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Neural network pruning is a popular technique used to reduce the inference costs of modern, potentially overparameterized, networks. Starting from a pre-trained network, the process is as follows: remove redundant parameters, retrain, and repeat while maintaining the same test accuracy. The result is a model that is a fraction of the size of the original with comparable predictive performance (test accuracy). Here, we reassess and evaluate whether the use of test accuracy alone in the terminating condition is sufficient to ensure that the resulting model performs well across a wide spectrum of "harder" metrics such as generalization to out-of-distribution data and resilience to noise. Across evaluations on varying architectures and data sets, we find that pruned networks effectively approximate the unpruned model, however, the prune ratio at which pruned networks achieve commensurate performance varies significantly across tasks. These results call into question the extent of \emph{genuine} overparameterization in deep learning and raise concerns about the practicability of deploying pruned networks, specifically in the context of safety-critical systems, unless they are widely evaluated beyond test accuracy to reliably predict their performance. Our code is available at https://github.com/lucaslie/torchprune., Comment: Published in MLSys 2021

We introduce the maximum $n$-times coverage problem that selects $k$ overlays to maximize the summed coverage of weighted elements, where each element must be covered at least $n$ times. We also define the min-cost $n$-times coverage problem where the objective is to select the minimum set of overlays such that the sum of the weights of elements that are covered at least $n$ times is at least $\tau$. Maximum $n$-times coverage is a generalization of the multi-set multi-cover problem, is NP-complete, and is not submodular. We introduce two new practical solutions for $n$-times coverage based on integer linear programming and sequential greedy optimization. We show that maximum $n$-times coverage is a natural way to frame peptide vaccine design, and find that it produces a pan-strain COVID-19 vaccine design that is superior to 29 other published designs in predicted population coverage and the expected number of peptides displayed by each individual's HLA molecules., Comment: ICLR 2022

Image classifiers are typically scored on their test set accuracy, but high accuracy can mask a subtle type of model failure. We find that high scoring convolutional neural networks (CNNs) on popular benchmarks exhibit troubling pathologies that allow them to display high accuracy even in the absence of semantically salient features. When a model provides a high-confidence decision without salient supporting input features, we say the classifier has overinterpreted its input, finding too much class-evidence in patterns that appear nonsensical to humans. Here, we demonstrate that neural networks trained on CIFAR-10 and ImageNet suffer from overinterpretation, and we find models on CIFAR-10 make confident predictions even when 95% of input images are masked and humans cannot discern salient features in the remaining pixel-subsets. We introduce Batched Gradient SIS, a new method for discovering sufficient input subsets for complex datasets, and use this method to show the sufficiency of border pixels in ImageNet for training and testing. Although these patterns portend potential model fragility in real-world deployment, they are in fact valid statistical patterns of the benchmark that alone suffice to attain high test accuracy. Unlike adversarial examples, overinterpretation relies upon unmodified image pixels. We find ensembling and input dropout can each help mitigate overinterpretation., Comment: NeurIPS 2021

Embeddings mapping high-dimensional discrete input to lower-dimensional continuous vector spaces have been widely adopted in machine learning applications as a way to capture domain semantics. Interviewing 13 embedding users across disciplines, we find comparing embeddings is a key task for deployment or downstream analysis but unfolds in a tedious fashion that poorly supports systematic exploration. In response, we present the Embedding Comparator, an interactive system that presents a global comparison of embedding spaces alongside fine-grained inspection of local neighborhoods. It systematically surfaces points of comparison by computing the similarity of the $k$-nearest neighbors of every embedded object between a pair of spaces. Through case studies across multiple modalities, we demonstrate our system rapidly reveals insights, such as semantic changes following fine-tuning, language changes over time, and differences between seemingly similar models. In evaluations with 15 participants, we find our system accelerates comparisons by shifting from laborious manual specification to browsing and manipulating visualizations., Comment: Published in IUI 2022; Equal contribution by first two authors

Local explanation frameworks aim to rationalize particular decisions made by a black-box prediction model. Existing techniques are often restricted to a specific type of predictor or based on input saliency, which may be undesirably sensitive to factors unrelated to the model's decision making process. We instead propose sufficient input subsets that identify minimal subsets of features whose observed values alone suffice for the same decision to be reached, even if all other input feature values are missing. General principles that globally govern a model's decision-making can also be revealed by searching for clusters of such input patterns across many data points. Our approach is conceptually straightforward, entirely model-agnostic, simply implemented using instance-wise backward selection, and able to produce more concise rationales than existing techniques. We demonstrate the utility of our interpretation method on various neural network models trained on text, image, and genomic data., Comment: Published in AISTATS 2019; Equal contribution by first two authors

