Re-evaluation of HER2 status in metastatic breast cancer and tumor-marker guided therapy with vinorelbine and trastuzumab

Background: HER2 is overexpressed in 20 - 30% of breast cancers. Compared to chemotherapy alone, chemotherapy with trastuzumab improves clinical outcome in patients with HER2- positive metastatic breast cancer ( MBC). In general, HER2 status in a primary lesion predicts the status of metastases, so that biopsy of metastatic lesions appears unnecessary. Case Report: A 39- year old woman was diagnosed with primary breast cancer in November 2000. Using the method and scoring system of the DAKO Hercep Test, the tumor has shown low HER2 expression ( DAKO score 1+). After failure of several chemotherapy regimens for metastatic disease ( liver, skeletal), the patient underwent CT- guided needle biopsy of the liver which showed HER2 positive adenocarcinoma ( DAKO score 3+). In consequence, the patient was treated with vinorelbine ( 30 mg/ m(2) d1,8,15 q4w) and trastuzumab ( 4 mg/ kg loading dose, 2 mg/ kg weekly). During a treatment period of 4 months imaging results as well as tumor marker kinetics indicated an excellent response with sustained decrease of tumor markers. A retrospective analysis of the HER2 shed antigen in metastatic stage revealed excessively increased serum levels and supports HER2 overexpression observed in liver metastasis. The kinetics of the HER2 shed antigen during therapy for metastatic disease were found to be in phase with the kinetics of CEA and CA15- 3. Conclusion: This case report demonstrates that re- evaluation of the HER2 status may be helpful in single patients not sufficiently responding to treatment of metastatic disease. Determination of HER2 overexpression may be facilitated by a determination of the HER2 shed antigen level in peripheral blood

General Upper Bounds on the Runtime of Parallel Evolutionary Algorithms

We present a general method for analyzing the runtime of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel runtime. This allows for a rigorous estimate of the speedup gained by parallelization. Tailored results are given for common migration topologies: ring graphs, torus graphs, hypercubes, and the complete graph. Example applications for pseudo-Boolean optimization show that our method is easy to apply and that it gives powerful results. In our examples the performance guarantees improve with the density of the topology. Surprisingly, even sparse topologies such as ring graphs lead to a significant speedup for many functions while not increasing the total number of function evaluations by more than a constant factor. We also identify which number of processors lead to the best guaranteed speedups, thus giving hints on how to parameterize parallel evolutionary algorithms

Evolutionary games and quasispecies

We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution of genomic regulation. Mathematically, it takes the form of a reaction-diffusion problem that is nonlinear in the population state. In our model system, the fitness is determined by a simple mathematical game, the hawk-dove game. The stationary population distribution is found to be a quasispecies with properties different from those which hold in fixed fitness landscapes.Comment: 7 pages, 2 figures. Typos corrected, references updated. An exact solution for the hawks-dove game is provide

Quantized Scaling of Growing Surfaces

The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should satisfy an operator product expansion and, unlike the correlations in a turbulent fluid, exhibit no multiscaling. These properties impose a quantization condition on the roughness exponent $\chi$ and the dynamic exponent $z$. Hence the exact values $\chi = 2/5, z = 8/5$ for two-dimensional and $\chi = 2/7, z = 12/7$ for three-dimensional surfaces are derived.Comment: 4 pages, revtex, no figure

Directed polymers in high dimensions

We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation theory we show that physical quantities develop singular behavior for d to 4. For example, the universal finite size amplitude of the free energy at the roughening transition is proportional to (4-d)^(1/2). This shows that the dimension d=4 plays a special role for this system and points towards d=4 as the upper critical dimension of the Kardar-Parisi-Zhang problem.Comment: 37 pages REVTEX including 4 PostScript figure

On Growth, Disorder, and Field Theory

This article reviews recent developments in statistical field theory far from equilibrium. It focuses on the Kardar-Parisi-Zhang equation of stochastic surface growth and its mathematical relatives, namely the stochastic Burgers equation in fluid mechanics and directed polymers in a medium with quenched disorder. At strong stochastic driving -- or at strong disorder, respectively -- these systems develop nonperturbative scale-invariance. Presumably exact values of the scaling exponents follow from a self-consistent asymptotic theory. This theory is based on the concept of an operator product expansion formed by the local scaling fields. The key difference to standard Lagrangian field theory is the appearance of a dangerous irrelevant coupling constant generating dynamical anomalies in the continuum limit.Comment: review article, 50 pages (latex), 10 figures (eps), minor modification of original versio

Universality of Long-Range Correlations in Expansion-Randomization Systems

We study the stochastic dynamics of sequences evolving by single site mutations, segmental duplications, deletions, and random insertions. These processes are relevant for the evolution of genomic DNA. They define a universality class of non-equilibrium 1D expansion-randomization systems with generic stationary long-range correlations in a regime of growing sequence length. We obtain explicitly the two-point correlation function of the sequence composition and the distribution function of the composition bias in sequences of finite length. The characteristic exponent $\chi$ of these quantities is determined by the ratio of two effective rates, which are explicitly calculated for several specific sequence evolution dynamics of the universality class. Depending on the value of $\chi$, we find two different scaling regimes, which are distinguished by the detectability of the initial composition bias. All analytic results are accurately verified by numerical simulations. We also discuss the non-stationary build-up and decay of correlations, as well as more complex evolutionary scenarios, where the rates of the processes vary in time. Our findings provide a possible example for the emergence of universality in molecular biology.Comment: 23 pages, 15 figure

A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of $O(n \log n)$ for both cases, where $n$ is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page

Patterns in the Kardar-Parisi-Zhang equation

We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a network of localized growth modes. Scaling in 1d is associated with a gapless domain wall mode. The method also provides an independent argument for the existence of an upper critical dimension.Comment: 8 pages revtex, 4 eps figure

Renormalization group study of one-dimensional systems with roughening transitions

A recently introduced real space renormalization group technique, developed for the analysis of processes in the Kardar-Parisi-Zhang universality class, is generalized and tested by applying it to a different family of surface growth processes. In particular, we consider a growth model exhibiting a rich phenomenology even in one dimension. It has four different phases and a directed percolation related roughening transition. The renormalization method reproduces extremely well all the phase diagram, the roughness exponents in all the phases and the separatrix among them. This proves the versatility of the method and elucidates interesting physical mechanisms.Comment: Submitted to Phys. Rev.