arXiv subjects

Christian Hoffmann

Publications and source records attributed to Christian Hoffmann.

16 recordsLinked to original sources

arXiv2024

Why fixing alpha in the NRTL model might be a bad idea -- Identifiability analysis of a binary Vapor-Liquid equilibrium

New vapor-liquid equilibrium (VLE) data are continuously being measured and new parameter values, e.g., for the nonrandom two-liquid (NRTL) model are estimated and published. The parameter $\alpha$, the nonrandomness parameter of NRTL, is often heuristically fixed to a value in the range of 0.1 to 0.47. This can be seen as a manual application of a (subset selection) regularization method. In this work, the identifiability of the NRTL model for describing the VLE is analyzed. It is shown that fixing $\alpha$ is not always a good decision and sometimes leads to worse prediction properties of the final parameter estimates. Popular regularization techniques are compared and Generalized Orthogonalization is proposed as an alternative to this heuristic. In addition, the sequential Optimal Experimental Design and Parameter Estimation (sOED-PE) method is applied to study the influence of the regularization methods on the performance of the sOED-PE loop.

math.OC↗

arXiv2021

Semi-supervised Learning for Data-driven Soft-sensing of Biological and Chemical Processes

Continuously operated (bio-)chemical processes increasingly suffer from external disturbances, such as feed fluctuations or changes in market conditions. Product quality often hinges on control of rarely measured concentrations, which are expensive to measure. Semi-supervised regression is a possible building block and method from machine learning to construct soft-sensors for such infrequently measured states. Using two case studies, i.e., the Williams-Otto process and a bioethanol production process, semi-supervised regression is compared against standard regression to evaluate its merits and its possible scope of application for process control in the (bio-)chemical industry.

eess.SY↗

arXiv2020

$\mathrm{La}_{\mathrm{1-}x} \mathrm{Mn}_{\mathrm{1-}y} \mathrm{O}_{\mathrm{1\pm}δ}$ buffer layers on inclined substrate deposited MgO templates for coated conductors

Most commercial high-temperature superconducting coated conductors based on ion beam assisted MgO deposited templates use $\mathrm{LaMnO_3}$ (LMO) films as the terminating buffer layer. In contrast, coated conductors based on inclined substrate deposition (ISD)-MgO technology are still produced with homoepitaxial (homoepi)-MgO as the cap layer. In this work we report on the deposition of LMO buffer layers on ISD-MgO/homoepi-MgO by electron beam physical vapor deposition. The growth parameters of textured LMO films were studied systematically and their properties were optimized regarding the critical current densitiy ($J_\mathrm{c}$) of the subsequently deposited $\mathrm{DyBa_2Cu_3O}_{\mathrm{7-}δ}$ (DyBCO) superconducting films. LMO films without outgrowths at the surface were obtained at growth rates of up to $4\,\mathrm{Å/s}$. Despite the formation of non-stoichiometric LMO films containing $59\,\%$ La, single-phase films were obtained at substrate temperatures below $775^{\circ}\mathrm{C}$ and at oxygen partial pressures of up to $4\times10^{-4}\,\mathrm{mbar}$ due to a large homogeneity region towards La. The $J_\mathrm{c}$ values of DyBCO films deposited on LMO were found to be independent of the LMO thickness in a range from $50\,\mathrm{nm}$ to $450\,\mathrm{nm}$. DyBCO films on LMO reach $J_\mathrm{c}=0.83\,\mathrm{MA/cm^2}$ at $77\,\mathrm{K}$ in zero applied field. This value is up to $30\,\%$ higher than those of DyBCO films grown directly on homoepi-MgO. The wide range of LMO growth parameters and higher $J_\mathrm{c}$ values of DyBCO on LMO compared to DyBCO on homoepi-MgO make this material attractive for its use in manufacturing coated conductors based on ISD-MgO technology.

cond-mat.supr-con↗

arXiv2019

Controlled exploration of chemical space by machine learning of coarse-grained representations

The size of chemical compound space is too large to be probed exhaustively. This leads high-throughput protocols to drastically subsample and results in sparse and non-uniform datasets. Rather than arbitrarily selecting compounds, we systematically explore chemical space according to the target property of interest. We first perform importance sampling by introducing a Markov chain Monte Carlo scheme across compounds. We then train an ML model on the sampled data to expand the region of chemical space probed. Our boosting procedure enhances the number of compounds by a factor 2 to 10, enabled by the ML model's coarse-grained representation, which both simplifies the structure-property relationship and reduces the size of chemical space. The ML model correctly recovers linear relationships between transfer free energies. These linear relationships correspond to features that are global to the dataset, marking the region of chemical space up to which predictions are reliable---a more robust alternative to the predictive variance. Bridging coarse-grained simulations with ML gives rise to an unprecedented database of drug-membrane insertion free energies for 1.3 million compounds.

