Horst Trinker

Multifrequency Lock-In Detection With Nonsinusoidal References

We present a lock-in detection scheme, which simultaneously computes the amplitude and phase of several signals using nonsinusoidal references that have odd harmonics only. By stating constraints on the frequencies of the references and on the measurement time, we guarantee perfect discrimination of the sources. Using square-wave references, we simplify the lock-in algorithm, rendering it suitable to an implementation directly in logic. Furthermore, we apply this scheme to the design of a moisture sensor for industrial real-time measurement applications.

A simple derivation of the MacWilliams identity for linear ordered codes and orthogonal arrays

In (Can J Math 51(2):326–346, 1999), Martin and Stinson provide a generalized MacWilliams identity for linear ordered orthogonal arrays and linear ordered codes (introduced by Rosenbloom and Tsfasman (Prob Inform Transm 33(1):45–52, 1997) as “codes for the m-metric”) using association schemes. We give an elementary proof of this generalized MacWilliams identity using group characters and use it to derive an explicit formula for the dual type distribution of a linear ordered code or orthogonal array.

Brief Announcement: Rapid Asynchronous Plurality Consensus

We consider distributed plurality consensus on a complete graph of size n with k initial opinions in the following asynchronous communication model. Each node is equipped with a random Poisson clock with parameter lambda=1. Whenever a nodes clock ticks, it samples some neighbors uniformly at random and adjusts its opinion according to the sample. Distributed plurality consensus has been deeply studied in the synchronous communication model. A prominent example is the so-called Two-Choices protocol, where in each round, every node chooses two neighbors uniformly at random, and if the two sampled opinions coincide, then that opinion is adopted. This protocol is very efficient when k=2. If k=O(nε) for some small epsilon, we show that it converges to the initial plurality opinion within O(k log n) rounds, w.h.p., as long as the initial difference between the largest and second largest opinion is Omega(sqrt(n log n)). On the negative side, we show that there are cases in which Omega(k) rounds are needed, w.h.p. To beat this lower bound, we combine the Two-Choices protocol with push-pull broadcasting. We divide the process into several phases, where each phase consists of a two-choices round followed by several broadcasting rounds. Our main contribution is a non-trivial adaptation of this approach to the above asynchronous model. If the support of the most frequent opinion is at least (1+ε) times that of the second-most frequent one and k=O(Exp(log n / log log n)), then our protocol achieves the best possible run time of O(log n), w.h.p. Key to our adaptation is that we relax full synchronicity by allowing o(n) nodes to be poorly synchronized, and the well synchronized nodes are only required to be within a certain time difference from one another. We enforce this sufficient synchronicity by introducing a novel gadget into the protocol. Other parts of the adaptation are made to work using arguments and techniques based on a Pólya urn model.

New explicit bounds for ordered codes and (t,m ,s)-nets

We derive two explicit bounds from the linear programming bound for ordered codes and ordered orthogonal arrays. While ordered codes generalize the concept of error-correcting block codes in Hamming space, ordered orthogonal arrays play an important role in the context of numerical integration and quasi-Monte Carlo methods because of their equivalence to (t,m,s)-nets, low-discrepancy point sets in the s-dimensional unit cube whenever t is reasonably small. The first bound we prove is a refinement of the Plotkin bound; the second bound shares its parameter range with the quadratic bound by Bierbrauer as well as the Plotkin bound. Both bounds yield improvements for various parameters.

2.5.4 Reliable Online-Prediction of Characteristic Process Parameters by FTNIR-Spectroscopic Analysis

Within the industrial research project “Process Analytical Chemistry” (PAC) we are working on FTNIRspectroscopic measurement systems predicting characteristic parameters of industrial production processes. Those parameters are usually monitored offline or at-line with time consuming and expensive laboratory methods. In this contribution, we present a spectroscopic measurement configuration together with the required chemometric analysis, acting as an online-monitoring system. In order to demonstrate the potential of such a system we use the example of melamine resin production in an industrial process. At company partner Dynea the predicted value of the turbidity point is used as an indicator for the end of the batch reaction (turning off heating). Furthermore, we illustrate a way to verify the chemometric prediction by calculating a confidence interval for each predicted value.

The triple distribution of codes and ordered codes

We study the distribution of triples of codewords of codes and ordered codes. Schrijver [A. Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. Inform. Theory 51 (8) (2005) 2859–2866] used the triple distribution of a code to establish a bound on the number of codewords based on semidefinite programming. In the first part of this work, we generalize this approach for ordered codes. In the second part, we consider linear codes and linear ordered codes and present a MacWilliams-type identity for the triple distribution of their dual code. Based on the non-negativity of this linear transform, we establish a linear programming bound and conclude with a table of parameters for which this bound yields better results than the standard linear programming bound.

Cubic and higher degree bounds for codes and (t, m, s)-nets

The Plotkin bound and the quadratic bound for codes and (t, m, s)-nets can be obtained from the linear programming bound using certain linear and quadratic polynomials, respectively. We extend this approach by considering cubic and higher degree polynomials to find new explicit bounds as well as new non-existence results for codes and (t, m, s)-nets.