}(D+1, \mathbb{R})$. In this case, we can construct the metric \eqref{eq:k2metric},
\begin{equation}
G_{\mu\nu}^{(2)} \equiv g_{\mu\nu}-H^{-2}\nabla_\mu\nabla_\nu \hat{\phi}+H^{-2}\nabla_\mu \hat{\phi} \nabla_\nu \hat{\phi}, \quad \hat{\phi} \equiv -\frac{2 \alpha H^2}{\Lambda^{(D+2)/2}}\phi ,
\end{equation}
which transforms covariantly under the nonlinearly realized symmetries.\footnote{Actually, it transforms covariantly under a slightly larger set of symmetries, namely $\mathfrak{gl}(D+1, \mathbb{R})$. However, since the special galileon Lagrangian is a Wess--Zumino term, it cannot be written in terms of this metric, so it only has $\mathfrak{sl}(D+1, \mathbb{R})$ symmetry. Similarly, the appearance of $e^{-(D+1) \hat{\phi}}$ in Eq.~\eqref{eq:sgalEOM} breaks the symmetry of the equation of motion down to $\mathfrak{sl}(D+1, \mathbb{R})$.}
\end{itemize}
All of the above solutions can be written in the form
\begin{align}
\sigma = \left( \frac{1 - x^2 H^2 / 4}{1+x^2H^2/4} \right)^k P_k (y) \,, \label{sigma}
\end{align}
where $k \in \{0,1, 2\}$ and $P_k$ are $k$-th order polynomials in $y$, as given in Eqs.~\eqref{k1solepe} and \eqref{quadratic} for $k=1, 2$. These solutions can be lifted to the ambient space functions
\begin{equation}
\Sigma = \frac{1}{(X^2 H^2)^{k/2}}S_{A_1 \dots A_k} X^{A_1} \dots X^{A_k},
\end{equation}
where the overall factor of $(X^2H^2)^{-k/2}$ is chosen so that $\Sigma$ has weight zero. The nonlinear realization \eqref{phitransphie} of the exact diffeomorphisms on the Goldstone mode $\phi$ can then be written in ambient space as
\begin{align}
\label{eq:goldstone-ambient}
\delta \Phi = \Sigma + \frac{\alpha H^2 X^2}{ \Lambda^{(D+2)/2}} \nabla_A \Sigma \nabla^A \Phi \,,
\end{align}
where the ambient space field $\Phi$ has weight zero.
This discussion shows how we can identify the transformations of Goldstone scalars in dS space with various subsets of non-Killing diffeomorphisms. The trivial case $k=0$ yields a scalar field with a constant shift symmetry. The cases $k=1$ and $k=2$ are the curved-space analogues of the flat space dilaton and special galileon. For flat space, it is known that the corresponding algebras $\frak{so}(D, 2)$ and $\frak{igl}(D)=\frak{gl}(D,\mathbb{R}) \ltimes \mathbb{R}^D$ are the only finite-dimensional Lie subalgebras of the diffeomorphism algebra properly containing the Poincar\'e isometry algebra \cite{xthschool}.\footnote{Note that flat space DBI has as its symmetry algebra $\frak{iso}(D,1)$, which is not a subalgebra of $D$-dimensional diffeomorphisms, so it is not realized in this way.}
We do not know if a similar statement has been proven for dS space.
\section{Conclusions}
We have elucidated the structure of exceptional effective field theories of a single self-interacting scalar field on dS space. A particularly interesting example is the $k=2$ theory with a mass $m^2=-2(D+1)H^2$, which is the dS version of the special galileon. We found a simpler formulation of this theory and showed that it is related to the original formulation of Ref.~\cite{Bonifacio:2018zex} by a field transformation that can be thought of as a dS uplift of galileon duality. The $k=1$ theory, with a mass $m^2=-D\,H^2$, has two natural formulations: as the DBI theory of a dS$_D$ brane probing an AdS$_{D+1}$ bulk and as the dilaton of broken conformal symmetry on dS space. We found strong evidence that these two formulations are also equivalent, related by a field transformation that is a dS uplift of the transformation of Ref.~\cite{Bellucci:2002ji, Creminelli:2013fxa}. Finally, we gave a new interpretation of these symmetries as sets of broken diffeomorphisms.
The coset construction gives a systematic way to build Goldstone effective field theories that are invariant under a given symmetry breaking pattern for internal symmetries \cite{Coleman:1969sm, Callan:1969sn,Volkov:1973vd}. The effective field theories obtained are unique, in the sense that any two theories with the same breaking pattern will be equivalent under field redefinitions of the Goldstones. The Goldstones parametrize the coset, and the field redefinitions are different parameterizations of the coset. For spacetime symmetries, the coset construction is more involved \cite{Volkov:1973vd,xthschool}, and the number of the Goldstones is not generally equal to the dimension of the coset. As far as we know, there is no proof that effective field theories with the same spontaneous spacetime symmetry breaking pattern, and the same degrees of freedom, are always equivalent (this is expected to be the case, although there are subtleties when coupling to matter \cite{Creminelli:2014zxa,Dubovsky:2007ac}). Our results here give more evidence that they are in fact the same; different realizations of the same symmetry breaking pattern on the fields give theories whose Lagrangians look very different, but which are related by non-trivial field redefinitions involving all orders in powers of the field.
A natural extension of our study would be to explore where there are similarly simple (A)dS formulations of shift-symmetric theories that involve higher-spin particles. For example, there are shift-symmetric theories containing spin-1 fields on curved and flat space \cite{DeRham:2018axr,Bonifacio:2019hrj, Kampf:2021bet} that may have more unified formulations, and there may be higher-spin examples as well \cite{Bonifacio:2018zex}.
An important open question is to understand the on-shell avatar of the symmetries of these exceptional scalar theories in curved spacetimes, where the natural observable quantities are boundary correlation functions. This is the purview of the cosmological bootstrap, which aims to classify the space of possible cosmological correlators, and so constrain the physics of inflation (see, e.g., Refs.~\cite{Arkani-Hamed:2018kmz,Sleight:2019hfp,Baumann:2019oyu,Baumann:2020dch,Pajer:2020wxk,Meltzer:2020qbr,Goodhew:2020hob,Melville:2021lst,Jazayeri:2021fvk,Baumann:2021fxj,Bonifacio:2021azc,Meltzer:2021zin,Sleight:2021plv,Hogervorst:2021uvp,DiPietro:2021sjt} for recent developments). It is natural to wonder about the role of these scalar theories in the bootstrap construction: how precisely are their special properties reflected in their (A)dS correlators? We expect that, much like in the flat space case, their correlation functions will display a rich web of interconnections, which could help reveal some underlying general structures of cosmological correlators.
An intriguing direction to pursue is to search for (A)dS versions of the double copy and scattering equations. Some aspects of color-kinematics duality and the double copy have been studied in Refs.~\cite{Farrow:2018yni,Armstrong:2020woi,Albayrak:2020fyp,Alday:2021odx,Zhou:2021gnu,Sivaramakrishnan:2021srm}, but much of the structure remains mysterious. Similarly, scattering equations in AdS have just begun to be explored~\cite{Eberhardt:2020ewh,Roehrig:2020kck,Gomez:2021qfd}. It is natural to expect that these exceptional scalar theories will be similarly helpful in elucidating these structures as they were in flat space.
\paragraph{Acknowledgements:} We would like to thank Tanguy Grall, Hayden Lee, and David Stefanyszyn for helpful discussions. During this work we made use of the \texttt{Mathematica} package \texttt{xAct} \cite{xAct}. JB is supported by the research program VIDI with Project No.~680-47-535, which is partly financed by the Netherlands Organisation for Scientific Research (NWO), and partially supported by STFC HEP consolidated grant ST/T000694/1. KH acknowledges support from DOE grant DE-SC0009946 and from Simons Foundation Award Number 658908.
\renewcommand{\em}{}
\bibliographystyle{utphys}
\addcontentsline{toc}{section}{References}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 3,131
|
Q: Error ( No implicits found for parameter responseSerializer: MessageSerializer[Seq[SearchFormData], _] ) enter image description here
Getting error in scala rest API while passing Seq[] in response. And when I remove Seq it works fine.
Thank You
A: Maybe you need to check 1) if you have your own proper formatters for objects you have in your sequence. 2) And to check if you have play(or spray, or whatever you use to marshall and unmarshall) imported in your controller
maybe you need something like this on your controller layer
import de.heikoseeberger.akkahttpplayjson.PlayJsonSupport._
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,092
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Q: cant create new partition in dev/sdb1 sandisk pendrive While using the application "Disks" I am trying to format a USB and make a new partition on it. I am successfully able to format the drive but not make a new partition when i click the + sign. It shows an error.
And when i am selecting the erase option while creating a new partition with the + sign
It is showing this=
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,733
|
Jan Blachowicz Says It's UFC Title Shot Or Bust Next
Image Credit: Josh Hedges/Zuffa LLC via Getty Images
Jan Blachowicz feels there is no doubt that he deserves a crack at the UFC light heavyweight championship.
Blachowicz is coming off a first-round knockout victory over Corey Anderson. This was a rematch as Blachowicz lost their first encounter via unanimous decision. UFC light heavyweight champion Jon Jones was sitting near Octagon side and told reporters that Blachowicz is deserving of a title opportunity.
Jan Blachowicz Wants UFC Title Shot Next
Blachowicz doubled down on his belief that Dominick Reyes already had his chance and shouldn't get an immediate rematch. He told MMAJunkie.com that for him, it's title shot or bust next.
"I've done everything," Blachowicz said. "Dominick, he had his chance. He don't use it, and now it's my turn. It's a simple situation. I don't know why they think about the rematch. I know it was a good fight, close fight, but he lost the fight, and now it's my turn. Simple things. I'm next, and that's it."
Jones recently had a run-in with the law that had many questioning whether or not the UFC would take action. Some called for an interim title bout between Reyes and Blachowicz. Ultimately, "Bones" reached a plea deal for his DWI charge and avoided jail time.
Blachowicz is riding a three-fight winning streak. He hasn't suffered a loss since Feb. 2019. The fourth-ranked UFC light heavyweight has gone 7-1 in his last eight outings. In that span, he has earned two submissions and two knockouts.
Do you think Jan Blachowicz will get the next UFC light heavyweight title shot?
Jan Blachowicz Extends Retirement Challenge To Glover Teixeira
Jan Blachowicz Lashes Out At Joe Rogan Over UFC 282 Post-Fight Interview
Magomed Ankalaev Receives Hero's Welcome In Dagestan Despite UFC 282 Draw
Anthony Smith: Jan Blachowicz Beat Magomed Ankalaev At UFC 282
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 4,898
|
package generator.standard.field_types.primitives.valid;
import gsonpath.annotation.AutoGsonAdapter;
@AutoGsonAdapter
public class TestValidPrimitives {
public boolean value1;
public int value2;
public double value3;
public long value4;
public byte value5;
public short value6;
public float value7;
public char value8;
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,125
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{"url":"http:\/\/mathhelpforum.com\/advanced-algebra\/188591-definition-subfield.html","text":"# Thread: definition of a subfield\n\n1. ## definition of a subfield\n\nin the definition of a subfield we have that it contains both the 0 and 1 elements.\n\nprove- this condition can be replaced by \"it has at least 2 elements\"\n\nI'm quite confused as to how to start this, if someone could give me a hint to get started that would be great.\n\nthanks for any help\n\n2. ## Re: definition of a subfield\n\nOriginally Posted by hmmmm\nin the definition of a subfield we have that it contains both the 0 and 1 elements.\n\nprove- this condition can be replaced by \"it has at least 2 elements\"\n\nI'm quite confused as to how to start this, if someone could give me a hint to get started that would be great.\n\nthanks for any help\nWell, in a field you assume that $1\\ne 0$ and since every field has a multiplicative and additive identity.....","date":"2016-09-28 17:15:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 1, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8812734484672546, \"perplexity\": 237.10509454969318}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-40\/segments\/1474738661640.68\/warc\/CC-MAIN-20160924173741-00133-ip-10-143-35-109.ec2.internal.warc.gz\"}"}
| null | null |
Sigfredo Hillers de Luque (Madrid, 16 de desembre de 1934-Madrid, 24 de novembre de 2017) va ser un docent i polític espanyol d'extrema dreta.
Biografia
Nascut a Madrid el 16 de desembre de 1934, va ingressar en el Frente de Juventudes en 1944. Posteriorment, en 1953, va ingressar en la XVI Centúria de la Guàrdia de Franco. Obrer des dels 16 anys, va aconseguir matricular-se a la Universitat i llicenciar-se en Sociologia i Dret. Posteriorment va ampliar estudis a Berlín i Bonn. En 1975 va publicar la seva tesi doctoral, amb el títol España: Una revolución pendiente. Va obtenir plaça com a professor titular en la Facultat de Dret de la Universitat Complutense de Madrid.
En 1963 va fundar el Frente de Estudiantes Sindicalistas (FES) juntament amb Narciso Perales, Ceferino Maestú i Juan Diego. Aquest grup va néixer a la calor dels cercles falangistes dissidents amb la línia oficial del «Movimiento Nacional». No obstant això, a mesura que avançava la dècada van sorgir fortes dissidències entre Hillers, Perales i Maestú.
Hillers fundaria l'associació juvenil «Octubre»,germen de la posterior Falange Espanyola Independent.
Després de la mort de Franco es va posicionar com a líder de la Falange Espanyola Independent. El seu col·lectiu va competir per les sigles oficials de «FE de las JONS» amb els Cercles Doctrinals «José Antonio», la Falange Espanyola «Autèntica» i el Front Nacional Español de Raimundo Fernández Cuesta, que va aconseguir les sigles, mantenint Hillers conflictes amb aquesta formació. Va tenir un paper merament testimonial en la Transició i acabaria abandonant la política en 1984.Centrat en l'activitat docent, amb posterioritat va publicar diverses obres.
Va morir a Madrid el 24 de novembre de 2017.
Obra
—— (1974). Ética y estilo falangistas. Madrid: Gráficas Lázaro Carrasco.
—— (1975). España, una revolución pendiente. Madrid: FES.
Referències
Bibliografia
Falangistes
Morts el 2017
Alumnes de la Universitat Complutense de Madrid
Morts a Madrid
Polítics madrilenys
|
{
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| 1,575
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Environmental Lights is a leader in sustainable, energy-efficient LED lighting. We serve a variety of industries from Residential to Retail Stores, from Hotel Resorts to Theme Parks. We are proud to be a member of the Association for Retail Environments (A.R.E.), as it allows us to connect with our customers in the retail space and offer them products to improve their businesses and make their brands successful.
1. Do you need flexible lighting (strip) or rigid bars?
2. Do you need a solid color or color-changing flexibility?
3. Does the system need to dim?
4. Does the system need to create effects?
EnvironmentalLights.com offers a variety of premium LED cabinet lighting systems including the light bars, connectors, dimmers and power supplies needed to create beautiful retail displays. Our cabinet lighting systems feature low profile light bars, natural color options (soft and neutral white), flawless dimming performance and useful accessories. Illuminate countertop space, brighten display cases or highlight merchandise on shelves.
Another lighting option for a retail space is LED strip lighting. Strip lighting is flexible and sold in longer lengths than light bars (reel = 16.4 feet). In addition to four different brightness levels, there is a wider variety of color choices – a full range of white options plus red, green, blue, amber and RGB color-changing.
Our White Adjustable strip light lets you adjust the color of white you prefer, from warm white (2,400°K) to daylight white (6,500°K) and any color in between. Giving you versatility and control over your lighting environment.
Watch our video on retail lighting solutions to learn more about LED lighting and applications for lighting in your store. Learn about lighting features to help you get the most out of your lighting.
Learn how Barneys created the lighting effects in the 2011 Lady Gaga-inspired holiday window displays, designed with lighting from EnvironmentalLights.com.
(888) 880-1880 ext. 112 or email me your project details, product interests and any questions and I'll put together a quote to best fit your needs.
|
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"redpajama_set_name": "RedPajamaC4"
}
| 1,441
|
Natural Resources and Parks Water and Land Resources Division
Sections and programs
Environmental Lab Finance and Admin River and Floodplain Section
Projects Plans, reports, studies & surveys Levees and revetments
Rural and Regional Services Science Section Stormwater Section
Natural Resources and Parks
Water and Land Resources Division
River and Floodplain Section
River and Floodplain Management Section
Restoring rivers and reducing flood risks
POSTPONED: Jan. 14 public meeting about the Middle Fork Snoqualmie River Corridor Planning and Capital Investment Strategy.
The Middle Fork Snoqualmie River Capital Investment Strategy Community Meeting scheduled for Tuesday, January 14, 2020 in North Bend is POSTPONED due to winter weather.
The meeting will be rescheduled for a future date.
Sign up for free King County Flood Alerts.
Get free sand bags at a location near you and learn how to use them to fight flooding.
Download the free King County Flood Warning app.
Learn how to prepare for flooding.
Learn more about King County's rivers, from safety issues to flooding to river ecology. Follow The Downstream Blog.
River and Floodplain Management Section directory
Large wood in King County rivers
Known hazards in King County rivers
Boater safety
Watersheds, rivers and streams
Department of Natural Resources and Parks
Projects are designed to reduce risks to public health and safety, protect infrastructure and provide habitat components in compliance with natural resource regulations.
Levees and Revetments
Over 500 levees and revetments exist along King County rivers. Inspections and maintenance occur regularly on these river facilities.
Flood Warning System - The system is designed to warn and provide information to residents and agencies about impending floodwaters on major rivers so they can take action and prepare themselves before serious flooding occurs. The web site links to real-time river gage data and describes the local flooding homeowners can expect at different flood phases based on past flood events.
Home Buyouts and Elevations in flood prone areas - The home elevation program assists property owners with the costs of raising the finished floor of a home above the 100-year elevation, substantially reducing the threat of future damage. Home buyouts provide a permanent solution to the risks and damages of repetitive flooding.
Known Hazards in King County Rivers - Information about known hazards on the rivers of King County including maps and photos of projects containing large wood.
Grants Program - Grants from a variety of sources are pursued to fund flood hazard reduction projects and programmatic activities that mitigate flooding problems throughout the county.
Mapping, Floodplain Mapping and Channel Migration Hazard Mapping - These hazard areas are regulated to limit or prevent at-risk development. Since 1991, updated flood boundaries have been mapped on nearly 80 miles of river, and channel migration zones along 46 miles of river.
Planning and reports
2013 King County Flood Hazard Management Plan Update and Progress Report
2006 King County Flood Hazard Management Plan
Corridor plans
Biological Effects Analysis Report
Guidelines for Bank Stabilization Projects: in the Riverine Environments of King County
WRIA and watershed forum coordination - River and Floodplain Management Section has a lead role in WRIA 10, White River Watershed planning and participates in King County's Watershed Forums and the WRIA groups. Section staff work closely with the Watershed Coordinators and their interjurisdictional partners on Forum and WRIA efforts, including prioritization of watershed projects related to flooding, fish, and water quality; implementation of restoration projects; participation in the WRIA technical groups; and preliminary planning for WRIA conservation plans.
Flood hazard education - Flood hazard education efforts aim to educate the public about the risks of living in flood-prone areas, steps they should take to reduce flooding, and programs available to help them insure properties against flood losses.
Complaint response and enforcement - Staff investigates complaints about flooding, channel migration, severe bank erosion and logjams on a year-round basis and especially during and immediately following flood events. During large floods, two-person teams patrol flooded areas along the major rivers to provide rapid response to flooding complaints and evaluate whether logjams pose an imminent threat to public safety and/or public facilities. Patrols also inspect County river facilities for structural damage and other warning signs that indicate potential facility failure that could harm developed property and off channel habitat.
Violations of King County sensitive areas regulations, including floodplain regulations, are referred to the Department of Permitting and Environmental Review and/or other appropriate agencies for enforcement. Urban drainage complaints such as water quality problems and toxic waste dumping in unincorporated King County are referred to the Stormwater Services Section for investigation of potential violations of water quality codes. Other localized drainage and/or flooding complaints are also referred to the Stormwater Services Section for investigation. Water quality complaints found in cities are referred to the King County Trouble Call Coordinator, who will contact appropriate officials to initiate resolution of the problem. Large spills of toxic chemicals or petroleum products are referred to the Washington Department of Ecology. Fish kills are referred to the Washington Department of Fish and Wildlife.
Interlocal coordination - The River and Floodplain Management Section coordinates extensively with other King County agencies as well as numerous outside federal, state, local and tribal agencies on matters pertaining to floodplain management, flood control, and riverine and riparian habitat. The major coordination topics include:
Dam Operations: Participation in tabletop exercises related to dam safety, flood control, and fish habitat.
Flood hazard reduction policy and regulatory consistency with the State Department of Ecology and Department of Permitting and Environmental Review; Snohomish County, the Cities of Duvall, Carnation, Snoqualmie and North Bend, and the Tulalip Tribes in the Snoqualmie basin; the City of Renton and the Muckleshoot Indian Tribe (MIT) in the Cedar River basin; the Cities of Auburn, Kent, Renton and Tukwila and MIT in the Green/Duwamish basin; and Pierce County and the Cities of Auburn and Pacific, MIT and the Puyallup Indian Tribe in the White River basin.
WRIA coordination with federal and state natural resource agencies, Counties, Cities, tribes and citizen groups in the Snohomish, Cedar/Sammamish, Green/Duwamish and White River basins. Major areas of coordination are habitat restoration projects and flooding impacts on riverine and riparian habitats.
Technical assistance to the Department of Permitting and Environmental Review and federal, state and local agencies regarding public and private development projects affecting floodplains; as well as input and review of bank stabilization and vegetation management guidelines prepared by other agencies, including the Army Corps of Engineers, the U.S. Natural Resources Conservation Service, and the State Departments of Ecology and Fish and Wildlife.
FEMA and the State regarding floodplain land acquisitions, home buyouts and elevations, property owners request and applications for letters of Map Amendment and Revision, and the federal flood insurance program.
Fish habitat use research conducted by U.S. Fish and Wildlife Service at bank stabilization sites in King County.
For questions about this page, please contact Katy Vanderpool, Policy and Planning Supervisor, River and Floodplain Management Section.
|
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| 35
|
{"url":"https:\/\/earthscience.meta.stackexchange.com\/questions\/1615\/why-isnt-my-reputation-count-raising-when-my-post-gets-upvoted-on-meta","text":"# Why isn't my reputation count raising when my post gets upvoted on meta?\n\n## Here's my problem:\n\nI've had some upvoted posts that haven't raised my reputation count. It will sometimes take some time to notify me and raise my reputation count, but it's been 36 hours, and still no notification.\n\nHere's a couple of upvoted posts that haven't raised my reputation count:\n\nIt might just be another bug, but it could also be what is meant to happen.\n\n## Here's my theory:\n\nIt could just be whatever changes are made to you're reputation count on the main site (in this case it's earthscience.se) is what happens to your reputation count on meta.\n\nIf my theory os correct, than it would be much appreciated it i was told so. But if my theory is incorrect, than I ask for answers that tell me what's really going on.\n\nThanks for understanding :)\n\n\u2022 To quote the What is meta? help page: Votes on meta do not affect your reputation; your meta reputation is the same as your reputation on Earth Science Stack Exchange (synchronized hourly), though you earn separate badges. You must have 5 reputation to participate on meta. \u2013\u00a0plannapus Feb 7 '18 at 16:06\n\u2022 Incidentally: if it's important to you to acquire a high reputation score, Earth Science is not a good stackexchange for you. Firstly, the topics are mostly technical and can require a lot of expertise, time, and effort to address. Secondly, even good, high-effort questions and answers often get few votes simply because there are few active users here. By comparison, sites like Puzzling and English Language provide more reputation in less time, because they have more users and because posts are often quicker to write. \u2013\u00a0Pont Feb 14 '18 at 16:25","date":"2020-12-05 14:53:26","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.1863195151090622, \"perplexity\": 1607.449228177314}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-50\/segments\/1606141747887.95\/warc\/CC-MAIN-20201205135106-20201205165106-00485.warc.gz\"}"}
| null | null |
Tie up your horse and grab a pint as you prepare to put together this 1000piece jigsaw puzzle by famed master painter Charles Wysocki. Sleepy Town Westfeatures all of the classic icons from old western movies, including a generalstore, post office and saloon. The steam engine chugging in the distance andthe presence of horses and buggies in town offer an interesting contrast intransportation and progress. For more than 40 years, Charles Wysocki enjoyedhis love affair with life and Americana and through his imaginative andcolorful artwork, touched the hearts of millions worldwide. "Chuck" felt aspecial kinship with puzzlers, who share in the creative process by buildinghis paintings one piece at a time. Every Buffalo Games jigsaw puzzle ismanufactured in the U.S.A. from recycled puzzle board. A precision cuttingtechnique guarantees that every piece will fit soundly with the company'ssignature Perfect Snap. A bonus puzzle poster is also included so that youhave a handy reference of what the completed puzzle should look like while youput yours together.
|
{
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| 532
|
The United States District Court for the Northern District of Iowa (in case citations, N.D. Iowa) has jurisdiction over fifty-two of Iowa's ninety-nine counties. It is subject to the Eighth Circuit Court of Appeals (except for patent claims and claims against the U.S. government under the Tucker Act, which are appealed to the Federal Circuit).
The United States District Court for the District of Iowa, established on March 3, 1845, by , was subdivided into the current Northern and Southern Districts on July 20, 1882, by .
Presently, the court has two district judges, Chief Judge Leonard T. Strand and Judge C. J. Williams, one senior judge, Linda R. Reade, and two magistrate judges, Kelly Mahoney and Mark A. Roberts.
The court is headquartered in Cedar Rapids, with a satellite courthouse in Sioux City.
, the Acting United States Attorney is Timothy T. Duax.
Jurisdiction
The Northern District of Iowa has four court divisions, each covering the following counties:
The Cedar Rapids Division, covering Benton, Cedar, Grundy, Hardin, Iowa, Jones, Linn, and Tama counties.
The Central Division, covering Butler, Calhoun, Carroll, Cerro Gordo, Emmet, Franklin, Hamilton, Hancock, Humboldt, Kossuth, Palo Alto, Pocahontas, Webster, Winnebago, Worth, and Wright counties.
The Eastern Division, covering Allamakee, Black Hawk, Bremer, Buchanan, Chickasaw, Clayton, Delaware, Dubuque, Fayette, Floyd, Howard, Jackson, Mitchell, and Winneshiek counties.
The Western Division, covering Buena Vista, Cherokee, Clay, Crawford, Dickinson, Ida, Lyon, Monona, O'Brien, Osceola, Plymouth, Sac, Sioux, and Woodbury counties.
Current judges
:
Former judges
Chief judges
Succession of seats
See also
Courts of Iowa
List of current United States district judges
List of United States federal courthouses in Iowa
References
External links
Main page
Makeup
US Attorney
Iowa, Northern District
Iowa law
Cedar Rapids, Iowa
Webster County, Iowa
Sioux City, Iowa
1882 establishments in Iowa
Courthouses in Iowa
Courts and tribunals established in 1882
|
{
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| 8,541
|
\section{Introduction}
Protoplanetary disks link protostars and (extra-)solar planetary systems
physically and chemically. Understanding the chemical composition and
evolution of disks thus provides constraints on the nature of molecules
incorporated into planetesimals and planets.
A variety of simple species, including the organic molecules CN, HCN, and
H$_2$CO, have been detected towards a handful of disks in unresolved studies
\citep{Dutrey97, Thi04,Kastner08}, suggestive of an active chemistry. However, apart
from CO and to some extent HCO$^+$, the chemistry is poorly constrained \citep{Pietu07}.
Observations of the earlier stages of star formation and
of comets, the possible remnants of our own protoplanetary disk, reveal a
chemistry rich in simple and complex organics up to HCOC$_2$H$_5$ and
(CH$_2$OH)$_2$ in size \citep[e.g.][]{vanDishoeck95, Crovisier04, Belloche09}.
Pre-biotic pathways to chemical complexity thus exist. If theses pathways are active
in disks or if the observed cometary complexity is instead a fossil remnant from earlier stages remains to be shown. Recent experiments suggest that the combination
of icy grain mantles and UV irradiation efficiently produces the complex
molecules found around protostars \citep{Oberg09d}, and surely appropriate
conditions are common in disks as well \citep{vanZadelhoff03,Hersant09}.
The chemistry in disks is significantly more difficult to probe than in
protostellar cores because of their order-of-magnitude smaller angular size, which
necessitates the use of (sub-)millimeter arrays to resolve the chemistry of
the bulk of the disk material. The first observations of disk chemistry by \citet{Dutrey97} also revealed lower gas-phase abundances of most molecules compared to protostars. From a slightly larger sample consisting of four sources \citet{Thi04} showed that protoplanetary disks seem to generally contain orders of magnitude lower gas abundances compared to protostellar cores. This is reproduced by models of disks with a combination of
freeze-out onto grains toward the disk midplane and photodissociation in the
disk atmosphere \citep[e.g.][]{Aikawa99}. Gas phase molecules are only expected to be abundant in an intermediate zone that is warmer than common ice sublimation temperatures, but still deep
enough into the disk to be partly protected from stellar and interstellar UV
irradiation \citep[e.g.][]{Aikawa99, Bergin03}. The low molecular abundances result in
weak emission that requires long integration times at all existing
(sub-)millimeter facilities. The investment required for interferometers
in large part explains the small number of resolved chemistry studies of any species
more complicated than HCO$^+$ \citep{Qi03, Dutrey04, Dutrey07, Qi08, Henning10}.
Despite these impediments, single dish studies of the T Tauri stars
DM Tau, GG Tau, LkCa 15, TW Hya, V4046 Sgr and the Herbig Ae stars MWC 480
and HD 163296 have provided some constraints on the chemistry of protoplanetary
disks \citep{Dutrey97,Thi04,Kastner08}.
The species CN, HCN, DCN, HNC, CS, C$_2$H, H$_2$CO, HCO$^+$ and DCO$^+$ have
been detected toward at least one of these objects, with CN/HCN ratios that
only can be explained by high UV or X-ray fluxes penetrating into the disk -- CN is a photodissociation product of HCN.
The variations in molecular abundances among different systems are significant; H$_2$CO is only
detected toward DM Tau and LkCa 15, DCO$^+$ toward TW Hya, and HCN toward
all T Tauri stars but not toward either of the Herbig Ae stars. Suggested reasons
for these variations include higher photodissociation rates and a lack of cold chemistry products toward the more luminous Herbig Ae stars, different stages of
grain growth in different disks, and different disk structures. Differences in
the chemistry preceding the disk stage may also play a role.
Resolved studies of disk chemistry are few but intriguing. Using the
IRAM Plateau de Bure Interferometer, \citet{Dutrey07} reported low
signal-to-noise N$_2$H$^+$ detections toward DM Tau and LkCa 15 and an
upper limit toward MWC 480. Within the same project \citet{Schreyer08} tentatively detected
HCN toward AB Aur. More recently \citet{Henning10} resolved C$_2$H emission toward DM Tau and LkCa 15, while no C$_2$H was detected toward the more luminous MWC 480. The difference between the T Tauri stars and the Herbig Ae star was explained by a combination of high UV and low X-ray fluxes toward MWC 480. Using the SMA, \citet{Qi08} spatially resolved the
HCO$^+$ and DCO$^+$ emission toward TW Hydrae, revealing different
distributions of these
species -- DCO$^+$ is relatively more abundant at increasing radii out to
90 AU, consistent with its origins from cold disk chemistry. HCN and DCN were
both detected as well, but provide less constraints on the chemistry because
of the weak DCN signal. Overall, the combination of small samples of diverse
sources and even fewer resolved studies have so far prevented any strong
constraints on the main source of chemical diversity in protoplanetary disks.
