Points In Parameter Space Research Articles

On Parameter Identifiability in Non-Linear Biophysical Models

The quantitative modeling of biological phenomena allows for a deeper understanding of underlying mechanisms as well as the determination of biophysical parameters. However, we note that in many systems, the unique identification of relevant parameters is not possible with common experimental methods. The parameters of a model are said to be identifiable if there a unique point in parameter space that leads to an optimal agreement with particular data. In common non-linear models, however, there is not a unique map from parameter space to data space, and the confusion resulting from this lack of parameter identifiability may be slowing progress in many fields of biophysics. We use a simple example model to show analytically that this problem often results from rank-difficient regression, i.e., there are an infinite number of ways for the model parameters to fit the data equally well. Further, we use the same model to show that the identifiability problem can be resolved if additional experimental data is included for model constraint. Unfortunately, most models of interest will not be amenable to analytical examination. We present a numerical method based on Markov chain Monte Carlo (MCMC) sampling which can be used for any data and any model and will allow the diagnosis of these issues. We provide example uses of MCMC to asses parameter identifiability in a variety of systems. This method is an important tool that provides the ability to assess parameter identifiability for a given model and various potential experimental manipulations. This new kind of power analysis will lead to more precise conclusion and more fruitful experimentation.

Unbinding of Giant Vortices in States of Competing Order

We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O(M), near a point in parameter space where they couple to become a single O(2+M) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as 1/√Δ and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as 1/ln(1/Δ), where Δ denotes the distance from the high-symmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.

Using dark modes for high-fidelity optomechanical quantum state transfer

In a recent publication (Wang and Clerk 2012 Phys. Rev. Lett.108 153603), we demonstrated that one can use interference to significantly increase the fidelity of state transfer between two electromagnetic cavities coupled to a common mechanical resonator over a naive sequential-transfer scheme based on two swap operations. This involved making use of a delocalized electromagnetic mode which is decoupled from the mechanical resonator, a so-called ‘mechanically dark’ mode. Here, we demonstrate the existence of a new ‘hybrid’ state transfer scheme that incorporates the best elements of the dark-mode scheme (protection against mechanical dissipation) and the double-swap scheme (fast operation time). Importantly, this new scheme also does not require the mechanical resonator to be prepared initially in its ground state. We also provide additional details of the previously described interference-enhanced transfer schemes, and provide an enhanced discussion of how the interference physics here is intimately related to the optomechanical analogue of electromagnetically induced transparency. We also compare the various transfer schemes over a wide range of relevant experimental parameters, producing a ‘phase diagram’ showing the optimal transfer scheme for different points in parameter space.

A New Test for Testing Non Inferiority in Matched-Pairs Design

Non inferiority of one diagnostic method to another is a common issue in medical research. This article proposes a new test using an approximate p-value, which is based on only one point of the two-dimension nuisance parameter space. The sizes and powers of our test, the asymptotic normal test,Sidik and Hsueh's unconditional exact tests are considered. Simulation results suggest that our test can definitely control the Type I error rates with reasonable powers under all studied conditions while the asymptotic normal test cannot for most cases. Compared to Sidik and Hsueh's tests, our test is much easier to implement.

Three-dimensional tricritical gravity

We consider a class of parity even, six-derivative gravity theories in three dimensions. After linearizing around anti-de Sitter space, the theories have one massless and two massive graviton solutions for generic values of the parameters. At a special, so-called tricritical, point in parameter space the two massive graviton solutions become massless and they are replaced by two solutions with logarithmic and logarithmic-squared boundary behavior. The theory at this point is conjectured to be dual to a rank-3 Logarithmic Conformal Field Theory (LCFT) whose boundary stress tensor, central charges and new anomaly we calculate. We also calculate the conserved Abbott-Deser-Tekin charges. At the tricritical point, these vanish for excitations that obey Brown-Henneaux and logarithmic boundary conditions, while they are generically non-zero for excitations that show logarithmic-squared boundary behavior. This suggests that a truncation of the tricritical gravity theory and its corresponding dual LCFT can be realized either via boundary conditions on the allowed gravitational excitations, or via restriction to a zero charge sub-sector. We comment on the structure of the truncated theory.