The "regular" model presented here can be considered to be the most natural solution to the problem of constructing the simplest possible relativistic analogue of the category of classical Fourier--Euler thermally conducting fluid models as characterised by a pair of equations of state for just two dependent variables (an equilibrium density and a conducting scalar). The historically established but causally unsatisfactory solution to this problem due to Eckart is shown to be based on an ansatz that is interpretable as postulating a most unnatural relation between the (particle and entropy) velocities and their associated momenta, which accounts for the well known bad behaviour of that model which has recently been shown to have very pathological mixed-elliptic-hyperbolic comportments. The newer (and more elegant) solution of Landau and Lifshitz has a more mathematically respectable parabolic-hyperbolic comportment, but is still compatible with a well posed initial value problem only in such a restricted limit-case such as that of linearised perturbations of a static background. For mathematically acceptable behaviour undermore general circumstances, and a fortiori for the physically motivated requirement of subluminal signal propagation, only strictly hyperbolic behaviour is acceptable. Attention is drawn here to the availability of a more modern "regular" solution which, is fully satisfactory as far as all these requirements are concerned. This "regular" category of relativistic conducting fluid models arises naturally within a recently developed variational approach, in which the traditionally important stress--momentum-energy density tensor is relegated to a secondary role, while the relevant covariant 4-momentum co-vectors are instead brought to the fore., Comment: 10 pages Latex. Contribution to 5th M. Grossmann meeting, W. Australia, August, 1988; reprinted with corrections by Thomas Madler, September 2012

Although ultimately motivated by quantum theoretical considerations, Everett's many-world idea remains valid, as an approximation, in the classical limit. However to be applicable it must in any case be applied in conjunction with an appropriate anthropic principle, whose precise formulation involves an anthropic quotient that can be normalised to unity for adult humans but that would be lower for infants and other animals. The outcome is a deterministic multiverse in which the only function of chance is the specification of one's particular identity., Comment: 11 pages Latex contribution to J. Cosmology 14, with extra diagram showing age dependence of anthropic quotient. Also in Consciousness and the Universe: Quantum Physics, Evolution, Brain and Mind, ed. R. Penrose, S. Hameroff, S. Kak (Cosmology Science Publishers, Cambridge, Mass., 2011) 1077-1086

It is shown that a string carrying a field of harmonic type can have circular vorton states of a new "throbbing" kind, for which the worldsheet geometry is stationary but the internal structure undergoes periodic oscillation., Comment: 14 pages Latex, colored version of manuscript originally published in black and white

These notes offer an introductory overview of the essentials of classical brane dynamics in a space-time background of arbitrary dimension, using a systematic geometric treatment emphasising the role of the second fundamental tensor and its trace, the curvature vector $K^\mu$. This approach is applied to the problem of stability of vorton equilibrium states of cosmic string loops in an ordinary 4-dimensional background., Comment: 20 pages latex file of contribution to Proc. JGRG20 (Yukawa Inst., Kyoto, Sept., 2010) ed. T. Hiramatsu, M. Sasaki, M. Shibata, T, Shiromizu

The last few million years on planet Earth have witnessed two remarkable phases of hominid development, starting with a phase of biological evolution characterised by rather rapid increase of the size of the brain. This has been followed by a phase of even more rapid technological evolution and concomitant expansion of the size of the population, that began when our own particular `sapiens' species emerged, just a few hundred thousand years ago. The present investigation exploits the analogy between the neo-Darwinian genetic evolution mechanism governing the first phase, and the memetic evolution mechanism governing the second phase. From the outset of the latter until very recently -- about the year 2000 -- the growth of the global population N was roughly governed by an equation of the form dN/Ndt= N/T*, in which T* is a coefficient introduced (in 1960) by von Foerster, who evaluated it empirically as about two hundred thousand million years. It is shown here how the value of this hitherto mysterious timescale governing the memetic phase is explicable in terms of what happenned in the preceding genetic phase. The outcome is that the order of magnitude of the Foerster timescale can be accounted for as the product of the relevant (human) generation timescale, about 20 years, with the number of bits of information in the genome, of the order of ten thousand million. Whereas the origin of our `homo' genus may well have involved an evolutionary hard step, it transpires that the emergence of our particular `sapiens' species was rather an automatic process., Comment: 30 pages LaTex. Definitive (extended) version, as accepted by Int. J. Astrobiology

This article continues the study of the category of harmonious field models that was recently introduced as a kinetically non-linear generalisation of the well known harmonic category of multiscalar fields over a supporting brane wordsheet in a target space with a curved Riemannian metric. Like the perfectly harmonious case of which a familiar example is provided by ordinary barotropic perfect fluids, another important subcategory is the simply harmonious case, for which it is shown that as well as ``wiggle'' modes of the underlying brane world sheet, and sound type longitudinal modes, there will also be transverse shake modes that propagate at the speed of light. Models of this type are shown to arise from a non-Abelian generalisation of the Witten mechanism for conducting string formation by ordinary scalar fields with a suitable quartic self coupling term in the action., Comment: 22 pages Latex