With the DISCS (Disk Imaging Survey of Chemistry with SMA) Submillimeter Array legacy program, we aim to produce a resolved, systematic survey
of chemistry toward protoplanetary disks spanning a range of spectral types and
disk parameters. The targeted molecules are the simple species that
previous studies suggested may be detectable (CO, HCO$^+$, DCO$^+$, CN, HCN, DCN,
N$_2$H$^+$, C$_3$H$_2$, H$_2$CO and CH$_3$OH). The initial survey contains six
well known disks in the Taurus molecular clouds (DM Tau, AA Tau, LkCa 15,
GM Aur, CQ Tau and MWC 480) with central stars that span spectral types M1 to
A4.
The disk sample is presented in $\S$\ref{sec:sample} with special attention to
the properties that may affect the disk chemistry such as stellar luminosity, accretion rates,
disk size, disk structure and dust settling.
The spectral set-ups and observational details are described in
$\S$\ref{sec:obs}.
The channel maps toward one of the richest sources, moment maps for all disks
in the most abundant species, and spectra of all detected lines toward all
sources are shown in $\S$\ref{sec:res}.
The detection rates as well as source-to-source variations are discussed in
section $\S$\ref{sec:disc} followed by qualitative discussions on the origins
of the observed chemical variations.
\section{The Disk Sample\label{sec:sample}}
\subsection{Selection criteria}
The Taurus DISCS sample of protoplanetary disks was chosen to assess the impact
of spectral type or stellar irradiation field on the chemistry in the disk.
The target systems span the full range of stellar luminosities among the
T Tauri and Herbig Ae stars associated with the Taurus molecular cloud.
Table~\ref{tbl:star} lists the stellar properties.
The stellar masses in the sample range between 0.5 and 1.8--2.3 M$_{\odot}$,
corresponding to luminosities that span almost two orders of magnitude.
If stellar luminosity is the main driver of the outer disk chemical evolution,
then this sample should display a range of chemical behaviors. As discussed below there are other sources of radiation that may affect the chemistry as well, especially accretion luminosity and X-rays.
The sample is biased toward disks of large angular extent, since disks smaller
than a few hundred AU are not spatially resolved by the SMA in the compact
configuration. The observations are not sensitive to gas inside of 100~AU, which entails that there is a large gap in radii between these millimeter observations and infrared disk chemistry observations that typically probe the inner disk out to a few AUs. The sources were selected from disks previously mapped in CO
and thus may be biased toward gas-rich disks. Furthermore only disks clearly
isolated from the parent cloud emission are included to reduce confusion and
ensure that the detected molecules reside in the disks. Known harborers of
organic molecules were favored (DM Tau, LkCa 15 and MWC 480), but the sample
also contains disks that have only upper limits or that
have not been investigated for molecular lines other than CO. The focus on a single star
forming region allows us to probe disks of similar ages and likely similar chemical
starting points, reducing the sources of chemical variation.
\subsection{Star and Disk Properties affecting Disk Chemistry\label{sec:sample_prop}}
Stellar luminosity, accretion luminosity, X-rays, the interstellar irradiation field, disk geometry, disk gaps and holes, dust settling and dust growth may all affect the chemistry in the disk. The sample characteristics in terms of these properties are discussed in this section.
Observations of high CN and HCN abundances toward protoplanetary disks reveal
that a chemistry controlled by far-ultraviolet (FUV) or X-ray radiation or
both must contribute to the observed abundances
\citep[e.g.][]{vanZadelhoff01,Thi04}. FUV radiation below 2000~\AA~affects the chemistry by directly heating the gas in the disk surface layers, in limiting molecular abundances via photodissociation, increasing the amount of photochemistry products such as CN and liberating frozen species via photodesorption. The nature of the dominating source of radiation is however unknown.
The quiescent stellar luminosities in the sample range from 0.25 to 11.5
L$_{\odot}$, and if quiescent FUV radiation controls the photodissociation
rate in the disk surface, then there should be a clear trend in the CN/HCN
ratio between the low-luminosity T Tauri stars and the order of magnitude
more luminous Herbig Ae stars. However, Kurucz (1993) stellar atmosphere models show evidence that stars with a spectral type later than F do not have significant stellar continuum $<$2000~\AA~above that generated by accretion, and that it is only for A stars that stellar UV becomes more significant than accretion luminosity for the FUV field. This is confirmed by FUV observations toward the T Tauri star TW Hya, which is dominated by line emission generated from accretion shocks \citep{Herczeg02}.
The accretion FUV spectrum is dominated by line emission and especially Ly-$\alpha$ emission, which results in preferential HCN dissociation and therefore boosts the CN/HCN ratio \citep{Bergin03} beyond what is expected from a UV chemistry dominated by continuum radiation. Toward T Tauri stars, the FUV flux is expected to scale with the accretion rate \citep[e.g.][]{Calvet04}. The accretion rates probably vary over time however, as has been observed toward TW Hya, where \citet{Alencar02} found mass accretion rates between 10$^{-9}$ -- 10$^{-8}$ M$_{\sun}$ yr$^{-1}$ during a year and smaller variations on timescales of days. The measured accretion rate variability among the T Tauri stars in this sample are all within this range and it is unclear whether the average accretion luminosity vary significantly among the sources. In general more massive systems have higher accretion rates \citep{Calvet04} and it can therefore be expected that the FUV flux from accretion will be higher toward the intermediate mass Herbig Ae stars in the sample. As mentioned above, for the early type stars (e.g. A) the stellar continuum also adds a significant contribution to the FUV radiation field. Thus, even if accretion rather than quiescent luminosity controls the UV chemistry, one would expect to observe a higher CN/HCN ratio toward the more massive stars.
Observations of the FUV field in T Tauri systems find that accretion produces UV fluxes that are a few hundred to a thousand times stronger than the Interstellar Radiation Field (ISRF) at 100 AU \citep{Bergin04}. The ISRF may still be important at large radii, however.
The external irradiation field is presumed to be constant toward the Taurus sample of sources, i.e. none
of the disks are close to any O or B stars, but its impact may
differ between the different classes of sources; the ISRF may play a larger
role in driving the chemistry for the low luminosity objects, thus acting as a
chemical equalizer. A fourth possible driver of the disk chemistry is X-rays, which is predicted to be important for the ionization fraction in the disk
\citep{Markwick02}. X-rays are mainly attenuated by gas, while continuum UV photons are quickly absorbed by dust \citep{Glassgold97}. X-rays can therefore penetrate deeper into the disk compared to UV rays, and may be a main driver of both ion chemistry and molecular dissociation. This may result in observable differences in the molecular distribution if the chemistry is driven by X-rays instead of UV radiation. For individual objects X-ray measurements are notoriously variable and assessing their impact observationally may be possible only through monitoring of the X-ray flux and the chemical variation toward a single system \citep{Glassgold05}. On average the X-ray fluxes seem higher toward T Tauri stars compared to Herbig Ae stars and thus ion-driven chemical reactions may be faster in disks around T Tauri stars \citep{Gudel09}.
Regardless of whether the quiescent luminosity
of the central star is the main source of energetic radiation, it may still
control the disk temperature and thus the temperature sensitive chemistry,
e.g. deuterium fractionation efficiency probed by the DCO$^+$/HCO$^+$ ratio.
The stellar continuum photons are expected to be the primary agent for heating grains in the disk, particularly toward the midplane, setting the overall reservoir of warm or cold grains in the outer disk to which the SMA is most sensitive. Both the level of gas phase depletion and the chemistry dependent on CO depletion may then be regulated by the stellar continuum flux. For example a tracer of CO freeze-out such as the N$_2$H$^+$/HCO$^+$ ratio is expected to be higher toward low-luminosity systems \citep{Bergin02}.
The disk structure and dust properties determine how much of the stellar
radiation is intercepted by the disk and the penetration depth of
that radiation. These disk properties may be equally important to the
the strength of the radiation field for the chemical evolution in the disk. Table \ref{tbl:disk}
list the sample disk characteristics from previous CO and continuum
observations and modeling. Position angles and inclinations do not affect the
chemistry intrinsically, but the disk inclination affects which parts of
the disk are observed, and thus our view of the chemistry. The sizes of the disks are described in terms of CO gas disk radii and range
from 200 to 890~AU. Disk masses are less well constrained, since they are
derived from dust emission assuming a dust-to-gas ratio. In most studies the canonical interstellar dust-to-gas ratios of 1 to
100 is used. The actual dust-to-gas ratio may be different because of dust coagulation and photoevaporation, and also variable among the sources. Still it seems clear that two of the disks, AA Tau and CQ Tau,
are significantly less massive than LkCa 15, GM Aur and MWC 480, while DM Tau
falls in between (Table \ref{tbl:disk}). This difference in disk mass may affect their relative
abundances of different species, since more massive disks are expected to
contain more cold material per unit of incoming irradiation.
Three of the sample disks are so-called transition and pre-transition disks (DM Tau, GM Aur and
LkCa 15) with large inner holes or gaps \citep{Calvet04, Espaillat07,Dutrey08}. From a {\it Spitzer} survey of disk chemistry many transition disks, including GM Aur and LkCa 15 have CO gas in the disk hole \citep{Salyk09}. They do however lack emission from HCN and C$_2$H$_2$ transitions in the {\it inner} disk that are strong toward classical T Tauri stars \citep{Pascucci09}. It is unclear whether this is a chemistry or gas-mass effect. It is also unknown whether the chemistry in
the outer regions of these transition disks differ significantly from classical
T Tauri disks, although it is curious that these systems are the most chemically
rich in terms of the outer disk seen to date. This may be explained by increased radiation fluxes; more stellar radiation may reach the outer disk the larger the hole. In addition, large holes may be a tracer of overall grain growth and thus of increased UV penetration depth in both the inner and outer disk.
Grain properties can be traced by the millimeter slope of the Spectral Energy
Distributions (SEDs), parameterized by the power-law
index of the opacity spectrum, $\beta$, and this is the last disk
characteristic listed in Table \ref{tbl:disk}. The index $\beta$ is predicted to decrease with grain growth and the disks in the survey all
have $\beta$ below the expected 1.7 for interstellar grains \citep{Andrews07}. The $\beta$ estimates
are however different between different studies, which makes it difficult to
conclude on an order of dust coagulation among the disks, but AA Tau seems to
have a significantly lower $\beta$ compared to the other T Tauri disks. Most of the sources have also been observed by Spitzer in studies that constrain the grain properties in the inner disk \citep{Furlan09}. These measurements do not provide any straightforward constraints on the grain properties in the outer disk probed by the SMA, however.
Finally the disk structure, e.g. the amount of flaring, affects the amount of
stellar light intercepted by the disk. The disk structure, parameterized by the dust scale height, can be constrained by
modeling the SED, though degeneracy is a problem \citep{Chiang01}. As the dust settles towards the midplane the dust scale height decreases compared to the gas scale height. Five of the sample disk SEDs were modeled by \citet{Chiang01}, who concluded that MWC 480 and LkCa 15 are more settled than CQ Tau, GM Aur and AA Tau, i.e. in the disks of MWC 480 and LkCa 15 the upper disk layers are significantly depleted in micron-sized dust grains. This has been confirmed in more recent studies that find significantly less settling toward GM Aur compared to LkCa 15 \citep{Espaillat07, Hughes09}.
\section{Observations\label{sec:obs}}
\subsection{Spectral Setups}
Two frequency setups per source were selected to cover 4 to 8 spectral lines
in each setup, at the same time providing continuum observations.
The targeted molecules are DCO$^+$ and DCN (probing deuterium chemistry),
CN and HCN (probing photochemistry), HCO$^+$ and N$_2$H$^+$ (ions), H$_2$CO
and CH$_3$OH (potential grain chemistry products), $c$-C$_3$H$_2$ (carbon-chain chemistry) and CO (the disk kinematic tracer).
Tables ~\ref{tbl:setup1} and ~\ref{tbl:setup2} summarizes the two spectral
setups, centered at 1.1 mm and 1.4 mm, respectively.
The SMA correlator covers $\sim4$~GHz bandwidth in each of the two sidebands
using two Intermediate Frequency (IF) bands with widths of 1.968 GHz.
The first IF band is centered at 5 GHz, and the second IF band is centered
at 7 GHz. Each band is divided into 24 slightly overlapping ``chunks'' of
104 MHz width, which can have different spectral resolution.
For each spectral setting, the correlator was configured to increase the
spectral resolution on the key species with 128--256 channels per chunk, with
the exception of one H$_2$CO line observed with 64 channels. Chunks containing weaker lines were then binned to obtain higher signal to noise, while still recovering sufficient kinetic information. The remaining chunks were covered by 64 channels each and used to measure
the continuum. The continuum visibilities in each sideband and each IF band
were generated by averaging the central 82 MHz in all line-free chunks.
\subsection{Data Acquisition and Calibration}
The six disks were observed from 2009 November through December with the
compact configuration of the Submillimeter Array (SMA) interferometer
(Ho et al. 2004) at Mauna Kea, Hawaii. LkCa~15 was also observed on 2010 March 22nd with the subcompact configuration
for more short-spacing data to improve the signal-to-noise of deuterated
species detection. For each observation, at least six
of the eight 6~m SMA antennas were available, spanning baselines of 16--77~m
(Table ~\ref{tbl:obs}).
The observing sequence interleaved disk targets and two quasars in an
alternating pattern. Depending on their proximity to the disk targets
and fluxes at the time of the observations, a group of three quasars was used
as gain calibrators: 3C 111, J0510+180 and 3C 120. The observing conditions
were generally very good,
with $\tau_{\rm 225{\:GHz}}\sim0.04-0.1$ and stable atmospheric phase.
The data were edited and calibrated with the IDL-based MIR software
package\footnote{http://www.cfa.harvard.edu/$\sim$cqi/mircook.html}.
The bandpass response was calibrated with observations of Uranus and
the bright quasars available (3C 454.3, 3C 273, 3C 84).
Observations of Uranus provided the absolute scale for the calibration of
flux densities for all compact tracks and Vesta for the one LkCa 15 sub-compact track. The typical systematic uncertainty in the absolute flux
scale is $\sim$10\%. Continuum and spectral line images were generated
and CLEANed using MIRIAD. MIRIAD was also used to calculate synthesized beam sizes and position angles, which are listed in Table \ref{tbl:beam} for each setting and source.
\section{Results and simple analysis}\label{sec:res}
The first section presents the extracted spectra for all molecules detected toward at least one disk, channel maps toward DM Tau, which contain some of the strongest detections of the weaker lines in the survey and finally disk images and moment maps for strong
molecular lines toward all sources
($\S$\ref{ssec:overview}). The subsequent sections provide more details
on the observed CN/HCN ratios, ions and deuterated molecules and their
variation among the surveyed disks.
In general, we do not attempt to estimate column densities of molecules, but rather present the data in terms of integrated fluxes and flux ratios. The line fluxes and column densities are of course related, but the fluxes also depend on excitation temperatures and opacities. Determining molecular column densities therefore requires knowledge of the disk structure and the spatial distribution of molecules. Even for optically thin lines, estimated column densities may be off by an order of magnitude or more if the wrong emission regions/temperatures are adopted. For optically thick lines the estimates become even more uncertain and single dish studies including $^{13}$CO and H$^{13}$CO$^+$ have shown that the emission from $^{12}$CO and H$^{12}$CO$^+$ is mostly optically thick \citep{Dartois03,Thi04}. A proper derivation of column densities therefore requires detailed chemical modeling
of the disks, which we anticipate for a future DISCS publication. An exception from only reporting fluxes is made for the deuterium fractionation, where it is useful to derive abundance ratio limits assuming the same emission regions of molecules and their deuterated equivalents, to compare with previous studies. We also estimate the HCO$^+$/CO ratio toward CQ Tau for a rough consistency check with previous observations.
\subsection{Overview of Taurus disk chemistry\label{ssec:overview}}
Figure \ref{fig:spec} shows the extracted spectra of the targeted molecules toward DM Tau, AA Tau, LkCa 15, GM Aur, CQ Tau and MWC 480. The spectra are also tabulated in Table \ref{tbl:spec}. The four spectral lines, CO 2--1, HCO$^+$ 3--2, HCN 3--2 and CN 3--2, expected
to be strongest from previous studies were detected in all six disks except for HCN toward CQ Tau, with an order of magnitude variation in integrated fluxes between the different disks. Spectral lines from
N$_2$H$^+$ and H$_2$CO were detected toward three disks, DM Tau, LkCa 15 and
GM Aur, with tentative detections toward AA Tau. Lines from the two deuterated
molecules, DCO$^+$ and DCN, were detected toward LkCa 15 and the DCO$^+$ 3--2
line was also detected toward DM Tau. The spectral lines from CH$_3$OH and
c-C$_3$H$_2$ were not detected toward any of the disks.
Figure \ref{fig:dmtau} shows the velocity channel maps for all detected
spectral lines toward DM Tau. The peak intensities vary between $\sim$9 Jy beam$^{-1}$
for CO and $\sim$0.1 Jy beam$^{-1}$ for the weaker H$_2$CO line. All species, except for H$_2$CO, are apparent in
multiple velocity channel maps, and the stronger detections clearly follow
the velocity pattern indicative of a disk in Keplerian rotation. The relative intensity of different species in different velocity channels varies significantly, indicative of differences in emission regions between different lines.
Fig. \ref{fig:maps} shows integrated intensity and first moment maps derived
from the channel maps for CO, HCO$^+$, HCN and CN for each disk.
In addition, the first column in Figure \ref{fig:maps} shows millimeter
continuum SEDs compiled from the literature \footnote{\citet{Acke04,Adams90,Andrews05, Beckwith90, Beckwith91,Chapillon08,Dutrey96,Dutrey98,Duvert00,Guilloteau98,Hamidouche06,Hughes09,Isella09,Kitamura02,Koerner93,Looney00,Mannings94,Mannings97,Mannings00,Natta01,Osterloh95,Pietu06,Rodmann06,Testi01,Weintraub89}} together with new measurements
at 218 GHz and 267 GHz (Table \ref{tbl:int}), which show good agreement for all of the sources.
The dust continuum flux densities at $\sim$267 (and 218) GHz vary by about a factor of
four among these sources, with MWC 480 the strongest at 430 mJy and
AA Tau the weakest at 110 mJy. Note that there is not a one-to-one
correspondence between the strength of the 218 or 267 GHz dust continuum emission
and the CO 2-1 line emission.
The first-moment maps show the Keplerian rotation pattern of the disks, most
clearly in the CO 2-1 and HCO$^+$ 3-2 emission. The rotational velocity
pattern is also present to some extent in HCN and CN emission, which suffer
from lower signal-to-noise and, for CN, the blending of the
spectroscopic triplet.
Line spectra are extracted from the channel maps using elliptical masks
produced by fitting a Gaussian profile to the CO integrated intensity maps
toward each source to obtain major and minor axes and positions angles (listed in Fig. \ref{fig:maps}).
The size of the mask is scaled for each line, to optimize the signal-to-noise without losing any significant emission,
such that the major and minor axes are between 2-$\sigma$ and 1-$\sigma$ of
the Gaussian fitted to the CO emission -- a 2-$\sigma$ radius corresponds to
$\sim$1.7 $\times$ the radius at full-width-half-maximum (FWHM). All masks are large enough to not cut out any emission, i.e. the chosen masks results in no significant decrease in integrated line intensity compared to integrating over the full CO disk. Applying these
masks ensures that only disk emission and minimal noise are included in the
spectra. The derived CO full-width-half-maxima agree reasonably well with the disk
sizes from the literature compiled in Table \ref{tbl:disk}, i.e. all semi-major
axes are within $1''$ of the previously observed or derived CO radii, where
resolved data exist. In addition the position angles agree within
10$\degree$ except for the barely resolved disk of CQ Tau. The integrated spectra from CQ Tau are however not significantly affected by the choice of mask shape.
The resulting spectra in Fig. \ref{fig:spec} are used to derive the total intensities listed in Table \ref{tbl:int}. The 2-$\sigma$ upper limits are calculated from the rms when the spectra are binned to a spectral resolution of 3.3--4.3 km s$^{-1}$, the minimum resolution for resolving any lines, multiplied by the full width half maximum of the CO 2-1 line toward each source. This approximation is supported by the similarity in the line widths for different transitions toward the same disk in Fig. \ref{fig:spec}. Because of variable observing conditions and integration times, the flux upper limits vary between 0.09 and 0.78 Jy km s$^{-1}$ per beam. Most upper limits are however lower compared to detected fluxes toward other sources. Specifically the non-detections toward MWC 480 of DCO$^+$, N$_2$H$^+$ and one of the H$_2$CO lines are up to a factor of two lower than the detected fluxes toward the T Tauri stars DM Tau, GM Aur and LkCa 15.
\subsection{CN/HCN flux ratios}
As discussed above, deriving molecular abundances from disk spectra is complicated by the uncertainties in disk structures and the accompanying uncertainties in the emission conditions of the different molecules. Line flux ratios can however be used as a proxy for abundance ratios when the emission is optically thin and the upper energy levels are similar, canceling out the temperature effect, if the same emission region for the two molecules can be assumed. Models suggest that the emission regions are different for CN and HCN, however \citep{Jonkheid07}. It is still informative to compare the flux ratios between different sources if it can be assumed that the relative emission regions of the CN and HCN is stable between different disks, i.e. that CN is always present in a warmer layer closer to the surface compared to HCN. Then changes in the CN/HCN flux ratio can still be used to trace changes in abundance ratios if the emission is optically thin.
\citet{Thi04} suggested that HCN and CN line emission from protoplanetary
disks may be somewhat optically thick from comparisons of HCN and H$^{13}$CN
line intensities toward LkCa 15. This survey does not currently include any
rare isotopologues, but the CN optical depth can be estimated from the relative
integrated intensities of the 2$_3$-1$_2$ triplet transition and the $\sim$10 times weaker
2$_2$-1$_1$ singlet transition using the line strengths
from CDMS \citep[http://www.astro.uni-koeln.de/cdms/catalog and][]{Muller01}
at any of the reported temperatures between 9 and 300~K (the transitions have
the same excitation energy). Toward DM Tau and AA Tau the observed CN line
ratios are consistent with optically thin emission. Toward LkCa 15 and MWC 480, the emission from the CN triplet underestimates the CN abundance by factors of 1.3 and 1.6, respectively, indicative of somewhat optically thick
CN triplet emission.
Despite the complications introduced by modest
optical depth,
changes in CN 2$_3$-1$_2$ / HCN 3--2 ratios larger than a factor of 2,
assuming similar levels of optical depth for HCN emission, are expected to
trace real variations in the chemistry as discussed above.
The absolute CN and HCN integrated intensities range from 0.2 Jy km s$^{-1}$
toward CQ Tau to 5.5 Jy km s$^{-1}$ toward LkCa 15.
Figure \ref{fig:ratios} shows that the variation in CN/HCN line intensities
is smaller -- all sources have ratios of 0.8--1.6 except for AA Tau, which has
a CN/HCN emission ratio of 2.9. AA Tau is then the only significant outlier
in terms of CN/HCN flux ratios.
\subsection{Ions: HCO$^+$ (DCO$^+$) and N$_2$H$^+$}
HCO$^+$ is often used as a tracer of gas ionization and thus of high energy
radiation in disks. The high optical depth of HCO$^+$ and the lack of rare
isotopologues of CO prevent such an analysis at present, except for toward
CQ Tau where the CO 2--1 emission has been estimated to be optically thin
\citep{Chapillon08}. The ratio of column densities for species X and Y, for
optically thin, resolved emission, can be calculated from
\begin{equation}
\label{eq:ratio}
\frac{N_{\rm X}}{N_{\rm Y}} = \frac{\int T_{\rm mb}^{\rm X} d\nu}{\int T_{\rm mb}^{\rm Y} d\nu} \times \frac{Q_{\rm rot}^{\rm X}(T)}{Q_{\rm rot}^{\rm Y}(T)} \times \frac{e^{E_{\rm u}^{\rm X}/T_{\rm ex}}}{e^{E_{\rm u}^{\rm Y}/T_{\rm ex}}} \times \frac{\nu_{\rm Y} S_{\rm Y}\mu^2_{\rm Y}}{\nu_{\rm X} S_{\rm X}\mu^2_{\rm X}},
\end{equation}
\noindent where $N$ is the column density, $\int T_{\rm mb} d\nu$ is the integrated line
emission in K km s$^{-1}$, $Q_{\rm rot}(T)$ the temperature dependent
partition function, $E_{\rm u}$ the energy of the upper level in K,
$T_{\rm ex}$ the excitation temperature in K and $S_{\rm Y}\mu^2$ are the line
strength and dipole moment \citep[e.g.][]{Thi04}. Toward the same source, the
integrated line flux in Jy and line intensity in K are related by
$T_{\rm mb}[{\rm K}]\varpropto F[{\rm Jy}]\times\lambda^2[{\rm mm^2}]$.
Using partition functions, level energies and line strengths from CDMS and
assuming the same excitation conditions for HCO$^+$ 3--2 and CO 2--1 the
[HCO$^+$]/[CO] ratio is $1.0-1.3\times10^{-4}$ toward CQ Tau for excitation temperatures of
18--75~K.
The N$_2$H$^+$ observations toward DM Tau, LkCa 15 and GM Aur (and tentatively
toward AA Tau) provide unambiguous detections of this species in protoplanetary
disks, confirming previous claims by
\citet{Dutrey07}. Since N$_2$H$^+$ and DCO$^+$ both potentially trace the chemistry further toward the midplane compared to the more abundant molecules, their ratio provides important constraints on the cold chemistry in disks. The DCO$^+$/N$_2$H$^+$ line intensity ratio ranges from $<$0.1 toward GM Aur to 0.8 toward DM Tau (Fig. \ref{fig:ratios}). In contrast, there is no significant variation in the H$_2$CO/N$_2$H$^+$ ratio between the sources. Assuming that these molecules always reside in the colder regions of the disks, these differences in flux ratios suggest relative abundance variations of N$_2$H$^+$ and DCO$^+$ of an order of magnitude between the different sources.
\subsection{Deuteration: DCO$^+$/HCO$^+$ and DCN/HCN}
Because of the high optical depth of the HCO$^+$ line emission, the DCO$^+$/HCO$^+$ line intensity ratio can only be used to derive upper limits on the average HCO$^+$ deuteration fraction in the disk. The analysis is further complicated by evidence of different emission regions of DCO$^+$ and HCO$^+$ \citep{Qi08}. Assuming, however, the same emission region of DCO$^+$ and HCO$^+$ and optically thin emission for both ions, the upper limits on the deuteration fraction is calculated using Eq. \ref{eq:ratio} to vary between 0.32 toward DM Tau, 0.18 toward LkCa 15 and $<$0.07 toward GM Aur. An excitation temperature of 19 K is assumed, but the ratios are only marginally affected by the excitation temperature between 10 and 50~K. The variable ratios hint at differences in deuteration fractionation between different sources, especially since GM Aur has both lowest DCO$^+$/HCO$^+$ and DCO$^+$/N$_2$H$^+$ ratios, but radiative transfer modeling is needed to confirm this result.
DCN is only detected toward LkCa 15. The detection is at the $>$5-$\sigma$ level, and the moment maps shows an almost perfectly aligned velocity field compared to CO and HCO$^+$ and the detection appears secure. From the CN analysis above and previous single-dish observations, HCN line emission is expected to be much less optically thick than HCO$^+$ emission and the DCN/HCN ratio should provide stricter limits on the deuteration level in the disk. Assuming optically thin emission, the same emission region for DCN and HCN and an excitation temperature of $\sim$40~K, the upper limit on average deuteration in the disk around LkCa 15 is 0.06, a factor of three lower than the estimate from DCO$^+$/HCO$^+$.
\section{Discussion} \label{sec:disc}
\subsection{Detection rates and comparison with previous studies}
The reported images and spectra were acquired with only 3--7 hours on source integration, with the shorter time spent in the 1.1 mm setting. The detection rate of N$_2$H$^+$ and H$_2$CO in the 1.1 mm setting is then quite remarkable and can be attributed to the advantages of targeting higher $J$ lines when probing disks. For comparison, N$_2$H$^+$ was previously detected toward DM Tau and LkCa 15 through its 1--0 line using the Plateau de Bure Interferometer, with peak fluxes $<$0.02 Jy \citep{Dutrey07}, an order of magnitude or more lower than the $3-2$ line peak fluxes reported here. The 1-0 line in LkCa 15 was also detected by \citet{Qi03} using
the Owens Valley Radio Observatory Millimeter Array with integrated intensity four times larger than that with the PdBI.
The agreement with previous single-dish observations is generally good. All targeted molecular lines that have been previously reported in the
single dish studies of DM Tau, LkCa 15 and MWC 480 are also detected with the
SMA \citep{Dutrey97,Thi04, Guilloteau06}. Where the same lines have been
studied, most integrated intensities agree. HCN $J=3-2$ toward DM Tau is an exception,
where the reported upper limit in \citet{Dutrey97} is a factor of two below
the intensity observed with the SMA.
Using their detections, \citet{Dutrey07} derived [N$_2$H$^+$]/[HCO$^+$] ratios of 0.02--0.03 for DM Tau and LkCa 15 by fitting the line emission to disk models. Without such modeling we can only derive upper limits on the [N$_2$H$^+$]/[HCO$^+$] of 0.13--0.19 for the two disks because of the HCO$^+$ line optical depth. Considering that the HCO$^+$ abundance may be underestimated by up to an order of magnitude, the two data sets are consistent. Within the same observational program \citet{Chapillon08} searched for CO 2--1 and HCO$^+$ 1--0 emission toward CQ Tau and used the data to derive an upper limit on the [HCO$^+$]/[CO] abundance ratio. Assuming the same CO and HCO$^+$ distribution and excitation conditions and optically thin CO emission they find [CO]/[HCO$^+$]$>$4$\times10^3$. This is consistent with the abundance ratio of 10$^4$ reported above, which is calculated making similar assumptions, but without the detailed modeling in \citet{Chapillon08}.
CQ Tau is by far the most chemically poor of the investigated disks. It is interesting that despite the low abundances, the chemistry appears 'normal', the ratios of the integrated intensities toward MWC 480 and CQ Tau are the same within a factor of two, including the CN/HCN emission ratio. The only difference is that overall the gas toward CQ Tau is probably richer in CN and HCN with respect to CO, taking into account the large optical depth of the CO emission toward MWC 480 \citep{Thi04}, as might be expected for a smaller disk, completely exposed to UV radiation.
The upper limits on the [DCO$^+$]/[HCO$^+$] abundance ratio of $<$0.07--0.32 found toward the T Tauri systems in DISCS are consistent with the ratio of 0.035--0.05 observed toward TW Hydrae \citep{vanDishoeck03,Qi08}. The better constrained [DCN]/[HCN] ratio of 0.06 toward LkCa 15 is also consistent with the value of 0.02--0.05 toward TW Hydrae. While this ratio may be overestimated by a factor of a few, high levels of deuterium fractionation seems common toward T Tauri systems.