A numerical coarse-grained description of a binary alloy

We employ Monte Carlo simulation in the semi-grand canonical ensemble to obtain the coarse-grained free energy corresponding to an embedded-atom method description of a binary alloy. In particular, the Ginzburg-Landau free energy for a Cu-Ni alloy was determined from a tabulated histogram of the joint probability density of composition, energy, and volume. Using histogram reweighting techniques, the free energy is extrapolated to a range of points in parameter space from a small number of simulations. The results are interpreted by comparing the free energy with that corresponding to a regular solution model of an alloy. In addition, we obtain expressions for thermodynamic quantities in terms of the joint cumulants of the probability density at a given temperature and chemical potential difference. These expressions may then be likewise extrapolated to obtain the dependence of the composition on the temperature and the chemical potential difference over a wide range of parameter space.

Replacing Causal Faithfulness with Algorithmic Independence of Conditionals

Independence of Conditionals (IC) has recently been proposed as a basic rule for causal structure learning. If a Bayesian network represents the causal structure, its Conditional Probability Distributions (CPDs) should be algorithmically independent. In this paper we compare IC with causal faithfulness (FF), stating that only those conditional independences that are implied by the causal Markov condition hold true. The latter is a basic postulate in common approaches to causal structure learning. The common spirit of FF and IC is to reject causal graphs for which the joint distribution looks `non-generic'. The difference lies in the notion of genericity: FF sometimes rejects models just because one of the CPDs is simple, for instance if the CPD describes a deterministic relation. IC does not behave in this undesirable way. It only rejects a model when there is a non-generic relation between different CPDs although each CPD looks generic when considered separately. Moreover, it detects relations between CPDs that cannot be captured by conditional independences. IC therefore helps in distinguishing causal graphs that induce the same conditional independences (i.e., they belong to the same Markov equivalence class). The usual justification for FF implicitly assumes a prior that is a probability density on the parameter space. IC can be justified by Solomonoff's universal prior, assigning non-zero probability to those points in parameter space that have a finite description. In this way, it favours simple CPDs, and therefore respects Occam's razor. Since Kolmogorov complexity is uncomputable, IC is not directly applicable in practice. We argue that it is nevertheless helpful, since it has already served as inspiration and justification for novel causal inference algorithms.

Efficient Block-Based Parameterized Timing Analysis Covering All Potentially Critical Paths

In order for the results of timing analysis to be useful, they must provide insight and guidance on how the circuit may be improved so as to fix any reported timing problems. A limitation of many recent variability-aware timing analysis techniques is that, while they report delay distributions, or verify multiple corners, they do not provide the required guidance for re-design. We propose an efficient block-based parameterized timing analysis technique that can accurately capture circuit delay at every point in the parameter space, by reporting all paths that can become critical. Using an efficient pruning algorithm, only those potentially critical paths are carried forward, while all other paths are discarded during propagation. This allows one to examine local robustness to parameters in different regions of the parameter space, not by considering differential sensitivity at a point (that would be useless in this context) but by knowledge of the paths that can become critical at nearby points in parameter space. We give a formal definition of this problem and propose a technique for solving it, which improves on the state of the art, both in terms of theoretical computational complexity and in terms of runtime on various test circuits.

A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion

We address the solution of large-scale statistical inverse problems in the framework of Bayesian inference. The Markov chain Monte Carlo (MCMC) method is the most popular approach for sampling the posterior probability distribution that describes the solution of the statistical inverse problem. MCMC methods face two central difficulties when applied to large-scale inverse problems: first, the forward models (typically in the form of partial differential equations) that map uncertain parameters to observable quantities make the evaluation of the probability density at any point in parameter space very expensive; and second, the high-dimensional parameter spaces that arise upon discretization of infinite-dimensional parameter fields make the exploration of the probability density function prohibitive. The challenge for MCMC methods is to construct proposal functions that simultaneously provide a good approximation of the target density while being inexpensive to manipulate. Here we present a so-called Stoch...

