# J. P. Barrett - Universite Libre de Bruxelles

## Contact Details

NameJ. P. Barrett |
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AffiliationUniversite Libre de Bruxelles |
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CityBrussel |
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CountryBelgium |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesMathematics - Numerical Analysis (10) Physics - Computational Physics (9) Quantum Physics (8) Nuclear Experiment (6) General Relativity and Quantum Cosmology (6) Statistics - Theory (5) Mathematics - Statistics (5) Mathematical Physics (5) Mathematics - Mathematical Physics (5) High Energy Physics - Theory (4) Physics - Fluid Dynamics (4) Statistics - Methodology (3) Mathematics - Analysis of PDEs (3) Physics - Instrumentation and Detectors (3) Mathematics - Quantum Algebra (2) Physics - Superconductivity (2) Statistics - Applications (2) Quantitative Biology - Genomics (2) Computer Science - Computational Complexity (2) High Energy Astrophysical Phenomena (2) Physics - Biological Physics (1) Statistics - Machine Learning (1) Mathematics - Operator Algebras (1) High Energy Physics - Experiment (1) Physics - Soft Condensed Matter (1) Quantitative Biology - Populations and Evolution (1) Physics - Materials Science (1) Solar and Stellar Astrophysics (1) Physics - Other (1) Physics - Disordered Systems and Neural Networks (1) Physics - Data Analysis; Statistics and Probability (1) Astrophysics of Galaxies (1) Instrumentation and Methods for Astrophysics (1) Nuclear Theory (1) Quantitative Biology - Quantitative Methods (1) High Energy Physics - Lattice (1) |

## Publications Authored By J. P. Barrett

Overfitting, which happens when the number of parameters in a model is too large compared to the number of data points available for determining these parameters, is a serious and growing problem in survival analysis. While modern medicine presents us with data of unprecedented dimensionality, these data cannot yet be used effectively for clinical outcome prediction. Standard error measures in maximum likelihood regression, such as p-values and z-scores, are blind to overfitting, and even for Cox's proportional hazards model (the main tool of medical statisticians), one finds in literature only rules of thumb on the number of samples required to avoid overfitting. Read More

As we enter the era of gravitational wave astronomy, we are beginning to collect observations which will enable us to explore aspects of astrophysics of massive stellar binaries which were previously beyond reach. In this paper we describe COMPAS (Compact Object Mergers: Population Astrophysics and Statistics), a new platform to allow us to deepen our understanding of isolated binary evolution and the formation of gravitational-wave sources. We describe the computational challenges associated with their exploration, and present preliminary results on overcoming them using Gaussian process regression as a simulation emulation technique. Read More

During its first 4 months of taking data, Advanced LIGO has detected gravitational waves from two binary black hole mergers, GW150914 and GW151226, along with the statistically less significant binary black hole merger candidate LVT151012. We use our rapid binary population synthesis code COMPAS to show that all three events can be explained by a single evolutionary channel -- classical isolated binary evolution via mass transfer including a common envelope phase. We show all three events could have formed in low-metallicity environments (Z = 0. Read More

**Affiliations:**

^{1}MATHERIALS, Saint-Venant,

^{2}MATHERIALS, Saint-Venant

**Category:**Mathematics - Numerical Analysis

We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D $\subset$ R d , d = 2 or 3$, subject to no flow boundary conditions. Our schemes are based on approximating the pressure and the symmetric conforma-tion tensor by either (a) piecewise constants or (b) continuous piecewise linears. In case (a) the velocity field is approximated by continuous piecewise quadratics ($d = 2$) or a reduced version, where the tangential component on each simplicial edge ($d = 2$) or face ($d = 3$) is linear. Read More

The emergence of quantum computers has challenged long-held beliefs about what is efficiently computable given our current physical theories. However, going back to the work of Abrams and Lloyd, changing one aspect of quantum theory can result in yet more dramatic increases in computational power, as well as violations of fundamental physical principles. Here we focus on efficient computation within a framework of general physical theories that make good operational sense. Read More