The principles of a previously developed formalism for the covariant treatment of multi-scalar fields for which (as in a nonlinear sigma model) the relevant target space is not of affine type -- but curved -- are recapitulated. Their application is extended from ordinary harmonic models to a more general category of "harmonious" field models, with emphasis on cases in which the field is confined to a string or higher brane worldsheet, and for which the relevant internal symmetry group is non Abelian, so that the conditions for conservation of the corresponding charge currents become rather delicate, particularly when the symmetry is gauged. Attention is also given to the conditions for conservation of currents of a different kind -- representing surface fluxes of generalised momentum or energy -- associated with symmetries not of the internal target space but of the underlying spacetime background structure, including the metric and any relevant gauge field. For the corresponding current to be conserved the latter need not be manifestly invariant: preservation modulo a gauge adjustment will suffice. The simplest case is that of "strong" symmetry, meaning invariance under the action of an effective Lie derivative (an appropriately gauge adjusted modification of an ordinary Lie derivative). When the effective symmetry is of the more general "weak" kind, the kinetic part of the current is not conserved by itself but only after being supplemented by a suitable contribution from the background., Comment: 27 pages Latex (color)

The general purpose bitensorially gauge-covariant differentiation procedure set up in the preceding article is specialised to the particular case of bundles with nonlinear fibres that are endowed with a torsion free Riemannian or pseudo-Riemannian structure. This formalism is used to generalize the class of harmonic mappings between Riemannian or pseudo-Riemannian spaces to a natural gauge coupled extension in the form of a class of field sections of a bundle having the original image space as fibre, with a nonintegrable gauge connection $\Amr$ belonging to the algebra of the isometry group of the fibre space. The Bunting identity that can be used for establishing uniqueness in the strictly positive Riemannian case with negative image space curvature is shown to be generalizable to this gauge coupled extension., Comment: 12 page Latex file with some minor misprint corrections and added color for article originally published in black and white

The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the usual requirement that the base space should be flat or endowed with its own linear connection, and that there should be an ordinary gauge connection on the bundle, it is necessary to require also that there should be an intrinsic, bundle-group invariant connection on the fibre space. The procedure is based on the use of an appropriate primary-field (i.e. section) independent connector that is constructed in terms of the natural fibre-tangent-vector realisation of the gauge connection. The application to gauged harmonic mappings will be described in a following article., Comment: 17 page Latex file with some minor misprint corrections and added color for article originally published in black and white

This investigation follows up the suggestion that the equation of state for superconducting cosmic strings provided by Witten's prototype biscalar field model can be well represented by an effective Lagrangian of simple logarithmic form depending on only 3 independent parameters. The numerical work described here confirms the validity of this approximation, and initiates the evaluation of the 3 required parameters, as functions of the masses and other parameters specifying the underlying U(1) x U(1) scalar field model in the limit for which the relevant gauge coupling constants are small.In this limit, subject to calibration of the relevant length and mass scales, the scalar field model is characterised by just 3 dimensionless ratios which (in order to provide conducting strings) must be subject to three inequalities (of which two have obvious analytic expressions). It is found here that when all three of these inequalities are satisfied by a reasonably large margin, there is a simple empirical formula that can be used to provide a fairly accurate prescription for the algebraic dependence on these 3 dimensionless ratios of the 3 parameters required for the logarithmic equation of state., Comment: 15 pages including 5 figures; v2: notation used in eq. (6) clarified

The prediction that (due to the limited amount of hydrogen available as fuel in the Sun) the future duration of our favourable terrestrial environment will be short (compared with the present age of the Earth) has been interpreted as evidence for a hard step scenario. This means that some of the essential steps (such as the development of eukaryotes) in the evolution process leading to the ultimate emergence of intelligent life would have been hard, in the sense of being against the odds in the available time, so that they are unlikely to have been achieved in most of the earth-like planets that may one day be discovered in nearby extra-solar systems. It was originally estimated that only one or two of the essential evolutionary steps had to have been hard in this sense, but it has become apparent that this figure may need upward revision, because recent studies of climatic instability suggest that the possible future duration of our biologically favourable environment may be shorter than had been supposed, only about one Giga year rather than five. On the basis of the statistical requirement of roughly equal spacing between hard steps, it is argued that the best fit with the fossil record is now obtainable by postulating the number of hard steps to be five, if our evolution was exclusively terrestrial, or six if, as now seems very plausible, the first step occurred on Mars., Comment: 11 pages Latex