As found in single dish studies, the CN/HCN line intensity ratios toward the Taurus disks are high compared to interstellar clouds and cores. The line ratios all fall within the range of measurements toward other disks, where the total integrated flux ratio of CN/HCN is $\sim$1--5 \citep[see][for a compilation]{Kastner08}. A more quantitative comparison with previous observations is difficult without detailed modeling because different studies observed different transitions of CN and HCN.
\subsection{T Tauri vs. Herbig Ae stars}
In agreement with previous studies, we find that the disks surrounding T Tauri stars are more chemically rich in species with strong mm-transitions compared to disks around Herbig Ae stars \citep{Chapillon08,Schreyer08,Henning10}. The observed chemical poverty in the outer disks of Herbig Ae stars has been attributed to the more intense UV field around Herbig Ae stars compared to T Tauri stars, which may efficiently photodissociate most targeted molecules. In this sample, the most obvious difference between T Tauri and Herbig Ae stars is the lack of the cold chemistry tracers N$_2$H$^+$, DCO$^+$, DCN and H$_2$CO toward CQ Tau and MWC 480, while they are detected in 3/4, 2/4, 1/4 and 3/4 of the T Tauri systems. The upper limits toward CQ Tau are less informative because of its weak CO emission and observations toward more Herbig Ae stars are required to confirm that this difference between disks around low and medium mass stars is general.
In contrast the CN and HCN emission is similar toward the lowest and highest luminosity stars, DM Tau and MWC 480, in the sample. CN and HCN emission are modeled to originate mainly from the outer layers of the disk \citep{Willacy07} and this chemistry thus seems equally active toward low- and intermediate-mass pre-main sequence stars.
\subsection{CN and HCN}
CN is a photodissociation product of HCN and the CN/HCN ratio has been put forward to trace several different aspects of the UV field. The CN/HCN ratio is proposed to increase with the strength of the UV field \citep{vanZadelhoff03}, and it will be further enhanced if the UV radiation is dominated by line emission from accretion, since HCN is dissociated by Ly-$\alpha$ photons while CN is not \citep{Bergin03}. Dust settling or coagulation allows radiation to penetrate deeper into the disk, which is also predicted to enhance the CN/HCN ratio \citep{Jonkheid07}.
The quiescent UV luminosity increases with stellar mass. There is however no
visible trend in the emission ratio of CN/HCN with spectral type.
In fact, all CN/HCN ratios are the same within a factor of two, except toward AA Tau,
which has a factor of a few higher intensity ratio. This suggests that the
CN/HCN ratio is not set by the stellar luminosity though there are complications in comparing CN/HCN ratios toward disks around low- and intermediate-mass stars because of potentially different excitation conditions for HCN in the two sets of disks \citep{Thi04}. Within this sample the CN/HCN ratio also does not trace accretion luminosity; AA Tau has a comparable accretion rate to LkCa 15 and among the sources with comparable CN/HCN ratios the accretion rate varies by an order of magnitude. AA Tau is reported to have a lower power-law
index of the opacity spectrum, $\beta$, compared to the other disks, indicative of dust growth and it may be the dust properties rather than the stellar or accretion luminosities govern the importance of photochemistry in disks. A larger sample that spans a wider range of accretion rates and dust properties is clearly required to give a more definitive answer.
An additional complication is that the high CN/HCN ratio toward AA Tau may be a geometric effect. Compared to the other disks, AA Tau is almost edge-on \citep{Menard03}, which may result in preferential probing of the disk atmosphere compared to less inclined disks. Disk chemistry models (Fogel et al. submitted to ApJ) show that CN mainly emits from the disk surface, while HCN emission originates further into the molecular disk layer and the more inclined disk may offer a viewing angle that is biased toward CN emission. To estimate the effect of disk inclination on CN/HCN flux variations then requires a combination of chemical modeling and radiative transfer models.
In terms of absolute flux intensities, the weak CN and HCN emission toward GM Aur compared to LkCa 15 and DM Tau stands out. The difference between GM Aur and LkCa 15 may be due to the higher accretion rate and intenser FUV field toward LkCa 15. The difference between DM Tau and GM Aur is however difficult to explain in terms of UV flux, since DM Tau is a weaker accretor than GM Aur. There is some evidence for significantly more dust settling toward LkCa 15 and DM Tau compared to GM Aur \citep{Chiang01,Espaillat07,Hughes09}. This may expose more of the gas in the LkCa 15 and DM Tau disks to high-energy radiation, enhancing the photoproduction of CN and HCN as well as the ion chemistry deeper in toward the disk midplane.
\subsection{Cold chemistry tracers}
Lower abundances of DCO$^+$, DCN, N$_2$H$^+$ and H$_2$CO toward more luminous stars are qualitatively consistent with our current chemical understanding.
DCO$^+$ forms efficiently from gas phase reactions with H$_2$D$^+$, which is
only enhanced at low temperatures \citep{Roberts00,Willacy07} and should be enhanced
toward colder disks. Among the T Tauri stars the brightest DCO$^+$ emission is observed toward the disk around the least luminous star, DM Tau, consistent with a higher degree of deuterium fractionation around colder stars. The difference
in DCO$^+$ line flux around GM Aur and LkCa 15 is more difficult to explain. GM Aur has a more massive dust disk than LkCa 15 and the two stars have similar luminosities. Naively GM Aur should then be surrounded by at least as much cold disk material as LkCa 15. Instead, the upper limit on the DCO$^+$ flux is a factor of three lower toward GM Aur compared to LkCa 15. There is thus no one-to-one correlation between the ratio of disk dust mass over quiescent stellar luminosity and DCO$^+$ column densities.
N$_2$H$^+$ forms from protonation of N$_2$ by H$_3^+$ and is mainly destroyed by reactions with CO \citep{Bergin02}. Abundant N$_2$H$^+$ is therefore only expected where CO is depleted onto grains toward the disk midplane. N$_2$ freezes onto grains a few degrees below CO \citep{Oberg05} and in cold disks the N$_2$H$^+$ abundance should peak in a narrow region where the temperature is between the N$_2$ sublimation temperature of $\sim$16~K and the CO sublimation temperature of $\sim$19~K. As long as a cold region exists in the disk, the N$_2$H$^+$ abundances may be quite independent of the total amount of cold disk material. The observations are consistent with this disk abundance structure; within the T Tauri sample the N$_2$H$^+$ emission only varies by a factor of two, increasing slightly with increasing disk mass.
The variation in DCO$^+$/N$_2$H$^+$ flux ratios over the sample suggest that while both molecules trace a cold chemistry, their dependences on the physical environment is considerably different. The $>$8 times higher DCO$^+$/N$_2$H$^+$ flux ratios toward DM Tau and LkCa 15 compared to GM Aur may be related to the 5--6 times higher fluxes of CN and HCN toward DM Tau and LkCa 15 compared to GM Aur. This would suggest that both ratios depend on the amount of dust settling and that DCO$^+$ trace a cold radiation driven chemistry. Considering the ions involved in forming DCO$^+$ and DCN, it seems reasonable that their formation will be enhanced in regions that are irradiated, but not heated by FUV photons or X-rays. To test this hypothesis requires H$^{13}$CO$^+$ abundances toward both systems (to measure whether the DCO$^+$/HCO$^+$ abundance ratio varies as well) in combination with a model that simultaneously treat deuterium chemistry and UV and X-ray radiative transfer.
H$_2$CO can form both through gas and grain surface processes. The gas phase process starts with CH$_3^+$ reacting with H$_2$ \citep{Roberts07b} and is expected to be at least as efficient in disks around low and intermediate mass stars. In contrast, H$_2$CO formation on grains requires the freeze-out of CO, which is only efficient at low temperatures. The absence of H$_2$CO toward the more luminous stars suggests that the grain surface formation mechanism dominates in disks and it is also another indication
of the lack of a large cold chemistry reservoir toward disks around intermediate mass stars.
It also suggests that the organic molecules formed in the protostellar stage,
where H$_2$CO is common, do not survive in the gas phase in mature disks.
In summary, all potential tracers of cold chemistry imply the same lack of cold disk material around Herbig Ae stars, which is in agreement with a recent survey of CO gas toward Herbig Ae/Be stars \citep{Panic09}. In contrast, \citet{Pietu07} find that the disk around the Herbig Ae star MWC 480 contains large amounts of cold CO gas, below 17~K, indicative of cold material outside of 200 AU. At these temperatures CO should not be in the gas phase at all, however, since it is below the sublimation point of CO ice. Its presence is a sign of either efficient mixing in the disk or efficient non-thermal ice evaporation, perhaps through photodesorption \citep{Oberg07b,Hersant09}. Mixing may drag up material from the midplane on shorter timescales than the cold chemistry timescales, explaining the lack of cold chemistry tracers. Efficient photodesorption of CO into the gas phase would also explain the lack of N$_2$H$^+$ and H$_2$CO, while its impact on the deuterium fractionation is harder to assess. The same processes are probably present in disks around T Tauri stars as well, but because their disks are overall colder there is still enough material protected from vertical mixing and photodesorption on long enough timescales for large amounts of N$_2$H$^+$, DCO$^+$ and H$_2$CO to form.
The lack of CH$_3$OH detections does not put strong
constraints on the CH$_3$OH/H$_2$CO abundance ratio, since H$_2$CO is barely
detected and the CH$_3$OH transitions in this spectral region are more than an
order of magnitude weaker than the observed H$_2$CO transitions. To put stronger constraints on CH$_3$OH abundances in disks instead requires targeted observations of the most intense CH$_3$OH lines.
\section{Conclusions}
Protoplanetary disks exhibit a rich chemistry that varies significantly between different objects within the same star forming region. Some of this variation can be understood in terms of the central star and its heating of the disk -- the cold chemistry tracers N$_2$H$^+$, DCO$^+$, DCN and H$_2$CO are only detected toward T Tauri stars in our disk sample of four T Tauri stars and two Herbig Ae stars. Tracers of photochemistry, especially CN and HCN, show no clear dependence on quiescent stellar luminosity within the sample. Deuterium fractionation also seems to depend on parameters other than the disk temperature structure. For these chemical systems, the impact of other sources of irradiation, e.g. accretion shocks and X-rays, as well as the disk structure and grain characteristics may all be more important for the chemical evolution than the quiescent stellar luminosity. Investigating the relative importance of these different disk and star characteristics requires a combination of detailed modeling of the current sample, an increase in the number of sources to boost the statistics and span more parameters -- especially a larger range of accretion rates and disks around the intermediate F stars -- and targeted observations of rare isotopes of CO and HCO$^+$ to extract accurate abundance ratios. While the chemical evolution in protoplanetary disks is clearly complex, the qualitative agreement between at least parts of the early DISCS results and our current chemical understanding is promising for the ongoing modeling of these objects. The key results so far are listed below.
\begin{enumerate}
\item Six disks in Taurus (DM Tau, AA Tau, LkCa 15, GM Aur, CQ Tau and MWC 480) have been surveyed for 10 molecules, CO, HCO$^+$, DCO$^+$, CN, HCN, DCN, H$_2$CO, N$_2$H$^+$, CH$_3$OH and c-C$_3$H$_2$, with a high detection rate and large chemical variability.
\item The brightest molecular lines, CO 2-1, HCO$^+$ 3-2, CN 3-2 and HCN 3-2 are detected toward all disks, except for HCN toward CQ Tau. Other molecular lines tracing different types of cold chemistry, N$_2$H$^+$, DCO$^+$, DCN and H$_2$CO, are only detected toward disks around T Tauri stars, indicative of a lack of cold regions around Herbig Ae stars for long enough time scales.
\item Both the absolute CN flux and the CN/HCN ratio vary significantly among the observed disks and their variation seems independent of stellar luminosity, suggestive of that other parameters such as accretion luminosity and dust growth and dust settling play an important role for the chemical evolution in disks.
\item Among the cold chemistry tracers the DCO$^+$/N$_2$H$^+$ ratio varies by an order of magnitude suggesting that the deuterium fractionation depends on other parameters, including the radiation field, beyond the amount of cold material present in the disk.
\end{enumerate}
{\it Facilities:} \facility{SMA}
\acknowledgments
This work has benefitted from discussions with and comments from Ewine van Dishoeck, Geoffrey Blake and Michiel Hogerheijde, and from a helpful review by an anonymous referee. The SMA is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. Support for K.~I.~O. and S.~M.~A. is provided by NASA through Hubble Fellowship grants awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. C.~E. was supported by the National Science Foundation under Award No.~0901947. E.~A.~B. acknowledges support by NSF Grant \#0707777
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Monday, November 21 2022 - Welcome
Miami's first distillery will be open for tastings and Tours
by Helena Jose July 8, 2021
Miami-based company Tropical Distillers is thrilled to announce they are opening the only distillery in the City of Miami towards the latter part of the year which will produce their J.F. Haden's Craft Liqueurs. Located in the heart of the up-and-coming, Allapattah neighborhood at 2141 NW 10th Avenue, the distillery will offer guests a one-of-a-kind premium liqueur brand experience just steps away from the famous Wynwood Arts District. The distillery will feature J.F. Haden's Mango Liqueur, the first spirit to market from the Tropical Distillers brand portfolio launched a little over a year ago, a first-of-its-kind, small-batch liqueur made from all-natural home-grown Florida mangoes without preservatives, artificial colors, or flavors as well as the newest flavor J.F. Haden's Citrus Liqueur.
The distillery is a joint business venture between Tropical Distillers original brand partners CEO Buzzy Sklar, the newest brand partners, former NFL pros Mike and Maurkice Pouncey and Miami-based luxury realtor Kim Rodstein, and industry veteran Andrew Siegel. "This business endeavor has quickly turned into a family business that I am proud to be a part of. From ties to the Florida Gators to having the same work ethic, enjoying the same passions has made us all closer than we could have imagined. The future is bright!" says Mike Pouncey.
J.F. Haden's Craft Liqueur's new headquarters will be much more than a fully functioning distillery. "With the recent growth and buzz surrounding Miami as a new business hub, and my 30 plus years of experience in the hospitality industry, we are very excited about the potential success and feel the timing is perfect to be opening up the only distillery in the City of Miami," says CEO Buzzy Sklar. The 8,000 square foot space will include a fully automated craft distillery complete with an in-house cannery, a beautiful bar and tasting room decked out in colorful vintage wallpaper with old school Florida tropical touches throughout the space. In addition, the distillery will feature a retail and gift shop with branded merchandise and exclusive distillery only product from Tropical Distillers and J.F. Haden's Craft Liqueurs.
The distillery will be open daily offering premium tastings and behind-the-scenes tours of the company's meticulous small batching production process. The one-hour tours will be available in group or private sessions and will be able to be booked online. Following the tour, guests can indulge at the bar which will be serving up signature J.F. Haden's craft liqueurs cocktails while kicking back and enjoying live music from local musicians on certain nights. Guests will also have the option to grab a bite from various featured food trucks.
The Tropical Distillers premium brand experience is complete with a branded tour bus that will be available to book for private events providing transportation to and from the distillery. When not being used for private events, the bus will be cruising around Miami offering pick-ups to the distillery. In addition, the venue will be available for private and corporate events and will have parking accessible on-site as well as street parking.
Since the launch of J.F. Haden's Mango Liqueur in January 2020 they have been picked up by national distributors RNDC and is currently available in over 1,000 bars, restaurants, and retail stores across the country (700 of those in Florida). In addition, J.F. Haden's Mango Liqueur is now available in New York, New Jersey and Nevada.
www.jfhadens.com
@jfhmangoliqueur
BarsNewsUpcoming Events
9 Best places to Celebrate National Piña Colada day in Miami
Pineapple, Coconut, and Rum. There's nothing more tropical, tantalizing, or thrilling than this delicious combination. Just by reading or hearing the phrase, "Piña Colada," we are already dreaming of a vacation on a luxurious Caribbean Island, right? This mental transportation to paradise is probably why this Cocktail, originally from Puerto Rico, has become one of the most popular and beloved drinks around the world. In celebration of Piña Colada Day, this Saturday, July 10th, 2oz Mag would like to suggest the best places in Miami to enjoy this idyllic Cocktail. So find a venue, kick back, relax, and take a sip of paradise.
Sexy Colada
1600 NE 1st Ave, Miami, Fl. 33132
In Miami, 22400oz of Esotico's twist on the Piña Colada, "The Sexy Colada"($14) is sold every month, using around 1400 Pineapples monthly between their kitchen and bar, according to Elis Carriero, Bar Manager at Esotico Tiki Lounge. "To improve a Pina Colada is not easy, because it is already a beautiful and delicious drink, but our twist is definitely the best sellers in the house! We use everything from the pineapple since our concept is zero waste. We use 1/2 pineapple in the kitchen for our pineapple rice, chunk for cocktails, and for the fresh juice, with the skin we can prepare infusions and we use the leaves for garnishes as well. Our secret for the Sexy Colada is to do everything with love and very high-quality ingredients," says Elis.
The Sexy Colada is a recipe from Danielle Dallapolla with Coconut cream re'al, Ginger syrup re'al, Bacardi Carta Oro, Pineapple juice, Pinch of salt, Lime juice, Coconut water from fresh coconut
www.esoticomiami.com
Piña Colada by Havana Rum
FINKA
14690 Sw 26th St, Miami, Fl. 33175
On July 10th, Latin Gastropub Finka will host an event with Havana's Rum brand Ambassador, Gio Gutierrez who will be around spiking drinks and giving out Piña Colada Shirts. Order a virgin Piña Colada and you will get a free Havana Club Clasico Floater. And who doesn't love free t-shirts? Once your virgin Piña Colada is spiked, you will receive a hilarious, Piña Colada Day-inspired T-shirt to commemorate the occasion, while supplies last. Join the festivities from 6 pm to 11 pm.
www.finkarestaurant.com
Escape a la Orilla
ORILLA
426 Euclid Ave, Miami Beach, Fl. 33139
If you like piña coladas and gettin' caught in the rain… Come to Orilla and Escape… yes, if you are looking for an elevated experience, check Orilla restaurant and mixology bar, for their "Escape a la Orilla" Cocktail ($16), inspired by the famous song "Escape" by Rupert Holmes. This unique take on the Piña Colada will amaze you. To celebrate this glorious day, Bar Manager and Mixologist Rodrigo Turbet created a Piña Colada-meets-Highball Cocktail. "I'm looking to offer a more refreshing drink without the density of the classic recipe. I didn't want to use coconut cream but wanted the coconut flavor to be present so we'll use the coconut in different ways. We add Ultrasonic Bacardi Carta Blanca with coconut meat, Bacardi 4, Rectified Pineapple Juice, herbal notes from Yellow Chartreuse, and Natural Coconut soda, carbonated. The Glass is garnished with toasted coconut flakes. It's a simple cocktail that will transport you to a beach shore in every sip."
Available from Wednesday 7th until July 11th, this unique take on the Pina Colada will amaze you.
www.orilla.restaurant.com
Shaun's Colada
418 Meridian Ave, Miami Beach, Fl. 33139
If you are looking to just get a good drink, maybe a little mystery, romance, or some really good feelings, you can find your ideal spot at Minibar, inside of Urbanica Hotels. We recommend that you also look for "Shaun's Colada" ($13) on their Cocktail menu, with pineapple juice, coconut milk, Simple syrup, Velvet Falernum, Teeling Irish Whiskey, and a sprinkle of nutmeg. "It is the Original Vacation in a glass, once you drink it, you know it's time to kick your feet up," says David Cedeño, Director of Bars for Urbanica Hotel's Group.
www.minibarmiami.com
The Coco Club
1435 Brickell Ave, Miami. Fl. 33131
Nothing fights the summer heat better than an icy drink right by the pool. Add it into a coconut and you already feel like you're enjoying a staycation. Kick back with the tropical and delightfully creamy concoction "The Coco Club" – Havana club rum, pineapple juice, lime, served in a fresh coconut ($25). Presented in a gorgeous white coconut with an intricate design, this drink will elevate your summer vibes, your day, and your photos! Be sure to snap a picture and make all your friends envy your poolside delight this Piña Colada Day!
www.fourseasons.com
Our Piña Colada
SWEET BEACH POP UP
1801 Collins ave, Miami Beach, Fl. 33139
For a salty breeze experience, we recommend that you visit Sweet Beach Pop-up at the Shelborne Hotel. At the hotel, you can enjoy a Delicious Piña Colada honoring the classic recipe, while also laying down by the pool or enjoying their wonderful garden. Sip and enjoy "OUR PINA COLADA" ($16) with Bacardi Carta Blanca, Bacardi 8, Santa Teresa, Coco Lopez, Pineapple, Banana, Curry Powder, and Sea Salt.
@sweetbeachpopupmia
Frozen Piña Colada
LE CHICK
310 NW 24th St, Miami, Fl. 33127
The outdoor patio at Le Chick, screams for a Tropical drink, and what better one than a frozen Pina Colada? "We created our Rum blend with Bacardi Coconut and Havana Club añejo, a great combination of flavors, caramel, soft fruits, spiced oak, and manuka honey… paired with a Pina Colada mix made by Kelvin Slushy mixes and topped with Angostura Bitters. The bitters cut down the sweetness of the drink releasing flavors of clove, tamarind, and cinnamon," says Bar Manager Nikolas Mantzaridis. Piña Colada ($13
www.lechickmiami.com
Pina Colada with Teeling Whiskey
HOMETOWN BBQ
1200 NW 22nd Street, Miami, Fl. 33142
Find your ideal, classic, nostalgic Piña Colada here. It has a perfect balance of sweet coconut, tangy pineapple, and additional tropical fruits from Teeling Whiskey finished in Rum Barrels ($16). Enjoy live music every weekend because there is always a reason to celebrate a good time with good tunes!
www.hometownbbqmiami.com
Pepe Colada
LUCA OSTERIA
116 Giralda Ave, Coral Gables. Fl. 33134
Are you going to love the Pepe Colada? Claro que sí! This clarified cocktail has all of the refreshing, citrusy sweetness of a Piña Colada, but is much lighter and less filling. In celebration of Piña Colada Day, Luca Osteria is giving away free Clarified Piña Coladas sippers with any purchase of Havana Club drink on Saturday, July 10th during dinner service. Pepe Colada is made with The Real Havana Club Añejo Clásico, Pineapple Juice, Coconut Water, Velvet Falernum, Dorda Coconut Liquor, Fresh Lime Juice, and Whole Milk*
www.lucamiami.com
by Helena Jose June 16, 2021
Father's day is less than 5 days now and you haven't been able to buy a present for dad, we all been there. worry no more, here's a list of fine liquor to celebrate.
Stranahan's Blue Peak
This year, shoppers can order bottles of Stranahan's personalized with specialty engravings. Pick from Stranahan's latest offering, including their new and improved Original expression, or Stranahan's Blue Peak, perfect for sipping on the rocks or a strong cocktail.
Named for a 13-thousand-foot peak in Aspen, Blue Peak is built around a small batch of single malt whiskey that's been aged for 4 years before being finished with the time-honored Solera process, typically seen in winemaking. Blue Peak is chill filtered, bottled at 43% ABV and available nationwide to purchase for $42.99 MSRP at fine retailers nationwide.
Nose: Dried apricot, nutmeg, cinnamon toast, hints of leather and light tobacco
Palate: Creamy butterscotch and brown sugar, baked apples, with notes of cayenne and toasted oak
Finish: Rich and mellow, earthy malt gently fades into lingering spices
Proof: Blue Peak is bottled at 86 proof (43%ABV)
MSRP: $42.99 for a 750ml bottle
Available: https://www.reservebar.com/products/stranahans-blue-peak-single-malt-whiskey
Barceló Imperial Onyx.
Black onyx stones absorb and transform negative energy and aid in the development of emotional, physical strength and stamina, especially during times of stress, uncertainty or grief. Bold like the name, this dark añejo blend of 10-year-old rums in heavily charred ex-bourbon barrel, is then filtered through onyx stones, which attribute the mysticism of this unique super-premium rum. It is best enjoyed straight-up or over ice so as to fully appreciate its remarkably robust and full-bodied taste. ($46) The elegant, matte bottle would make a great addition on the table!
*Barcelo Imperial Onyx was recently awarded a Double Gold Medal at the 2021 San Francisco World Spirits Competition. This is one of the highest honors for a spirit brand at one of the most prestigious spirts competitions in the world.*
Color: Amber Mahogany
Aroma: Caramel aroma with intriguing hint of violet
Taste: The silky palate opens with caramel and brown butter, accented by dried fig and walnut, finishing long and gently spiced; Finish: It is best enjoyed straight up or over ice to fully appreciate its robust taste!
Find Barceló at Total Wines, or order online through ReserveBar with Free Shipping using code: BARCELOSHIP
BACARDI 8 years Aged Rum
Inspired by a family recipe from 1862, BACARDÍ Reserva Ocho is known as The Family Reserve. After minimun of eight years of ageing, Bacardi Reserva Ocho releases delightful flavors of stone, fruits and spices.
Nose: Dried apricot and banana leaf
Palate: The palate is sweet and rich with tropical fruits, oak and spices, peels and winter spice
Finish: Expansive and well-rounded, gentle and luscious
Available at Drizly
Past EventsNews
The prestigious American Fine Wine Competition, announced the result for The Invitational, which takes place annually in south Florida. With the Pandemic wreaking havoc for the past year, the judging was delayed, and took place on Memorial Day Weekend. More than 550 wines from 125 wineries vied for top honors at this INVITATION-only event. The Judging — conducted by a 28-member blue ribbon panel of wine industry educators, restaurateurs, retailers, journalists, and top sommeliers from across the country — was held at the Chaplin School of Hospitality & Tourism Management at Florida International University, Biscayne Bay Campus.
As usual, the results did not disappoint! There were ties for Best of Show Red wine AND Best of Show Sparkling. And the Sparkling wines were from the same winery! Equally exciting, there was also a tie for Best of Class Riesling, which was the case last year as well.
Co-founder and President Shari Gherman said, "At AFWC, we look for the very best wines the country has to offer, and so they must be vetted before being invited. This year was challenging since the country was pretty much shut down. But with some creativity, we persevered, and as one can see by the results, we found stunning wines yet again."
The Judges had an incredibly difficult time coming up with the Best of Class results. Judge Wendy Rosano said, "Of the 11 double gold medal winning Red Bordeaux Blends, it was almost impossible to pick one!" Judge Patrick Sullivan said, "The 12 Double Gold medal winning Syrah's were so awesome, we actually finished drinking our glasses!" In the Cabernet Sauvignon category, there were five flights where ALL the wines were awarded double gold medals.
Fourteen years of careful scouting and judging means this competition starts where others end. Four-team judging panels evaluate, describe, debate and assign medals and scores. "Our Judges take their time and really care about getting it right" observed Greg Miseyko, Chief Judge and Judging Coordinator. Wines earn Gold, Silver or Bronze medals and "Double Gold" honors when every judge agrees the wine deserves a Gold Medal. Points from a 100-point scale are also awarded. Miseyko added "We want to direct the public to America's finest wines, to become the most trusted source of information about finding quality wines."
Remember, Price doesn't always dictate the finest. Quality does.
Attached are the complete results.
AFWC 2021 Best Of final 06-09-21
They are also posted at www.AmericanFineWineCompetition.org
EventsNewsPast Events
by Helena Jose June 2, 2021
Last Monday May 24th, BACARDI honored Miami's trailblazers and culture movers with Premium cocktails & delicious food pairings.
An evening to celebrate creatives, philanthropists, tech titans, business and community leaders who are blazing a trail in respective industries and making the world a better place through the work that they are committed to doing.
Hotel Nacional
Hosted by Master of Rum David Cid and Janet Benitez, guests were welcome with a refreshing "Hotel Nacional" cocktail ( Bacardi Reserva Ocho Rum, Pineapple juice, Lime juice, Simple Syrup, Apricot Liqueur) and invited to the table for a pairing dinner and the Red Rooster restaurant in Overtown, featuring aged rum Bacardi Reserva 8 and Bacardi Reserva 10 cocktails. The second Cocktail was the "Old Cuban" (Bacardi Reserva Ocho Rum, Martini & Rossi Prosecco, Sugar Syrup, Lime Juice, Dashes bitters) paired with Chef Marcus Samuelson famous dishes such as the devil eggs, Marcus cornbread, fried yardbird, shrimp & grits, grilled Yellowtail Snapper and finished with I'm in love with cocoa, a chocolate feast dessert paired with the "Cane collective Ocho old Fashioned" cocktail.
Cane Collective Ocho Old Fashioned
David educated all patrons about aged rums with a tasting of Bacardi Reserva 8 and Bacardi Reserva 10 between meals. As the night ended, the guests were greeted with a beautiful gift that included a wooden box with a bottle of Bacardi Reserva Ocho Rum, a bottle of Cane collective Sweet Potato On Syrup to make your own Old Fashion and a cigar to pair with.
Images by @Nickjustchill
FIU students win People Choice Awards at the Art of Tiki event
by Helena Jose May 24, 2021
FIU students celebrated when they were announced as the winners of the People's Choice Award at this year's South Beach Wine & Food Festival Art of Tiki Cocktail Showdown, celebrated at the Kimpton Surfcomber Hotel on South Beach, on Saturday, May 22nd.
Students participating from the Hospitality School and Bacardi Center of Excellence Bartender's Guild club, alongside professional mixologists and bartenders took home the top prize for their cocktail, The Sunblazer. The drink was made with six ingredients including: pineapple juice, lemon juice, Bacardi Ocho and even honey syrup cultivated by the FIU Beekeeping Association.
Judges gave their top prize to Landon Nero of Freehold Miami in Wynwood.
100% of the net proceeds from the Festival benefit FIU's Chaplin School of Hospitality & Tourism Management. Each year, over 1,200 students and volunteers gain invaluable real-world experience at the Festival. To date, SOBEWFF® – which serves as an interactive educational platform for future leaders of the hospitality industry – has raised more than $31.8 million for the School.
Video Courtesy of FIU Chaplin School of Hospitality & Tourism Management
CreatorsNews
Co-Founder Juan Coronado & Maestra Tequilera Ana Maria Romero present Mijenta Tequila
As a sommelier, mixologist, and Co-Founder of Mijenta Tequila, Juan Coronado has been in the food and beverage industry for more than thirty years. Whether serving as the founder and Creative Director for Colada Shop or embarking on a brand new venture, any brand or business that Juan graces will thrive as a direct result of his experience, passion, and community-oriented mindset. So too, as a writer, Master Distiller, and passionate student of all things Tequila, Ana Maria Romero Mena brings her experience, expertise, and admiration for Tequila to the forefront of Mijenta's aesthetic. As two incredible individuals in the rapidly growing industry, it is no wonder that the renowned Master Distiller Ana and Industry Vet Juan have joined forces to create Mijenta Tequila's stylish and stunning look. With her impeccable designs, Ana has captured the essence of Mijenta Tequila which is as delicious as it is respectable, as smooth as it is captivating, as versatile as it is celebratory. At a glance, consumers will notice that Mijenta Tequila is a brand for the land, for the people, and for life.
Tell us your story and hospitality background. What's your connection?
JC: I jumped into the hospitality and service industry about 30+ years ago. I have a background in Engineering and Art. I also have an interest in the hospitality industry which led to my curiosity in cocktails, spirits, wines, and distillates. I went to The Culinary Institute of America (CIA) and became a sommelier. I got interested in diving into wine. I used to be part owner of a champagne bottle bar called the Bubble Lounge in San Francisco and New York. Then, I ventured out and did a Mixology craft cocktail bar. Afterward, I started working with brands through consulting. The whole deal with Brand Ambassadors was not a position that existed. Due to my knowledge, I got into a position as a Brand Master with Bacardi years later. This was a great opportunity because I took part in the production and marketing. I used my voice to design certain rums and to market to different countries. I became the Global person and figure for Bacardi while also being a part-owner of Colada shops, Serenata, and Bresca. I had three businesses in Washington D.C. In the case of Serenata, it is free for all for Latin spirits and Latin-inspired combinations. We cover every distillate from Patagonia to Spain.