We consider the existence of global-in-time weak solutions in two spatial dimensions to the Hookean dumbbell model, which arises as a microscopic-macroscopic bead-spring model from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. This model involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. Read More

Motivation: Epigenetic heterogeneity within a tumour can play an important role in tumour evolution and the emergence of resistance to treatment. It is increasingly recognised that the study of DNA methylation (DNAm) patterns along the genome -- so-called `epialleles' -- offers greater insight into epigenetic dynamics than conventional analyses which examine DNAm marks individually. Results: We have developed a Bayesian model to infer which epialleles are present in multiple regions of the same tumour. Read More

**Authors:**Daniel Furse, Stefan Groh, Nikolaus Trost, Martin Babutzka, John P. Barrett, Jan Behrens, Nicholas Buzinksy, Thomas Corona, Sanshiro Enomoto, Moritz Erhard, Joseph A. Formaggio, Ferenc Glück, Fabian Harms, Florian Heizmann, Daniel Hilk, Wolfgang Käfer, Marco Kleesiek, Benjamin Leiber, Susanne Mertens, Noah S. Oblath, Pascal Renschler, Johannes Schwarz, Penny L. Slocum, Nancy Wandkowsky, Kevin Wierman, Michael Zacher

The Kassiopeia particle tracking framework is an object-oriented software package using modern C++ techniques, written originally to meet the needs of the KATRIN collaboration. Kassiopeia features a new algorithmic paradigm for particle tracking simulations which targets experiments containing complex geometries and electromagnetic fields, with high priority put on calculation efficiency, customizability, extensibility, and ease of use for novice programmers. To solve Kassiopeia's target physics problem the software is capable of simulating particle trajectories governed by arbitrarily complex differential equations of motion, continuous physics processes that may in part be modeled as terms perturbing that equation of motion, stochastic processes that occur in flight such as bulk scattering and decay, and stochastic surface processes occuring at interfaces, including transmission and reflection effects. Read More

Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn--Hilliard model on an evolving hypersurface coupled to Navier--Stokes equations on the surface and in the surrounding medium to model these phenomena. The evolution is driven by a curvature energy, modelling the elasticity of the membrane, and by a Cahn--Hilliard type energy, modelling line energy effects. Read More

We present a composable security proof, valid against arbitrary attacks and including finite-size effects, for a high dimensional time-frequency quantum key distribution (TFQKD) protocol based upon spectrally entangled photons. Previous works have focused on TFQKD schemes as it combines the impressive loss tolerance of single-photon QKD with the large alphabets of continuous variable (CV) schemes, which enables the potential for more than one bit of secret key per transmission. However, the finite-size security of such schemes has only been proven under the assumption of collective Gaussian attacks. Read More

Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. Read More

A compressible Oldroyd--B type model with stress diffusion is derived from a compressible Navier--Stokes--Fokker--Planck system arising in the kinetic theory of dilute polymeric fluids, where polymer chains immersed in a barotropic, compressible, isothermal, viscous Newtonian solvent, are idealized as pairs of massless beads connected with Hookean springs. We develop a-priori bounds for the model, including a logarithmic bound, which guarantee the nonnegativity of the elastic extra stress tensor, and we prove the existence of large data global-in-time finite-energy weak solutions in two space dimensions. Read More

Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behavior should arguably satisfy. In the framework of generalized probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. Read More

Standard quantum theory represents a composite system at a given time by a joint state, but it does not prescribe a joint state for a composite of systems at different times. If a more even-handed treatment of space and time is possible, then such a joint state should be definable, and one might expect it to satisfy the following five conditions: that it is a Hermitian operator on the tensor product of the single-time Hilbert spaces; that it represents probabilistic mixing appropriately; that it has the appropriate classical limit; that it has the appropriate single-time marginals; that composing over multiple time-steps is associative. We show that no construction satisfies all these requirements. Read More