cond-mat.soft↗

arXiv2019

Wormholes Immersed in Rotating Matter

We consider Ellis wormholes immersed in rotating matter in the form of an ordinary complex boson field. The resulting wormholes may possess full reflection symmetry with respect to the two asymptotically flat spacetime regions. However, there arise also wormhole solutions where the reflection symmetry is broken. The latter always appear in pairs. We analyse the properties of these rotating wormholes and show that their geometry may feature single throats or double throats. We also discuss the ergoregions and the lightring structure of these wormholes.

gr-qc↗

arXiv2019

On Approximate Nonlinear Gaussian Message Passing On Factor Graphs

Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the factor graph tool kit is the ability to handle deterministic nonlinear transformations, such as those occurring in nonlinear filtering and smoothing problems, using tabulated message passing rules. In this contribution, we provide general forward (filtering) and backward (smoothing) approximate Gaussian message passing rules for deterministic nonlinear transformation nodes in arbitrary factor graphs fulfilling a Markov property, based on numerical quadrature procedures for the forward pass and a Rauch-Tung-Striebel-type approximation of the backward pass. These message passing rules can be employed for deriving many algorithms for solving nonlinear problems using factor graphs, as is illustrated by the proposition of a nonlinear modified Bryson-Frazier (MBF) smoother based on the presented message passing rules.

stat.ML↗

arXiv2018

Symmetric and Asymmetric Wormholes Immersed In Rotating Matter

We consider four-dimensional wormholes immersed in bosonic matter. While their existence is based on the presence of a phantom field, many of their interesting physical properties are bestowed upon them by an ordinary complex scalar field, which carries only a mass term, but no self-interactions. For instance, the rotation of the scalar field induces a rotation of the throat as well. Moreover, the bosonic matter need not be symmetrically distributed in both asymptotically flat regions, leading to symmetric and asymmetric rotating wormhole spacetimes. The presence of the rotating matter also allows for wormholes with a double throat.

gr-qc↗

arXiv2017

Wormholes Immersed in Rotating Matter

We demonstrate that rotating matter sets the throat of an Ellis wormhole into rotation, allowing for wormholes which possess full reflection symmetry with respect to the two asymptotically flat spacetime regions. We analyze the properties of this new type of rotating wormholes and show that the wormhole geometry can change from a single throat to a double throat configuration. We further discuss the ergoregions and the lightring structure of these wormholes.

gr-qc↗

arXiv2017

Spontaneous Symmetry Breaking in Wormholes Spacetimes with Matter

When bosonic matter in the form of a complex scalar field is added to Ellis wormholes, the phenomenon of spontaneous symmetry breaking is observed. Symmetric solutions possess full reflection symmetry with respect to the radial coordinate of the two asymptotically flat spacetime regions connected by the wormhole, whereas asymmetric solutions do not possess this symmetry. Depending on the size of the throat, at bifurcation points pairs of asymmetric solutions arise from or merge with the symmetric solutions. These asymmetric solutions are energetically favoured. When the backreaction of the boson field is taken into account, this phenomenon is retained. Moreover, in a certain region of the solution space both symmetric and asymmetric solutions exhibit a transition from single throat to double throat configurations.

gr-qc↗

arXiv2014

Boson Stars with Nontrivial Topology

We construct boson star solutions in the presence of a phantom field, allowing for a nontrivial topology of the solutions. The wormholes residing at the core of the configurations lead to a number of qualitative changes of the boson star solutions. In particular, the typical spiraling dependence of the mass and the particle number on the frequency of the boson stars is lost. Instead, the boson stars with nontrivial topology approach a singular configuration in the limit of vanishing frequency. Depending on the value of the coupling constant, the wormhole geometry changes from a single throat configuration to a double throat configuration, featuring a belly inbetween the two throats. Depending on the mass of the boson field and its self-interaction, the mass and the size of these objects cover many orders of magnitude, making them amenable to various astrophysical observations. A stability analysis reveals, that the unstable mode of the Ellis wormhole is retained in the presence of the bosonic matter. However, the negative eigenvalue can get very close to zero, by tuning the parameters of the self-interaction potential appropriately.