NMSDECAY: A Fortran code for supersymmetric particle decays in the Next-to-Minimal Supersymmetric Standard Model

The code NMSDECAY allows to compute widths and branching ratios of sparticle decays in the Next-to-Minimal Supersymmetric Standard Model. It is based on a generalization of SDECAY, to include the extended Higgs and neutralino sectors of the NMSSM. Slepton 3-body decays, possibly relevant in the case of a singlino-like lightest supersymmetric particle, have been added. NMSDECAY will be part of the NMSSMTools package, which computes Higgs, sparticle masses and Higgs decays in the NMSSM. Program summary Program title: NMSDECAY Catalogue identifier: AELC_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELC_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 188 177 No. of bytes in distributed program, including test data, etc.: 1 896 478 Distribution format: tar.gz Programming language: FORTRAN77 Computer: All supporting g77, gfortran, ifort Operating system: All supporting g77, gfortran, ifort Classification: 11.1 External routines: Routines in the NMSSMTools package: At least one of the routines in the directory main (e.g. nmhdecay.f), all routines in the directory sources. (All software is included in the distribution package.) Nature of problem: Calculation of all decay widths and decay branching fractions of all particles in the Next-to-Minimal Supersymmetric Standard Model. Solution method: Suitable generalization of the code SDECAY [1] including the extended Higgs and neutralino sector of the Next-to-Minimal Supersymmetric Standard Model, and slepton 3-body decays. Additional comments: NMSDECAY is interfaced with NMSSMTools, available on the web page http://www.th.u-psud.fr/NMHDECAY/nmssmtools.html. Running time: On an Intel Core i7 with 2.8 GHZ: about 2 seconds per point in parameter space, if all flags flagqcd, flagmulti and flagloop are switched on.

A numerical analysis model for interpretation of flow cytometric studies of ex vivo phagocytosis.

The study of ex vivo phagocytosis via flow cytometry requires that one distinguish experimentally between uptake and adsorption of fluorescently labeled targets by phagocytes. Removal of the latter quantity from the analysis is the most common means of analyzing such data. Because the probability of phagocytosis is a function of the probability of adsorption, and because partially quenched fluorescence after uptake often overlaps with that of negative controls, this approach is suboptimal at best. Here, we describe a numerical analysis model which overcomes these limitations. We posit that the random adsorption of targets to macrophages, and subsequent phagocytosis, is a function of three parameters: the ratio of targets to macrophages (m), the mean fluorescence intensity imparted to the phagocyte by the internalized target (alpha), and the probability of phagocytosis per adsorbed target (p). The potential values of these parameters define a parameter space and their values at any point in parameter space can be used to predict the fraction of adsorption(+) and [adsorption(−), phagocytosis(+)] cells that might be observed experimentally. By systematically evaluating the points in parameter space for the latter two values and comparing them to experimental data, the model arrives at sets of parameter values that optimally predict such data. Using activated THP-1 cells as macrophages and platelets as targets, we validate the model by demonstrating that it can distinguish between the effects of experimental changes in m, alpha, and p. Finally, we use the model to demonstrate that platelets from a congenitally thrombocytopenic WAS patient show an increased probability of ex vivo phagocytosis. This finding correlates with other evidence that rapid in vivo platelet consumption contributes significantly to the thrombocytopenia of WAS. Our numerical analysis method represents a useful and innovative approach to multivariate analysis.

On Critical Massive (Super)Gravity in adS3

We review the status of three-dimensional "general massive gravity" (GMG) in its linearization about an anti-de Sitter (adS) vacuum, focusing on critical points in parameter space that yield generalizations of "chiral gravity". We then show how these results extend to \U0001d4a9 = 1 super-GMG, expanded about a supersymmetric adS vacuum, and also to the most general 'curvature-squared' \U0001d4a9 = 1 supergravity model.

Discovery reach for generic supersymmetry at the LHC: M T2 versus missing transverse momentum selections for pMSSM searches

Different search strategies for supersymmetry have been employed by the LHC general-purpose experiments using early data. As proven by their early results, these strategies are promising, but raise the question of how well they will generalize for the future. We address this question by studying two thousand phenomenological minimal supersymmetric standard model parameter space points that come from a fit to indirect and cosmological data. We examine the 5σ discoverability of the points employing a typical ATLAS-type search based on missing transverse momentum (MET), a search based on an optimised M T2 cut and a combination of the two, taking into account standard model backgrounds. The discovery reach of the strategies can depend strongly on the systematic uncertainty in the background, subject to the stringency of the cuts and the details of the background simulation. By combining the MET and M T2 based strategies, with an integrated luminosity of 1 fb−1 (10 fb−1) at 7 TeV, 4-8%(42%) of the points are discoverable, depending on the systematic uncertainty on the background. At 14TeVand with10fb−1, 96% of the points are discoverable. While the majority of points can be discovered by both strategies at \( \sqrt {s} = 14 \) TeV and with 1fb−1, there are some that are left undiscovered by a MET search strategy, but which are discovered by the M T2 strategy, and vice versa, therefore it is essential that one performs both in parallel. We discuss some of the factors that can make points more difficult to observe.