I did approach Ana Maria Romero. For us, it was instant Tequila love. I could tell that she was the right person to create this beautiful, delicate, aromatic, and traditional profile through the phone. That's the way I like to describe it.
AM: I started studying wines 30 years ago. I studied at Davis University, not as an oenologist but as a sensory evaluation. It was my passion to know about wines, and as I made visits to different parts of the world, they asked me about Tequila. There is a specific case that happened to me when I was visiting the Martell wineries. Someone asked me, "Hey, aren't you from Jalisco? Well, let's talk about Tequila." I didn't know anything, just the basics. I knew that Tequila was a liquor that came from agave. I began to study Tequila. I visited all the distilleries, and I learned that Tequila is sophisticated and complex. It does not have a unique process. It has several ways of being made. Even if it is a single plant, it behaves differently depending on the region, the climate, and the processes. I started doing Tequila sensory evaluation seminars. A client in 2007 told me, "if you like Tequila so much, why don't you do one?" And he invited me to work in his factory. That's when I realized that this is what I liked. I liked to understand Tequila, what happens in each process, the grinding, and each phase of the process. That was how I discovered the olfactory imprint of Tequila. I have an aromatic circle of Tequila. That is how I started working with big brands until I got to know Juan Coronado, who wanted to develop a Culinary Tequila. I said yes, and today I am a Tequila designer.
What inspired you to create Mijenta?
JC:. Behind the inspiration of Mijenta Tequila is a strong feeling for the land, for what Arandas means. We wanted to create a Tequila that brings and exposes all the biodiversities, aromas, flavors, and colors of the land of Arandas. That unique red soil that governs the whole terrain is unique because of the nutrients and the iron content it possesses. We wanted to bring everything into the production and the design of Mijenta Tequila's profile. With an eye on sustainability, an eye on the land, and an eye on the people, we can bring it all together and bring it to life. Our motto is por la tierra, por la gente, y por la vida.
AM: All Tequilas are made from the same plant. However, when a customer asks you for something specific, and you see through their eyes, being able to satisfy that dream is fascinating in the development of the product. If they tell you," I want a Tequila that is Mineral, that represents the earth, that speaks of tradition," you have to know what points you are going to focus on for that product. We implement a much longer cooking time for the agave. We select agaves only from regions close to Arandas, an Alteña region because that is the area we want to know. We know that its reddish color is due to the high concentration of iron that is present. We also know that there are other components that we are learning about to create the Añejo, which has more time in the barrel than another Tequila. We are studying whether the Ph influences that or not. Another topic that we found exciting when designing Tequila was selecting the yeast. We discovered which yeast would highlight all the characteristics of the highlands region. We did a study and chose one. From there, we went on to fermentation. The long or short fermentation process gives us the aromatic characteristics, and finally, the distillation issue. We also decided that this Tequila was not filtered so as not to remove aromatic characteristics. When you take care of all the points of a process, you do not need any fixes. This consideration was part of the philosophy requested by Juan Coronado and Mr. Dolan. Our Reposado is to express everything that we achieve in the Blanco, with very used barrels and very new European and American barrels. We want the barrels to be a framework for our drinks. Let Tequila not become wood. We want to transport people to what Tequila is when they taste it, and we succeeded.
What are Mijenta Tequilas Values? How do these values intersect with your principles and standards for yourself as well as for the industry?
AM: The first thing is that it is a real, honest Tequila. It is a Tequila that expresses the naked soul of the agave. This Tequila brings us its letters of nobility through the attributes of the land. We investigate, see, and talk with the agaveros that have good agricultural practices. For us, it is very important that they take care of the soil and land. We firmly believe that without soil there is no agave. We want to take care of it and from my point of view as a Tequila teacher, people fall in love with Tequila.
JC: For us, it is very important to have safe practices when it comes to production. We consider the agricultural methods. We deal with the jimadores. We don't own the land, but we care so much about the practices that happen on the land. We want to make sure that the voices in our work of the jimadores are understood. We want to make sure, during our process, that the hands of our team, the production team, and Ana Maria and I, the rest, are important. We want to get the final product into the right hands. We also want those with the right hands to come to understand when they taste our product, all the care that was taken during the process. Our motto is por la tierra, por la gente, y por la vida. For the land, for the people, and for life. We take these practices seriously because they involve all the pillars of Mijenta. If we do not have a good agave, we cannot create a great production. If we do not have good production, we cannot have a good product or good Tequila at the end of the day. The land is the most important thing. The hands of the people that work the land are the most important thing. Those are the true values of our brand. The care of the land, the care of the people, and how we celebrate life is our main difference.
What contributes to a successful business partnership?
JC: We believe in doing right. At Mijenta, we believe in doing right by doing well. We want to create a good flavor profile that respects traditions, Mother Nature, and the processes that we are establishing. We always say that we are not in a rush. The product will be ready when it is ready. We cannot force Mother Nature to give us what we want. It happens when it happens, and we take that presence from Mother Nature, and then we turn it into an art. That's what we are trying to do. It takes time, so we are very patient. Ana Maria and I, when it comes to production, ride the wave with Mother Nature. We cannot isolate the process. We are getting used to spending time and using our senses. When all distilleries smell like Mijenta, we know that we did it. It takes time.
AM: It is very important to have common points of view about the product and the management of the image. Because in the end, each taster is a taster who will say yes or no to the product, which is a high commitment. We also consider the global vision to make a high-end product and take it to international markets. We selected very successful, capable people with a good track record to carry out this task. They are capable of not only developing a Tequila. They are also, with the correct marketing, capable of making and taking it to the people. We also believe a lot in the educational part of Tequila. We believe that the commitment to lead people to learn about our history, our land, and how to enjoy Tequila is very important. We want to have a community that buys our Tequila because it is valuable and conquers the senses. That is the educational part that we want to achieve.
Ana Maria Romero
What do the two of you bring to Mijenta separately? What do you bring to the brand collectively?
AM: I have contributed my experience and my knowledge of the industry. I have also contributed to doing different things, but at the same time in conjunction with Juan. Juan can understand the tastes of American palates and European and Asian ones because of his background as a world Mixologist. That vision has made this process and this product very enriching. We work together by adding ideas. We talk about creative processes, etc.
JC: In my case, since I have more than 30 years in the beverage industry, I have been able to tame the knowledge of understanding. I have been moving forward when it comes to forecasting. I bring in knowledge from the wine industry. I have made wine. I have made beers. I have consulted for big brands such as King Cognac. I have worked with Gins, Vodkas, Rums. I have experience in production and the knowledge that I have in consumers, the market, and the trends. Each market reacts differently. All of this has given me the ability to be the eyes and ears of our brand Mijenta.
What have you enjoyed the most from all the processes creating a Tequila?
JC: My favorite part of my journey through Mijenta is the interaction with consumers and bar professionals. I have been doing this for years. It makes me feel like I'm in my grandma's house with my big family. I love sharing good energies and stories among ourselves. It's key to foster what is the need, where the trends are going, and what are the challenges that we are facing. I love the communication part of it. Sharing is caring for me. At Mijenta, of course, we have a beautiful product that we would like to spread the gospel of Mijenta. We would like to spread the values of Mijenta all around. Of course, the history and traditions of Mexico are key. We are a brand new brand. This is going to be a long journey. I enjoy it. I am going to be able to go to market and impact others. I let them know the best part about creating a good brand versus us staying still and waiting to see what happens. I am a go-getter. I am always going to be out on guard when it comes to the teaching of the Tequila and the process that we meticulously create with Ana Maria. I am going to be the guardian of it forever- that is my favorite part of it.
AM: What I have enjoyed the most is the leadership. I love that people get motivated, do the work, train the staff, share their knowledge with others, in addition to designing Tequila, which is my passion.
What have been some challenges of being a New Tequila brand next to the others with many years of history?
AM: The challenge is to have your own personality and achieve your own style. This is a differentiating characteristic from powerful brands that may be our competition. That is different. That people can say, this is a Mijenta.
JC: I echo Ana Maria. The real challenge here is not us being a new brand. The real challenge is just us creating a unique profile. We can taste thousands of Tequila, but there is always room for improvement. We have improved and taken Tequila to a different platform because we are hogging the platform of tradition and authenticity. We are also in love with the Culinary experience. We wanted to have a GM that is so smooth and delicious that people can sip it. Or, they enjoy it with ice or in a cocktail. Being able to understand the meaning of that Aranda's perfume, as Ana Maria said before, is key for us. If there is a challenge, it would be for the other brands looking at us.
Ana Maria, how do you differ from other Master distillers? What qualities should a successful MD possess?
AM: A deep knowledge about the processes is the differentiating aspect. Know each phase from the agricultural part to the creative part. One of the things that distinguish me is the creativity of not always falling into the same thing that everyone else does. I look for different things, different opportunities. I play with different variables that can occur in the process. This approach makes a difference in a successful MT, but also the part of forming a good team.
Ana Maria, you just recently won Best Maestra Tequilera 2020 by Tequila Aficionado Magazine. What was it like to receive such recognition? Who has helped you along the way?
AM: It was unexpected. When you love your work and are passionate about it, you don't expect recognition because you were hired to do something excellent. However, I am very grateful to Tequila Aficionado magazine for giving me that recognition. I believe that it commits me more to doing better than not keeping what I have. Having this type of recognition is a commitment because you have to inspire others.
Ana Maria, what other achievements/ opportunities have you had or hope to have in the future?
AM: I write books. My first book won 3rd place in Le Gourmand Award which is a very powerful gastronomy contest in France. I took third place globally with this book on the theme of the pairing of Tequila. I aspire to continue educating people who want to believe in Tequila, to continue promoting the culture of Mexico and its values. I also want to inspire women who believe in their dreams. Talent does not have a gender. Talent is talent. I believe that when talent is real, it opens doors and tranverses borders.
Mijenta
Juan, how do you want to position Mijenta in the consumer's mind?
JC: Mijenta will find its niche in Culinary applications and opportunities such as restaurants, tastings, degustations, etc. In the case of the Blanco, it is the best partner that a cocktail may have. The cocktail will taste like Arandas, and it will have the olfactory sense and taste profile of land that is so unique and pristine. For consumers, I always tell everybody to bring their favorite Tequila and taste it next to Mijenta, and you'll decide what is good for you. We don't want to sound cocky because we are humble people. We took all the Tequilas that we tasted in our careers into consideration.
Juan, What is your vision for Mijenta?
JC: We wanted to deliver something that has an opportunity on a table. Mijenta Tequila is best enjoyed with friends. If my Tequila can pass the test of culinary dishes and be fine with citrus dishes, cooked stews, salads, and desserts, we're somewhere. Everywhere two or three people have a bite to eat, there is room for Mijenta. There is room to enhance their experience.
How may we follow your journey?
Instagram: @mijentatequila
Facebook: @mijentatequila
Website: https://shopmijenta.com
BarsNews
CH'I, the newest Latin-Chinese concept lands in Brickell City Center
South Florida-based restaurant groups, Grove Bay Hospitality Group and Breakwater Hospitality Group are pleased to announce the highly-anticipated opening of their first collaboration, CH'I, set to open in the coming weeks in Brickell City Centre. The multi-faceted entertainment venue fuses multiple immersive concepts – the Garden; Mercado; Lounge; and Main Dining Room – into one dynamic and incomparable experience. CH'I's high-energy ambiance is infused into every corner of the massive 12,000 square foot indoor and outdoor space that boasts three full-service bars; two DJ booths; several lounge and dining areas; and a unique menu of Chino-Latino cuisine that is intensely flavored, imaginatively prepared, and equally celebratory of its heritage. Inspired by the Chinese cafes that first dotted the streets of Latin America, and then of Miami and New York, CH'I has created a style of entertainment, food, and service all its own.
"We could not be more thrilled to launch our first venture together with Breakwater," said Francesco Balli Co-CEO of Grove Bay. "We're also thrilled to be adding more than 125 new job opportunities for the local community. Job seekers are highly encouraged to apply before the grand opening – we are offering a $1,000 signing bonus for all positions that employees will receive after three months of employment."
"Imagine if you had the opportunity to enter one restaurant that offered four unique concepts to create one immersive experience…that is the magic of CH'I," said Emi Guerra, co-owner of Breakwater Hospitality. "It's clear that today, people expect so much more from restaurants and hospitality, and this partnership has allowed us to combine what we each specialize in best to deliver something special and unique to Miami. From the outdoor garden and market area, to the cocktail lounge and upscale dining room, there is something for just about everyone to enjoy."
"This is one of the most exciting and unique concepts we've ever done," adds Ignacio Garcia-Menocal Co-CEO of Grove Bay. "I can't wait for everyone to check it out!"
In CH'I's Garden, guests can take advantage of Miami's gorgeous weather and the stunning views in the verdant open-air terrace. The full-service concept features an island bar with a complete beverage menu, plenty of outdoor seating, and cozy cabanas centered around a large-scale dynamic light installation. Guests can order from the menu available from the adjacent Mercado, like dim sum and other casual bites.
Upon entering the space, guests find themselves in the Mercado, modeled after an Asian-themed market featuring menu items like Soups, Salads, Bao Buns, Rotisserie and Wok items available via grab-and-go or counter service. Visitors will feel like they are transported to a secret hole-in-the-wall market in New York's Chinatown with bright neon signs mixed with vintage design, dimmed lighting and a floor to ceiling display of antique objects and curious knick-knacks. While waiting for their orders, patrons can entertain themselves with retro games.
Through a large wooden door in the back of the Mercado, the cool and vibrant Lounge can be accessed. There, guests are greeted with two large impactful murals by artist Mallory Dawn – pieces curated by The Art Plug –– atop a mirrored wall, and more than 150 lanterns strung overhead. Diners can check in at the hostess stand and, while waiting for a table or to simply enjoy the scene, partake in a vast selection of libations at a sprawling full-service bar.
CH'I's Main Dining Room is a chic and sophisticated space with large plush booths, tropical décor, and Asian-inspired stylistic elements. The variety of textures and aesthetic components combine earthy brown and green velvets with hints of gold, vibrant jewel tones and sultry crimsons. Juxtaposing crystal chandeliers hang above with columns lined with wallpaper depicting tropical palm fronds running alongside wooden slats and exposed brick walls. Adjacent to the large luminescent bar, is additional seating perfect for large parties or celebrations. The menu, like the Mercado, features a variety of Soups, Salads, Dim Sum, and Small Plates, as well as more substantial Rotisserie; Wok items; and larger For The Table dishes ideal for family-style sharing. Lighting will play an integral part in the guest experience, depending on the time of day the space will be lit up in radiant jewel tones, glowing shades of blues, and muted ambers. Following dinner service, the lights go down, the music turns up and the celebration begins. A full bar and bottle service is available until close, as well as the Mercado's late-night selection of culinary delights.
From its décor to food and beverage, CH'I embodies the veritable melting pot that is South Florida. The vibe is the ultimate combination of laid-back meets heart thumping high energy. It's the type of concept that you can visit when looking for a great meal with family, or to stay up late dancing and enjoying copious drinks with friends.
CH'I is located at 701 S Miami Ave #339a in Miami's Brickell City Centre. Website: chibrickell.com.
To apply for a job or sign up to receive an invitation to opening festivities, please visit chibrickell.com.
Instagram @Chibrickell
UncategorizedNews
Let's Do Our Part This Earth Day
by Helena Jose April 20, 2021
There is no occasion more significant than the celebration of our home. Our beloved planet Earth is the cradle of countless wonders, resources, and species. Today, we highlight celebrations that pay tribute to our world with sustainable practices. Many bars and restaurants dedicate themselves to planting the seed of education about the care and preservation of our land. Most of them use agave or paper straws and recyclable to-go packaging. This week you can participate in activities such as cleaning the beach. You may also choose to try the cocktail in honor of Earth Day. Bars and restaurants will direct proceeds of the Earth Day cocktails to specific organizations that benefit the environment.
Mijenta, a carbon-neutral artisanal Tequila, is well known for its sustainable practices and respect for the land. They will host the following activations:
Earth Week at the Lido, The holistic Standard hotel at Miami Beach will be featuring a specialty Mijenta Cocktail throughout the week. A portion of the profits will be donated to Miami Waterkeeper.
Beach Day Clean up at 1 beach club $15, give a gift to Mother Earth by cleaning up the beach to preserve our water, and receive a refreshing Mijenta cocktail. Proceeds benefiting Debris Free Ocean. Thursday 22nd, 10:30am – 11:30am. Register at bit.ly/1HotelClean
Enjoy "La Madre" Earth month specialty cocktail at 1 Beach club, available throughout the month of April, with Serrano infused Mijenta, Basil infused simple Syrup, sun-dried tomato, green Chartreuse, and lime. Featured Image*
Hop at KYU and receive a liquid hug with the "Tequila hugger" cocktail, a mix of Mijenta Tequila Blanco, St George Green Chile Vodka, Cap Corse Blanc, Thai Basil Syrup, Thai Chili Tincture. Proceeds benefiting Debris Free Ocean.
Tequila Hugger @ KYU
SLS south beach is joining forces with Clean This Beach Up & Clear View Kayaks to clean up the canal on Miami Beach. Tickets are $20 and include Kayaks and paddleboards. 100% of the proceeds will support our partners with supplies to continue the fight against pollution in Miami. Afterward, join volunteers at SLS South Beach for Ketel One complimentary refreshments at the beach hut. Spend the day on the lounge chairs and soak up the sun after your hard work. This event takes place at 10 AM on Thursday, April 22nd. Meet at 23rd/ Collins Ave. Clear View Kayak Rentals. RSVP [email protected]
Earth Day cocktail @ Tanuki
TANUKI Miami, a pan-Asian hotspot located in Miami Beach, will celebrate Earth Day with a special Earth Day cocktail that they are creating exclusively for the holiday $15. (Yoshikazu, Roku Gin, Domain Canton, Hibiscus-Sage, Lemon, Ginger Candy) . A portion of proceeds from every sold cocktail will go to Clean This Beach Up, specifically for their Earth Day Clean-Up event on April 24th, from xx . Register at volunteercleanup.org/cleanthisbeachup.
Let's not forget that our art neighborhood needs some cleaning too. Join Buya on Earth Day, Thursday 22nd from 5-7 PM to register and receive your clean-up equipment provided by Debris free Ocean and help clean up WYNWOOD. Complimentary Boozy drinks & snacks at BUYA afterward for all participants. You can RSVP at [email protected]
Let's all do our part!
The Sylvester – Reopens with a revamped Cocktail menu
The Sylvester is thrilled to announce their reopening on April 15, 2021. Located in the heart of Midtown, The Sylvester is a vintage eclectic cocktail bar where Miami nostalgia meets cutting-edge cocktails in a fun and familiar atmosphere. "We're serious about cocktails, but we don't take ourselves too seriously," is still our bar motto says Bar Director and co-owner Ben Potts.
Having survived the year long Covid shutdown the team is beyond excited to get the doors open again. "After being closed for over a year, we feel it is the right time to reopen the Sylvester responsibly. We are really excited to show our guests our exciting improvements and welcome them back to an even better bar with more thoughtful menus, programming, and ambiance," says Potts.
The new cocktail menu will feature upgraded classics using next-level techniques, locally sourced sustainable ingredients, and Instagram-worthy presentations. Led by Ben Potts, the bar team will showcase the creations executed by Bar Manager Rensel (Ice) Cabrera, along with Tim Christakis, General Manager combined with the concept expertise from Gui Jaroschy and cultural flair provided by Josue Gonzalez. In addition to the exciting new cocktails, there is a crave-worthy menu of Miami-familiar bar bites to compliment the libations created by Chef and co-owner, Brian Nasajon of Beaker & Gray.
Floradora
The cocktail menu pays homage to old and new Miami think: "The Floradora" an upgraded Moscow Mule using Ketel One Botanicals Grapefruit-Rose, raspberry syrup, fresh citrus, ginger beer and a fortified rosé aperitivo or the "Pink Panther," a pretty in pink tropical gin sour made with Sipsmith Gin, guava-lavender syrup, Martini Bitter, bianco vermouth, fresh citrus and egg glair. Another sure to be fan favorite will be the "Vaxxxed & Waxxxed" a spicy take on the modern classic "Naked & Famous" featuring Don Julio Blanco Tequila, Vida Mezcal, thai-chili infused Aperol, Chinola Passion Fruit liqueur and fresh citrus juice. The menu also includes a rotating and unique wine list and as well as a selection of locally brewed craft beers.
The Sylvester will also be adding large format cocktails to the menu by putting their own spin on the current, seafood tower trend. In true Florida fashion, guests at the Sylvester will be given the pleasure to embark on a tower adventure of their own. Imagine instead of oysters, crabs, shrimp, and all the fun things you normally find on a seafood tower being replaced by an assortment of pony beers, Lambrusco, curated shots and specialty cocktails all bottled and ready to go. Guests will be able to select from a few options to build their very own cocktail tower style large format drinking experience. There will be three sizes available, Deluxe, Royale, and Grand for those high ballers.
The 3,400 square foot space is decked out in colorful vintage wallpaper combined with tropical touches that play up the retro vibe while the repurposed antique furniture balances out the overall ambiance creating a cozy and relaxed feel. "We wanted to create a unique, inclusive space with something for everyone, a place where you would want to be stuck in a hurricane," says Potts.
The Sylvester is open Wednesday through Sunday, starting at 5PM with a casual and laid-back atmosphere for bites and drinks then transforming into a congenial cocktail bar with an elevated menu set to the tone of hand-selected contemporary sounds courtesy of your local DJ faves until 2AM on weekdays and 3AM on Fridays and Saturdays.
For more information please visit: www.thesylvesterbar.com or @thesylvesterbar on Instagram.
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}
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\section{1. Introduction}
One challenge to understanding disordered solids is the complex
geometry of their phase spaces, including the relative positions and
interconnections between the different metastable states. Phase
spaces are usually too large and complicated to be directly studied.
For example, an $N$-particle system typically has a vast abstract
$6N$-dimension phase space ($3N$ for position, $3N$ for velocity).
Here, we propose that some simple models of disordered solids, such
as geometrical frustrated spin models, provide an ideal platform for
phase-space studies. Their phase spaces can be mapped as nontrivial
complex networks, so that the recently developed large tool box of
network analysis \cite{Albert02,Newman03,Costa07} can be used to
understand phase spaces. On the other hand, these phase spaces
provide a new class of complex networks with novel topologies.
When a system has competing interactions, there is no way to
simultaneously satisfy all interactions, a situation known as
frustration. Frustration widely exists in systems ranging from
neural networks to disordered solids. Frustration can also arise in
an ordered lattice solely from geometric incompatibility
\cite{Moessner06}. For example, consider the three antiferromagnetic
Ising spins on the triangle shown in Fig.~\ref{fig:cubenet}A. Once
two of them are antiparallel to satisfy their antiferromagnetic
interaction, there is no way that the third one can be antiparallel
to both of the other two spins. Frustration leads to highly
degenerated ground states and, subsequently, to complex materials
with peculiar dynamics such as water ice \cite{Pauling35}, spin ice
\cite{Bramwel01}, frustrated magnets \cite{Bramwel01}, artificial
frustrated systems \cite{Wang06} and soft frustrated materials
\cite{Han08}.
In geometrical frustrated systems, spins on lattices have discrete
degrees of freedom, such that their phase spaces are discrete and
can be viewed as networks. A node in the network corresponds to a
state of the system. Two nodes are connected by an edge (i.e. a
link) if the system can directly evolve from one state to the other
without passing through intermediate states. Edges are undirected
because dynamic processes at the microscopic level are time
reversible. The challenge is how to construct and analyze such large
phase-space networks. For example, how do we identify whether or not
two nodes are connected?
\section{2. Antiferromagnets on triangular lattices.}
The first model we consider is antiferromagnetic Ising spins on a
two-dimensional (2D) triangular lattice \cite{Wannier50}. For a
large system with periodic boundary conditions, it has $\sim
e^{0.323N_{spin}}$ degenerated ground states where $N_{spin}$ is the
number of spins \cite{Wannier50}. For example, configuration 3A in
Fig.~\ref{fig:cubenet}C is one ground state in the hexagonal area.
We refer to pairs of neighbouring spins in opposite states as
satisfied bonds, i.e., they satisfy the antiferromagnetic
interaction. Since one triangle has at most two satisfied bonds (see
Fig.~\ref{fig:cubenet}A), the ground state should have 1/3 of its
bonds frustrated and 2/3 of its bonds satisfied \cite{Wannier50}. If
we plot only satisfied bonds, a ground state can be mapped to a
random lozenge tiling \cite{Blote94}, see configuration 3A in
Fig.~\ref{fig:cubenet}C. A lozenge is a rhombus with $60^{\circ}$
angles. By colouring lozenges with different orientations with
different grey scales, the tiling can be viewed as a stack of 3D
cubes, or as a simple cubic crystal surface projected in the [1,1,1]
direction \cite{Blote94}, see Fig.~\ref{fig:cubenet}C.
\begin{figure}
\centering
\includegraphics[width=1\columnwidth]{cubenet.jpg}
\caption{\textbf{A phase-space network of cube stacks.} (A): Three
antiferromagnetic spins on a triangle cannot simultaneously satisfy
all their interactions. (B): The central spin has three up and three
down neighbours, so that it can flip freely without energy change.
Satisfied bonds can be viewed as cubes. The +/- free spin flip
corresponds to adding/removing a cube. (C): The $2 \times 2 \times
2$ cube stacks are stable against gravity along the [1,1,1]
direction. Stack configurations have one-to-one correspondence to
Ising ground states under `hexagon boundary condition', e.g., see
configuration 3A. In the right 3A configuration, the black lines are
satisfied bonds forming rhombuses and the blue lines are frustrated
bonds. In total, there are 20 legal stacks, i.e., 20 nodes in the
phase-space network. The network is bipartite, i.e., consisting of
alternating red (even number of cubes) and black (odd number of
cubes) states.}
\label{fig:cubenet}
\end{figure}
The ground state has a local zero-energy mode, as shown in
Fig.~\ref{fig:cubenet}B: the central particle can flip without
changing the energy since it has 3 up and 3 down neighbours. The
system can evolve via a sequence of such single spin flips, even at
zero temperature. We call such a local zero-energy mode the
\textit{basic flip}. Any configuration change can be viewed as a
sequence of such basic flips. Recently, we directly observed such
flips in a colloidal monolayer \cite{Han08}. In the language of
cubes, a basic flip is equivalent to adding or removing a cube, see
Fig.~\ref{fig:cubenet}B. By continuing to add or remove one cube
from the stack surface, we can access all possible stack
configurations in the large box. Thus, the ground-state phase space
is connected by this `hexagonal boundary condition'. The
corresponding cube stacking in a large box is equivalent to the
boxed plane partition problem in combinatorics \cite{Andrews04}. The
total number of ways to stack unit cubes in an $L^3$ box is given by
the MacMahon formula: \cite{MacMahon}
\begin{eqnarray}
N_n(L)&=&\prod_{1\le i, j, k \le L}\frac{i+j+k-1}{i+j+k-2}
=\frac{H^3(L)H(3L)}{H^3(2L)} \nonumber \\
&\sim & \left(\frac{27}{16}\right)^{\frac{3}{2}L^2} \textrm{when }
L\to \infty, \label{eq:g}
\end{eqnarray}
where the hyperfactorial function $H(L)=\prod_{k=0}^{L-1} k!$. The
first several $N_n(L=2,3,4,5,\cdots)$ are 20, 980, 232848,
267227532,$\cdots$ (see the number sequence A008793 in
ref.~\cite{sequence}). When $L=2$, all 20 ground-state
configurations in Fig.~\ref{fig:cubenet}C have the same minimum
possible energy, i.e., 12 frustrated bonds in 12 rhombuses.
\section{3. Network properties.} The 20-node phase-space network shown
in Fig.~\ref{fig:cubenet}C can be constructed based on the following
two facts: (1) Spins have discrete degrees of freedom, such that the
phase space is a discrete network; (2) Any configuration change can
be decomposed to a sequence of basic flips. Consequently, we can
define an edge between two nodes if the two states differ by only
one basic flip (i.e., one cube), such that the system can
\textit{directly} change from one node to the other without passing
through intermediate nodes.
Numerically, we can handle networks only up to $L=4$ stacks with
$N_n=232848$ nodes; nevertheless many general properties have
emerged from such small systems. Figure \ref{fig:histok}A shows the
connectivity (i.e. degree) distribution
\cite{Albert02,Newman03,Costa07} of cube-stack networks. The
connectivity, $k_i$, is the number of edges incident with the node
$i$. The connectivities of various frustrated systems appear to have
Gaussian distributions (see Fig.~\ref{fig:histok}). This behavior is
similar to that of small-world networks \cite{Watts98,Costa07} and
Poisson random networks \cite{Newman03,Costa07} and different from
that of scale-free networks \cite{Costa07,{Barabasi99}}.
\begin{figure}
\centering
\includegraphics[width=1\columnwidth]{histok.jpg}
\caption{\textbf{Connectivity distributions.} Histograms of the
connectivities of ground-state phase-space networks for (A)
antiferromagnets on triangular lattices, and (B, C, D) square ices
under different boundary conditions. (A): $L=4$ (circles) and $L=3$
(squares) cube stacks. (B): Spheres stacks in $L=6$ (circles) and
$L=5$ (squares) tetrahedra. (C): Spheres stacks in $L=4$ (circles)
and $L=3$ (squares) octahedra. (D): Sphere stacks in $L=6$
(circles), $L=5$ (squares) and $L=4$ (diamonds) containers shown in
Fig.~\ref{fig:alterboundary}. Insets: semi-log plots. The curves in
the main plots and insets show the best Gaussian fits.}
\label{fig:histok}
\end{figure}
Other network properties, such as the diameter and the cluster
coefficient, can be readily derived from the cube stack picture. The
shortest path length between two nodes is simply the number of
different sites among all the $L^3$ sites. The largest distance,
i.e. the diameter of the network, is $L^3$ between the `vacant' and
the `full' states. Here, we define the vacant state as no cube
(i.e., $L^3$ vacant sites) and the full state as no vacant site
(i.e., $L^3$ cubes). The networks have small-world properties
\cite{Watts98,Costa07} in the sense that the diameter, $L^3$, is
almost logarithmically small compared with the network size, $\sim
e^{N_{spin}}\sim e^{L^2}$. The network is bipartite (see the black
and red circles in Fig.~\ref{fig:cubenet}C) because a cube stack
comes back to its initial configuration only by adding and removing
the same number of cubes, i.e., an even number of basic flips.
Consequently, the cluster coefficient \cite{Costa07}, which
characterizes the density of triangles in the network, is 0.
Spectral analysis provides global measures of network properties.
For an $N_n$-node network, the connectivity (or adjacent) matrix
$\mathbf{A}$ is an $N_n\times N_n$ matrix with $A_{ij}=1$ if nodes
$i$ and $j$ are connected, and zero otherwise. Since edges in
phase-space networks are undirected, $\mathbf{A}$ is symmetric and
all its eigenvalues, $\lambda_i$, are real. The spectral density of
the network is the probability distribution of these $N_n$
eigenvalues:
$\rho(\lambda)=\frac{1}{N_n}\sum_{i=1}^{N_n}\delta(\lambda-\lambda_i)$.
