The Glansdorff–Prigogine stability criterion for biochemical reaction networks

Local stability analysis of steady states in mathematical models of biochemical reaction networks is an important tool for systems biology. The second variation of the Gibbs energy around a steady state is a positive definite function and a candidate for a Lyapunov function. A sufficient condition for the local stability is the local negative definiteness of the time derivative of this function. This is expressed by the Glansdorff–Prigogine stability criterion. Previously, the criterion was criticized to be overly conservative and difficult to check. Here, we derive an easily testable form of the criterion for models of biochemical networks. The criterion can be evaluated with incomplete knowledge of the parameters. For ideal mass-action kinetics, it depends only on the steady state fluxes. For reaction systems in ideal solutions, the Glansdorff–Prigogine criterion is overly conservative and we give a tighter criterion that depends on the same subset of the parameters as the Glansdorff–Prigogine criterion. Whenever these criteria are indefinite, there exist parameter values such that the steady state is unstable. By means of simple example systems we explore these aspects and discuss the possible uses of the criteria for systems biology.     

Numerical lower bound shakedown analysis of engineering structures

We propose a numerical method for the computation of shakedown loads of engineering structures subjected to varying thermo-mechanical loading. The method is based on Melan’s lower bound shakedown theorem using the von Mises yield criterion. The resulting nonlinear convex optimization problem is presented in a generalized formulation and then solved by an interior-point algorithm, which is characterized by a problem-tailored solution strategy, particularly suitable for application to large-scale engineering structures.Theoretical and numerical issues of the algorithm are described. It’s efficiency is shown by application to thermo-mechanical problems from power plant engineering. The results are compared to those found in literature as well as to calculations with other optimization codes lancelot, ipopt and ipdca.     

Interactive Disassembly Planning for Complex Objects

We present an approach for the automatic generation, interactive exploration and real‐time modification of disassembly procedures for complex, multipartite CAD data sets. In order to lift the performance barriers prohibiting interactive disassembly planning, we run a detailed analysis on the input model to identify recurring part constellations and efficiently determine blocked part motions in parallel on the GPU. Building on the extracted information, we present an interface for computing and editing extensive disassembly sequences in real‐time while considering user‐defined constraints and avoiding unstable configurations. To evaluate the performance of our C++/CUDA implementation, we use a variety of openly available CAD data sets, ranging from simple to highly complex. In contrast to previous approaches, our work enables interactive disassembly planning for objects which consist of several thousand parts and require cascaded translations during part removal.     

Space Hierarchy Results for Randomized and other Semantic Models

We prove space hierarchy and separation results for randomized and other semantic models of computation with advice where a machine is only required to behave appropriately when given the correct advice sequence. Previous works on hierarchy and separation theorems for such models focused on time as the resource. We obtain tighter results with space as the resource. Our main theorems deal with space-bounded randomized machines that always halt. Let s(n) be any space-constructible monotone function that is Ω(log n) and let s′(n) be any function such that s′(n) = ω(s(n + as(n))) for all constants a.

Comparative analysis of multidimensional, quantitative data

When analyzing multidimensional, quantitative data, the comparison of two or more groups of dimensions is a common task. Typical sources of such data are experiments in biology, physics or engineering, which are conducted in different configurations and use replicates to ensure statistically significant results. One common way to analyze this data is to filter it using statistical methods and then run clustering algorithms to group similar values. The clustering results can be visualized using heat maps, which show differences between groups as changes in color. However, in cases where groups of dimensions have an a priori meaning, it is not desirable to cluster all dimensions combined, since a clustering algorithm can fragment continuous blocks of records. Furthermore, identifying relevant elements in heat maps becomes more difficult as the number of dimensions increases. To aid in such situations, we have developed Matchmaker, a visualization technique that allows researchers to arbitrarily arrange and compare multiple groups of dimensions at the same time. We create separate groups of dimensions which can be clustered individually, and place them in an arrangement of heat maps reminiscent of parallel coordinates. To identify relations, we render bundled curves and ribbons between related records in different groups. We then allow interactive drill-downs using enlarged detail views of the data, which enable in-depth comparisons of clusters between groups. To reduce visual clutter, we minimize crossings between the views. This paper concludes with two case studies. The first demonstrates the value of our technique for the comparison of clustering algorithms. In the second, biologists use our system to investigate why certain strains of mice develop liver disease while others remain healthy, informally showing the efficacy of our system when analyzing multidimensional data containing distinct groups of dimensions.     

Neighborhood Relations between Fields with Applications to Cellular Networks

In some spatial applications the objects of interest are fields, caused by spatially distributed sources, and one of the central questions is to find neighborhood relations between these fields. The motivating example for this paper is a cellular network: base transceiver stations transmit signals with continuous distribution, the signal strength, in an urban environment. In order to avoid interference, neighbored transceivers must not use the same frequency, so that neighborhood knowledge is one key to frequency planning. In this paper we define a concept of neighborhood for fields, and we propose a vector-based model to determine neighborhoods between given fields. In contrast to this vector-based model, the commonly used raster-based models suffer in urban areas from their resolution as well as from the prediction of signal propagation.     

The influence of electrolytes on gas hold-up and regime transition in bubble columns

Experiments were conducted in a 0.12-m-in-diameter bubble column to investigate the effect of electrolytes on gas hold-up (ε) and on the regime transition point in bubble columns. Air was used as the dispersed phase and aqueous solutions of three different salts (NaCl, Na₂SO₄ and NaI), as well as double-distilled water, were utilised as the continuous phase, varying the gas superficial velocity (u_G) in the range 0-0.26 m/s. The ε×u_G curves were a function of both the chemical nature and the concentration of the electrolytes. However, similar ε×u_G profiles were obtained regardless of the electrolyte for a given ratio between the concentration in the solution and the critical concentration of the electrolyte for bubble coalescence. This ratio therefore presents itself as a promising modelling parameter to account for the chemical nature of electrolytes. The gas hold-up data were employed to compute the regime transition point according to two different methods, evidencing its non-linear dependence on the concentration of electrolytes in the liquid.     

Flow dependence of spin susceptibilities in superfluid3He

The flow dependence of spin susceptibilities in superfluid ³ He-A and -B is studied theoretically. It is shown that in the A phase _A, the component of the static spin susceptibility parallel to , increases rapidly in the presence of mass current. A similar behavior is found for all components of _B, the susceptibility tensor of the B phase.Work supported by the National Science Foundation under grant No. DMR76-21032.Recipient of a scholarship from the Studienstiftung des Deutschen Volkes.     

Preparation of amorphous composite materials

Composite meterialoconuioting of an amorphous Ni₇₅B₁₇Si₈ matrix and containing one or two reinforcing tungsten wire(s) were prepared by a modified melt-spinning technique, With this method it was possible to incorporate a single 10, 26 and 60m wire in the entire length of an amorphous ribbon, as well as two 26m wires. The process is continuous and allows the praparation of arbitrarily long composite ribbons.