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Christian Wagner

Publications and source records attributed to Christian Wagner.

At least 109 records · Page 6Linked to original sources
arXiv2012

Perturbation theory approach for the power spectrum: from dark matter in real space to massive haloes in redshift space

We investigate the accuracy of Eulerian perturbation theory for describing the matter and galaxy power spectra in real and redshift space in light of future observational probes for precision cosmology. Comparing the analytical results with a large suite of N-body simulations (160 independent boxes of 13.8 (Gpc/h)^3 volume each, which are publicly available), we find that re-summing terms in the standard perturbative approach predicts the real-space matter power spectrum with an accuracy of < 2% for k < 0.20 h/Mpc at redshifts z < 1.5. This is obtained following the widespread technique of writing the resummed propagator in terms of 1-loop contributions. We show that the accuracy of this scheme increases by considering higher-order terms in the resummed propagator. By combining resummed perturbation theories with several models for the mappings from real to redshift space discussed in the literature, the multipoles of the dark-matter power spectrum can be described with sub-percent deviations from N-body results for k < 0.15h/Mpc at z < 1. As a consequence, the logarithmic growth rate, f, can be recovered with sub-percent accuracy on these scales. Extending the models to massive dark-matter haloes in redshift space, our results describe the monopole term from N-body data within 2% accuracy for scales k < 0.15 h/Mpc at z < 0.5; here f can be recovered within < 5% when the halo bias is known. We conclude that these techniques are suitable to extract cosmological information from future galaxy surveys.

astro-ph.CO↗
arXiv2012

Mirror-Descent Methods in Mixed-Integer Convex Optimization

In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an algorithmic approach to this problem, postponing its hardness to the realization of an oracle. If this oracle can be realized in polynomial time, then the problem can be solved in polynomial time as well. For problems with two integer variables, we show that the oracle can be implemented efficiently, that is, in O(ln(B)) approximate minimizations of f over the continuous variables, where B is a known bound on the absolute value of the integer variables.Our algorithm can be adapted to find the second best point of a purely integer convex optimization problem in two dimensions, and more generally its k-th best point. This observation allows us to formulate a finite-time algorithm for mixed-integer convex optimization.

math.OC↗
arXiv2012

Bayesian Analysis of Inflation III: Slow Roll Reconstruction Using Model Selection

We implement Slow Roll Reconstruction -- an optimal solution to the inverse problem for inflationary cosmology -- within ModeCode, a publicly available solver for the inflationary dynamics. We obtain up-to-date constraints on the reconstructed inflationary potential, derived from the WMAP 7-year dataset and South Pole Telescope observations, combined with large scale structure data derived from SDSS Data Release 7. Using ModeCode in conjunction with the MultiNest sampler, we compute Bayesian evidence for the reconstructed potential at each order in the truncated slow roll hierarchy. We find that the data are well-described by the first two slow roll parameters, εand η, and that there is no need to include a nontrivial ξparameter.

astro-ph.CO↗
arXiv2012

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the Data Release 9 Spectroscopic Galaxy Sample

We present measurements of galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), which is part of the Sloan Digital Sky Survey III (SDSS-III). These use the Data Release 9 (DR9) CMASS sample, which contains 264,283 massive galaxies covering 3275 square degrees with an effective redshift z=0.57 and redshift range 0.43 < z < 0.7. Assuming a concordance Lambda-CDM cosmological model, this sample covers an effective volume of 2.2 Gpc^3, and represents the largest sample of the Universe ever surveyed at this density, n = 3 x 10^-4 h^-3 Mpc^3. We measure the angle-averaged galaxy correlation function and power spectrum, including density-field reconstruction of the baryon acoustic oscillation (BAO) feature. The acoustic features are detected at a significance of 5σin both the correlation function and power spectrum. Combining with the SDSS-II Luminous Red Galaxy Sample, the detection significance increases to 6.7σ. Fitting for the position of the acoustic features measures the distance to z=0.57 relative to the sound horizon DV /rs = 13.67 +/- 0.22 at z=0.57. Assuming a fiducial sound horizon of 153.19 Mpc, which matches cosmic microwave background constraints, this corresponds to a distance DV(z=0.57) = 2094 +/- 34 Mpc. At 1.7 per cent, this is the most precise distance constraint ever obtained from a galaxy survey. We place this result alongside previous BAO measurements in a cosmological distance ladder and find excellent agreement with the current supernova measurements. We use these distance measurements to constrain various cosmological models, finding continuing support for a flat Universe with a cosmological constant.