We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution is based on a parametric description allowing for tangential motion, whereas the discretisation for the PDE on the curve uses an idea from [6]. We prove optimal error bounds for the resulting fully discrete approximation and present numerical experiments. Read More

We have measured the total kinetic energy (TKE) release for the $^{235}$U(n,f) reaction for $E_{n}$=2-100 MeV using the 2E method with an array of Si PIN diode detectors. The neutron energies were determined by time of flight measurements using the white spectrum neutron beam at the LANSCE facility. To benchmark the TKE measurement, the TKE release for $^{235}$U(n$_{th}$,f) was also measured using a thermal neutron beam from the Oregon State University TRIGA reactor, giving pre-neutron emission $E^*_{TKE}=170. Read More

We consider the quasi-static magnetic hysteresis model based on a dry-friction like representation of magnetization. The model has a consistent energy interpretation, is intrinsically vectorial, and ensures a direct calculation of the stored and dissipated energies at any moment in time, and hence not only on the completion of a closed hysteresis loop. We discuss the variational formulation of this model and derive an efficient numerical scheme, avoiding the usually employed approximation which can be inaccurate in the vectorial case. Read More

Molecules with hyperfine splitting of their rotational line spectra are useful probes of optical depth, via the relative line strengths of their hyperfine components.The hyperfine splitting is particularly advantageous in interpreting the physical conditions of the emitting gas because with a second rotational transition, both gas density and temperature can be derived. For HCN however, the relative strengths of the hyperfine lines are anomalous. Read More

**Authors:**M. Arenz, M. Babutzka, M. Bahr, J. P. Barrett, S. Bauer, M. Beck, A. Beglarian, J. Behrens, T. Bergmann, U. Besserer, J. Blümer, L. I. Bodine, K. Bokeloh, J. Bonn, B. Bornschein, L. Bornschein, S. Büsch, T. H. Burritt, S. Chilingaryan, T. J. Corona, L. De Viveiros, P. J. Doe, O. Dragoun, G. Drexlin, S. Dyba, S. Ebenhöch, K. Eitel, E. Ellinger, S. Enomoto, M. Erhard, D. Eversheim, M. Fedkevych, A. Felden, S. Fischer, J. A. Formaggio, F. Fränkle, D. Furse, M. Ghilea, W. Gil, F. Glück, A. Gonzalez Urena, S. Görhardt, S. Groh, S. Grohmann, R. Grössle, R. Gumbsheimer, M. Hackenjos, V. Hannen, F. Harms, N. Hauÿmann, F. Heizmann, K. Helbing, W. Herz, S. Hickford, D. Hilk, B. Hillen, T. Höhn, B. Holzapfel, M. Hötzel, M. A. Howe, A. Huber, A. Jansen, N. Kernert, L. Kippenbrock, M. Kleesiek, M. Klein, A. Kopmann, A. Kosmider, A. Kovalík, B. Krasch, M. Kraus, H. Krause, M. Krause, L. Kuckert, B. Kuffner, L. La Cascio, O. Lebeda, B. Leiber, J. Letnev, V. M. Lobashev, A. Lokhov, E. Malcherek, M. Mark, E. L. Martin, S. Mertens, S. Mirz, B. Monreal, K. Müller, M. Neuberger, H. Neumann, S. Niemes, M. Noe, N. S. Oblath, A. Off, H. -W. Ortjohann, A. Osipowicz, E. Otten, D. S. Parno, P. Plischke, A. W. P. Poon, M. Prall, F. Priester, P. C. -O. Ranitzsch, J. Reich, O. Rest, R. G. H. Robertson, M. Röllig, S. Rosendahl, S. Rupp, M. Rysavy, K. Schlösser, M. Schlösser, K. Schönung, M. Schrank, J. Schwarz, W. Seiler, H. Seitz-Moskaliuk, J. Sentkerestiova, A. Skasyrskaya, M. Slezak, A. Spalek, M. Steidl, N. Steinbrink, M. Sturm, M. Suesser, H. H. Telle, T. Thümmler, N. Titov, I. Tkachev, N. Trost, A. Unru, K. Valerius, D. Venos, R. Vianden, S. Vöcking, B. L. Wall, N. Wandkowsky, M. Weber, C. Weinheimer, C. Weiss, S. Welte, J. Wendel, K. L. Wierman, J. F. Wilkerson, D. Winzen, J. Wolf, S. Wüstling, M. Zacher, S. Zadoroghny, M. Zboril