This is the first part of a survey whose ultimate purpose is to clarify the significance of the famous coincidence between the Hubble age of the universe and a certain combination of microphysical parameters. In this part the way is prepared by a discussion of the manner in which familiar local phenomena depend qualitatively, and in order of magnitude, quantitatively on the fundamental parameters of microphysics. In order to keep the account concise while remaining self contained, only the barest essentials of the standard nuclear physical and astrophysical calculations involved are given. Only six of the fundamental parameters play a dominant part, namely the coupling constants of the strong, electromagnetic, and gravitational forces, and the mass ratios of the proton, neutron, electron and pi-meson. Attention is drawn to the important consequences of three coincidental relationships between these parameters. It is shown that most of the principle limiting masses of astrophysics arise (in fundamental units) simply as the reciprocal of the gravitational fine structure constant, with relatively small adjustment factors. The dividing point between red dwarf and blue giant stars turns out to be an exception: this division occurs within the range of the main sequence stars only as a consequence of the rather exotic coincidence that the ninth power of the electromagnetic fine structure constant is roughly equal to the square root of the gravitational fine structure constant., Comment: 73 latex pages, consisting of 5 page postscript appended to transcript (with original figures by photocopy) of 68 page manuscript printed by stencil in 1967 under subheading ``The role of fundamental microphysical parameters in cosmogony'', as a foundation for what was to become known as the anthropic principle

The original formulation of the (weak) anthropic principle was prompted by a question about objective time at a macroscopic level, namely the age of the universe when ``anthropic'' observers such as ourselves would be most likely to emerge. Theoretical interpretation of what one observes requires the theory to indicate what is expected, which will commonly depend on where, and particularly when, the observation can be expected to occur. In response to the question of where and when, the original version of the anthropic principle proposed an {it a priori} probability weighting proportional to the number of ``anthropic'' observers present. The present discussion takes up the question of the time unit characterising the biological clock controlling our subjective internal time, using a revised alternative to a line of argument due to Press, who postulated that animal size is limited by the brittleness of bone. On the basis of a static support condition depending on the tensile strength of flesh rather than bone, it is reasoned here that our size should be subject to a limit inversely proportional to the terrestrial gravitation field g, which is itself found to be proportional (with a factor given by the 5/2 power of the fine structure constant) to the gravitational coupling constant.This provides an animal size limit that will in all cases be of the order of a thousandth of the maximum mountain height, which will itself be of the order of a thousandth of the planetary radius. The upshot, via the (strong) anthropic principle, is that the need for brains, and therefore planets, that are large in terms of baryon number may be what explains the weakness of gravity relative to electromagnetism., Comment: 15 pages Latex, work prepared at SR21 meeting, Salonika, May, 2007 and 12th Peyresq Physics workshop, June 2007, new version with corrected typos and some additional comments and references for presentation at SR21 meeting, Athens, September 2007

In a flat background, simple non-conducting string loops have no strictly stationary equilibrium states, but for cosmic string loops of superconducting kind such ``vorton'' states will exist, with rotating circular configurations appropriately describable as ``cosmic rings'' (which may conceivably be a significant contributor to the material content of the universe) whose equilibrium is obtained for zero angular velocity of retrograde characteristics. Such a ``cosmic ring'' is characterised by its mass M and angular momentum J say, corresponding at a microscopic level to two independent quantum numbers, namely charge number C and a topological phase number N whose product determines the angular momentum, J=CN, while their ratio determines the local intrinsic state of the string, which may be qualitatively classified as being of ``electric'' or ``magnetic'' type depending on whether C/N is greater or less than a critical value dependent on the underlying theoretical model., Comment: 9 page TeX file (with typo corrections and completed references) of article on generic properties of circular vorton states published in Physics Letters

A brief explanation of the meaning of the anthropic principle - as a prescription for the attribution of a priori probability weighting - is illustrated by various cosmological and local applications, in which the relevant conclusions are contrasted with those that could be obtained from (less plausible) alternative prescriptions such as the vaguer and less restrictive ubiquity principle, or the more sterile and restrictive autocentric principle., Comment: 6 pages, latex: contribution to Colloquium ``Cosmology: Facts and problems'', Paris, 2004

At densities below the neutron drip threshold, a purely elastic solid model (including, if necessary, a frozen-in magnetic field) can provide an adequate description of a neutron star crust, but at higher densities it will be necessary to allow for the penetration of the solid lattice by an independently moving current of superfluid neutrons. In order to do this, the previously available category of relativistic elasticity models is combined here with a separately developed category of relativistic superfluidity models in a unified treatment based on the use of an appropriate Lagrangian master function. As well as models of the purely variational kind, in which the vortices flow freely with the fluid, such a master function also provides a corresponding category of non-dissipative models in which the vortices are pinned to the solid structure., Comment: 29 pages, Latex. V. 2. Minor changes, matches published version