astro-ph.CO↗
arXiv2012

Thinking Outside the Box: Effects of Modes Larger than the Survey on Matter Power Spectrum Covariance

Considering the matter power spectrum covariance matrix, it has recently been found that there is a potentially dominant effect on mildly non-linear scales due to power in modes of size equal to and larger than the survey volume. This {\it beat coupling} effect has been derived analytically in perturbation theory and while it has been tested with simulations, some questions remain unanswered. Moreover, there is an additional effect of these large modes, which has so far not been included in analytic studies, namely the effect on the estimated {\it average} density which enters the power spectrum estimate. In this article, we work out analytic, perturbation theory based expressions including both the beat coupling and this {\it local average effect} and we show that while, when isolated, beat coupling indeed causes large excess covariance in agreement with the literature, in a realistic scenario this is compensated almost entirely by the local average effect, leaving only $\sim 10 %$ of the excess. We test our analytic expressions by comparison to a suite of large N-body simulations. For the variances, we find excellent agreement with the analytic expressions for $k < 0.2 h$Mpc$^{-1}$ at $z=0.5$, while the correlation coefficients agree to beyond $k=0.4 h$Mpc$^{-1}$. As expected, the range of agreement increases towards higher redshift and decreases slightly towards $z=0$. We finish by including the large-mode effects in a full covariance matrix description for arbitrary survey geometry and confirming its validity using simulations. This may be useful as a stepping stone towards building an actual galaxy (or other tracer's) power spectrum covariance matrix. [abridged]

astro-ph.CO↗
arXiv2012

Effects of the neutrino mass splitting on the non-linear matter power spectrum

We have performed cosmological N-body simulations which include the effect of the masses of the individual neutrino species. The simulations were aimed at studying the effect of different neutrino hierarchies on the matter power spectrum. Compared to the linear theory predictions, we find that non-linearities enhance the effect of hierarchy on the matter power spectrum at mildly non-linear scales. The difference between the different hierarchies is about 0.5% for a sum of neutrino masses of 0.1eV. Albeit this is a small effect, it is potentially measurable from upcoming surveys. In combination with neutrinoless double-beta decay experiments, this opens up the possibility of using the sky to determine if neutrinos are Majorana or Dirac fermions.

astro-ph.CO↗
arXiv2012

An improved fitting formula for the dark matter bispectrum

In this paper we present an improved fitting formula for the dark matter bispectrum motivated by the previous phenomenological approach of Scoccimarro & Couchman (2001). We use a set of LCDM simulations to calibrate the fitting parameters in the k-range of 0.03 h/Mpc<k<0.4 h/Mpc and in the redshift range of 0<z<1.5. This new proposed fit describes well the BAO-features although it was not designed to. The deviation between the simulations output and our analytic prediction is typically less than 5% and in the worst case is never above 10%. We envision that this new analytic fitting formula will be very useful in providing reliable predictions for the non-linear dark matter bispectrum for LCDM models.

astro-ph.CO↗
arXiv2012

Quantification of depletion-induced adhesion of Red Blood Cells

Red blood cells (RBC) are known to form aggregates in the forms of rouleaux due to the presence of plasma proteins under physiological conditions. Rouleaux formation can be also induced in vitro by the addition of macromolecules to the RBC solution. Current data on the adhesion strength between red blood cells in their natural discocyte shapes mostly rely on indirect measurements like flow chamber experiments, but on the single cell level data is lacking. Here we present measurements on the dextran induced aggregation of red blood cells by use of atomic force microscopy based single cell force spectroscopy (SCFS). The effects of dextran concentration and molecular weight on the interaction energy of adhering RBCs was determined. The results are in good agreement with a model based on the depletion effect and former experimental studies.