**Category:**Physics - Instrumentation and Detectors

The KATRIN experiment will probe the neutrino mass by measuring the beta-electron energy spectrum near the endpoint of tritium beta-decay. An integral energy analysis will be performed by an electro-static spectrometer (Main Spectrometer), an ultra-high vacuum vessel with a length of 23.2 m, a volume of 1240 m^3, and a complex inner electrode system with about 120000 individual parts. Read More

**Authors:**Jin Koda

^{1}, James Barrett

^{2}, Tetsuo Hasegawa

^{3}, Masahiko Hayashi

^{4}, Gene Shafto

^{5}, Jeff Slechta

^{6}, Stanimir Metchev

^{7}

**Affiliations:**

^{1}Stony Brook,

^{2}Stony Brook,

^{3}NAOJ Chile,

^{4}NAOJ,

^{5}Stony Brook,

^{6}Stony Brook,

^{7}Stony Brook

We report development of a simple and affordable radio interferometer suitable as an educational laboratory experiment. With the increasing importance of interferometry in astronomy, the lack of educational interferometers is an obstacle to training the future generation of astronomers. This interferometer provides the hands-on experience needed to fully understand the basic concepts of interferometry. Read More

A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parameterised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Read More

We have measured the total kinetic energy (TKE) release for the $^{235}$U(n,f) reaction for $E_{n}$=2-100 MeV using the 2E method with an array of Si PIN diode detectors. The neutron energies were determined by time of flight measurements using the white spectrum neutron beam at the LANSCE facility. (To calibrate the apparatus, the TKE release for $^{235}$U(n$_{th}$,f) was also measured using a thermal neutron beam from the OSU TRIGA reactor). Read More

Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated using Monte Carlo simulations to compute the integrals. Various qualitatively different types of behaviour of these random Dirac operators are exhibited. Read More

Information-adaptive designs estimate how much statistical information an individual is expected to provide and allocates them to treatment arms in a manner that maximises information gain. Information-adaptive designs with selective recruitment preferentially recruit individuals that are estimated to be statistically informative onto a clinical trial. Individuals that are expected to contribute less information have a lower probability of recruitment. Read More

**Affiliations:**

^{1}University of New Mexico,

^{2}University of Oxford,

^{3}University of Heidelberg, University of Western Ontario,

^{4}University of Heidelberg, University of Western Ontario, Perimeter Institute for Theoretical Physics

In this note we lay some groundwork for the resource theory of thermodynamics in general probabilistic theories (GPTs). We consider theories satisfying a purely convex abstraction of the spectral decomposition of density matrices: that every state has a decomposition, with unique probabilities, into perfectly distinguishable pure states. The spectral entropy, and analogues using other Schur-concave functions, can be defined as the entropy of these probabilities. Read More

The yields of over 200 projectile-like fragments (PLFs) and target-like fragments (TLFs) from the interaction of (E$_{c.m.}$=450 MeV) $^{136}$Xe with a thick target of $^{208}$Pb were measured using Gammasphere and off-line $\gamma$-ray spectroscopy, giving a comprehensive picture of the production cross sections in this reaction. Read More

Vesicles and many biological membranes are made of two monolayers of lipid molecules and form closed lipid bilayers. The dynamical behaviour of vesicles is very complex and a variety of forms and shapes appear. Lipid bilayers can be considered as a surface fluid and hence the governing equations for the evolution include the surface (Navier--)Stokes equations, which in particular take the membrane viscosity into account. Read More