This work confirms the stability of a class of domain wall lattice models that can produce accelerated cosmological expansion, with pressure to density ratio $w=-1/3$ at early times, and with $w=-2/3$ at late times when the lattice scale becomes large compared to the wall thickness. For walls of tension $T_{I}$, the relevant X type junctions could be unstable (for a sufficiently acute intersection angle $\alpha$) against separation into a pair of Y type junctions joined by a compound wall, only if the tension $T_{II}$ of the latter were less than $2T_{I}$ (and for an approximately right-angled intersection if it were less that $\sqrt{2} T_{I}$) which can not occur in the class considered here. In an extensive category of multicomponent scalar field models of forced harmonic (linear or non-linear) type it is shown how the relevant tension -- which is the same as the surface energy density $U$ of the wall -- can be calculated as the minimum (geodesic) distance between the relevant vacuum states as measured on the space of field values $\Phi^i$ using a positive definite (Riemannian) energy metric $dU^2=\tilde G_{ij} d\Phi^i d\Phi^j$ that is obtained from the usual kinetic metric (which is flat for a model with ordinary linear kinetic part) by application of a conformal factor proportional to the relevant potential function $V$. For suitably periodic potential functions there will be corresponding periodic configurations -- with parallel walls characterised by incrementation of a winding number -- in which the condition for stability of large scale bunching modes is shown to be satisfied automatically. It is suggested that such a configuration -- with a lattice lengthscale comparable to intergalactic separation distances -- might have been produced by a late stage of cosmological inflation., Comment: 30 pages Latex. December 2007 update (published version, with new appendix) of contribution for 'Macro and Micro Structures of Spacetime', 11th Peyresq Physics Meeting, June 2006, and for 'Condensates in Physics: from Atoms to Cosmology', COSLAB workshop, Nottingham, April, 2006

This article provides a unified treatment of an extensive category of non-linear classical field models whereby the universe is represented (perhaps as a brane in a higher dimensional background) in terms of a structure of a mathematically convenient type describable as hyperelastic, for which a complete set of equations of motion is provided just by the energy-momentum conservation law. Particular cases include those of a perfect fluid in quintessential backgrounds of various kinds, as well as models of the elastic solid kind that has been proposed to account for cosmic acceleration. It is shown how an appropriately generalised Hadamard operator can be used to construct a symplectic structure that controles the evolution of small perturbations, and that provides a characteristic equation governing the propagation of weak discontinuities of diverse (extrinsic and extrinsic) kinds. The special case of a poly-essential model - the k-essential analogue of an ordinary polytropic fluid - is examined and shown to be well behaved (like the fluid) only if the pressure to density ratio $w$ is positive., Comment: 16 pages Latex, Contrib. to 10th Peyresq Pysics Meeting, June 2005: Micro and Macro Structures of Spacetime

Although implicit in the discovery of the Schwarzschild solution 40 years earlier, the issues raised by the theory of what are now known as black holes were so unsettling to physicists of Einstein's generation that the subject remained in a state of semiclandestine gestation until his demise. That turning point -- just half a century after Einstein's original foundation of relativity theory, and just half a century ago today -- can be considered to mark the birth of black hole theory as a subject of systematic development by physicists of a new and less inhibited generation, whose enthusastic investigations have revealed structures of unforeseen mathematical beauty, even though questions about the physical significance of the concomitant singularities remain controversial., Comment: 30 pages latex. Contrib. to Encuentros Relativistas Espanoles: A Century of Relativity Theory, Oviedo, 2005 (ed. L. Mornas)

To account for pulsar frequency glitches, it is necessary to use a neutron star crust model allowing not only for neutron superfluidity but also for elastic solidity. These features have been treated separarately in previous treatments of crust matter, but are combined here in a unified treatment that is based on the use of a Lagrangian master functon, so that the coherence the system is ensured by the relevant Noether identities. As well as the model obtained directly from the variation principle, the same master function can provide other conservative alternatives, allowing in particular for the effect of perfect vortex pinning. It is also shown how such models can be generalised to allow for dissipative effects, including that of imperfect pinning, meaning vortex drag or creep., Comment: 31 pages Latex

This work develops the dynamics of perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type) magneto-elastic perturbation modes., Comment: 39 pages Latex

Probabilistic models (developped by workers such as Boltzmann, on foundations due to pioneers such as Bayes) were commonly regarded merely as approximations to a deterministic reality before the roles were reversed by the quantum revolution (under the leadership of Heisenberg and Dirac) whereby it was the deterministic description that was reduced to the status of an approximation, while the role of the observer became particularly prominent. The concomitant problem of lack of objectivity in the original Copenhagen interpretation has not been satisfactorily resolved in newer approaches of the kind pioneered by Everett. The deficiency of such interpretations is attributable to failure to allow for the anthropic aspect of the problem, meaning {\it a priori} uncertainty about the identity of the observer. The required reconciliation of subjectivity with objectivity is achieved here by distinguishing the concept of an observer from that of a perceptor, whose chances of identification with a particular observer need to be prescribed by a suitable anthropic principle. It is proposed that this should be done by an entropy ansatz according to which the relevant micro-anthropic weighting is taken to be proportional to the logarithm of the relevant number of Everett type branch-channels., Comment: 29 pages Latex, 1 figure. Contribution to `Universe or Multiverse?' ed. B.J. Carr, for Cambridge U.P