physics.med-ph↗
arXiv2011

N-body simulations with generic non-Gaussian initial conditions II: Halo bias

We present N-body simulations for generic non-Gaussian initial conditions with the aim of exploring and modelling the scale-dependent halo bias. This effect is evident at very large scales requiring large simulation boxes. In addition, the previously available prescription to implement generic non-Gaussian initial conditions has been improved to keep under control higher-order terms which were spoiling the power spectrum on large scales. We pay particular attention to the differences between physical, inflation-motivated primordial bispectra and their factorizable templates, and to the operational definition of the non-Gaussian halo bias (which has both a scale-dependent and an approximately scale-independent contributions). We find that analytic predictions for both the non-Gaussian halo mass function and halo bias work well once a calibration factor (which was introduced before) is calibrated on simulations. The halo bias remains therefore an extremely promising tool to probe primordial non-Gaussianity and thus to give insights into the physical mechanism that generated the primordial perturbations. The simulation outputs and tables of the analytic predictions will be made publicly available via the non-Gaussian comparison project web site http://icc.ub.edu/~liciaverde/NGSCP.html

astro-ph.CO↗
arXiv2011

Stimulation of human red blood cells leads to Ca2+-mediated intercellular adhesion

Red blood cells (RBCs) are a major component of blood clots, which form physiologically as a response to injury or pathologically in thrombosis. The active participation of RBCs in thrombus solidification has been previously proposed but not yet experimentally proven. Holographic optical tweezers and single-cell force spectroscopy were used to study potential cell-cell adhesion between RBCs. Irreversible intercellular adhesion of RBCs could be induced by stimulation with lysophosphatidic acid (LPA), a compound known to be released by activated platelets. We identified Ca2+ as an essential player in the signaling cascade by directly inducing Ca2+ influx using A23187. Elevation of the internal Ca2+ concentration leads to an intercellular adhesion of RBCs similar to that induced by LPA stimulation. Using single-cell force spectroscopy, the adhesion of the RBCs was identified to be approximately 100 pN, a value large enough to be of significance inside a blood clot or in pathological situations like the vasco-occlusive crisis in sickle cell disease patients.

physics.bio-ph↗
arXiv2011

Maximal lattice-free polyhedra: finiteness and an explicit description in dimension three

A convex set with nonempty interior is maximal lattice-free if it is inclusion-maximal with respect to the property of not containing integer points in its interior. Maximal lattice-free convex sets are known to be polyhedra. The precision of a rational polyhedron $P$ in $\mathbb{R}^d$ is the smallest integer $s$ such that $sP$ is an integral polyhedron. In this paper we show that, up to affine mappings preserving $\mathbb{Z}^d$, the number of maximal lattice-free rational polyhedra of a given precision $s$ is finite. Furthermore, we present the complete list of all maximal lattice-free integral polyhedra in dimension three. Our results are motivated by recent research on cutting plane theory in mixed-integer linear optimization.

math.OC↗
arXiv2011

Mass Function Predictions Beyond LCDM

The mass distribution of halos, as specified by the halo mass function, is a key input for several cosmological probes. The sizes of $N$-body simulations are now such that, for the most part, results need no longer be statistics-limited, but are still subject to various systematic uncertainties. We investigate and discuss some of the reasons for these differences. Quantifying error sources and compensating for them as appropriate, we carry out a high-statistics study of dark matter halos from 67 $N$-body simulations to investigate the mass function and its evolution for a reference $Λ$CDM cosmology and for a set of $w$CDM cosmologies. For the reference $Λ$CDM cosmology (close to WMAP5), we quantify the breaking of universality in the form of the mass function as a function of redshift, finding an evolution of as much as 10% away from the universal form between redshifts $z=0$ and $z=2$. For cosmologies very close to this reference we provide a fitting formula to our results for the (evolving) $Λ$CDM mass function over a mass range of $6\cdot 10^{11}-3\cdot 10^{15}$ M$_{\odot}$ to an estimated accuracy of about 2%. The set of $w$CDM cosmologies is taken from the Coyote Universe simulation suite. The mass functions from this suite (which includes a $Λ$CDM cosmology and others with $w\simeq-1$) are described by the fitting formula for the reference $Λ$CDM case at an accuracy level of 10%, but with clear systematic deviations. We argue that, as a consequence, fitting formulae based on a universal form for the mass function may have limited utility in high precision cosmological applications.