$\rho(\lambda)$'s $q$th moment, $M_q$, is directly related to the
network's topological feature.
$D_q=N_nM_q=\sum_{i=1}^{N}(\lambda_i)^q$ is the number of paths (or
loops) that return back to the original node after $q$ steps
\cite{Costa07}. In a bipartite network, all closed paths have even
steps so that all odd moments are zero. Consequently, the spectral
density is symmetric and centered at zero. The $i$th node with $k_i$
neighbours has $k_i$ ways to return back after two steps; hence, the
variance $\sigma^2=M_2=\sum_i k_i/N_n=\bar{k}$, where
$\bar{k}=2N_{edge}/N_n$ is the mean connectivity. We rescale the
spectral densities by $\bar{k}^{1/2}$ to the unit variance (see Fig
\ref{fig:specdensity}). The rescaled spectral densities of different
frustration models collapse onto the same \textit{Gaussian}
distribution. By counting $D_q$, we show that spectral densities are
Gaussian at the infinite-sized limit (see Section I of Supplementary
Information (SI)). This distinguishes phase spaces from other
complex networks. For example, the spectral density of a random
network is the semicircle in Fig.~\ref{fig:specdensity}. The
spectral densities have triangular distributions for scale-free
networks and irregular distributions for small-world, modular
hierarchical and many real-world networks
\cite{deAguiar05,Farkas01}.
\begin{figure}
\centering
\includegraphics[width=1\columnwidth]{specdensity.jpg}
\caption{\textbf{Spectral densities of phase-space networks.}
Variances are rescaled to 1 by
$\lambda'=\lambda/\bar{k}^{-\frac{1}{2}}$. Black curve: Gaussian
distribution $e^{-\lambda'^2/2}/\sqrt{2\pi}$. Dashed curve: Wigner's
semicircle law for random networks.
$\rho(\lambda)=\sqrt{4\sigma^2-\lambda^2}/(2\pi \sigma^2)$ if
$|\lambda|<2\sigma$ and zero otherwise. The variance $\sigma^2$ is
also rescaled to 1. Red curve: the spectral density of the 980-node
network of $L=3$ cube stacks. Blue curve: the 7436-node network of
$L=6$ sphere stacks in a tetrahedron, i.e., $7\times7$ square ice
under the domain wall boundary condition. Green curve: 7782-node
network of $2\times 5$ square ice under the free boundary condition.
Their Gaussian fits are indistinguishable from the black curve.}
\label{fig:specdensity}
\end{figure}
Spectral analysis can also detect the network's community (or
modular) structures \cite{Newman06PNAS} if there are any. The
algorithm in ref. \cite{Newman06PNAS} identifies some relatively
highly connected subnetworks (i.e., communities). However, we still
observe a number of edges between subnetworks such that the whole
phase space has to be considered as fully ergodic. Our simulation
shows that the system can easily travel through the whole
phase-space network via basic flips and will not be trapped in a
local community for a long time.
\section{4. Poisson processes and equal probability in phase spaces.}
The fundamental assumption of statistical mechanics is that the
dynamic trajectory of a system wanders through all its phase spaces
and spends the same amount of time in each equally sized region of
the phase space. However, this `equal a priori probability
postulate' (essentially the same as the `ergordic hypothesis'
\cite{Patrascioiu87}) is not necessarily true, as Einstein noted
\cite{Cohen07}. How the system moves from one configuration to the
next depends on the details of the molecules' interactions (e.g.
nearest-neighbor antiferromagnetic interactions here); these
microscopic dynamics may make some configurations more likely than
others.
Network analysis provides an opportunity to study ergodicity. Unlike
billiards with deterministic trajectory, we assume the spin flipping
is due to the random thermal motion and not depends on history. Thus
the dynamical evolution of the system can be viewed as a random walk
on its phase-space network. It still interesting to ask whether
this random walk can uniformly visit each node given the complex
topology of the network. In another word, whether the system can
visit each possible microstate configuration under the complex
constraint of local nearest-neighbor interactions.
Random walks on a network are rather chaotic, and nodes with higher
connectivities will be visited more frequently. Thanks to the
theorem in ref.\cite{Noh04}, the mean visiting frequency for node
$i$ is $k_i/N_{edge}$, which only depends on local connectivity,
$k_i$, and does not depend on the global structure of the network.
Here, $N_{edge}$ is the total number of edges. This theorem is a
direct consequence of the undirectedness of edges. Although highly
connected nodes are visited more frequently ($\sim k_i$),
interestingly, the equal-probability postulate does not break down
because the average time stayed at node $i$ is $\sim 1/k_i$. Basic
flips are random and independent of history, meaning that it is a
Poisson process. We define the flipping probability of a basic flip
within a unit of time as $\nu$, which is the intensity of the
Poisson process. In Poisson processes, the time interval between
flips (i.e., the staying time) has an exponential distribution,
$e^{-\nu t}$, and the mean staying time is $1/\nu$. Note that
multiple flips will \textit{not} flip \textit{exactly
simultaneously} because time is continuous. Therefore we do not need
to worry about possible illegal configurations if \textit{neighbor}
free spins flip simultaneously. For a node with connectivity $k$,
the superposition of $k$ Poisson processes is still a Poisson
process with intensity $k\nu$ and, consequently, the mean staying
time is $1/(k\nu)$. A random walker has higher frequency ($\sim k$)
to visit a high-$k$ node, but will stay there for a shorter time
($\sim 1/k$), so that the equal-probability postulate is recovered.
Boltzmann assumed that molecules shift from one microscopic
configuration to the next in such a way that every possible
arrangement is equally likely, i.e., all edges have the same weight.
We find that the equal-probability postulate still holds if edges
have different weights (see Appendix B), which, for example, can
represent different potential barriers in complex energy landscapes
in phase spaces.
\section{5. Square ice.} We further study another frustration model
called square ice to identify the more general properties of phase
spaces. Square ice is the two-dimensional version of water ice as
shown in Fig.~\ref{fig:water}. It can be viewed as jigsaw tiling
\cite{Bressoud99} or spin ice
\cite{Bramwel01,Bressoud99,Wang06,Propp01} (see
Figs.~\ref{fig:squareiceall}A,D). Oxygen atoms are represented by
vertices and the relative directions of hydrogen atoms are
represented by arrows. The ground state of the system follows the
\textit{ice rule}, i.e., each vertex has two incoming and two
outgoing arrows. It is also known as the six-vertex model since each
vertex has six possible configurations (i.e., six types of jigsaw
tiles). For a vertex associated with four ferromagnetic spins,
frustration is inevitable (see the example in
Fig.~\ref{fig:squareiceall}C).
Flipping a closed loop of arrows from clockwise to counterclockwise
(or vice versa) does not break the ice rule. The smallest four-spin
loops in Figs.~\ref{fig:squareiceall}D,G are labeled in red
(clockwise) and yellow (counterclockwise). They are basic flips
since any configuration change can be decomposed as a sequence of
such flips \cite{Eloranta99}. Similar to cube stacking, all the
legal configurations of square ice are connected via basic flips
\cite{Eloranta99}. Consequently, the phase-space network of square
ice can be constructed.
The square ices in Figs.~\ref{fig:squareiceall}A,D have domain wall
boundary conditions (DWB) as shown by the black arrows in
Fig.~\ref{fig:squareiceall}D. There is a one-to-one correspondance
between jigsaw tiling with DWB and alternating sign matrices (ASM)
\cite{Bressoud99} (see Fig.~\ref{fig:squareiceall}A). ASM are square
matrices with entries 0 or $\pm$1 such that each row and column has
an alternating sequence of +1 and -1 (zeros excluded) starting and
ending with +1. The number of $n\times n$ ASM is \cite{Bressoud99}
\begin{eqnarray}
W&=&\prod_{1\le i \le j \le n}\frac{n+i+j-1}{2i+j-1}
=\prod_{j=0}^{n-1}\frac{(3j+1)!}{(n+j)!} \nonumber \\
&\sim & \left(\frac{27}{16}\right)^{\frac{n^2}{2}} \textrm{when }
n\to \infty, \label{eq:ASM}
\end{eqnarray} i.e., the number of nodes of the
phase-space network of an $n\times n$ square ice with DWB.
\section{6. Mapping square ices to sphere stacks.} Mapping 2D triangular
antiferromagnets to 3D cube stacks greatly simplifies the picture of
the phase space and allows combinatorial analysis to generate
quantitative results such as Eq.~\ref{eq:g} and Gaussian spectral
densities. Here, we show that square ices can be mapped to 3D
close-packed spheres in face-centered cubic (FCC) lattices. Each
square plaquette in Figs.~\ref{fig:squareiceall}D,G is assigned a
height \cite{Beijeren77,Eloranta99} based on the rule shown in
Fig.~\ref{fig:squareiceall}B: When walking from the plaquette with
height $h$ to its neighbor, the height increases by 1 if it crosses
a left arrow and decreases by 1 if it crosses a right arrow. The ice
rule guarantees that the height change around a vertex is zero and
$h$ is independent of the path along which it was computed. From the
minimum and maximum possible heights, we found that DWB yields a
stack of building blocks in a tetrahedron (see Fig. S5 of SI). A
plaquette can be flipped only when its four neighbor plaquettes have
the same height. Since each building block is `supported' by four
underneath blocks in an effective `gravity field', the stack can be
viewed as an FCC lattice along the [100] direction, see section III
of SI. Thus, the stacking blocks should be rhombic dodecahedra,
which are primitive unit cells of FCC lattices. FCC lattices can be
conveniently represented by close-packing of spheres. Sphere stacks
in side length $L$ tetrahedra have one-to-one correspondence to
$(L+1)\times (L+1)$ square ices with DWB (see Fig. S5 of SI). The
stack of red spheres in Fig.~\ref{fig:squareiceall}E corresponds to
the configurations in Figs.~\ref{fig:squareiceall}A,D. The physical
heights of the red spheres on the top surface are the heights of the
corresponding plaquettes in the square ice. At the interface between
the red spheres and the yellow vacant sites, the four removable red
spheres on the top surface correspond to the red plaquettes and the
four addable yellow sites correspond to the yellow plaquettes in
Fig.~\ref{fig:squareiceall}C. Similar to the cube stacking, here, a
basic flip from counterclockwise to clockwise (or vice versa)
corresponds to adding (or removing) a sphere. By adding spheres from
the vacant state shown in Figs.~\ref{fig:squareicetetra}A,G, we can
generate all possible stack configurations, i.e., all the nodes of
the phase-space network. Similar to the cube stack case, we can
construct the phase-space network of sphere stacks by adding an edge
between two nodes if the two stacks are different by one sphere.
\begin{figure}
\centering
\includegraphics[width=1\columnwidth]{squareiceall.jpg}
\caption{\textbf{Square ice.} (A): A $5\times 5$ square ice under
the domain wall boundary condition. Each jigsaw tile can be viewed
as a water molecule with one oxygen atom in the center and two
hydrogen atoms at the two bulges (see Fig.~S4 of SI). By assigning
vertical tiles to be 1, horizontal tiles to be -1 and the other four
types to be 0, a $5\times 5$ alternating sign matrix
\cite{Bressoud99} is obtained. (B): The height rule used in (D) and
(G). (C): Four magnets placed at a cross inevitably have
frustrations. (D): The spin ice mapped from (A). The arrows
represent bulge directions in (A). The blue arrows may flip under
the ice rule. Each plaquette is assigned a height based on the rule
in (B). The upper left corner is defined as height zero. Basic flips
(i.e., four-arrow loops) are labeled in red (clockwise) and yellow
(counterclockwise). (E): The corresponding sphere stack of (D).
Yellow spheres are vacant sites. (F): A typical sphere stack in an
$L=100$ tetrahedron. The sphere centers are connected so that it
appears to be a stack of polyhedra. (G): A spin ice configuration in
an Aztec diamond area under the constant-height boundary condition.
(H): The corresponding sphere stack of (G) in an octahedron.}
\label{fig:squareiceall}
\end{figure}
\section{7. Network properties of sphere stacks.} We numerically studied
phase-space networks of small square ices under various boundary
conditions. Our largest network contains 2068146 nodes and 13640060
edges ($4\times5$ ice under free boundary conditions). All networks
have the small-world property. Their connectivity distributions in
Figs.~\ref{fig:histok}B,C,D and the spectral densities in
Fig.~\ref{fig:specdensity} are similar to those of cube stacks.
Apparently, both cube-stack and sphere-stack phase spaces have
Poisson processes with equal probability and Gaussian spectral
densities.
\section{8. Boundary effects.} Stacks in higher dimensions provide a
vivid means for qualitative visualization of the boundary effect,
which has not been well understood in geometrical frustration
\cite{Millane04}. One peculiar property of geometrical frustration
is that boundary effects often percolate through the entire system
even in the infinite-sized limit \cite{Millane04,Destainville98}.
This can be visualized from a typical sphere stack in the $L=100$
tetrahedron shown in Fig.~\ref{fig:squareiceall}F, which has a
central disordered region and four frozen (ordered) corners known as
the arctic circle phenomenon \cite{Jockush98}. The disordered region
is not uniformly random since different positions have different
mean surface curvatures and entropy densities \cite{Destainville98}
(see Appendix C). Consequently, the infinitely large limit under DWB
\textit{cannot} be called the thermodynamic limit due to the lack of
homogeneity.
Different boundary conditions in square ice correspond to different
container shapes in sphere stacking. For example, the boundary
condition shown in Fig.~\ref{fig:squareiceall}G corresponds to
sphere stacks in an octahedron (see Fig.~\ref{fig:squareiceall}H)
because the lowest possible heights form an inverted pyramid (i.e.
the container) and the highest heights form an upright pyramid (i.e.
the lid). Appendix D shows another boundary condition whose
container and lid have different shapes. At a given boundary
condition, the lid and the container form an interesting pair of
dual surfaces. Some boundary conditions do not have the arctic
circle phenomenon, as illustrated by the sphere stacking in Appendix
C.
We found that phase spaces are ergodic under free or fixed boundary
conditions, but nonergrodic under periodic boundary conditions whose
networks consist of disconnected subnetworks. As an example,
Fig.~\ref{fig:period34phase} is the phase-space network of the
$2\times 3$ square ice wrapped on toroid, i.e., under periodic
boundary conditions. It contains two nontrivial (12-node)
subnetworks and 20 trivial isolated nodes. The corresponding 44
configurations are shown in Fig.~\ref{fig:period34all}. For $m\times
n$ periodic square ice wrapped on a toroid, we show that its phase
space contains $2^{n+1}+2^{m+1}-4$ trivial isolated nodes,
$(m-1)\times (n-1)$ nontrivial subnetworks and the smallest
non-trivial subnetwork has $\frac{(m+n-1)!}{(n-1)!(m-1)!}$ nodes
(see Appendix E). These results are confirmed numerically.
\begin{figure}
\centering
\includegraphics[width=0.6\columnwidth]{period34phase.jpg}
\caption{\textbf{The phase-space network of $2\times 3$ square ice
under periodic boundary conditions.} There are 44 possible states
(see their detailed configurations in Figs. S9A,B of SI). States 1
to 12 are connected via basic flips; states 13 to 24 are connected;
and states 25 to 44 do not contain any basic flips, thus they are
isolated nodes.} \label{fig:period34phase}
\end{figure}
\section{9. Discussion and outlook.} We build novel connections between
geometrical frustration, combinatorics (e.g., plane partition and
sphere stacking) and complex networks to exploit open questions and
analysis tools from these fields. Other frustration models, such as
triangular and kagom\'{e} ices, antiferromagnets in 2D kagom\'{e}
and 3D pyrochlore lattices \cite{Moessner98,Lee02}, have height
functions and basic flips so that their phase-space networks can be
similarly constructed. In principle, these models can be mapped to
polyhedra stacking in higher dimensions, so that their rich
symmetries and boundary effects become more transparent.
Quasicrystals can also be mapped to higher-dimensional lattices.
Projecting the high-dimensional lattices to lower dimensions could
result in periodic lattices (i.e., geometrical frustration) at
certain projection angles, or aperiodic structures (i.e.,
quasicrystals) at other angles. Phasons in quasicrystals correspond
to basic flips in geometrical frustration \cite{Destainville98},
thus similar phase-space analysis may be applied to quasicrystals.
In fact, the infinitely degenerated ($\sim e^N$ where $N\to \infty$)
ground states in both geometrical frustration and quasicrystals are
essentially metastable states since the third law of thermodynamics
dictates that the true ground state of real materials must have
finite degeneracy. Network analysis may provide a possible approach
to understanding the observed glassy dynamics in frustrated systems
\cite{Han08}. At finite temperatures, phase-space networks can be
similarly constructed. The nodes are all configurations on the
hypersurface in the phase space determined by the conservation laws.
Configurations change via basic flips and diffusion of thermal
excitations \cite{Han08,Blunt08}. These motions are represented by
edges. The weight of each edge can be assigned by a Boltzmann factor
or defined by the physical details of the real system
\cite{Blunt08}. Height representation can be recovered by assigning
vector heights \cite{Moore00}, so that systems at finite
temperatures might be mapped to stacks in even higher dimensions.
Compared with intensively studied social networks, information
networks, biological networks and technological networks
\cite{Newman03}, phase-space networks belong to a new class with
unique Gaussian spectral densities. A large tool box \cite{Costa07}
has been developed in the recent decade to study network dynamics,
correlations, centrality, community structures, fractal properties
\cite{Song05}, coarse graining \cite{Gfeller07}, etc. These tools
can be readily applied to phase-space studies. In particular, phase
spaces might have fractal structures because stacks of cubes or
spheres have self-repeating patterns on various length scales. This
may cast new light on the highly controversial Tsallis's
nonextensive entropy \cite{Cho02,GellMann04}, which is based on the
assumption that nonequilibrium systems have fractal phase spaces. To
date, a real example to support this assumption has not been
available. Indeed, geometrical frustrated ground states share the
same features as the long-range interacting systems typically
discussed in the context of Tsallis entropy. One example is boundary
effects percolating through the entire system so that the system is
not uniform at the infinite-sized limit and cannot be viewed as a
simple sum of its subsystems (i.e., non-extensive).
In statistical physics, the two models we studied here are
considered as exactly solvable \cite{Baxter82} under periodic
boundary conditions at the infinite-sized limit. Combinatoric
analysis, although challenging, provides an alternative approach to
yield exact results about finite systems and at various boundary
conditions. Cube stacking (i.e., rhombus tiling or plane partition
\cite{Bressoud99}), naturally appears in many chemical and physical
problems, such as counting benzenoid hydrocarbons, percolation,
crystal melting and string theory \cite{Okounkov03}. In contrast to
the intensively studied cube stacking, sphere stacking has not been
explored. Only some combinatoric properties of sphere stacking in
tetrahedra are available since we can map them to ASM. Our numerical
calculations show that there are $2, 7, 42, 429, 7436, 218348\cdots$
ways to pack spheres in $L=1, 2, 3, 4, 5, 6,\cdots$ tetrahedra; and
$2, 18, 868, 230274,\cdots$ ways in $L=1, 2, 3, 4,\cdots$ octahedra.
The former number sequence (i.e., sequence A005130 in
ref.\cite{sequence}) is given by Eq. \ref{eq:ASM}, while the formula
for the latter is not available. Moreover, many questions studied in
cube stacking can be asked about FCC sphere stacking. For example,
how many ways are there to pack $N$ spheres into a tetrahedron? Is
there a similar generating function as cube stacking for sphere
stacking in a tetrahedron \cite{MacMahon}? What is the
ensemble-averaged surface in Fig.~\ref{fig:meansurf100}A, i.e., what
are the entropy density distributions at the infinite-sized limit
\cite{Destainville98,Kenyon07}? These questions can also be asked
about other container shapes. Furthermore, square ice has one-to-one
mappings to other 2D models, such as three-color graphs, dimers,
fully packed loops, etc. \cite{Propp01}. It also has one-to-multiple
mapping to the domino tiling \cite{Elkies92}. Sphere stacking
provides a simple 3D picture and casts new light on these 2D models.
\section{Acknowledgements} We thank Michael Wong for helpful
discussions.
\section{Appendix A: Proof of the Gaussian spectral density}
The characteristic function, i.e., the Fourier transform of the
probability function, uniquely describes a statistical distribution.
It can be written as a series of moments of the distribution. Hence,
to prove that the spectral density is Gaussian, we only need to show
that all orders of the moments are the same as those of a Gaussian
distribution. For a Gaussian distribution centered at 0, its odd
moments are zero and its even moments (of order $q$) are
$M(q)=\frac{(q)!}{2^{q/2}(q/2)!}\sigma^{q}=(q-1)!!\sigma^{q}$, where
$\sigma^2$ is the variance. For an $N_n$-node undirected network,
$D(q)=N_nM(q)$ is the number of directed paths that return to their
starting node after $q$ steps \cite{Costa07}. We count $D_q$ by
stacking cubes/spheres and show that $M(q)=D(q)/N_n$ follows the
Gaussian $M(q)$.
The phase-space networks are bipartite since walking an odd number
of steps (i.e., adding/removing cubes/spheres an odd number of
times) cannot return back to the original state. Consequently, all
odd moments are zero, i.e., the distribution is symmetric and
centered at 0. $D(2)$ is the number of ways to have one basic flip,
$f_1$, and its reverse flip, $\bar{f}_1$. Given a stack
configuration, $i$, with $k_i$ available basic flips, i.e., node $i$
with connectivity $k_i$ in the phase-space network, its
$D(2)_i=k_i$. Thus, the total $D(2)=\sum_i k_i=N_n\bar{k}$ where
$\bar{k}=2N_{edge}/N_n$ is the mean connectivity. Compared with the
second moment, $M(2)=\sigma^2$, we have $\bar{k}=\sigma^2$. $D(4)$
is the number of ways to have two basic flips, $f_1$, $f_2$, and
reverse flips, $\bar{f}_1$, $\bar{f}_2$. Subscripts 1 and 2 denote
the time order. Given $f_1$ and $f_2$, typically there are three
ways to arrange them in legal order:
$f_1$-$\bar{f}_1$-$f_2$-$\bar{f}_2$,
$f_1$-$f_2$-$\bar{f}_1$-$\bar{f}_2$ and
$f_1$-$f_2$-$\bar{f}_2$-$\bar{f}_1$. Note that the reverse flip,
$\bar{f}_j$, must be later than $f_j$. $f_j$ represents either
adding or removing a cube/sphere. If $f_1$ and $f_2$ are flips of
the same spin or neighbor spins, they are not independent so that
only $f_1$-$\bar{f}_1$-$f_2$-$\bar{f}_2$ is legal. However, the
probability of such a case approaches 0 in infinitely large systems
such that we can neglect the `interference' between basic flips in
large systems and assume that all flips are independent. Next, we
consider how many choices of $f_1$ and $f_2$ we have. Given the
initial state, $i$, $f_1$ has $k_i$ choices and $f_2$ has $k_{i1}$
choices. Here, $k_{i1}$ is the connectivity of a node after walking
one step away from state $i$. In large systems, a dominant number of
states have large $k$ diverging with the rough surface area, $\sim
L^2$. Hence, $k_{i1}\simeq k_i$. Moreover, the dominant number of
states is close to the mean surface, such as
Fig.~\ref{fig:meansurf100}A under the domain wall boundary
condition. The surface shape distribution peaks around this maximum
possible surface and becomes like a Dirac delta distribution when
approaching the infinite-sized limit \cite{Destainville98}. The
probability distribution of normalized connectivity approaches a
Dirac delta distribution as well (see Fig.~\ref{fig:normhistok} and
its caption). Thus the leading term in $k_ik_{i1}$ is $\bar{k}^2$.
At the infinite-sized limit, there are $k_ik_{i1}\simeq \bar{k}^2$
choices of $f_1$ and $f_2$, and three ways to flip them in different
time orders; therefore, $D(4)=3\bar{k}^2$.
Similarly, we count $D(2n)$ by considering $2n$ flips, $f_1,
\bar{f}_1,f_2,\bar{f}_2,\cdots,f_n,\bar{f}_n$. They are placed in a
$2n$-long sequence in time order. First, $f_1$ must be placed at
step 1. Then, there are $2n-1$ choices for placing $\bar{f}_1$.
Then, $f_2$ must be placed at the earliest available step (i.e.,
step 2 if $\bar{f}_1$ is not occupying that step), Then, $\bar{f}_2$
has $2n-3$ choices. Thus, in total, there are $(2n-1)!!$ legal
sequences. Note that this is accurate because a finite number of
$f_j$'s are diluted enough to be considered as independent in an
infinitely large system. Next, we consider how many choices of
$f_j$'s there are. Given the initial state, $i$, $f_1$ has $k_i$
choices, $f_2$ has $k_{i1}$ choices, ... $f_n$ has $k_{i(n-1)}$
choices. Here, $k_{ij}$ is the connectivity of a node after walking
$j$ steps away from the initial node, $i$. $k_{ij}$ depends on the
pathway of the $j$ steps and is not a constant. In total, there are
$\prod_{j=0}^{n-1} k_{ij}$ choices for $\{f_1,f_2,\cdots,f_n\}$ if
node $i$ is chosen as the starting point. When the system size $L\to
\infty$, there will be $N_n(1-\delta)$ states ($\delta \to 0$) with
large connectivity, $k_i \sim L^2$. In cube stacks, adding one cube
can change $k$ by 3 at most because one cube is supported by three
underlying cubes. If the shortest path between two nodes has $j$
steps, their connectivity difference is $|\delta k_{ij}|\le 3j$. In
sphere stacks, one sphere is supported by four underlying spheres;
thus, $|\delta k_{ij}|\le 4j$. Therefore, when $L\to \infty$, $j \ll
L$ and $\prod_{j=0}^{n-1} k_{ij}=\prod_{j=0}^{n-1} (k_i+\delta
k_{ij}) \simeq k_i^n\simeq \bar{k}^n$ by dropping the high-order
terms. The last step uses the fact that the surface shape
distribution becomes a delta distribution when approaching the
infinite-sized limit.
\begin{figure}
\centering
\includegraphics[width=1\columnwidth]{meansurf100.jpg}
\caption{(A): The mean sphere stack surface in an $L=100$
tetrahedron. The surface is obtained by averaging over $10^9$ stacks
at equilibrium. A typical surface at equilibrium is shown in Fig. 4F
of the main text. (B): The corresponding probability of basic flips
measured from $10^9$ step simulation. The probability distribution
appears to be a hemisphere. (C): The flipping probability in (B)
represented by brightness. The bright non-frozen region is circular,
which agrees with the arctic circle theorem \cite{Jockush98}.}
\label{fig:meansurf100}
\end{figure}
Combining the above results, $D(2n) \simeq \sum_{i=1}^{N_n} (2n-1)!!
\prod_{j=0}^{n-1} k_{ij}\simeq (2n-1)!! N_n \bar{k}^n$, which
becomes exact at the infinite-sized limit. Since $D(2)=N_n
\bar{k}=N_n \sigma^2$, the $2n$th moment of the eigenvalue
distribution $M(2n)=D(2n)/N_n=(2n-1)!!\sigma^{2n}$ is identical to
the $2n$th moment of a Gaussian distribution. Therefore, spectral
densities of phase-space networks are Gaussian at the infinite-sized
limit. In fact, Fig.~3 in the main text shows that spectral
densities are already very close to the Gaussian distribution when
systems are small ($\sim 10^3$ nodes).
\begin{figure}
\centering
\includegraphics[width=0.5\columnwidth]{normhistok.jpg}
\caption{The probability distribution of normalized connectivity,
$k'=k/k_{max}$, where the maximum connectivity is $k_{max} \propto
N_{spin} \propto L^2$. This figure is normalized from Fig.~2 in the
main text. Black curves: cube stacks in $L=4$ (thick curve) and
$L=3$ (thin) boxes. Red curves: sphere stacks in $L=7$ (thick) and
$L=6$ (thin) tetrahedra. Blue curves: 2D square stacks (i.e., 2D
sphere stack as shown in Fig.~\ref{fig:2Dstack}A) with $L=11, 10, 9,
8$ (thicker curves for larger $L$). The peaks are in the middle bin
at 0.5, i.e., $k=k_{max}/2$ has the highest number of stack
configurations. In the infinite-sized limit, the normalized
distributions will be asymptotic to a specific functional form. For
a histogram of Fig.~2 in the main text before the normalization, the
peak height, $H$, increases exponentially with the system size,
while the heights at $k_{max}$ are always 1 or 2 (for example, see
Fig.~\ref{fig:cube4}). Thus, their ratio $2/H \to 0$ in infinitely
large systems. This indicates that the asymptotic distribution is
indeed a Dirac delta function as described in ref.
\cite{Destainville98}.} \label{fig:normhistok}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.6\columnwidth]{cube4.jpg}
\caption{The two highest connectivity ($k=13$) states in $L=3$ (odd)
cube stacks and the highest connectivity ($k=24$) state in $L=4$
cube stacks.} \label{fig:cube4}
\end{figure}
\section{Appendix B: Dynamics in phase-space networks with weighted edges}
In the main text, we show that trajectories spend equal amounts of
time at every node on average. This can be easily generalized to
networks with weighted edges, which, for example, can represent
different potential barriers at finite temperatures. We replace an
edge, $i$, with weight $w_i$ with $w_i$ equivalent edges. By
applying such replacement to all edges, we get a new network with
all equally weighted edges. The new connectivity for node $i$ is
$k_i^{w}=\sum_{j=1}^{N_{node}}w_{ij}$. For the same reason as shown
in the main text, the mean staying time at node $i$ is $\propto
1/k_i^w$. The visiting probability is $\propto k_i^w$ by
generalizing the theorem in ref.\cite{Noh04} to weighted networks
\cite{Wu07}. In fact, the proof in ref.\cite{Noh04} can be directly
applied to weighted networks. For a weighted network, the
connectivity matrix, $A_{ij}=w_{ij}$, where $w_{ij}$ is the weight
of the edge between nodes $i$ and $j$. The weighted connectivity is
$k_i^w=\sum_j A_{ij}$. The transition probability from node $i$ to
node $j$ is $A_{ij}/k_i^w$. Suppose a walker starts at node $i$ at
time $t=0$. Then, the master equation for the probability, $P_{ij}$,
to find the walker at node $j$ at time $t$ is given by \cite{Noh04}:
\begin{equation}
P_{i\to j}(t) = \sum_{j_{t-1}} \frac{A_{j_{t-1}j}}{k^w_{j_{t-1}}}
P_{i,j_{t-1}}(t-1). \label{eq:master}
\end{equation}
The transition probability, $P_{ij}(t)$, from node $i$ to node $j$
in $t$ steps can be explicitly expressed by iterating
Eq.~\ref{eq:master},
\begin{equation}
P_{i\to j}(t) = \sum_{j_1,\cdots,j_{t-1}} \frac{A_{ij_1}}{k^w_i}
\frac{A_{j_1j_2}}{k^w_{j_1}} \cdots
\frac{A_{j_{t-1}j}}{k^w_{j_{t-1}}}. \label{eq:itoj}
\end{equation}
By comparing the expressions of $P_{i\to j}(t)$ and $P_{j\to i}(t)$,
we get
\begin{equation}
k_i^w P_{i\to j}(t) = k_j^w P_{j\to i}(t). \label{eq:kp}
\end{equation}
We define the stationary probability, $P_i^{\infty}$, as $t\to
\infty$. Eq.~\ref{eq:kp} implies that $k_i P_{j}^{\infty} = k_j
P_{i}^{\infty}$ and, consequently, we obtain
\begin{equation}
P_i^{\infty} = \frac{k_i^w}{\sum_ik_i^w}=\frac{\sum_i
A_{ij}}{\sum_{i,j}A_{i,j}}. \label{eq:p}
\end{equation}
A random walker visits node $i$ at frequency $P_i^{\infty}\sim
k_i^w$ and stays at node $i$ for the time period $\sim 1/k_i^w$ on
average. Thus the walker spends the same amount of time at each
node.