The build up of the stress whose relaxation is presumed to account for pulsar frequency glitches can be attributed to various mechanisms, of which the most efficient involve differential rotation of the neutron superfluid in the inner layers of the (magnetically braked) solid crust of a rotating neutron star. In such a case it is usually supposed that the stress is attributable to pinning of superfluid vortices to crust nuclei, but it has been suggested that, even if the pinning effect is too weak, a comparably large stress might still arise just from the deficit of centrifugal buoyancy in the slowed down crust. The present work is a re-examination that investigates the way such processes may be affected by considerations that were overlooked in the previous work -- notably uncertainties about the ``effective'' masses that have to be attributed to the ``free'' superfluid neutrons to allow for their entrainment by the ionic crust material. Though restricted to a Newtonian formulation, this analysis distinguishes more carefully than has been usual between true velocities, which are contravariantly vectorial, and so called ``superfluid velocities'' that are proportional to momenta, which are essentially covectorial, a technicality that is important when more than one independent current is involved. The results include a Proudman type theorem to the effect that the superfluid angular velocity must be constant on slightly deformed Taylor cylinders in the force free case, and it is shown how to construct a pair of integral constants of the motion that determine the solution for the pinned case assuming beta equilibrium., Comment: 17 pages Latex. Revised version has been extended to include generalised Proudman theorem

Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to freeze out into static lattice type configurations with energy contribution ultimately be provided by the membranes. It has been suggested by Bucher and Spergel that on scales large compared with the relevant (interstellar separation) distance characterising the relevant mesh length, such a system may behave as a rigidity - stabilised solid, having an approximately isotropic stress energy tensor with negative pressure, as given by a polytropic index $\gamma=w+1=1/3$. It has recently been shown that such a system can be rigid enough to be stable if the number of membranes meeting at a junction is even (though not if it is odd). Using as examples an approximately O(3) symmetric scalar field model that can provide an ``8 color'' (body centered) cubic lattice, and an approximate U(1)$\times$ U(1) model offering a disordered ``5 color'' lattice, it is argued that such a mechanism can account naturally for the observed dark energy dominance of the universe, without ad hoc assumptions, other than that the relevant symmetry breaking phase transition should have occurred somewhere about the Kev energy range., Comment: 14 pages, LaTex. Contrib. to Micro and Macro Structures of Spacetime, Peyresq, June, 2004, extended to include illustrations of "8 color" and "5 color" examples of "even" (as opposed to "odd") lattices

We compute the regularized force density and renormalized action due to fields of external origin coupled to a brane of arbitrary dimension in a spacetime of any dimension. Specifically, we consider forces generated by gravitational, dilatonic and generalized antisymmetric form-fields. The force density is regularized using a recently developed gradient operator. For the case of a Nambu--Goto brane, we show that the regularization leads to a renormalization of the tension, which is seen to be the same in both approaches. We discuss the specific couplings which lead to cancellation of the self-force in this case., Comment: 15 pages

This course is designed to give a mathematically coherent introduction to the classical thory of black holes and also of strings and membranes (which are like the horizon of a black hole in being examples of physical systems based on a dynamically evolving world sheet) giving particular attention given to the study of the geometry of their equilibrium states., Comment: 93 page latex file (with typo corrections and redrafted C.P. diagrams) of contribution to BLACK HOLE PHYSICS (NATO ASI C364) ed. V. de Sabbata, Z. Zhang (Kluwer, Dordrecht, 1992) 283-357

As a follow up to articles dealing firstly with a convective variational formulation in a Milne-Cartan framework for non-dissipative multi fluid models, and secondly with various ensuing stress energy conservation laws and generalised virial theorems, this work continues a series showing how analytical procedures developed in the context of General Relativity can be usefully adapted for implementation in a purely Newtonian framework where they provide physical insights that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. The present article describes the 4-dimensionally covariant treatment of various dissipative mechanisms, including viscosity in non-superfluid constituents, superfluid vortex drag, ordinary resistivity (mutual friction) between relatively moving non-superfluid constituents, and the transvective dissipation that occurs when matter is transformed from one constituent to another due to chemical disequilibrium such as may be produced by meridional circulation in neutron stars. The corresponding non dissipative limit cases of vortex pinning, convection, and chemical equilibrium are also considered., Comment: 27 pages latex