A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy spaces defined as real spectral triples. Fuzzy 2-spheres are investigated in detail, and it is shown that the fuzzy analogues correspond to two spinor fields on the commutative sphere. Read More

We propose a novel adaptive design for clinical trials with time-to-event outcomes and covariates (which may consist of or include biomarkers). Our method is based on the expected entropy of the posterior distribution of a proportional hazards model. The expected entropy is evaluated as a function of a patient's covariates, and the information gained due to a patient is defined as the decrease in the corresponding entropy. Read More

From the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation is that BQP is in AWPP. This work investigates limits on computational power that are imposed by physical principles. Read More

Low-coverage short-read resequencing experiments have the potential to expand our understanding of Y chromosome haplogroups. However, the uncertainty associated with these experiments mean that haplogroups must be assigned probabilistically to avoid false inferences. We propose an efficient dynamic programming algorithm that can assign haplogroups by maximum likelihood, and represent the uncertainty in assignment. Read More

We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains with finitely extensible nonlinear elastic (FENE) type spring potentials. The class of models under consideration involves the unsteady, compressible, isentropic, isothermal Navier-Stokes system in a bounded domain $\Omega$ in $\mathbb{R}^d$, $d = 2$ or $3$, for the density, the velocity and the pressure of the fluid. The right-hand side of the Navier-Stokes momentum equation includes an elastic extra-stress tensor, which is the sum of the classical Kramers expression and a quadratic interaction term. Read More

The analysis of high dimensional survival data is challenging, primarily due to the problem of overfitting which occurs when spurious relationships are inferred from data that subsequently fail to exist in test data. Here we propose a novel method of extracting a low dimensional representation of covariates in survival data by combining the popular Gaussian Process Latent Variable Model (GPLVM) with a Weibull Proportional Hazards Model (WPHM). The combined model offers a flexible non-linear probabilistic method of detecting and extracting any intrinsic low dimensional structure from high dimensional data. Read More

Magnetic traps for cold atoms have become a powerful tool of cold atom physics and condense matter research. The traps on superconducting chips allow one to increase the trapped atom life- and coherence time by decreasing the thermal noise by several orders of magnitude compared to that of the typical normal-metal conductors. A thin superconducting film in the mixed state is, usually, the main element of such a chip. Read More

We consider two-phase Navier--Stokes flow with a Boussinesq--Scriven surface fluid. In such a fluid the rheological behaviour at the interface includes surface viscosity effects, in addition to the classical surface tension effects. We introduce and analyze parametric finite element approximations, and show, in particular, stability results for semi-discrete versions of the methods, by demonstrating that a free energy inequality also holds on the discrete level. Read More

**Authors:**J. F. Amsbaugh, J. Barrett, A. Beglarian, T. Bergmann, H. Bichsel, L. I. Bodine, J. Bonn, N. M. Boyd, T. H. Burritt, Z. Chaoui, S. Chilingaryan, T. J. Corona, P. J. Doe, J. A. Dunmore, S. Enomoto, J. Fischer, J. A. Formaggio, F. M. Fränkle, D. Furse, H. Gemmeke, F. Glück, F. Harms, G. C. Harper, J. Hartmann, M. A. Howe, A. Kaboth, J. Kelsey, M. Knauer, A. Kopmann, M. L. Leber, E. L. Martin, K. J. Middleman, A. W. Myers, N. S. Oblath, D. S. Parno, D. A. Peterson, L. Petzold, D. G. Phillips II, P. Renschler, R. G. H. Robertson, J. Schwarz, M. Steidl, D. Tcherniakhovski, T. Thümmler, T. D. Van Wechel, B. A. VanDevender, S. Vöcking, B. L. Wall, K. L. Wierman, J. F. Wilkerson, S. Wüstling