\section{Appendix C: Square ice and sphere stacks}
\begin{figure}
\centering
\includegraphics[width=0.5\columnwidth]{water.jpg}
\caption{(A) Square ice with a domain wall boundary condition. Water
molecules are frozen into a square lattice. This configuration
corresponds to Figs. 4A, D, E in the main text.} \label{fig:water}
\end{figure}
Figure~\ref{fig:water} shows a $5\times 5$ square ice with the
domain wall boundary condition (DWB) corresponding to Figs. 4A, D,
E. in the main text. Figure~\ref{fig:squareicetetra} shows $6\times
6$ spin ices with DWB and their corresponding FCC sphere stacks in
an $L=5$ tetrahedron. Flipping all counterclockwise four-spin loops
to clockwise corresponds to adding one layer of spheres. The
tetrahedron emerges from the maximum packing, i.e., the full state.
A square plaquette can flip only when its four neighbors have the
same height, which indicates that one building block in the 3D stack
should be supported by four building blocks underneath. Thus, the
stack can also be viewed as a body-centered cubic (BCC) lattice
\cite{Beijeren77}. Both FCC and BCC stacking have the same
combinatoric properties since they are only different by a stretch
(see a 2D analogy in Fig.~\ref{fig:2Dstack}A). FCC is better than
BCC because (1) FCC can be viewed as close-packed spheres in simple
container shapes; (2) FCC has simple polyhedra stacking under
gravity. The Wigner-Seitz cell of an FCC lattice is a rhombic
dodecahedron, which is supported by four rhombic dodecahedra
underneath, while the Wigner-Seitz cell of a BCC lattice can be
supported by one block underneath since it has a flat square on the
top.
\begin{figure}
\centering
\includegraphics[width=1\columnwidth]{squareicetetra.jpg}
\caption{The one-to-one mapping between square ice and sphere
stacks. (A-F): $6\times 6$ square ices. The domain wall boundary
condition is labeled in grey. The height of each square plaquette is
labeled with a number ranging from 0 to 6. The upper left corner is
defined as zero height. Other heights are generated by the height
rule in Fig.~5B in the main text. (A): the vacant state with the
lowest possible heights. Heights in (F) define a container
consisting of two yellow triangles shown in (G). Counterclockwise
four-spin loops are labeled in yellow. Flipping all of them in (A)
leads to the configuration in (B). Clockwise four-spin loops are
labeled in red. Flipping the yellow plaquettes results a series of
states shown in (C, D, E, and F). (F) has the highest possible
heights without yellow plaquettes. These heights define a lid, which
is an upside-down container in (G). All legal square ice
configurations can be generated by flipping yellow plaquettes from
the vacant state or, reversely, by flipping red plaquettes from the
full state. A plaquette can be flipped only when its four neighbour
plaquettes have the same height. The height of each plaquette is the
physical height of the corresponding spheres on the top surface of
the stack. Each basic flip can be viewed as adding or removing a
sphere. (H-L): the red sphere stacks corresponding to (B-F). The
yellow spheres are vacant sites.} \label{fig:squareicetetra}
\end{figure}
\section{Appendix D: Boundary effects}
We use the `alternating boundary condition' shown in
\ref{fig:alterboundary}A, B to elucidate the lid-container duality.
Given a boundary condition, the minimum (or maximum) possible
heights can be directly written out, for example see
Figs.~\ref{fig:alterboundary}A, B. These heights define the lid and
the container. The lid and the container have different shapes. The
container contains multiple height minima and the lid contains one
height maximum (see the colored squares in
Figs.~\ref{fig:alterboundary}A, B). They form an interesting pair of
dual surfaces: using one as the container, the other will emerge as
the surface of the highest `sand pile' of small spheres. In fact,
given a fixed boundary condition, the container and the lid are dual
surfaces because, if we reverse the height rule in Fig.4(B), the
container and the lid switch roles. Packing spheres in the container
is equivalent to packing buoyant spheres in the corresponding lid.
The height difference between a lid and container is a pyramid; for
example, see Figs.~\ref{fig:alterboundary} and
\ref{fig:tetracontainer}.
\begin{figure}
\centering
\includegraphics[width=0.8\columnwidth]{alterboundary.jpg}
\caption{$6\times 6$ square ice with the `alternating boundary
condition'. (A): The maximum possible heights, i.e., the lid,
contains one clockwise basic flip labeled in red. (B): the minimum
possible height, i.e., the container, contains multiple
counterclockwise basic flips labeled in yellow. (C): The 3D shape of
a full stack, including a lid (D) and a container (E). (F): The
height difference between the lid and the container is a pyramid.
(G-J): Upside-down geometries of (C-F). The lid (H) emerges from the
maximum packing in the container (I), which is the upside-down
version of (D).} \label{fig:alterboundary}
\end{figure}
Some boundary conditions do not exhibit the arctic circle phenomenon
shown in Fig.~\ref{fig:meansurf100}. Their disordered region may not
have a circular shape or may not even have a frozen area
\cite{Eloranta99}. The container shape provides an intuitive
understanding about how boundaries affect the disordered region. In
a tetrahedron, the largest horizontal cross section is a square in
the middle height that is circumscribed by the disordered region. In
an octahedron, the largest horizontal cross section is the total
square ice area so that there is no frozen region under the boundary
condition shown in Fig.~4G of the main text. This is confirmed by
our simulation. Other boundary conditions may lead to the
non-circular disordered region. For example, the flower shape
observed in ref. \cite{Eloranta99} (see
Fig.~\ref{fig:tilt100meanandfluc}B) is a direct consequence of the
container shown in Fig.~\ref{fig:tilt100meanandfluc}A.
The ensemble average over random stacks results a mean surface shown
in Fig.~S1A. At the infinite-sized limit, dominate states are close
to this mean surface \cite{Destainville98}, i.e., the typical
surface in Fig.~4F approaches the mean surface in Fig.~S1A when
$L\to \infty$. In the space of the stack surface, the distribution
peaks around this maximum possible surface and becomes more and more
like a Dirac delta distribution when approaching the infinite-sized
limit \cite{Destainville98}. The local gradient of the surface
determines the density of the basic flips, i.e., the density of
configurational entropy $s_0$ \cite{Destainville98}. In Fig.~S1A ,
the $s_0$ is zero in the frozen areas and continuously varies to
reach its maximum value near the center of the square ice, with a
non-zero gradient everywhere except near the center
\cite{Destainville98}. Consequently, the infinitely large limit of
the DWB \textit{cannot} be called the thermodynamic limit due to the
lack of homogeneity. In contrast, the boundary condition in Fig.~4G
has the thermodynamic limit since the limiting surface in the
octahedron is flat everywhere. The flat surface has the maximum
possible $s_0$ (for example, see Fig.~S3) so that its spatial
averaged, $\bar{s}_0$, is as high as that of the free boundary
condition. The boundary condition in Fig.~4G is a subset of the
periodic boundary condition, so that the periodic boundary condition
has the same $\bar{s}_0$ as the free boundary condition at the
infinite-sized limit. This explains why the $\bar{s}_0$ calculated
from the periodic boundary condition \cite{Nagle66} agrees so well
with the experimental results on water ice obtained under the free
boundary condition \cite{Giauque33}. When the height difference of a
fixed boundary is comparable to $L$, the limiting surface is not
flat and $\bar{s}_0$ is smaller. For example, the zero-point entropy
of $L\times L$ square ice in the infinite-sized limit under DWB is
$\bar{s}_0=k_BL^2\ln{N_n}= k_B \ln(\sqrt{27/16})$ \cite{Elkies92}
based on Eq.~2 in the main text, which is smaller than $k_B
L^2\ln(\sqrt{64/27})$ under the periodic boundary condition
\cite{Lieb67}. For cube stacks, $\bar{s}_0=k_B \ln(\sqrt{27/16})$
under the hexagonal boundary condition based on Eq.~1 in the main
text, which is smaller than $0.323k_B$ under the periodic boundary
condition \cite{Wannier50}.
The typical stack configuration in a tetrahedron or octahedron is
$\sim$ 50\% filled because the lid and the container have the same
shape. When they have different shapes, a typical stack
configuration may not be $\sim$ 50\% filled. Figure
\ref{fig:tilt100meanandfluc}A is the averaged surface in an $L=100$
container. The total volume has $L(L^2-1)/6$ spheres, and $\sim$42\%
of the volume is filled with spheres on average. Note that the
largest horizontal cross-section is at $h=\sqrt{2}/3$ with a
corresponding filled fraction of 4/9.
\begin{figure}
\centering
\includegraphics[width=1\columnwidth]{tilt100meanandfluc.jpg}
\caption{(A): The ensemble-averaged height surface for $L=100$
square ice with alternating boundary condition shown in
Fig.~\ref{fig:alterboundary}A, B. The heights are rounded off to
integers to show equal-height contours. The container shape is shown
in Fig.~\ref{fig:alterboundary}E. (B): The flipping probability
represented by the brightness.} \label{fig:tilt100meanandfluc}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.8\columnwidth]{tetracontainer.jpg}
\caption{The lid, container and their height difference of a
tetrahedron.} \label{fig:tetracontainer}
\end{figure}
\section{Appendix E: square ice with periodic boundary condition}
Here, we use the $2\times 3$ square ices to illustrate that periodic
boundary conditions result in disconnected phase-space networks.
Figure~\ref{fig:period34all} shows the 44 configurations of the
$2\times 3$ square ice wrapped on a toroid. Note that this periodic
boundary condition is for spins, not for heights. The upper left
corner is defined as zero height. The 12 configurations in
Fig.~\ref{fig:period34all}A are connected by basic flips and form a
12-node cluster as shown in Fig.~\ref{fig:period34all}D. The other
12 configurations in Fig.~\ref{fig:period34all}B form another
12-node cluster in Fig.~\ref{fig:period34all}D. The height
difference between the top corners and bottom corners is +1 in
Fig.~\ref{fig:period34all}A and -1 in Fig.~\ref{fig:period34all}B.
Note that the four corners are essentially the same plaquette on the
toroid, so they must be either all inside or all outside of a loop,
such as the one shown in Fig.~\ref{fig:period34all}E. Consequently,
the height difference between the corners cannot be changed by
flipping a closed spin loop. Therefore, the nodes in
Fig.~\ref{fig:period34all}A and B form two disconnected clusters.
The 20 isolated nodes in Fig.~\ref{fig:period34all}D correspond to
the 20 configurations in Fig.~\ref{fig:period34all}C, which contain
no basic flips.
\begin{figure}[!t]
\centering
\includegraphics[width=1\columnwidth]{period34all.jpg}
\caption{Configurations and the phase-space network of $2\times 3$
square ice wrapped on a toroid, i.e., with the periodic boundary
condition. (A): Configurations 1 to 12. The upper left plaquette is
defined as zero height and other heights are derived from it by
using the height rule in Fig.~4B in the main text. (B):
Configurations 13 to 24. (C): 20 configurations that contain no
basic flip. They are categorized into four types: all horizontal
spins are (1) leftwards; (2) rightwards; all vertical spins are (3)
upwards; (4) downwards. Four configurations are double counted, so
the total number of configurations is $2\times 2^2+2\times 2^3-4$.
(D): The phase-space network. Two nodes are connected if they are
different by one basic flip (i.e., the flip of a four-spin loop).
(E): The flip of a spin loop does not change the height difference,
$h_a-h_b$ if $h_a$ and $h_b$ are both inside or outside the loop.
(F): $m\times n$ square ice ($m=3$, $n=4$) with periodic boundary
conditions. There are $(m-1)\times (n-1)=6$ types of different
$(\Delta h_x,\Delta h_y)$. Configurations with the same $(\Delta
h_x,\Delta h_y)$ form one cluster by adding/removing spheres in the
corresponding container, while configurations with different
$(\Delta h_x,\Delta h_y)$ are disconnected because zero energy flips
cannot change the height mismatches. Each state has a unique lowest
height plaquette labeled in yellow.} \label{fig:period34all}
\end{figure}
We generalize the above results to the $m\times n$ periodic lattice
and prove that it has $(m-1)\times (n-1)$ non-trivial clusters and
$2^{n+1}+2^{m+1}-4$ isolated nodes. Unlike fixed boundary
conditions, after walking along a closed loop in the $x$ or $y$
direction on a toroid and coming back to the original plaquette, the
height may change. Such height differences, $\Delta h_x$ and $\Delta
h_y$, uniquely characterize each disconnected subnetwork. Consider
an arbitrary plaquette on a toroid. We unwrap the lattice onto a
plane so that this plaquette is at the upper left corner with the
height defined as 0, e.g., see Fig.~\ref{fig:period34all}F. As shown
in Fig.~\ref{fig:period34all}E, any zero energy flip of a spin loop
cannot change the height differences between the four corners since
they are essentially the same plaquette on the toroid. Consequently,
configurations with different $\Delta h_x$ or $\Delta h_y$ cannot be
connected by basic flips. On the other hand, if configurations have
the same $\Delta h_x$ and $\Delta h_y$, they must be connected
because they have essentially the same fixed boundary condition
after being unwrapped onto a plane (see
Fig.~\ref{fig:period34all}F). Here, we use the fact that all legal
configurations at a fixed boundary condition are connected by basic
flips \cite{Eloranta99}. Since they are connected, we can choose the
configuration whose bulk spins are along the boundary spins to
represent each subnetwork (see examples in
Figs.~\ref{fig:period34all}C, F). Next, we consider the number of
representative configurations, i.e., the number of subnetworks. If a
representative configuration has no basic flips, all of its
horizontal spins or vertical spins have to be along the same
direction as shown in Fig.~\ref{fig:period34all}C. The `energy
barriers' between these states are large for large systems because
$m$ or $n$ spins need to flipped simultaneously in order to change
from one state to another without breaking the ice rule. If all
horizontal spins are leftwards (or rightwards), there are $2^m$
configurations for vertical spins (see Fig.~\ref{fig:period34all}C).
If all vertical spins are upwards (or downwards), there are $2^n$
configurations for horizontal spins. In total, the four
configurations are double counted so that there are
$2^{n+1}+2^{m+1}-4$ isolated nodes, i.e., configurations without
basic flips. Next, we consider nontrivial clusters with multiple
nodes. The corner height difference, $\Delta h_x$, has $m-1$
possible values, and $\Delta h_y$ has $n-1$ possible values (see
Fig.~\ref{fig:period34all}F), so that there are $(m-1)\times (n-1)$
nontrivial subnetworks in total. The representative configurations
of the six subnetworks shown in Fig.~\ref{fig:period34all}F are
chosen to have the lowest possible heights, i.e., vacant containers
for sphere stacking. Each configuration is characterized by one
basic flip labeled as yellow squares, i.e., the lowest point of the
vacant container. Apparently, there are $(m-1)\times (n-1)$
positions for a yellow square, i.e., $(m-1)\times (n-1)$
subnetworks. This result confirms that the zero-point entropy
$\bar{s}_0$ of the whole network is the same as that of the largest
subnetwork under the constant-height boundary condition (see section
IV) because $(m-1)\times (n-1)$ is logarithmically small compared
with the total number of configuration $\sim e^{N_{spin}}\sim
e^{m\cdot n}$.
Next, we show that the smallest nontrivial cluster has
$\frac{(m+n-1)!}{(n-1)!(m-1)!}$ nodes. In Fig.
\ref{fig:period34all}F, the two middle configurations represent
132-node subnetworks and the other four configurations represent
60-node subnetworks. When the yellow square is at the corner, the
height function indicates that the container shape is a tilted 2D
container rather than a 3D container. Thus, the number of spheres
packing in such a container is much smaller than that in 3D
containers whose lowest point (the yellow plaquette) is not at the
corner. To count the number of states in a tilted 2D container, we
first consider the simple case in Fig.~\ref{fig:period34all}A.
Configuration 1 in Fig.~\ref{fig:period34all}A is the representative
state with the lowest height of -3. Configurations 1 to 4 in
Fig.~\ref{fig:period34all}A have the same boundary spins so that we
can view them as the 2D sphere stacks in the same $1\times 3$-sized
2D rectangle. Such a blue $1\times 3$ container has three possible
positions relative to the zero height plaquette (see configurations
1, 5 and 9 in Fig. \ref{fig:period34all}A). In total the subnetwork
has $3\times 4=12$ nodes. It is easy to generalize this counting to
$m\times n$ square ice on a toroid. There are $m$ possible positions
for the $m\times (n-1)$-sized rectangle. With 2D sphere stacking in
an $a\times b$ container, there are $C_{a+b}^{a}=(a+b)!/(a!b!)$
configurations (see Fig.~\ref{fig:2Dstack} and its caption).
Consequently, there are
$mC_{m+n-1}^{m}=\frac{(m+n-1)!}{(n-1)!(m-1)!}$ nodes in the smallest
nontrivial subnetworks. We confirm the above results numerically.
Our numerical results also confirm the number sequence A054759 in
ref.\cite{sequence} for the $n\times n$ square ice under periodic
boundary conditions.
\begin{figure}[!t]
\centering
\includegraphics[width=0.5\columnwidth]{2Dstack.jpg}
\caption{(A): 2D circle stacking is combinatorically equivalent to
2D square stacking because each circle or square is supported by two
circles underneath in a gravity field. (B): Mapping a 2D stack of
squares in an $a\times b=7\times 9$ container to a chain of $a$
solid particles and $b$ holes \cite{Okounkov03}. The dynamics, i.e.,
the diffusion of particles, is described as a symmetric simple
exclusion process (SSEP). The number of 2D stack configurations in a
container is $C_{a+b}^a=(a+b)!/(a!b!)$, i.e., the number of ways to
put $a$ particles onto $a+b$ sites.} \label{fig:2Dstack}
\end{figure}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 3,355
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{"url":"https:\/\/www.lmfdb.org\/ModularForm\/GL2\/Q\/holomorphic\/192\/4\/d\/c\/","text":"# Properties\n\n Label 192.4.d.c Level $192$ Weight $4$ Character orbit 192.d Analytic conductor $11.328$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$\n\n# Related objects\n\n## Newspace parameters\n\n Level: $$N$$ $$=$$ $$192 = 2^{6} \\cdot 3$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\\chi]$$ $$=$$ 192.d (of order $$2$$, degree $$1$$, minimal)\n\n## Newform invariants\n\n Self dual: no Analytic conductor: $$11.3283667211$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\\Q(\\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\\Z[a_1, \\ldots, a_{19}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: yes Sato-Tate group: $\\mathrm{SU}(2)[C_{2}]$\n\n## $q$-expansion\n\nCoefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\\beta_1,\\beta_2,\\beta_3$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.\n\n $$f(q)$$ $$=$$ $$q - 3 \\beta_1 q^{3} - \\beta_{2} q^{5} - 7 \\beta_{3} q^{7} - 9 q^{9}+O(q^{10})$$ q - 3*b1 * q^3 - b2 * q^5 - 7*b3 * q^7 - 9 * q^9 $$q - 3 \\beta_1 q^{3} - \\beta_{2} q^{5} - 7 \\beta_{3} q^{7} - 9 q^{9} + 48 \\beta_1 q^{11} + 12 \\beta_{2} q^{13} - 3 \\beta_{3} q^{15} + 54 q^{17} + 4 \\beta_1 q^{19} + 21 \\beta_{2} q^{21} - 50 \\beta_{3} q^{23} + 113 q^{25} + 27 \\beta_1 q^{27} + 47 \\beta_{2} q^{29} - 17 \\beta_{3} q^{31} + 144 q^{33} + 84 \\beta_1 q^{35} + 94 \\beta_{2} q^{37} + 36 \\beta_{3} q^{39} - 294 q^{41} + 188 \\beta_1 q^{43} + 9 \\beta_{2} q^{45} - 146 \\beta_{3} q^{47} + 245 q^{49} - 162 \\beta_1 q^{51} - 215 \\beta_{2} q^{53} + 48 \\beta_{3} q^{55} + 12 q^{57} + 252 \\beta_1 q^{59} - 26 \\beta_{2} q^{61} + 63 \\beta_{3} q^{63} + 144 q^{65} - 628 \\beta_1 q^{67} + 150 \\beta_{2} q^{69} + 2 \\beta_{3} q^{71} - 1006 q^{73} - 339 \\beta_1 q^{75} - 336 \\beta_{2} q^{77} + 387 \\beta_{3} q^{79} + 81 q^{81} + 720 \\beta_1 q^{83} - 54 \\beta_{2} q^{85} + 141 \\beta_{3} q^{87} - 1482 q^{89} - 1008 \\beta_1 q^{91} + 51 \\beta_{2} q^{93} + 4 \\beta_{3} q^{95} + 1822 q^{97} - 432 \\beta_1 q^{99}+O(q^{100})$$ q - 3*b1 * q^3 - b2 * q^5 - 7*b3 * q^7 - 9 * q^9 + 48*b1 * q^11 + 12*b2 * q^13 - 3*b3 * q^15 + 54 * q^17 + 4*b1 * q^19 + 21*b2 * q^21 - 50*b3 * q^23 + 113 * q^25 + 27*b1 * q^27 + 47*b2 * q^29 - 17*b3 * q^31 + 144 * q^33 + 84*b1 * q^35 + 94*b2 * q^37 + 36*b3 * q^39 - 294 * q^41 + 188*b1 * q^43 + 9*b2 * q^45 - 146*b3 * q^47 + 245 * q^49 - 162*b1 * q^51 - 215*b2 * q^53 + 48*b3 * q^55 + 12 * q^57 + 252*b1 * q^59 - 26*b2 * q^61 + 63*b3 * q^63 + 144 * q^65 - 628*b1 * q^67 + 150*b2 * q^69 + 2*b3 * q^71 - 1006 * q^73 - 339*b1 * q^75 - 336*b2 * q^77 + 387*b3 * q^79 + 81 * q^81 + 720*b1 * q^83 - 54*b2 * q^85 + 141*b3 * q^87 - 1482 * q^89 - 1008*b1 * q^91 + 51*b2 * q^93 + 4*b3 * q^95 + 1822 * q^97 - 432*b1 * q^99 $$\\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 36 q^{9}+O(q^{10})$$ 4 * q - 36 * q^9 $$4 q - 36 q^{9} + 216 q^{17} + 452 q^{25} + 576 q^{33} - 1176 q^{41} + 980 q^{49} + 48 q^{57} + 576 q^{65} - 4024 q^{73} + 324 q^{81} - 5928 q^{89} + 7288 q^{97}+O(q^{100})$$ 4 * q - 36 * q^9 + 216 * q^17 + 452 * q^25 + 576 * q^33 - 1176 * q^41 + 980 * q^49 + 48 * q^57 + 576 * q^65 - 4024 * q^73 + 324 * q^81 - 5928 * q^89 + 7288 * q^97\n\nBasis of coefficient ring\n\n $$\\beta_{1}$$ $$=$$ $$\\zeta_{12}^{3}$$ v^3 $$\\beta_{2}$$ $$=$$ $$4\\zeta_{12}^{2} - 2$$ 4*v^2 - 2 $$\\beta_{3}$$ $$=$$ $$-2\\zeta_{12}^{3} + 4\\zeta_{12}$$ -2*v^3 + 4*v\n $$\\zeta_{12}$$ $$=$$ $$( \\beta_{3} + 2\\beta_1 ) \/ 4$$ (b3 + 2*b1) \/ 4 $$\\zeta_{12}^{2}$$ $$=$$ $$( \\beta_{2} + 2 ) \/ 4$$ (b2 + 2) \/ 4 $$\\zeta_{12}^{3}$$ $$=$$ $$\\beta_1$$ b1\n\n## Character values\n\nWe give the values of $$\\chi$$ on generators for $$\\left(\\mathbb{Z}\/192\\mathbb{Z}\\right)^\\times$$.\n\n $$n$$ $$65$$ $$127$$ $$133$$ $$\\chi(n)$$ $$1$$ $$1$$ $$-1$$\n\n## Embeddings\n\nFor each embedding $$\\iota_m$$ of the coefficient field, the values $$\\iota_m(a_n)$$ are shown below.\n\nFor more information on an embedded modular form you can click on its label.\n\nLabel $$\\iota_m(\\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$\n97.1\n 0.866025 + 0.500000i \u22120.866025 + 0.500000i \u22120.866025 \u2212 0.500000i 0.866025 \u2212 0.500000i\n0 3.00000i 0 3.46410i 0 \u221224.2487 0 \u22129.00000 0\n97.2 0 3.00000i 0 3.46410i 0 24.2487 0 \u22129.00000 0\n97.3 0 3.00000i 0 3.46410i 0 24.2487 0 \u22129.00000 0\n97.4 0 3.00000i 0 3.46410i 0 \u221224.2487 0 \u22129.00000 0\n $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles\n\n## Inner twists\n\nChar Parity Ord Mult Type\n1.a even 1 1 trivial\n4.b odd 2 1 inner\n8.b even 2 1 inner\n8.d odd 2 1 inner\n\n## Twists\n\nBy twisting character orbit\nChar Parity Ord Mult Type Twist Min Dim\n1.a even 1 1 trivial 192.4.d.c 4\n3.b odd 2 1 576.4.d.c 4\n4.b odd 2 1 inner 192.4.d.c 4\n8.b even 2 1 inner 192.4.d.c 4\n8.d odd 2 1 inner 192.4.d.c 4\n12.b even 2 1 576.4.d.c 4\n16.e even 4 1 768.4.a.f 2\n16.e even 4 1 768.4.a.o 2\n16.f odd 4 1 768.4.a.f 2\n16.f odd 4 1 768.4.a.o 2\n24.f even 2 1 576.4.d.c 4\n24.h odd 2 1 576.4.d.c 4\n48.i odd 4 1 2304.4.a.x 2\n48.i odd 4 1 2304.4.a.bk 2\n48.k even 4 1 2304.4.a.x 2\n48.k even 4 1 2304.4.a.bk 2\n\nBy twisted newform orbit\nTwist Min Dim Char Parity Ord Mult Type\n192.4.d.c 4 1.a even 1 1 trivial\n192.4.d.c 4 4.b odd 2 1 inner\n192.4.d.c 4 8.b even 2 1 inner\n192.4.d.c 4 8.d odd 2 1 inner\n576.4.d.c 4 3.b odd 2 1\n576.4.d.c 4 12.b even 2 1\n576.4.d.c 4 24.f even 2 1\n576.4.d.c 4 24.h odd 2 1\n768.4.a.f 2 16.e even 4 1\n768.4.a.f 2 16.f odd 4 1\n768.4.a.o 2 16.e even 4 1\n768.4.a.o 2 16.f odd 4 1\n2304.4.a.x 2 48.i odd 4 1\n2304.4.a.x 2 48.k even 4 1\n2304.4.a.bk 2 48.i odd 4 1\n2304.4.a.bk 2 48.k even 4 1\n\n## Hecke kernels\n\nThis newform subspace can be constructed as the kernel of the linear operator $$T_{5}^{2} + 12$$ acting on $$S_{4}^{\\mathrm{new}}(192, [\\chi])$$.\n\n## Hecke characteristic polynomials\n\n$p$ $F_p(T)$\n$2$ $$T^{4}$$\n$3$ $$(T^{2} + 9)^{2}$$\n$5$ $$(T^{2} + 12)^{2}$$\n$7$ $$(T^{2} - 588)^{2}$$\n$11$ $$(T^{2} + 2304)^{2}$$\n$13$ $$(T^{2} + 1728)^{2}$$\n$17$ $$(T - 54)^{4}$$\n$19$ $$(T^{2} + 16)^{2}$$\n$23$ $$(T^{2} - 30000)^{2}$$\n$29$ $$(T^{2} + 26508)^{2}$$\n$31$ $$(T^{2} - 3468)^{2}$$\n$37$ $$(T^{2} + 106032)^{2}$$\n$41$ $$(T + 294)^{4}$$\n$43$ $$(T^{2} + 35344)^{2}$$\n$47$ $$(T^{2} - 255792)^{2}$$\n$53$ $$(T^{2} + 554700)^{2}$$\n$59$ $$(T^{2} + 63504)^{2}$$\n$61$ $$(T^{2} + 8112)^{2}$$\n$67$ $$(T^{2} + 394384)^{2}$$\n$71$ $$(T^{2} - 48)^{2}$$\n$73$ $$(T + 1006)^{4}$$\n$79$ $$(T^{2} - 1797228)^{2}$$\n$83$ $$(T^{2} + 518400)^{2}$$\n$89$ $$(T + 1482)^{4}$$\n$97$ $$(T - 1822)^{4}$$","date":"2022-11-29 18:10:09","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9950892925262451, \"perplexity\": 9244.963861430728}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710710.91\/warc\/CC-MAIN-20221129164449-20221129194449-00652.warc.gz\"}"}
| null | null |
Maricaona reimoseri är en insektsart som beskrevs av Rauno E. Linnavuori 1959. Maricaona reimoseri ingår i släktet Maricaona och familjen dvärgstritar. Inga underarter finns listade i Catalogue of Life.
Källor
Dvärgstritar
reimoseri
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,856
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Becoming an Odyssey of the Mind Coach will probably be one of the most rewarding volunteer roles you will ever have.
By becoming a coach you will have the opportunity to work with a team of 7 kids to facilitate creative problem solving, team building and brainstorming. You do not need to be an expert in a particular area, you just need to have a passion to see kids grow and learn.
Coaches facilitate the team's needs (meeting place, transportation, review of program rules, etc), but the students do all the work! The coach keeps the team on task, encourages them to be creative and work as a team, but does not provide assistance to the solution of the problem.
More detailed guidance will be sent as part of the membership package and program guide once the national membership dues are paid. As a coach, you will be honored and entertained while keeping your team on track. Teams tend to meet a couple of hours once every 1 or 2 weeks in the fall, then may increase the time or frequency as the tournament nears.
All coaches are required to attend regional training (new and veteran) and long term training. Please make sure to RSVP to confirm your attendance and receive further training details. We look forward to seeing you at one of the following meetings.
No current coaches training dates yet. Please check back soon.
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{
"redpajama_set_name": "RedPajamaC4"
}
| 9,334
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Q: How to call system with VAR=$VAL passed to called program? I'm using Strawberry Perl (latest) on Windows 7 (fully patched). I'm trying to invoke nmake to compile a library. The makefile is OK and I use it manually. Next I want to automate it.
I'm having trouble getting some Perl correct. I have the following:
#!/usr/bin/env perl
use strict;
use warnings;
my $DEBUG32_CXXFLAGS="/DDEBUG";
system('nmake', '/f', 'cryptest.nmake', 'CXXFLAGS="$DEBUG32_CXXFLAGS"');
It results in:
cl.exe EBUG32_CXXFLAGS /Yc"pch.h" /Fp"pch.pch" /c pch.cpp
Microsoft (R) C/C++ Optimizing Compiler Version 16.00.40219.01 for x64
Copyright (C) Microsoft Corporation. All rights reserved.
cl : Command line warning D9024 : unrecognized source file type 'EBUG32_CXXFLAGS
', object file assumed
cl : Command line warning D9027 : source file 'EBUG32_CXXFLAGS' ignored
pch.cpp
cl.exe EBUG32_CXXFLAGS /c cryptlib.cpp
According to how to pass arguments to system command in perl, I'm supposed to use the dollar sign for the scalar variable. Searching for terms like "how to pass a scalar variable through system" keeps leading back to the Stack Overflow question and answer.