gr-qc↗

arXiv2010

Exponential Time Complexity of Weighted Counting of Independent Sets

We consider weighted counting of independent sets using a rational weight x: Given a graph with n vertices, count its independent sets such that each set of size k contributes x^k. This is equivalent to computation of the partition function of the lattice gas with hard-core self-repulsion and hard-core pair interaction. We show the following conditional lower bounds: If counting the satisfying assignments of a 3-CNF formula in n variables (#3SAT) needs time 2^{Ω(n)} (i.e. there is a c>0 such that no algorithm can solve #3SAT in time 2^{cn}), counting the independent sets of size n/3 of an n-vertex graph needs time 2^{Ω(n)} and weighted counting of independent sets needs time 2^{Ω(n/log^3 n)} for all rational weights x\neq 0. We have two technical ingredients: The first is a reduction from 3SAT to independent sets that preserves the number of solutions and increases the instance size only by a constant factor. Second, we devise a combination of vertex cloning and path addition. This graph transformation allows us to adapt a recent technique by Dell, Husfeldt, and Wahlen which enables interpolation by a family of reductions, each of which increases the instance size only polylogarithmically.

cs.CC↗

arXiv2010

Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth

We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k)*n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context of tree decompositions, we give a faster and more direct algorithm. Our algorithm uses 2^{3k^2+O(k)}*n arithmetic operations and can be efficiently implemented in parallel.

cs.DS↗

arXiv2008

On the Complexity of the Interlace Polynomial

We consider the two-variable interlace polynomial introduced by Arratia, Bollobas and Sorkin (2004). We develop graph transformations which allow us to derive point-to-point reductions for the interlace polynomial. Exploiting these reductions we obtain new results concerning the computational complexity of evaluating the interlace polynomial at a fixed point. Regarding exact evaluation, we prove that the interlace polynomial is #P-hard to evaluate at every point of the plane, except on one line, where it is trivially polynomial time computable, and four lines, where the complexity is still open. This solves a problem posed by Arratia, Bollobas and Sorkin (2004). In particular, three specializations of the two-variable interlace polynomial, the vertex-nullity interlace polynomial, the vertex-rank interlace polynomial and the independent set polynomial, are almost everywhere #P-hard to evaluate, too. For the independent set polynomial, our reductions allow us to prove that it is even hard to approximate at any point except at 0.

cs.CC↗

arXiv2008

A Most General Edge Elimination Polynomial - Thickening of Edges

We consider a graph polynomial ξ(G;x,y,z) introduced by Averbouch, Godlin, and Makowsky (2007). This graph polynomial simultaneously generalizes the Tutte polynomial as well as a bivariate chromatic polynomial defined by Dohmen, Poenitz and Tittmann (2003). We derive an identity which relates the graph polynomial of a thicked graph (i.e. a graph with each edge replaced by k copies of it) to the graph polynomial of the original graph. As a consequence, we observe that at every point (x,y,z), except for points lying within some set of dimension 2, evaluating ξis #P-hard.

math.CO↗

arXiv2005

Electric Field Control of Spin Transport

Spintronics is an approach to electronics in which the spin of the electrons is exploited to control the electric resistance R of devices. One basic building block is the spin-valve, which is formed if two ferromagnetic electrodes are separated by a thin tunneling barrier. In such devices, R depends on the orientation of the magnetisation of the electrodes. It is usually larger in the antiparallel than in the parallel configuration. The relative difference of R, the so-called magneto-resistance (MR), is then positive. Common devices, such as the giant magneto-resistance sensor used in reading heads of hard disks, are based on this phenomenon. The MR may become anomalous (negative), if the transmission probability of electrons through the device is spin or energy dependent. This offers a route to the realisation of gate-tunable MR devices, because transmission probabilities can readily be tuned in many devices with an electrical gate signal. Such devices have, however, been elusive so far. We report here on a pronounced gate-field controlled MR in devices made from carbon nanotubes with ferromagnetic contacts. Both the amplitude and the sign of the MR are tunable with the gate voltage in a predictable manner. We emphasise that this spin-field effect is not restricted to carbon nanotubes but constitutes a generic effect which can in principle be exploited in all resonant tunneling devices.

cond-mat.mes-hall↗

arXiv1999

Pseudogap and Superconducting Gap in Y-123: A Raman Study

We present results of electronic Raman-scattering experiments in differently doped Y-123. In B2g symmetry, an analysis of the data in terms of a memory function approach is presented and dynamical relaxation rates $Γ(ω,T)$ and mass-enhancement factors $1+λ(ω,T)$ for the carriers are obtained. Starting from temperatures T > 180K, $Γ(ω,T)$ and $1+λ(ω,T)$ are extrapolated to lower temperatures and used to re-calculate Raman spectra. By comparison with our data, we find a loss of spectral weight between Tc < T < T* at all doping levels x. T* is comparable to the pseudogap temperature found in other experiments. Below Tc, the superconducting gap is observed. It depends on x and scales with Tc whereas the energy scale of the pseudogap remains the same.

cond-mat.supr-con↗