Phenomena such as pulsar frequency glitches are believed to be attributable to differential rotation of a current of ``free'' superfluid neutrons at densities above the ``drip'' threshold in the ionic crust of a neutron star. Such relative flow is shown to be locally describable by adaption of a canonical two fluid treatment that emphasizes the role of the momentum covectors constructed by differentiation of action with respect to the currents, with allowance for stratification whereby the ionic number current may be conserved even when the ionic charge number Z is altered by beta processes. It is demonstrated that the gauge freedom to make different choices of the chemical basis determining which neutrons are counted as ``free'' does not affect their ``superfluid'' momentum covector, which must locally have the form of a gradient (though it does affect the ``normal'' momentum covector characterising the protons and those neutrons that are considered to be ``confined'' in the nuclei). It is shown how the effect of ``entrainment'' (whereby the momentum directions deviate from those of the currents) is controlled by the (gauge independent) mobility coefficient K, estimated in recent microscopical quantum mechanical investigations, which suggest that the corresponding (gauge dependent) ``effective mass'' m* of the free neutrons can become very large in some layers. The relation between this treatment of the crust layers and related work (using different definitions of ``effective mass'') intended for the deeper core layers is discussed., Comment: 21 pages Latex. Part II of article whose Part I (Simple microscopic models) is given by nucl-th/0402057. New version extended to include figures

The relative current density $n^i$ of conduction neutrons in a neutron star crust beyond the neutron drip threshold can be expected to be related to the corresponding particle momentum covector $p_i$ by a linear relation of the form $n^i=K^{ij}p_j$ in terms of a physically well defined mobility tensor $K^{ij}$. This result is describable as an ``entrainment'' whose effect - wherever the crust lattice is isotropic - will simply be to change the ordinary neutron mass m to an effective mass $m_\star$ such that in terms of the relevant number density n of unconfined neutrons we shall have $K^{ij}=n/m_\star\gamma^{ij}$. In a preceding analysis based on an independent particle treatment using Bloch boundary conditions to obtain the distribution of energy $E_k$ and associated group velocity $v_k^i=\partial E_k/\partial\hbar k_i$ as a function of wavenumber $k_i$, it was shown that the mobility tensor would be given by $K^{ij}\propto\int d^3 k v_k^i v_k^j\delta\{E_k-\mu\}$, where $\mu$ is the Fermi energy. Using the approach due to Bogoliubov, it is shown here that the effect of BCS pairing with an energy gap \Delta_F and corresponding quasiparticle energy function \EE_k=\sqrt{(E_k-\mu)^2+\Delta_F^2}$ will just be to replace the Dirac distributional integrand by a smoother distribution : $K^{ij}\propto \int d^3 k v_k^i v_k^j \Delta_F^2 /\EE^3_k$. It is also shown how the pairing condensation gives rise to superfluidity in the technical sense of providing (meta) stability against resistive perturbations for a current that is not too strong (its momentum $p_i$ must be small enough to give $2|p_i v_k^i|<\EE_k^2/|E_k-\mu|$ for all modes). It is concluded that the prediction of a very large effective mass enhancement in the middle layers of the crust will not be significantly affected by the pairing mechanism., Comment: 30 pages, revised published version

The problem of interpreting quantum theory on a large (e.g. cosmological) scale has been commonly conceived as a search for objective reality in a framework that is fundamentally probabilistic. The Everett programme attempts to evade the issue by the reintroduction of determinism at the global level of a ``state vector of the universe''. The present approach is based on the recognition that, like determinism, objective reality is an unrealistic objective. It is shown how an objective theory of an essentially subjective reality can be set up using an appropriately weighted probability measure on the relevant set of Hilbert subspaces. It is suggested that an entropy principle (superseding the weak anthropic principle) should be used to provide the weighting that is needed., Comment: Latex file (7 pages) for exposition presented at Interdisciplinary Colloquium ``La Philosophie de la Nature aujourd'hui?'', Paris, March 2003, and 8th Peyresq Physics Meeting ``The Early Universe'', June 2003

In the inner crust of a neutron star, at densities above the ``drip'' threshold, unbound ``conduction'' neutrons can move freely past through the ionic lattice formed by the nuclei. The relative current density $n^i= n \bar v^i$ of such conduction neutrons will be related to the corresponding mean particle momentum $p_i$ by a proportionality relation of the form $n^i= {\cal K}p^i$ in terms of a physically well defined mobility coefficient $\cal K$ whose value in this context has not been calculated before. Using methods from ordinary solid state and nuclear physics, a simple quantum mechanical treatment based on the independent particle approximation, is used here to formulate $\cal K$ as the phase space integral of the relevant group velocity over the neutron Fermi surface. The result can be described as an ``entrainment'' that changes the ordinary neutron mass m to a macroscopic effective mass per neutron that will be given -- subject to adoption of a convention specifying the precise number density n of the neutrons that are considered to be ``free'' -- by $m_\star=n/{\cal K}$. The numerical evaluation of the mobility coefficient is carried out for nuclear configurations of the ``lasagna'' and ``spaghetti'' type that may be relevant at the base of the crust. Extrapolation to the middle layers of the inner crust leads to the unexpected prediction that $m_\star$ will become very large compared with m., Comment: 27 pages, latex. Revised published version