Attempting to use variations, like 'CXXFLAGS="DEBUG32_CXXFLAGS"', 'CXXFLAGS="${DEBUG32_CXXFLAGS}"' and others results in similar Perl breaks.
I'm using single quotes because system(nmake, /f, cryptest.nmake); and system("nmake", "/f", "cryptest.nmake") did not work as expected. These are close to the cited question and answer.
Eventually I am going to need to pass a real name value pair. That would be closer to something like DEBUG_CXXFLAGS = /nologo /W4 /wd4511 /D_MBCS /Zi /TP /GR /EHsc /MD /FI sdkddkver.h /FI winapifamily.h
How do I call system with VAR=$VAL passed as an argument to the called program?
Thanks in advance
> perl.exe --version
This is perl 5, version 22, subversion 1 (v5.22.1) built for MSWin32-x64-multi-thread
A: Variables only get expanded in double quoted strings. You can use single quotes around the parameters that don't include variables, but you'll need to switch to double quotes for the ones that do.
The next problem is that you want to include a double quote character in the string that uses double quotes as a delimiter. To achieve that, use a backslash character to escape each double quote inside the string:
my $DEBUG32_CXXFLAGS="/DDEBUG";
system('nmake', '/f', 'cryptest.nmake', "CXXFLAGS=\"$DEBUG32_CXXFLAGS\"");
Another approach is to use the qq double quote operator which provides the double quote context you need for variable interpolation, but allows you to chose the delimiter. In this example I chose to use curly braces to delimit the string:
system('nmake', '/f', 'cryptest.nmake', qq{CXXFLAGS="$DEBUG32_CXXFLAGS"});
More details can be found in the docs on Quote and Quote like Operators.
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,476
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/**
*
*/
package com.xinfan.msgbox.http.common;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
/**
* @author cyp
*
*/
public class ServiceContext {
private static ThreadLocal<HttpServletRequest> requestLocal = new ThreadLocal<HttpServletRequest>();
private static ThreadLocal<HttpServletResponse> responseLocal = new ThreadLocal<HttpServletResponse>();
public static void bind(HttpServletRequest request, HttpServletResponse response) {
requestLocal.set(request);
responseLocal.set(response);
}
public static void unbind(HttpServletRequest request, HttpServletResponse response) {
requestLocal.remove();
responseLocal.remove();
}
public static HttpServletRequest getRequest() {
return requestLocal.get();
}
public static HttpServletResponse getResponse() {
return responseLocal.get();
}
}
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{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,148
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Lance still isn't entirely comfortable with this.
Larry said he wasn't sorry.
Judith wanted to find out who was the artist who was playing violin in such a manner in an Arkansas forest.
Howard doesn't want to sleep.
Krzysztof and I both agree with you.
Jeffie is a man of many talents.
Is it possible that a Hungarian sea has ever existed?
Please write down what Tollefsen says.
Srinivasan did more than that.
Nhan sang while he worked.
You should tell Anne what happened.
Dean doesn't think that Dawson was the one who did that.
Bucky posted an unboxing video, but it's extremely boring.
Dave told Harold to listen carefully, but she didn't.
Marcos and Archie both wanted to make each other happy.
Bernie is going to come and visit.
Nathaniel and Ted's relationship became strained.
Betsy had expected Joel to be there, too.
Pitawas tried to ignore the problem.
Irfan had a new scar on his forehead since the last time Janos had seen him.
Laurel has run away from home.
Jakob saves about 30% of what he earns.
Jenine was afraid he was going to die.
Adrian was disturbed at the direction of his thoughts.
This car was cheap enough for him to buy.
Nicholas got into his car.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,903
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Just practiced texture and metals tonight. More tomorrow.
Hi, I'm an artist and designer living in Atlanta. I love game design, logos, and lately a bit of oil painting. Have a look around and feel free to follow me on instagram, tumblr, or twitter to keep up with newly shared images. Also I stream my painting and dev occasionally on Twitch. Thanks for visiting!
Use these social media links to stay in touch.
The cards came in today & they look great! Thanks for such a cool logo.
I've used Joseph Knight for many of my priority projects the last 5 years and he never ceases to impress me! Anyone would be impressed by his creativity and technical skills as well as his knowledgeable, efficient, and friendly personality. Joseph's advice and assistance continues to be invaluable to myself and my network.
I can't thank you enough for your attention to detail and hard work. You have a client for life!!!! I compared our logo to some of the major companies like GE, Microsoft, etc and I swear I think ours is better.
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{
"redpajama_set_name": "RedPajamaC4"
}
| 8,773
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Matches for "Jugette"
Alexa's Power strong horse in $230,700 Jugette
Alexa's Power proved to be the strong horse Wednesday as she overpowered pacesetter Strong Opinion at the top of the stretch to capture the 48th annual $230,7000 Jugette at Delaware, Ohio. The classic grand circuit event for harness racing three-year-old pacing fillies saw the 19th race feature began with betting favorite Youaremycandygirl and driver Yannick Gingras going off-stride at the start of the race and was never in contention. Strong Opinion and driver Chris Page go right to the front from post one with Alexa's Power and driver Tim Tetrick grabbing the two-hole spot as they sped to the opening quarter mile in :26.4. Then coming to the half mile marker, driver Tim Tetrick came out from the inside in post two and sit there as no one was coming from behind to force him to go on as they went to the half in :55.2. E Dee's Well Said (Jim Pantaleano) at 62-1 odds, filled the gap behind Strong Opinion. Going to the three-quarters in 1:22.4, Strong Opinion was still in command with Alexa's Power stalking them on the outside. Then in the stretch, Alexa's Power and Tetrick wore down Strong Opinion and went on to win by one length in 1:51.2. E Dee's Well Said came on for second place with Strong Opinion third. "I had about 100 ideas flowing through my head behind the starting gate," said winning driver Tim Tetrick. "I saw Yannick's (Gingras) horse (Youaremycandygirl) make a misstep and I didn't want to fall too far back so we went to the two-hole and figured to outmuscle most of them from there. "She really raced her butt off today," Tetrick said. "She was just super." Sired by Somebeachsomewhere, it was the 9th win in 15 starts this year for Alexa's Power. She is trained by Jim Campbell and owned and bred by Jeffery and Michael Snyder of New York, NY. She paid $3.80 to win. "This is my first Jugette," said winning trainer Jim Campbell. "It's so exciting. We've had a really good year with Alexa all season, Timmy has driven her since her first qualifier. We have had a lot of fun and this win is the best." Jim Campbell did say that they had made an equipment change on Alexa's Power, adding a pull-down bridle that she was using for the first time today. This year's Jugette was named in Memory of Hall of Fame Communicator, Laverne A. Hill. To see the 2018 Jugette replay go to https://youtu.be/emEv23NX-io On Thursday is the $627,000 Little Brown Jug for the colts with two elimination divisions followed by heats until one horse has won twice. By Steve Wolf, for Harnesslink
$642,000 Little Brown Jug heads huge Grand Circuit
This Week: Delaware Grand Circuit, Delaware County Fair, Delaware, Ohio; Caesars Trot, Hoosier Park Pacing Derby, Jenna's Beach Boy, Kentuckiana Stallion Management Stakes, Moni Maker and The Elevation, Hoosier Park, Anderson, Ind.; and Metro, She's A Great Lady and Milton finals, Woodbine Mohawk Park, Milton, Ontario. Schedule of events: Grand Circuit harness racing action kicks into full gear on Wednesday (Sept. 19) at Delaware with the $230,700 Jugette for 3-year-old filly pacers, the $82,200 Buckette for 3-year-old filly trotters, the $40,918 Standardbred for 2-year-old filly trotters and the $39,318 Standardbred for 2-year-old filly pacers. The Thursday (Sept. 20) card at Delaware is highlighted by the $642,000 Little Brown Jug, the third leg of Pacing's Triple Crown for 3-year-olds. Also on tap that day is the $107,000 Miss Versatility final for older trotting mares, the $111,075 Old Oaken Bucket for 3-year-old male trotters, the $48,218 Standardbred for 2-year-old colt trotters and the $40,418 Standardbred for 2-year-old colt pacers. Grand Circuit racing at Hoosier Park will be held on Friday (Sept. 21) with the $200,000 Caesars Classic for Open trotters, the $236,000 Kentuckiana Stallion Management stakes for 2-year-old filly trotters, the $207,000 Kentuckiana Stallion Management stakes for 2-year-old filly pacers, the $177,000 Hoosier Park Pacing Derby for Open pacers, the $172,000 Moni Maker for 3-year-old filly trotters, the $155,000 Jenna's Beach Boy for 3-year-old colt pacers, and the $120,000 Elevation for 2-year-old colt pacers. Grand Circuit action at Woodbine Mohawk will be held on Saturday (Sept. 22) with the C$890,000 Metro final for 2-year-old open pacers, the C$590,000 She's A Great Lady for 2-year-old filly pacers and the C$255,000 Milton for older pacing mares. Complete entries for the races at the U.S. tracks are available at this link. Entries for the Woodbine Mohawk Park races are available at this link. Last time: The Grand Circuit spotlight was on Woodbine Mohawk Park this past Saturday, with the finals of four major stakes, led by the $512,050 Canadian Trotting Classic. It was a hoof-to-hoof heavyweight battle from start to finish, with Crystal Fashion coming out on top in the final strides. Crystal Fashion was a 1:52.1 winner in the Canadian Trotting Classic. Saddled with the daunting post 10, Crystal Fashion, a bay son of Cantab Hall, needed a little racing luck and plenty of grit to get the job done in Canada's richest trotting event of 2018 and the Jim Campbell trainee had plenty of the latter. Sent off as the 5-2 second choice to 3-5 Met's Hall, Crystal Fashion, piloted by Tim Tetrick, was full of trot as the gate took off from the field of 11 sophomore stars. After taking his rivals through an opening quarter in :27.3, Crystal Fashion then found himself sitting in the second spot once Met's Hall, with Andy Miller driving, went from second to first. The see-saw tussle between the leaders continued through a half in :56.2 and three-quarters in 1:25, with the final round coming as the field straightened for home. Down the stretch, Crystal Fashion, on the outside, and Met's Hall, to his inside, put on a show for the packed house at Woodbine Mohawk Park. At the wire, Crystal Fashion ($7.90 to win) eked out a hard-fought half-length triumph over his rival, in 1:52.1. Fiftydallarbill was third, while Lawmaker was fourth. "It worked out good today," said Tetrick who two races earlier teamed with Green Manalishi S to win the William Wellwood Memorial. "We got out of there good and got on the right foot. He crossed over well, in-hand, and the favorite came and we had to let him go, so I got a dream trip." It was lifetime win No. 13 from 25 starts for the bay gelding, owned by Fashion Farms. In 13 starts this year, Crystal Fashion, bred by Hanover Shoe Farms, has nine wins and a trio of seconds. Complete recaps of all the races are available at the Grand Circuit website. Grand Circuit Standings: In 2018, the Grand Circuit leaders in three categories (driver, trainer and owner) will once again be tracked on a points system (20-10-5 for the top three finishers in divisions/finals and 10-5-2 for the top three finishers in eliminations/legs). Winbak Farms is the sponsor for the 2018 Grand Circuit awards. Here are the leaders following the past weekend. Drivers: 1. Tim Tetrick - 910.5; 2. Yannick Gingras - 862.5; 3. David Miller - 571.5; 4. Scott Zeron - 409; 5. Jordan Stratton - 288. Trainers: 1. Ron Burke - 712.5; 2. Jimmy Takter - 664; 3. Tony Alagna - 464; 4. Jim Campbell - 296; 5. Erv Miller - 267. Owners: 1. Fashion Farms - 209; 2. Burke Racing Stable - 158.2; 3. Weaver Bruscemi - 151.9; 4. Brittany Farms - 149.9; 5. Brad Grant - 124.3. Looking ahead: Grand Circuit action will be taking place next week at Lexington's historic Red Mile. There will be eight Bluegrass stakes for 2- and 3-year-olds of both sexes and gaits. Hollywood Dayton Raceway will also be hosting a pair of Grand Circuit events, the Dayton Pacing Derby and the Dayton Trotting Derby for older horses and Harrah's Philadelphia will contest John Simpson Stakes for 2-year-old pacers and trotters of both sexes. by Paul Ramlow, for the Grand Circuit
Youaremycandygirl leads entries for $230,700 Jugette
Youaremycandygirl, winner of fifteen of 22 career races, headlines a field of eight filly pacers in the $230,700 Jugette on Wednesday, September 19th at the Delaware County Fair. The fillies will race one heat to determine the Jugette champion. The daughter of American Ideal owns a lifetime mark of 1:48 2/5 and has earned $1,263,536. The Ron Burke trainee will leave from post #3 and will be piloted by Yannick Gingras for owner W. J. Donovan. She was the 207 Breeders Crown champion and in 2018 won the $270,425 Empire Breeders Classic and the $96,600 Shady Daisy. The main challenge to Youaremycandygirl should come from Alexa's Power from post #5. The Somebeachsomewhere lass has earned $405,195 for Jeffrey and Michael Snyder and trainer Jim Campbell. The ultra-consistent Alexa's Power has finished on the board in 11 straight races and will be piloted by Trace Tetrick. Post time for the Wednesday card at the Delaware County Fair will be 11:00 AM. The simulcast program will start at 10:30 AM. Post positions for the $230,700 Jugette PP - Horse (Driver/Trainer) 1. Strong Opinion (Chris Page/Ron Burke) 2. Sansovina Hanover (Matt Kakaley/Ron Burke) 3. Youaremycandygirl (Yannick Gingras/Ron Burke) 4. E Dee's Well Said (Jim Pantaleano/Christen Pantaleano) 5. Alexa's Power (Trace Tetrick/Jim Campbell) 6. Sidewalk Dancer (Scott Zeron/Chris Oakes) 7. Solitary (Brett Miller/Nick Surick) 8. Aldine Hanover (Marcus Miller/Erv Miller) by Jau Wolf, for the Little Brown Jug
Jugette Entry Box remains open
The entry box of the 48th Jugette will remain open until Sunday (September 16) at 10:00 AM. Race officials discovered that the entry information on a website contained conflicting information. "In an overabundance of caution, we want to make sure no horsemen were using the conflicting information to make their entires. Therefore, we are going to use a three day box for this year's Jugette," noted Tom Wright, Director of Racing. The 73rd Little Brown Jug will remain in a five day box and entries must be received by Saturday, September 15 at 10:00 AM. Questions and concerns should directed to the Log Cabin by calling (740) 363-6000. by Jay Wolf, for the Little Brown Jug
Caviart dreams come true
Trenton, NJ --- Judy and Buck Chaffee have been parents and harness racing horse owners for more than three decades. But they never had the pleasure of both coming together so joyfully as they did during a four-day span last month. On Sept. 20, the Chaffees experienced the biggest racing triumph of their 33 years in the business when Caviart Ally won the $163,950 Jugette Stakes final for 3-year-old female pacers in Delaware, Ohio. While they could not witness the event in person, it was for a good reason as they were at their Vienna, Va., home with daughter Drew and her husband Kevin, awaiting the arrival of their grandson. "The baby was due at any moment," Judy Chaffee said. "She was having contractions that day, which did stop." They re-started and remained four days later, when Tyler Grayson Fahrendorff came into the world at 20 inches long; weighing 7 pounds, 14 ounces. "It's been quite an experience for us," said Judy, who said she and Buck had not come off Cloud Nine more than a week later. "I don't think we've ever had a more stressful day. Not only could the baby have come but we actually had two fillies racing in the Jugette that day and it was quite a rollercoaster of emotions. "Our filly, Jaye's A Lady, raced first. We were hoping she would do well and make the final, and she broke stride right at the start. So, that was a low feeling at that moment. Then we went from Jaye to Ally. We went from one extreme to the other. It was quite a day. We've experienced it all over the years, but I think this is the highest we ever felt." The Chaffees watched it all unfold on the Internet and were also getting phone updates from son Terry, who operates their Caviart Farms in Paris, Ky. They wanted to be at the race, but they knew they would not have enjoyed it had they left Drew and Kevin alone. "Their little girl was staying with us in case she had to go to the hospital," Judy said. "As much as we would have loved to have been there, we opted to stay home for our daughter because we'd be taking care of their little girl while she was in the hospital. We had a choice to make, and like with everything else, I think family has to come first." Especially when it comes to the Chaffees, as their current standing as breeders and owners has been handed down through the generations. Judy's maternal grandfather, Lowell Chapman, was a Standardbred owner in Maine who raced on the New England and Canadian circuits. Judy met him a few times but was so young, that the two never really talked about racing. "But I think I inherited the love of horses from him," Chaffee said. "My mother and father went to the races and I used to have to babysit my sister when they went. I got to go sometimes, but I never realized I would ever be part of it. My mother (who has passed away) would speak about that, and we both agreed my grandfather and I would have a ball together. We would be going to (the sales) together. It would have been quite a bonding experience and we would have loved experiencing it." Photo courtesy of Judy Chaffee Judy Chaffee's love of horses has been handed down through the generations. In 1978, however, Judy saw herself as a career journalist. Working as a reporter for the Portland Press Herald, she met architect Clarence "Buck" Chaffee at a project meeting at the selectman's office. Judy met him as "Buck", which probably helped get the relationship started as opposed to the alternative of the given name. "He was named after his father, and they were looking for something to call him so they wouldn't be called the same," Judy said. "His aunt came up with the name Buck; I'm glad she did." Their chemistry was immediate and the two began dating. Shortly thereafter, Buck was moving from Maine back to his home state of Virginia and Judy gave up her newspaper career to join him. When it came time to meet her future in-laws, Buck and Judy were greeted by a note on the door that said, "Meet us at Rosecroft." It was then, that Judy discovered Buck's parents raised and raced horses in the Mid-Atlantic area, most notably at Rosecroft and Freestate. "It's funny, when Buck and I met each other we never even mentioned horses," Judy said. "It turned out we both loved the horses and the racing." The two married within the same year they met and the first of seven children came shortly thereafter. "I expected to work as a reporter, I guess, forever," Judy said. "When Buck and I started to have a family, I became a stay at home mom and raised the family." As the family grew, so did their love of racing. One day in 1984, Buck and Judy decided to attend the Standardbred Horse Sale in Harrisburg, Pa., as spectators only. It would turn out to be a milestone day in their lives. "We were watching the sale progress; and Buck turned to me and said, 'Which would you rather have, a house or a horse?' and I said, 'A horse,'" Judy recalled. "We bought our first horse, her name was Good Tal. So that was the beginning, and we've had horses ever since." But not without some immediate trepidation. "When we bought her," Judy said with a laugh, "Buck looked at me and said, 'What do we do now?'" As luck would have it, an Ohio resident sitting behind them was eavesdropping. "He told us, 'Send it to Joe Adamsky, he's a good, honest horseman,'" Judy said. Photo courtesy of Judy Chaffee Buck and Judy Chaffee with trainer Nancy Johansson. The Chaffees did just that, and Good Tal became a stakes champion in Ohio. The couple remained lifelong friends with Joe (who has since passed away) and his wife and had him train several other horses. After Good Tal, Buck and Judy began adding to their stable and raising them on Buck's parents' family farm in Fredericksburg, Va. "Every year we tried to buy a horse or two and we had some success," Chaffee said. "Nothing that was like Ally or anything, but we enjoyed it. We've had horses with (Ohio trainer) Jim Arledge for quite a while." Arledge worked with Caviart Sydney, whose biggest win came over My Little Dragon in the 2006 Matron Stakes for 3-year-old filly pacers, and Sydney's mother, Caviart Sierra. "Basically, Sydney was racing against My Little Dragon and Darlin's Delight during those 2- and 3-year-old years," Judy said. "She didn't beat them except for this one race. But she was there all the time. Sierra won her first five races, which were all stakes races, but then she was injured and it basically ended her career and she became a broodmare for us." In 2007, after several years of intense research, the Chaffees purchased their Kentucky farm on Winchester Road -- the famed Avenue of Champions. "We always wanted to have a breeding farm once we got in the business," Judy said. "We used to go to Kentucky and we just looked for a farm there. Buck was busy working so Terry and I went and picked out a farm. It's 225 acres and it works well for us, there's room to expand. We have 18 broodmares, and the yearlings and the foals." They named it Caviart Farms because of Judy's penchant for the 1980s TV show "Lifestyles of the Rich & Famous," hosted by Robin Leach. "He would end the show and say, 'Champagne wishes and caviar dreams,'" Judy said. "I liked the caviar dreams and we did have caviar dreams. Buck said, 'I like it better with a T on the end,' so that's where Caviart came from." So, it was a case of pretty much making up words? "Basically, yes," Judy said with a laugh. Terry runs the farm and is on the phone with his mom constantly while Buck tends to his consulting business that he started 10 years ago. "This is my profession now," Judy said. "I pick out the stallions, I keep track of the ovulation of the mares and tell Terry who to check each date and so forth. I handle the paperwork part of it and Terry runs the farm. He's amazing and so good with the horses, I can't speak highly enough of him. We couldn't possibly have the business without him. "Terry is the only one who's fulltime but all our kids take an interest. After we won the Jugette, I was on the phone with my daughter Drew and I was like, 'We just won the Jugette!' She texted all the other brothers and sisters and everyone was watching the replay. They're all very interested in how we're doing but they don't actually work in the business." Nigel Soult photo In her first start since the Jugette, Caviart Ally won the second of two divisions of the Bluegrass 3-year-old filly pace in 1:51 on Oct. 1 at Red Mile. Caviart's main trainers are Arledge, Nancy Johansson and Noel Daley, who trains Caviart Ally. Daley recommended the purchase of Caviart Ally, as he worked with family member All Speed Hanover. The Chaffees were actually looking to upgrade by purchasing a filly broodmare at Harrisburg, but figured if the horse could race, they would do that as well. They got Caviart Ally for $35,000. "Noel looked at her and said she didn't look like All Speed because he was taller, but he thought she was the right size and looked perfect for a Bettor's Delight (sired horse) so we bought her and she has become everything," Chaffee said. "She's become our best racing filly ever and will certainly be at the top of our list for broodmares once she gets there. We'll race her at least another year, maybe two years before we look to breed her. "Ally certainly owns our hearts. It's been a long time coming and it's been a dream, and it finally happened." After the win, Judy posted on her Facebook page, "The biggest and best day ever in racing!!! Thank you Caviart Ally -- and trainer Noel Daley, driver Andy McCarthy, son Terry Chaffee who is COO of our farm and represented us at Delaware -- and all of Team Daley. And thank you to my husband who allows me to fulfill my dreams with the horses!!!" Indeed, the happiest part of this story is that going into the horse business together only helped to strengthen Buck and Judy's already solid marriage. "It's been great," Judy said. "We generally agree on everything and if we don't, we work it out. So, we've never had any problems. We both love the horses, we love the racing. We both get excited together and we share the experience. So, if anything I think it's a wonderful thing for a marriage." A marriage that experienced four days in September that will certainly be one of its high points. by Rich Fisher, USTA Web Newsroom Senior Correspondent
Noel Daley & Andrew McCarthy win Jugette
Caviart Ally and harness racing driver Andrew McCarthy showed why they were the best Wednesday afternoon as the pair won the 47th $273,250 Jugette at the Delaware County Fair on Wednesday afternoon. In the $163,950 second and final heat, Blazin Britches (Trace Tetrick) and Caviart Ally used the inside positions that they earned in the eliminations to sprint out the early lead as the field of eight passed the quarter mile pole in :27 3/5. Blazin Britches kept Caviart Ally behind her through the half in :55 4/5. McCarthy tipped the eventual winner off the rail at the three-quarters in 1:23 3/5. The crowd urged the pair down the lane and Caviart Ally cleared by ¾ of a length in 1:51 3/5. Obvious Blue Chip (Scott Zeron) rounded out the top three. New Zealand native, Noel Daley trains the Bettor's Delight filly for Caviart Farms. McCarthy, an Australian native, won the Jugette for the first time, capping a three win day at the Delaware County Fair. In the second elimination, Caviart Ally used the inside post and took control of the race and went by the ¼ mile pole in :27 1/5. Idyllic Beach (Yannick Gingras) was the first to challenge the pacesetter as the field approached the half mile station in :56 3/5. McCarthy asked his charge for more and Caviart Ally opened up at the three-quarters in 1:23 4/5. Caviart Lady won by 5 lengths over Tequila Monday (David Miller). Idyllic Beach hung on for third and Ella Christina (Tim Tetrick) advanced to the final with her fourth place finish. The first $54,650 elimination went to Blazin Britches by 2¼ lengths over Obvious Blue Chip in 1:52 1/5. The Brian Brown trainee is owned by Emerald Highlands Farm. That pair hope to win the 72nd Little Brown Jug on Thursday. Jugette Day Undercard Driver Andrew McCarthy and trainer Noel Daley teamed up after their Jugette elimination win to take the $80,575 Buckette for three-year-old filly trotters. McCarthy used a perfect drive with Cool Cates to keep Satin Dancer (Ronnie Wrenn, Jr.) locked on the rail and sprinted home to win in 1:56. The Yankee Glide filly, a $35,000 yearling purchase, has now won more than $250,000 for the All Laid Out Stables. Seventeen three-year-old colt trotters competed in the $94,334 Ohio Breeders Championship. Trainer Chris Beaver swept the two divisions with Buckeye Boss (Aaron Merriman) in the first division and Fraser Ridge (Ronnie Wrenn, Jr.) in the second. Fraser Ridge established a national season's record of 1:55 in the second $47,167 division with a 4½ length win over Full Surge (Mike Wilder). Fraser Ridge has won three in a row for Donald Robinson, Robert Mondillo, Beaver and RBH Ventures. Buckeye Boss took the second division in 1:55 3/5 over Jailhouse Sam (Hugh Beatty) and Dejarover (David Miller). The winner is owned by Beaver, Marion Beachy and Synerco Ventures. Three divisions of the $130,000 OBCs for freshman pacing fillies were held with Prsntpretynperfect taking the fastest division in 1:54 3/5. Prsntpretynperfect (Kayne Kauffman) overcame post #7 and was able to sit behind the leading Princess Rougarou (Yannick Gingras) until the final turn and sprinted clear to score by three lengths. The daughter of Big Bad John has now won six of seven starts this season for owners Jennifer Brown, Richard Lombardo and Joshua Green and trainer Brian Brown. Baron Remy (Chris Page) won the second $43,333 division in 1:54 4/5. Baron Remy belongs to Burke Racing Stable, Silva, Pumel & Libby, Lawrence Karr and Weaver Bruscemi. The nation's leading trainer Ron Burke conditions the Yankee Cruiser filly. Pearl Crush (Ryan Stahl) took the first division over Shadows On Time (Ronnie Wrenn, Jr.) and Delicate Arch (Yannick Gingras) in a lifetime best 1:55 3/5. The Yankee Cruiser filly is conditioned by Ron Potter for Clyde Perfect. Two-year-old filly trotters competed in a pair of divisions of the $113,400 (div) Ohio Breeders Championships. The first division featured a classic stretch duel between Looking For Zelda (Tony Hall) and Risky Deal (David Miller). The Break The Bank K fillies were nose-to-nose through the lane with Risky Deal getting the last call in a lifetime best 1:57. Crist Hershberger trains the winner for Deborah Kvernmo To Russia (Ryan Stahl) used a final turn move to win the second $56,700 division in 1:58 2/5 over Red Storm (Aaron Merriman) and She's Got Pizazz (Brett Miller). The Manofmanymissions filly now has $104,380 on her card for owner Parent Racing Stable and trainer Scott Cox. The $12,900 OBC for aged trotters went to A Tc Queenie (Dan Noble) in 1:54 3/5. The 4 year-old Triumphant Caviar mare is owned by Trish Soulsby and Richard Schault and trained by Ron Steck. The 22 race Jug Day card features the $590,400 Little Brown Jug. Post time is 11:00 am. Jay Wolf
Jugette eliminations
Delaware, OH --- Blazin Britches won the $54,650 first elimination of the Jugette for harness racing 3-year-old female pacers in 1:52.1 on Wednesday (Sept. 20) at the Delaware County Fairgrounds. Obvious Blue Chip finished second, followed by Terrortina and Rockin Serena to advance to the final later this afternoon. Sent off at odds of 1-9, Blazin Britches and driver Trace Tetrick went to the lead on the first turn and never looked back, winning by 2-1/4 lengths. The filly, who has won 10 of 11 races this year, is trained by Brian Brown and owned by breeder Emerald Highlands Farm. Blazin Britches set fractions of :28.1, :57 and 1:24.4. Obvious Blue Chip tried to challenge heading around the final turn, but was unable to get within striking distance. "I wanted to be on the move to the front by the backside to try to control the race," Tetrick said. "I had plenty of mare left; it was just trying to get her to pay attention. She kind of got to daydreaming there a little bit. "She loves her job. When it was time to race she wanted to go forward. "She was a little headstrong earlier on and Brian went ahead and changed bits on her. Since then she has been perfect. She really loves her work." Caviart Ally romped to victory in the second $54,650 Jugette elimination, winning by open lengths in 1:52 for driver Andy McCarthy and trainer Noel Daley. Caviart Ally, the 8-5 favorite, led every step of the way. She pulled away from her rivals on the backstretch and was unthreatened from there. Tequila Monday finished second, followed by Idyllic Beach and Ella Christina to reach the final. Caviart Ally, a daughter of Bettor's Delight-Allamerican Cool owned by Caviart Farms, has won five of 14 races this year. She set fractions of :27.1, :56.3, and 1:23.4 on her way to victory. "She's very handy off the gate," McCarthy said. "You just have to chirp to her a little bit and she will get out of there as much as you want to. That definitely helped. She actually got a little bumpy on me coming out of the third turn. I think we were going too slow; she just wanted to get going. I had to let her pace out a little bit to get her smoothed out and she was good. "Over the last few months she has become much stronger," added McCarthy. "I used to always race from off the pace for that reason but I don't have to anymore. They did add Lasix as well, so that may have helped, but she is coming into her own." The post-position order for the $163,950 final is: 1. Blazin Britches, 2. Caviart Ally, 3. Obvious Blue Chip, 4. Tequila Monday, 5. Terrortina, 6. Idyllic Beach, 7. Ella Christina, 8. Rockin Serena. -- Kim French contributed to this report by Ken Weingartner, Harness Racing Communications