Fast frequency-domain algorithm for gravitational self-force: Circular orbits in Schwarzschild spacetime

Fast, reliable orbital evolutions of compact objects around massive black holes will be needed as input for gravitational wave search algorithms in the data stream generated by the planned Laser Interferometer Space Antenna (LISA). Currently, the state of the art is a time-domain code by [Phys. Rev. D{\bf 81}, 084021, (2010)] that computes the gravitational self-force on a point-particle in an eccentric orbit around a Schwarzschild black hole. Currently, time-domain codes take up to a few days to compute just one point in parameter space. In a series of articles, we advocate the use of a frequency-domain approach to the problem of gravitational self-force (GSF) with the ultimate goal of orbital evolution in mind. Here, we compute the GSF for a particle in a circular orbit in Schwarzschild spacetime. We solve the linearized Einstein equations for the metric perturbation in Lorenz gauge. Our frequency-domain code reproduces the time-domain results for the GSF up to $\sim 1000$ times faster for small orbital radii. In forthcoming companion papers, we will generalize our frequency-domain methods to include bound (eccentric) orbits in Schwarzschild and (eventually) Kerr spacetimes for computing the GSF, where we will employ the method of extended homogeneous solutions [Phys. Rev. D {\bf 78}, 084021 (2008)].

A laboratory study of global-scale wave interactions in baroclinic flow with topography I: multiple flow regimes

A laboratory investigation is presented with the aim of studying systematically the diversity of flows resulting from the interaction of a baroclinic flow with periodic bottom topography. Flow visualisation and particle-tracking experiments were performed using a differentially heated rotating annulus of fluid with sinusoidal bottom topography. Multi-directional regime scans with varying initial locations in parameter space revealed a rich variety of flow regimes, including those with near-axisymmetric flow at upper levels and a weak stationary wave forced by the topography which is evanescent at upper levels, and flows with a strong forced wave at all heights both with and without travelling baroclinic waves. A range of time-dependent and vacillating flows was also found. The parametric occurrence of the principal regimes agrees well with a number of earlier studies, which covered a more limited range and at lower resolution in parameter space. It is clear from these results that multiple flow states at the same point in parameter space are very common in baroclinically unstable flows with topography. The parametric extent of the influence of the topographically forced stationary waves was shown to be qualitatively consistent with the well-known Charney–Drazin criterion for vertical wave propagation.

Leptogenesis: The other cuts

For standard leptogenesis from the decay of singlet right-handed neutrinos, we derive source terms for the lepton asymmetry that are present in a finite density background but absent in the vacuum. These arise from cuts through the vertex correction to the decay asymmetry, where in the loop either the Higgs boson and the right-handed neutrino or the left-handed lepton and the right-handed neutrino are simultaneously on-shell. We evaluate the source terms numerically and use them to calculate the lepton asymmetry for illustrative points in parameter space, where we consider only two right-handed neutrinos for simplicity. Compared to calculations where only the standard cut through the propagators of left-handed lepton and Higgs boson is included, sizable corrections arise when the masses of the right-handed neutrinos are of the same order, but the new sources are found to be most relevant when the decaying right-handed neutrino is heavier than the one in the loop. In that situation, they can yield the dominant contribution to the lepton asymmetry.