The 4-dimensionally covariant approach to multiconstituent Newtonian fluid dynamics presented in the preceding article of this series is developed by construction of the relevant 4-dimensional stress energy tensor whose conservation in the non-dissipative variational case is shown to be interpretable as a Noether identity of the Milne spacetime structure. The formalism is illustrated by the application to homogeneously expanding cosmological models, for which appropriately generalised local Bernouilli constants are constructed. Another application is to the Iordanski type generalisation of the Joukowski formula for the Magnus force on a vortex. Finally, at a global level, a new (formally simpler but more generally applicable) version of the ``virial theorem'' is obtained for multiconsituent -- neutron or other -- fluid star models as a special case within an extensive category of formulae whereby the time evolution of variously weighted mass moment integrals is determined by corresponding space integrals of stress tensor components, with the implication that all such stress integrals must vanish for any stationary equilibrium configuration., Comment: 32 pages, Latex

Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium (i.e. vorton) state of a closed string loop it is shown that the fundamental axisymmetric ($n=0$) and lowest order ($n=1$) nonaxisymmetric perturbation modes can never be unstable. However, stability for modes of higher order ($n\geq 2$) is found to be non-trivially dependent on the values of the characteristic propagation velocity, $c$ say, of longitudinal perturbations and of the corresponding extrinsic perturbation velocity, $v$ say. For each mode number the criterion for instability is the existence of nonreal roots for a certain cubic eigenvalue equation for the corresponding mode frequency. A very simple sufficient but not necessary condition for reality of the roots and therefore absence of instability is that the characteristic velocity ratio, $c/v$ be greater than or equal to unity. Closer examination of the low velocity (experimentally accessible) nonrelativistic regime shows that in that limit the criterion for instability is just that the dimensionless characteristic ratio $c/v$ be less than a critical value $\chi_c$ whose numerical value is approximately $1\over 2$. In the relativistic regime that is relevant to superconducting cosmic strings the situation is rather delicate, calling for more detailed investigation that is postponed for future work., Comment: 20 page TeX file (with typo corrections and added reference) of manuscript published (with shorter title) in Annals of Physics

This is the first of a series of articles showing how 4 dimensionally covariant analytical procedures developed in the context of General Relativity can be usefully adapted for application in a purely Newtonian framework where they provide physical insights (e.g. concerning helicity currents) that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. After an introductory presentation of the relevant Milne spacetime structure and the associated Cartan connection, the essential principles are illustrated by application to the variational formulation of simple barotropic perfect fluid models. This variational treatment is then extended to conservative multiconstituent self gravitating fluid models of the more general kind that is needed for treating the effects of superfluidity in neutron stars., Comment: 35 pages Latex, with typo corrections and updated references

This article treats the generalisation to brane dynamics of the covariant canonical variational procedure leading to the construction of a conserved bilinear symplectic current in the manner originally developped by Witten, Zuckerman and others in the context of field theory. After a general presentation, including a review of the relationships between the various (Lagrangian, Eulerian and other) relevant kinds of variation, the procedure is illustrated by application to the particularly simple case of branes of the Dirac-Goto-Nambu type, in which internal fields are absent., Comment: 13 pages Latex; Contribution to 2002 Peyresq - 7 workshop

The dynamical behaviour of a cosmic string is strongly affected by any reduction of the effective string tension $T$ below the constant value $T=m^2$ say that characterizes the simple, longitudinally Lorentz invariant, Goto Nambu string model in terms of a fixed mass scale $m$ whose magnitude depends on that of the Higgs field responsible for the existence of the string. Such a reduction occurs in the standard "hot" cosmic string model in which the effect of thermal perturbations of a simple Goto Nambu model is expressed by the formula $T^2=m^2(m^2-2\pi\Theta^2/3)$, where $\Theta$ is the string temperature. A qualitatively similar though analytically more complicated tension reduction phenomenon occurs in "cold" conducting cosmic string models where the role of the temperature is played by an effective chemical potential $\mu$ that is constructed as the magnitude of the phase $\phi$ of a bosonic condensate of the kind whose existence was first proposed by Witten. The present article describes the construction and essential mechanical properties of a category of "warm" cosmic string models that are intermediate between these "hot" and "cold" extremes. These "warm" models are the string analogues of the standard Landau model for a 2-constituent finite temperature superfluid, and as such involve two independent currents interpretable as that of the entropy on one hand and that of the bosonic condensate on the other. It is surmised that the stationary (in particular ring) equilibrium states of such "warm" cosmic strings may be of cosmological significance., Comment: 31 pages, Tex preprint version of manuscript subsequently published (with editorial modifications) in Nuclear Physics B

The general relativistic mass-energy variation formula for axisymmetric equilibrium states of a selfgravitating system is developed in the particular case for which the relevant matter consists of a perfectly conducting multiconstituent fluid (or superfluid) with stationary circular or convective motion., Comment: 11 pages, Tex version of manuscript originally distributed with restricted circulation in Journees Relativistes, 1979, ed. I. Moret-Bailly, C. Latremoliere, pp 166-182 (Faculte des Sciences, Angers, 1979)