The focal-plane detector system for the KArlsruhe TRItium Neutrino (KATRIN) experiment consists of a multi-pixel silicon p-i-n-diode array, custom readout electronics, two superconducting solenoid magnets, an ultra high-vacuum system, a high-vacuum system, calibration and monitoring devices, a scintillating veto, and a custom data-acquisition system. It is designed to detect the low-energy electrons selected by the KATRIN main spectrometer. We describe the system and summarize its performance after its final installation. Read More

We describe a technique to analytically compute the multipole moments of a charge distribution confined to a planar triangle, which may be useful in solving the Laplace equation using the fast multipole boundary element method (FMBEM) and for charged particle tracking. This algorithm proceeds by performing the necessary integration recursively within a specific coordinate system, and then transforming the moments into the global coordinate system through the application of rotation and translation operators. This method has been implemented and found use in conjunction with a simple piecewise constant collocation scheme, but is generalizable to non-uniform charge densities. Read More

We have studied the fission-neutron emission competition in highly excited $^{274}$Hs (Z=108) (where the fission barrier is due to shell effects) formed by a hot fusion reaction. Matching cross bombardments ($^{26}$Mg + $^{248}$Cm and $^{25}$Mg + $^{248}$Cm) were used to identify the properties of first chance fission of $^{274}$Hs. A Harding-Farley analysis of the fission neutrons emitted in the $^{25,26}$Mg + $^{248}$Cm was performed to identify the pre- and post-scission components of the neutron multiplicities in each system. Read More

The state sum models in two dimensions introduced by Fukuma, Hosono and Kawai are generalised by allowing algebraic data from a non-symmetric Frobenius algebra. Without any further data, this leads to a state sum model on the sphere. When the data is augmented with a crossing map, the partition function is defined for any oriented surface with a spin structure. Read More

We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates are regarded as the `inputs' and the event times are the `outputs'. This allows for highly flexible inference of non-linear relationships between covariates and event times. Read More

We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport equation for the insoluble surfactant on the interface that separates the two phases. We combine the evolving surface finite element method with an approach previously introduced by the authors for two-phase Navier--Stokes flow, which maintains good mesh properties. Read More

According to a recent no-go theorem (M. Pusey, J. Barrett and T. Read More

The gauge gravity action for general relativity in any dimension using a connection for the Euclidean or Poincar\'e group and a symmetry-breaking scalar field is written using a particularly simple matrix technique. A discrete version of the gauge gravity action for variables on a triangulated 3-manifold is given and it is shown how, for a certain class of triangulations of the three-sphere, the discrete quantum model this defines is equivalent to the Ponzano-Regge model of quantum gravity. Read More

We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface. Read More

The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP) estimation of the latent variables and hyperparameters can be used for model selection and hence we can determine the optimal number or latent variables and the most appropriate model. This is an alternative to the variational approaches developed recently and may be useful when we want to use a non-Gaussian prior or kernel functions that don't have automatic relevance determination (ARD) parameters. Read More

Similar evolutionary variational and quasi-variational inequalities with gradient constraints arise in the modeling of growing sandpiles and type-II superconductors. Recently, mixed formulations of these inequalities were used for establishing existence results in the quasi-variational inequality case. Such formulations, and this is an additional advantage, made it possible to determine numerically not only the primal variables, e. Read More

Background: The cross section for forming a heavy evaporation residue in fusion reactions depends on the capture cross section, the fusion probability, PCN, i.e., the probability that the projectile-target system will evolve inside the fission saddle point to form a completely fused system rather than re-separating (quasifission), and the survival of the completely fused system against fission. Read More

We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface. Read More

Thin film magnetization problems in type-II superconductivity are usually formulated in terms of the magnetization function alone, which allows one to compute the sheet current density and the magnetic field but often inhibits computing the electric field in the film. Accounting for the current leads presents an additional difficulty encountered in thin film transport current problems. We generalize, to the presence of a transport current, the two-variable variational formulation proposed recently for thin film magnetization problems. Read More

We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Particular emphasis is put on Stefan problems, and their quasi-static variants, with applications to crystal growth. New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem. Read More