Eleven fillies vie for $273,250 47th Jugette
Blazin Britches, winner of nine of ten races this season, has been installed as the 6/5 morning line harness racing favorite in the $273,250 Little Brown Jugette three-year-old filly pace on Wednesday, September 20th at the Delaware County Fair. The daughter of the 2010 Little Brown Jug champion, Rock N Roll Heaven, owns a lifetime mark of 1:48 4/5 and has earned $203,392. The Brian Brown trainee will leave from post #3 in the first of two eliminations and will be piloted by Trace Tetrick for Emerald Highlands Farm. During her current five race win streak are wins in the $63,475 Adioo Volo, the $113,950 Shady Daisy and the $160,000 Nadia Lobell. Emerald Highlands and Brian Brown are also expected to challenge in the 72nd Little Brown Jug with Fear The Dragon. Obvious Blue Chip (Scott Zeron) is the second choice at 4-1 from post #4. Mark Steacy trains the daughter of Roll For Joe for NLG Racing and Stephen Klunowski. Obvious Blue Chip has earned $264,073 during her career. Caviart Alley is the favorite in the six horse second $54,650 elimination. Andrew McCarthy was named to pilot the daughter of Bettor's Delight for Caviart Farm. The Noel Daley trainee has been first or second in her last five starts. She owns a 1:50 2/5 mark and has earned $475,700 during her career. The second and third choices in the second elimination are Tequila Monday (Brett Miller) and Idyllic Beach (Yannick Gingras). The top four elimination finishers will advance to the $163,950 second heat. The winner of the second heat will be declared the Jugette champion. The complete Jugette field and announced drivers: PP Horse (Driver/Trainer) Morning Line Odds $54,650 First Elimination 1. Rockin Serena by Rockin Image - (Peter Wrenn/Melanie Wrenn) 9/2 2. Jaye's A Lady by Mcardle - (Yannick Gingras/Nancy Johansson) 8-1 3. Blazin Britches by Rock N Roll Heaven - (Trace Tetrick/Brian Brown) 6-5 4. Obvious Blue Chip by Roll With Joe - (Scot Zeron/Mark Steacy) 4-1 5. Terrortina by Western Terror - (Tony Hall/Norm Parker) 12-1 $54,650 Second Elimination 1. Caviart Ally by Bettor's Delight - (Andrew McCarthy/Noel Daley) 2-1 2. Roaring To Go by Art Major - (Brett Miller/Kevin Lare) 5-1 3. Tequila Monday by American Ideal - (Brett Miller/Chrs Oakes) 3-1 4. Ella Christina by Western Ideal - (Tim Tetrick/Nick Surrick) 6-1 5. Zoe Ellasen by Santanna Blue Chip - (Ronnie Wrenn, Jr./Ron Potter) 8-1 6. Idyllic Beach by Somebeachsomewhere - (Yannick Gingras/Jimmy Takter) 4-1 Jay Wolf
Campbell & McIntosh's Jugette
Delaware, Ohio - L A Delight and John Campbell in the sulky used a perfect pocket trip to win the $239,400 46th Jugette at the Delaware County Fair on Wednesday. First heat winner Call Me Queen Be (Scott Zeron) used his rail position to take the early lead. A leaving attempt by Blue Moon Stride (Andrew McCarthy) was thwarted by a break in stride allowing L A Delight into the two-hole and Pure Country (Brett Miller) into third. The top trio raced without further movement through the quarters of :27 1/5, :56 2/5 and 1:25. Campbell eased the winner off the rail in the final turn and edged past the pacesetting Call Me Queen Be by ¾ length in 1:51.3. Yankee Moonshine (Yannick Gingras) rallied for third and Pure Country (Brett Miller) held on for fourth. Robert McIntosh Stables, CSX Stables and Al McIntosh Holdings own the homebred daughter of Bettor's Delight, who earned $98,578 for her efforts. John Campbell hoisted the Jugette trophy for a record fifth time and trainer Bob McIntosh won for record tying third time. Campbell and McIntosh teamed up with So Fresh to capture the 1992 Jugette. World record set in first heat of Jugette In the $95,760 first heat, Call Me Queen Be grabbed the racetrack and took the lead before the field hit the first turn. Yankee Moonshine protected his rail position and sat second at the quarter in :26 4/5. Second tier starter Pure Country was the first to challenge the leader and was parked second at the half in :55. As the field headed to the ¾ mile pole, Scott Zeron asked his horse for more and she responded by opening drawing away from Pure Country. Using a :27 1/5 last quarter, Call Me Queen Be won by 4½ lengths over L A Delight and Pure Country in a world record record clocking of 1:50.1. Ella Christina Takes 2FP Standardbred David Miller guided Ella Christina to a narrow neck win over Caviart Cherie (Andrew McCarthy) and Kim's Desire (Yannick Gingras) in lifetime best 1:54 3/5. Miller sent the daughter of Western Ideal after the early lead and was allowed to control the field of eight through fractions of :27 4/5, :57 4/5 and 1:26 1/5. Pittstop Danika (Matt Kakaley) tried to pressure the winner but could not get past the leader and her :28 2/5 last quarter. Ella Christina is owned and trained by Nancy Johansson. Miss Tezsla Takes Buckette Miss Tezsla (Brett Miller) came off the rail at the three quarter pole and wore down the pacesetting Haughty III (Peter Wrenn) to win the $86,200 Buckette for three-year-old filly trotters in 1:55 1/5. Haughty III held on for second and Ultimate Shopper (Tim Tetrick) closed for third. Jimmy Takter trains the Andover Hall filly for the Miss Tezsla Stable. Ohio Breds In Action Uncle Leroy (Mike Wilder) took the lead just before the quarter mile pole and pulled away from his competitors to win the first division of the $96,300 (div.) Ohio Breeders Championships for sophomore colt trotters. The Neely Dunn gelding was a half length clear of Deep Question (David Miller) and Chips So Fast (Aaron Merriman) in 1:55 3/5. Uncle Leroy is owned by Cheryl Vigneron and trained by Charles Vigneron. The Ohio Sire Stake champion, Wegoferdaprize (Chris Page) took the second division in 1:56 2/5. The Next Triumph (Ronnie Wrenn, Jr.) and MJB Got Faith (Kayne Kauffman) and the eventual winner all battled for the lead in the final turn and late breaks in stride by The Next Triumph and MJB Got Faith sealed the victory for the And Away We Go gelding. The 3 1/2 length score was his eight win in a row for Curran Racing and trainer Jessica Millner. The final division was won by Lets Go Bucks (Dan Noble). The partisan crowd cheered the And Away We Go gelding to a 6 1/2 length victory over Roundtown Rocker (Peter Wrenn) and Speedy Translation (Kurt Sugg) in 1:54 4/5. Jim Dailey trains Lets Go Bucks for Jim S. Burnett and Tim S. Homan. The two divisions of the $114,440 (div.) two-year-old filly trot went to Let's Get Started (Josh Sutton) and Chim Swift (David Miller). Let's Get Stated scored a 1 1/4 length victory over Rose Run Sydney (Ryan Holton) in a stakes record 1:57.4. In the second division, Chim Swift overcame the outside post #8 and defeated Renee Lu (Yannick Gingras) in 1:58. by Jay Wolf, for the Delaware County Fair
Jugette and Little Brown Jug notes
I Said Diamonds has been scratched from Wednesday's harness racing Jugette by the judges. The Well Said filly was to leave from post #6. Jugette Day Post Time Moved To 12:00 Noon Wednesday's Post Time has been moved back to 12:00 p.m. The 15 race card will start one hour later than the originally announced time. Guaranteed Pools On Jugette and Jug Day The Delaware County Fair in partnership with the USTA's Strategic Wagering Initiative will offer several guaranteed pools on Wednesday and Thursday: Wednesday: $20,000 Pick 4 and $30,000 Pick 4 Thursday: $10,000 Pick 3, $30,000 Pick 4 and $50,000 Pick 4 Final Jug Drivers Announced In the first Jug elimination, Matt Kakaley will drive Stolen Glimpse (Post #2) and Sylvain Filion will pilot Lyons Snyder (Post #3). In the second $92,500 elimination, Big Top Hanover will pick up the services of Yannick Gingras. The complete Jug field: First Elim 1. Dr J Hanover (Scott Zeron) 2. Stolen Glimpse (Matt Kakaley) 3. Lyons Snyder (Sylvain Filion) 4. Check Six (Yannick Gingras) 5. Betting Line (David Miller) 6. Fernando Hanover (Tim Tetrick) Second Elim 1. Western Fame (Mark MacDonald) 2. Racing Hill (Brett Miller) 3. Big Top Hanover (Yannick Gingras) 4. Manhattan Beach (Matt Kakaley) 5. Spider Man Hanover (Andy Miller) Jay Wolf
Filly to put connections in the record books
Columbus, OH --- While Dan Patch Award winner Pure Country and her extremely accomplished rival Darlinonthebeach are dominating the headlines for the 46th edition of the Jugette, Canadian L A Delight is not only a force to be reckoned with, but if she secures the victory, she will not only redeem her dam's loss in this very event, but will secure her pilot and her harness racing breeder/owner/trainer a place in Jugette history. "I think she is not receiving much attention because she has only raced twice outside of Canada," said John Campbell, who will be guiding the filly over the Delaware County Fair oval on Wednesday (Sept. 21) in the $239,400 Jugette. "The first time she raced in the U.S. she made that break on me at the Meadowlands (on July 16 in the Mistletoe Shalee) for some reason we have never determined, but in the Nadia Lobell, her second start here (Aug. 27) she beat some quality fillies at The Meadows with Dave Palone driving her in a personal best 1:49.1 and just missed setting a track record. She certainly has a very good chance to win this race." A daughter of Bettor's Delight-West Of L A, L A Delight was the 2015 O'Brien Award winner as the sport's best 2-year-old pacing filly in Canada. In last year's campaign, she finished third in her first start and continued her season with 11 consecutive trips to the winner's circle. Trained by Bob McIntosh, who captured this very contest in 1994 with Electric Slide and in 1992 with So Fresh, she competes as a homebred for her trainer in conjunction with C S X Stables and Al McIntosh Holdings. L A Delight will leave from post position three in rein to the most prolific driver in the race's history, as Campbell has captured the Jugette on four occasions. Rated as the fourth selection on the morning line, behind Pure Country (5-2, post nine), Darlinonthebeach (7-2, post seven) and Call Me Queen Be (9-2, post five), the filly merits serious consideration after a sophomore season that has netted $310,548 with a resume of 11-6-1-1. If she hits the finish line ahead of her eight rivals, the victory will indeed be sweet for her connections, as it will place McIntosh in a tie with Bill Haughton for the most wins by a trainer in this race and will reverse the sting of her mother's seventh place finish to Showherthemoney in 2009. McIntosh also trained, owned and bred West Of L A with the same parties and always takes great pride when a product of his breeding program gets their picture taken. "Winning any race is always special," he said last fall. "But there is something extra special when it's a horse you bred and raised from a baby and were responsible for generations of the family. There is a sense of great pride that comes when one of your very own horses wins a big race." It certainly increases the filly's chances to become a Jugette winner when a pilot with Campbell's expertise is satisfied with how the draw unfolded for the duo's journey at Delaware. "It is very important to have an inside post draw over this specific track," he said. "I am pleased with our post position as we can get our nose right on the gate, which is key in races at Delaware. When you are six or seven lengths off the pace, it is extremely difficult to make that up in any races there, even with a very nice horse. When you have a post position like this it definitely helps and allows you to put your horse right in the race off the starting gate." When asked if an unrivaled fifth Jugette win would hold especially high esteem within the context of his storied career, Campbell, as usual, was exceptionally humble and blatantly honest. "I have been fortunate with the opportunities I have been offered to drive horses of this caliber in races like this," he said. "Of course winning this race is always enjoyable, but being in the winner's circle for any race at Delaware is special. It does not matter what race it is. You have such a big audience that is so close to the track and they are so involved and supportive. There is also the history there and it holds a unique place within the industry. Any win there is one you will always remember." Wednesday's Jugette will be raced in two heats. All the first heat finishers will advance to the second heat. The winner of the second heat will be declared the Jugette champion. The first heat will be raced for $95,760 and the second heat will carry a purse of $143,640. The complete Jugette field: PP-Horse-Sire-(Driver/Trainer)-Morning Line Odds 1. Yankee Moonshine - Yankee Cruiser - (Yannick Gingras/Ron Burke)-8/1 2. Marty Party Two - Yankee Cruiser - (Ronnie Wrenn Jr./Ron Steck)-15/1 3. L A Delight - Bettor's Delight - (John Campbell/Robert McIntosh)-6/1 4. Hug A Dragoness - Dragon Again - (Matt Kakaley/Ron Burke)-10/1 5. Call Me Queen B - Somebeachsomewhere - (Scott Zeron/Ross Croghan)-9/2 6. I Said Diamonds - Well Said - (Tim Tetrick/Matias Ruiz)-12/1 7. Darlinonthebeach - Somebeachsomewhere - (David Miller/Nancy Johansson)-7/2 8. Blue Moon Stride - Rocknroll Hanover - (Andrew McCarthy-Mark Harder)-12/1 9. Pure Country - Somebeachsomewhere - (Brett Miller/Jimmy Takter)-5/2 by Kim French, USTA Internet News Editor
Nine fillies entered into $239,400 Jugette
Pure Country, the number 8 ranked standardbred in North America, is the 5/2 morning line harness racing favorite in the $239,400 Jugette three-year-old filly pace on Wedensday,September 21st at the Delaware County Fair. The daughter of Sombeachsomewhere was undefeated at two and has won half of her 14 starts this season. She has banked more than $1.5 million in career earnings. The Jimmy Takter trainee will leave from the second tier in post #9 and will be piloted by Brett Miller for Diamond Creek Racing. Earlier this summer Pure Country raced against the boys in the $320,000 Cane Pace and the $300,000 Carl Milstein Memorial finishing a competitive fourth and second, respectively. Darlinonthebeach (David Miller) is the second choice at 7/2 from post #7. Nancy Johansson, Takter's daughter, trains the daughter of Somebeachsomewhere for the White Birch Farm. Darlinonthebeach has eight victories and has earned $519,644 on the season. She is the fastest filly in the field with her 1:48 4/5 mark at Pocono Downs. Third choice Call Me Queen Be (Scott Zeron) upset Pure Country in her last start, the $252,000 Pennsylvania Sire Stakes Final on September 10. Call Me Queen Be is trained by Ross Croghan for the Let It Ride Stable and Dana Parham. All the elimination finishers will advance to the second heat. The winner of the second heat will be declared the Jugette champion. The first heat will be raced for $95,760 and the second heat will carry a purse of $143,640. The complete Jugette field and announced drivers: PP Horse (Driver/Trainer) Morning Line Odds 1. Yankee Moonshine - Yanke Cruiser - (Yannick Gingras/Ron Burke) 8-1 2. Marty Party Two - Yanke Cruiser - (Ronnie Wrenn, Jr./Ron Steck) 15-1 3. LA Delight - Bettors Delight - (John Campbell/Robert McIntosh) 6-1 4. Hug A Dragoness - Dragon Again - (Yannick Gingras/Ron Burke) 10-1 5. Call Me Queen B - Somebeachsomewhere - (Scott Zeron/Ross Croghan) 9/2 6. I Said Diamonds - Well Said - (Tim Tetrick/Matias Ruiz) 12-1 7. Darlinonthebeach - Somebeachsomewhere - (David Miller/Nancy Johansson) 7/2 8. Blue Moon Stride - Rocknroll Hanover - (Andrew McCarthy) 12-1 9. Pure Country - Somebeachsomewhere - (Brett Miller/Jimmy Takter) 5/2 Jay Wolf
Sassa Hanover dominant in Jugette
Sassa Hanover showed her versatility in winning the 45th Jugette in Wednesday action at the the harness racing meeting at the Delaware County Fairgrounds. In the $151,350 second heat, Matt Kakaley sent Sassa Hanover after the lead from the rail position. Southwind Roulette (Corey Callahan) improved from her third starting position to sit behind the leader. The first elimination winner Bettor N Better (Yannick Gingras) was the first to challenge but could not get past the eventual winner. Sassa Hanover drew clear of the field and scored a two length victory over Southwind Roulette and Somewhere Sweet (Jim Morrill, Jr.) in 1:51 1/5. The daughter of Rock N Roll Heaven, winner of the 2010 Little Brown Jug, is owned by Burke Racing Stable, Panhellenic Stable, Weaver Bruscemi and Lawrence Karr. The win was trainer Ron Burke's second Jugette crown and Kakaley's first. "I was second the past two years, so this feels good," noted Kakaley. The two heat time of 3:42 established a new two-heat world record. In the second elimination, Sassa Hanover came from off the pace and went from last to first to score in a stakes record equaling 1:50 4/5. Momas Got A Gun (David Miller) was hustled off the gates wings to take early command of the field of six. Kakaley dropped Sassa Hanover to the back of the pack and was content to sit there until midway down the backstretch. Sassa Hanover swooped past the field and beat Somewhere Sweet by ¾ of a length. Bedroomconfessions (Tim Tetrick) and Serious Filly (Scott Zeron) advanced to the final. In the first elimination Bettor N Better came from off the pace to score in 1:51 1/5. David Miller and Triple V Hanover protected his rail position and led the field through the first three-quarters of a mile. Yannick Gingras eased Bettor N Better off the rail going down the backstretch and drew off by 2 ¼ lengths over the pocket sitting Southwind Roulette (Matt Kakaley) and Moremercy Bluechip (Andy Miller) in 1:51 1/5. Wicked Little Minx (Brett Miller) also advanced to the final. Two Divisions of the Buckette Held Classical Annie and Aaron Merriman took the faster of the two divisions in the $109,200 (div.) Buckette for three-year-old distaff trotters. The field of six raced in post-position order through the first three-quarters of the mile. The leader Katniss (Yannick Gingras) made a break in stride and was taken into the safety lane handing the lead over to the pocket sitting Classical Annie. The daughter of Andover Hall held off a late rally by Smexi (Corey Callahan) by a neck in a lifetime best 1:54 1/5. Jim Arledge, Jr. conditions the filly for Laura Baker, John Schmucker and Thomas York, Jr. The second $54,600 division was won by a fast closing Speak To Me (Brett Miller) who swooped past four rivals in the deep stretch to win in 1:55 1/5. Jimmy Takter trains the Muscle Massive lass, who has earned $324,418, for Brittany Farms. Tipton Teeez Survives Tough Trip to Win the $44,200 Standardbred (2FP) Tipton Teeez and Yannick Gingras never saw the rail, but still had enough in the tank to win the Standardbred for freshmen filly pacers. When the gates wings folded, Montrell Teague hustled Miss Me Yet after the early lead, forcing the eventual winner to race on the outside. As the field of nine rounded the final turn five fillies were within two lengths of the pacesetting Miss Me Yet. Tipton Teeez gutted out a 3/4 length victory over Rockin Rum Springa (David Miller) and Hug A Dragoness (Matt Kakaley). Miss Me Yet hung on for fourth. Brian Brown trains the Wester Terror filly for Jennifer Brown and Richard Lombardo. Beaver Trainees Sweep OBC Two-Year Filly Trot Trainer Chris Beaver won both divisions of the $98,000 Ohio Breeders Championship. Kestrel (Aaron Merriman) rebounded from a narrow defeat in the recent Ohio Sires Stake Championship to score a decisive nine length victory over Bellesvictoryring (John Konesky III) in 1:58, shattering the stakes record. The daughter of Triumphant Caviar is owned by Wilbur Stoll Lang and Beaver. Beaver was back in the Delaware winner's circle a few races later with Evanora (Ryan Stahl). The daughter of Pilgrims Taj scored in 1:58 4/5 over the pacesetting Count On Cami (Kurt Sugg). Evanora is owned by Sandra Burnett. Neely's Messenger, David Miller Score in OBC Neely's Messenger scored a mild upset over I Know My Chip (Chris Page) in the final strides to win the $75,000 Ohio Breeders Championship for sophomore colt trotters in 1:57. Miller is the winningest driver in the history of the Delaware County Fair with 206 victories. Neely's Messenger is conditioned by Marty Wollam for Dale and Julie Ann Sweet. Jay Wolf
Band Of Angels eyes $212,250 Jugette
Bill Donovan is looking forward to seeing Band Of Angels compete in Wednesday's $212,250 Jugette for 3-year-old female pacers at the harness racing meeting at Delaware County Fairgrounds in central Ohio, but the longtime owner will watch from afar. "Of course, I'm excited," Donovan said. "Anytime you have a horse good enough to go into one of the premier races in the sport, you're excited. She's earned her way in, for sure. "(But) I'm very superstitious," he added with a laugh. "Every time I go to a big race, it seems like disaster strikes." Band Of Angels is one of 12 fillies entered in the Jugette, and one of four horses in the race from the stable of trainer Ron Burke. She will start from post No. 3 with driver Yannick Gingras in the second of two $50,450 eliminations and is the 3-1 second choice on the morning line. The top four finishers from each division return later in the day for the $151,150 final. A horse must only win the final to be declared the Jugette champion. Post time is noon for Wednesday's first race at the Delaware County Fairgrounds, located 30 miles north of Columbus. The Jugette eliminations are races 12 and 13. The final is race 17. Band Of Angels heads to the Jugette off a nose win over Devil Child in the New York Sire Stakes championship on Sept. 12 at Yonkers Raceway. Band Of Angels and driver Jason Bartlett started from the outside, post eight, but got the lead in the opening quarter-mile and went on to victory. "I think most people wrote her off from winning the sire stakes final, but she persevered," Donovan said. "I was surprised myself. Jason Bartlett gave her an aggressive drive getting her off the (starting) gate and she did the rest. She's just been a real pleasure." Band Of Angels has won six of 13 races this year and 12 of 23 lifetime starts, with total earnings of $462,745. She has finished worse than third only once in her most recent 11 races. In 11 career races on half-mile tracks, such as the oval at the Delaware County Fairgrounds, she has posted eight wins, one second, and one third. "She is awful good on a half-mile track, so I think she'll give a good accounting of herself on Wednesday," Donovan said. "She's been a solid horse this year. When they make the money she's made this year, it's obviously a good year." "We've been fortunate with Band Of Angels in that she did come out of a terrific 2-year-old season and she has more than held her own at 3. I think she belongs there. I think she's definitely in the top 10 of 3-year-old fillies this year." Band Of Angels is a daughter of Rock N Roll Heaven, the 2010 Little Brown Jug winner and Horse of the Year honoree, and the mare Time N Again. She is a half-sister to millionaire Romantic Moment and was purchased as a yearling for $100,000 at the 2013 Lexington Selected Sale. Donovan is making his second appearance in the Jugette as an owner. His filly Bettor B Lucky finished second to Darena Hanover in the 2012 Jugette. Both horses were trained by Burke. "I'm hoping to turn the tables on that finish this year," Donovan said. The morning line favorite at 5-2 in the second elimination is trainer Virgil Morgan Jr.'s Momas Got A Gun, who will start from post No. 2 with driver David Miller. She is coming off back-to-back second-place finishes in the Pennsylvania Sire Stakes championship, where she missed by a head, and Valley Forge Stakes. A daughter of stallion Somebeachsomewhere out of the mare Benear, she is a full sister to 2014 Little Brown Jug winner Limelight Beach. She has won three of 14 races in 2015 and earned $313,368. Triple V Hanover is the 3-1 morning line favorite in the first elimination. The Brian Brown trainee will start from post one, also with Miller in the sulky. She has won four of 11 races this year and earned $105,265 for owners Donald Robinson, King McNamara, and Strollin Stable. Following are the Jugette elimination fields in post order with drivers, trainers and morning line odds. $50,450 First Elimination Post-Horse-Driver-Trainer-Morning Line 1. Triple V Hanover-David Miller-Brian Brown-3-1 2. Southwind Roulette-Matt Kakaley-Ron Burke-7-2 3. Bettor N Better-Yannick Gingras-Ron Burke-6-1 4. Moremercy Bluechip-Andy Miller-Julie Miller-10-1 5. Wicked Little Minx-Brett Miller-Nancy Johansson-12-1 6. Mosquito Blue Chip-Jim Morrill Jr.-Paul Jessop-7-2 $50,450 Second Elimination 1. Serious Filly-Scott Zeron-Brian Brown-6-1 2. Momas Got A Gun-David Miller-Virgil Morgan Jr.-5-2 3. Band Of Angels-Yannick Gingras-Ron Burke-3-1 4. Bedroomconfessions-Tim Tetrick-Tony Alagna-12-1 5. Somewhere Sweet-Jim Morrill Jr.-Brian Brown-8-1 6. Sassa Hanover-Matt Kakaley-Ron Burke-4-1 Ken Weingartner
New York bred fillies well represented in Jugette
Latham, NY---When you look at the entries for this year's 3-year-old pacing filly classic, the Jugette, one thing seems fairly obvious: New York breds are well represented. In fact, half of the entrants of the harness racing stake are from the Empire State. One week ago, five of the six who are entered in Wednesday's (Sept. 23) Jugette competed in the New York Sire Stakes (NYSS) $225,000 Night of Champions final at Yonkers Raceway. Those five contested over a rain-soaked track in 1:54, finishing only three-lengths apart from each other. That was clearly a great tune-up for the Grand Circuit test ahead of them in Delaware, Ohio. The group is led by a trio of Ron Burke trainees; Band Of Angels, Sassa Hanover and Bettor N Better. Band Of Angels (Rock N Roll Heaven-Time N Again) 1:50 $462,745, was crowned the New York State champion at Yonkers this year after cutting the whole mile and winning by a nose with a fast :27.4 final quarter. Prior to that, Band Of Angels was used hard twice in the $269,000 Empire Breeders Classic at Tioga Downs before coming up just a length short in 1:49.3. The filly left in :26.4 and led the field past three-eighths before yielding the lead. Band Of Angels was asked for more late and responded well, but could only manage third behind the hard charging Mosquito Blue Chip who was the winner. Earlier this year she had a very impressive effort in the $207,350 Mistletoe Shallee Stake at the Meadowlands. After winning her elimination heat in 1:50, Band Of Angels got locked in early in the final. When she was finally able to clear, the filly flew through the stretch before coming up just a long-length short in 1:49.2. Sassa Hanover (Rock N Roll Heaven-Sayo Hanover) 1:49.4 $704,002, did not compete in the NYSS final, opting instead to race in the Nadia Lobell at the Meadows on September 16. Coming into that race off a two-week layoff, Sassa Hanover cut the mile with stiff fractions of :26.3, :54.4 and 1:22.2 before tiring down the lane to get beat three-lengths in 1:50.4. Although wins weren't as prevalent this year as last, her performances did not lack for effort. Sassa Hanover was second in the $117,724 Lismore Final at Yonkers, fourth in the $387,990 Fan Hanover at Mohawk Raceway and third in the $350,000 Valley Forge at Pocono Downs. None of those defeats were more than two-lengths. Last year Sassa Hanover finished second to Horse of the Year, JK She'salady, in the $500,000 Breeders Crown. Bettor N Better (Bettor's Delight-Vanite Semalu) 1:51 $318,568, raced in-state all year and didn't see the Grand Circuit action some of the other entrants have. She did score convincing wins of 1:53.3 at Saratoga Raceway and 1:54.4 at Monticello Raceway and finished the year as the fourth highest point-getter in the series. Aside from the Burke contingent, the other three New York breds have very impressive credentials of their own. The Paul Jessop trained Mosquito Blue Chip (Bettor's Delight-Sandfly Hanover) 1:49.3 $504,511, had a hard act to follow this year after coming away the NYSS 2-year-old pacing filly champion in 2014. However she acquitted herself well, besting both her mark and earnings of a year ago. After starting off the year somewhat slowly, Mosquito Blue Chip turned it up in June. She strung together eight solid efforts where she didn't miss the board that included wins at Buffalo Raceway (1:53.3), Saratoga (1:53.3) and Harrah's Philadelphia (1:52.3). In August she got away fourth in the $269,000 Empire Breeders Classic at Tioga and laid-in-wait behind fast fractions. When she got loose in the lane and fanned three-deep, Mosquito Blue Chip powered her way to the lead and the winner's share of the purse in her career best time of 1:49.3. Tony Alagna's Bedroomconfessions (American Ideal-Turnoffthelights) 1:50.2, $318,791, has seen action in some major stakes this year but has come away with minor prizes. Her two best outings were wins in consolation events of the Shady Daisy at the Meadowlands where she won by three in 1:50.2 and the Empire Breeders Classic at Tioga where she was victorious again in 1:51. Bedroomconfessions only had one win in NYSS competition all year (1:52.1 at Yonkers) but collected a lot of points along the way to make the final. In that event she drew post seven in the mud but closed very well; beaten by three lengths. Moremercy Hanover (Rock N Roll Heaven-Mercy Mercy Mercy) 1:50.2, $112,017 is from the Julie Miller Stable and is one of the more lightly raced fillies in the field. After having only four starts as a 2-year-old, she started this year in the second-tier NYSS Excelsior A series. She won at that level in 1:54.4 at Yonkers before moving up to the top-tier sire stakes with victories in 1:53.1 at Saratoga and 1:53.4 at Monticello. In the state final at Yonkers, Moremercy Hanover got away third and after not pulling first-over, got locked in and shuffled to fifth before finding racing room at the pylons in the lane. She closed well and was beaten only two-lengths in 1:54 over the sloppy track. The best of this sex and gait the Empire State has to offer will represent its breeding program well in the 2015 Jugette and having routinely competed over New York's five fast half-mile tracks for the last two years, these fillies bring with them the expertise needed to be successful at Delaware , Ohio. By Tim Bojarski for the Harness Horse Breeders of New York
12 enter for $252,000 45th annual Jugette
Delaware, OH - The 45th edition of the Jugette saw entries for twelve sophomore filly pacers forcing race officials to divide the field into two $50,450 eliminations on September 23 with the top four finishers advancing to the $151,350 second heat. Due to a clerical error, the race officials were forced to conduct a redraw. The second elimination features the two of the richest entries, Sassa Hanover and Band Of Angels. World champion Sassa Hanover drew the outside post in the field of six. The daughter of Rock N Roll Heaven owns a lifetime mark of 1:49.4 and has earned $704,002 for Burke Racing Stable, The Panhellenic Stable, Weaver Bruscemi and Lawrence Karr. Band Of Angels won the $225,000 New York Sires Stake Final on September 12 and has earned $462,745 for her owner W. J. Donovan of Ft. Lauderdale, FL. The daughter of the 2010 Little Brown Jug champion Rock N Roll Heaven will leave from post #3. Yannick Gingras was named to drive both fillies. The first elimination's morning line favorite is Southwind Roulette with post position #2. Although winless in 2015 the daughter of Somebeachsomewhere has amassed $405,971 in career earnings for Bradley Grant and Howard Taylor. Southwind Roulette was third in the $350,000 Pennsylvania Sire Stake Final in her last start on September 5. Matt Kakaley was named to drive. Mosquito Blue Chip and driver Jim Morrill, Jr. should provide a stiff challenge to Southwind Roulette. The sophomore daughter of Bettor's Delight has earned more than a half million dollars for Our Three Sons Stable, D. Falcicchio and Paul Jessop. Mosquito Blue Chip won the $269,000 Empire Breeders Championship at Tioga Downs on August 23. The complete Jugette field with listed drivers: $50,450 First Elimination 1. Triple V Hanover (David Miller) 2. Southwind Roulette (Matt Kakaley) 3. Bettor N Better (Matt Kakaley) 4. Moremercy Blue Chip (Andy Miller) 5. Wicked Little Minx (Brett Miller) 6. Mosquito Blue Chip (Jim Morrill, Jr.) $50,450 Second Elimination 1. Serious Filly (Tim Tetrick) 2. Moma's Got A Gun (David Miller) 3. Band Of Angels (Yannick Gingras) 4. Bedroomconfessions (Tim Tetrick) 5. Somewhere Sweet (David Miller) 6. Sassa Hanover (Yannick Gingras) The Second Heat (top four finishers in the eliminations) will race for a purse of $151,350. by Jay Wolf, for the Little Brown Jug
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