astro-ph.CO↗
arXiv2011

Evidence Feed Forward Hidden Markov Model: A New Type of Hidden Markov Model

The ability to predict the intentions of people based solely on their visual actions is a skill only performed by humans and animals. The intelligence of current computer algorithms has not reached this level of complexity, but there are several research efforts that are working towards it. With the number of classification algorithms available, it is hard to determine which algorithm works best for a particular situation. In classification of visual human intent data, Hidden Markov Models (HMM), and their variants, are leading candidates. The inability of HMMs to provide a probability in the observation to observation linkages is a big downfall in this classification technique. If a person is visually identifying an action of another person, they monitor patterns in the observations. By estimating the next observation, people have the ability to summarize the actions, and thus determine, with pretty good accuracy, the intention of the person performing the action. These visual cues and linkages are important in creating intelligent algorithms for determining human actions based on visual observations. The Evidence Feed Forward Hidden Markov Model is a newly developed algorithm which provides observation to observation linkages. The following research addresses the theory behind Evidence Feed Forward HMMs, provides mathematical proofs of their learning of these parameters to optimize the likelihood of observations with a Evidence Feed Forwards HMM, which is important in all computational intelligence algorithm, and gives comparative examples with standard HMMs in classification of both visual action data and measurement data; thus providing a strong base for Evidence Feed Forward HMMs in classification of many types of problems.

cs.AI↗
arXiv2011

A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts (extended version)

We consider mixed integer linear sets defined by two equations involving two integer variables and any number of non-negative continuous variables. The non-trivial valid inequalities of such sets can be classified into split, type 1, type 2, type 3, and quadrilateral inequalities. We use a strength measure of Goemans to analyze the benefit from adding a non-split inequality on top of the split closure. Applying a probabilistic model, we show that the importance of a type 2 inequality decreases with decreasing lattice width, on average. Our results suggest that this is also true for type 3 and quadrilateral inequalities.

math.OC↗
arXiv2010

The Coyote Universe II: Cosmological Models and Precision Emulation of the Nonlinear Matter Power Spectrum

The power spectrum of density fluctuations is a foundational source of cosmological information. Precision cosmological probes targeted primarily at investigations of dark energy require accurate theoretical determinations of the power spectrum in the nonlinear regime. To exploit the observational power of future cosmological surveys, accuracy demands on the theory are at the one percent level or better. Numerical simulations are currently the only way to produce sufficiently error-controlled predictions for the power spectrum. The very high computational cost of (precision) N-body simulations is a major obstacle to obtaining predictions in the nonlinear regime, while scanning over cosmological parameters. Near-future observations, however, are likely to provide a meaningful constraint only on constant dark energy equation of state 'wCDM' cosmologies. In this paper we demonstrate that a limited set of only 37 cosmological models -- the "Coyote Universe" suite -- can be used to predict the nonlinear matter power spectrum at the required accuracy over a prior parameter range set by cosmic microwave background observations. This paper is the second in a series of three, with the final aim to provide a high-accuracy prediction scheme for the nonlinear matter power spectrum for wCDM cosmologies.

astro-ph.CO↗
arXiv2010

The Coyote Universe I: Precision Determination of the Nonlinear Matter Power Spectrum

Near-future cosmological observations targeted at investigations of dark energy pose stringent requirements on the accuracy of theoretical predictions for the clustering of matter. Currently, N-body simulations comprise the only viable approach to this problem. In this paper we demonstrate that N-body simulations can indeed be sufficiently controlled to fulfill these requirements for the needs of ongoing and near-future weak lensing surveys. By performing a large suite of cosmological simulation comparison and convergence tests we show that results for the nonlinear matter power spectrum can be obtained at 1% accuracy out to k~1 h/Mpc. The key components of these high accuracy simulations are: precise initial conditions, very large simulation volumes, sufficient mass resolution, and accurate time stepping. This paper is the first in a series of three, with the final aim to provide a high-accuracy prediction scheme for the nonlinear matter power spectrum.

astro-ph↗
arXiv2010

Inequalities for the lattice width of lattice-free convex sets in the plane

A closed, convex set $K$ in $\mathbb{R}^2$ with non-empty interior is called lattice-free if the interior of $K$ is disjoint with $\mathbb{Z}^2$. In this paper we study the relation between the area and the lattice width of a planar lattice-free convex set in the general and centrally symmetric case. A correspondence between lattice width on the one hand and covering minima on the other, allows us to reformulate our results in terms of covering minima introduced by Kannan and Lovász. We obtain a sharp upper bound for the area for any given value of the lattice width. The lattice-free convex sets satisfying the upper bound are characterized. Lower bounds are studied as well. Parts of our results are applied in a paper by the authors and Weismantel for cutting plane generation in mixed integer linear optimization, which was the original inducement for this paper. We further rectify a result of Kannan and Lovász with a new proof.

math.MG↗