Accuracy and effectualness of closed-form, frequency-domain waveforms for nonspinning black hole binaries

The coalescences of binary black hole (BBH) systems, here taken to be non-spinning, are among the most promising sources for gravitational wave (GW) ground-based detectors, such as LIGO and Virgo. To detect the GW signals emitted by BBHs, and measure the parameters of the source, one needs to have in hand a bank of GW templates that are both effectual (for detection), and accurate (for measurement). We study the effectualness and the accuracy of the two types of parametrized banks of templates that are directly defined in the frequency-domain by means of closed-form expressions, namely 'post-Newtonian' (PN) and 'phenomenological' models. In absence of knowledge of the exact waveforms, our study assumes as fiducial, target waveforms the ones generated by the most accurate version of the effective one body (EOB) formalism. We find that, for initial GW detectors the use, at each point of parameter space, of the best closed-form template (among PN and phenomenological models) leads to an effectualness >97% over the entire mass range and >99% in an important fraction of parameter space; however, when considering advanced detectors, both of the closed-form frequency-domain models fail to be effectual enough in significant domains of the two-dimensional [total mass and mass ratio] parameter space. Moreover, we find that, both for initial and advanced detectors, the two closed-form frequency-domain models fail to satisfy the minimal required accuracy standard in a very large domain of the two-dimensional parameter space. In addition, a side result of our study is the determination, as a function of the mass ratio, of the maximum frequency at which a frequency-domain PN waveform can be 'joined' onto a NR-calibrated EOB waveform without undue loss of accuracy.

Exceptional Points for Nonlinear Schroedinger Equations Describing Bose-Einstein Condensates of Ultracold Atomic Gases

The coalescence of two eigenfunctions with the same energy eigenvalue is not possible in Hermitian Hamiltonians. It is, however, a phenomenon well known from non-hermitian quantum mechanics. It can appear, e.g., for resonances in open systems, with complex energy eigenvalues. If two eigenvalues of a quantum mechanical system which depends on two or more parameters pass through such a branch point singularity at a critical set of parameters, the point in the parameter space is called an exceptional point. We will demonstrate that exceptional points occur not only for non-hermitean Hamiltonians but also in the nonlinear Schroedinger equations which describe Bose-Einstein condensates, i.e., the Gross-Pitaevskii equation for condensates with a short-range contact interaction, and with additional long-range interactions. Typically, in these condensates the exceptional points are also found to be bifurcation points in parameter space. For condensates with a gravity-like interaction between the atoms, these findings can be confirmed in an analytical way.

Methodological Bridges for Multi-Level Systems

“All models are wrong, but some are useful.” George Box, statistician Nowdays since modeling is growing of importance, this sentence would reflect many things: the continuous improvement of developing new models in all scientific fields, the different level of abstractions that a model could express and our difficulties in modelling multiscale dynamical systems. If the scientific progress relies on asking the right questions, we observe that different modelling methodologies often suggest slightly different questions and provide similar or different answers. In the figure on the right, a point in parameter space, given by a set of parameter values, defines a dynamics on the state space. If the system is prepared in an initial condition, then the dynamics typically lead to an attractor, pictured here as a star. We believe that a better understanding of the compositional framework of different modelling will bring easiness in making sense of large amount of heterogenesous data gathered on varison scales and also in robust parameter estimation and reverse engineering properties of various types of networks and parameters relationship. We found that when the system has a multiscale structure, formal methods help in guiding the exploration across dimensionality. In particular we report that Shape Calculus can effectively interface with a wide range of methodologies for example: Hybrid Automata, Stochastic Simulations (implemented as Gillespie algorithm or software Agent) and Model Checking, Bayesian inference and Model Checking, ODE (Ordinary Differential Equation) and PDE. We can imagine Shape Calculus as “high order” set of levers that pull the low order procedures implemented. Here we investigate the emerging behavior of connecting the Shape high levers (the tissue, the social network) with the low lever types of gear-bevel, spur-lever, helical gear constituents, etc (the cells, the individuals). Multi-Method Multi-Level approach

Line detection with adaptive random samples

This paper examines the detection of parameterized shapes in multidimensional noisy grayscale images. A novel shape detection algorithm utilizing random sample theory is presented. Although the method can be generalized, line detection is detailed. Each line in the image corresponds to a point in the line parameter space. The method creates hypothesis lines by randomly selecting parameter space points and tests the surrounding regions for acceptable linear features. The information obtained from each randomly selected line is used to update the parameter distribution, which reducesi the required number of random trials. The selected lines are re-estimated within a smaller search space with a more accurate algorithm like the Hough transform (HT). Faster results are obtained compared to HT, without losing performance as in other faster HT variants. The method is robust and suitable for binary or grayscale images. Results are given from both simulated and experimental subsurface seismic and ground penetrating radar (GPR) images when searching for features like pipes or tunnels.