Sparse polynomial division using a heap

In 1974, Johnson showed how to multiply and divide sparse polynomials using a binary heap. This paper introduces a new algorithm that uses a heap to divide with the same complexity as multiplication. It is a fraction-free method that also reduces the number of integer operations for divisions of polynomials with integer coefficients over the rationals. Heap-based algorithms use very little memory and do not generate garbage. They can run in the CPU cache and achieve high performance. We compare our C implementation of sparse polynomial multiplication and division with integer coefficients to the routines of the Magma, Maple, Pari, Singular and Trip computer algebra systems.     

Hidden Markov models for the stimulus-response relationships of multistate neural systems

Given recent experimental results suggesting that neural circuits may evolve through multiple firing states, we develop a framework for estimating state-dependent neural response properties from spike train data. We modify the traditional hidden Markov model (HMM) framework to incorporate stimulus-driven, non-Poisson point-process observations. For maximal flexibility, we allow external, time-varying stimuli and the neurons' own spike histories to drive both the spiking behavior in each state and the transitioning behavior between states. We employ an appropriately modified expectation-maximization algorithm to estimate the model parameters. The expectation step is solved by the standard forward-backward algorithm for HMMs. The maximization step reduces to a set of separable concave optimization problems if the model is restricted slightly. We first test our algorithm on simulated data and are able to fully recover the parameters used to generate the data and accurately recapitulate the sequence of hidden states. We then apply our algorithm to a recently published data set in which the observed neuronal ensembles displayed multistate behavior and show that inclusion of spike history information significantly improves the fit of the model. Additionally, we show that a simple reformulation of the state space of the underlying Markov chain allows us to implement a hybrid half-multistate, half-histogram model that may be more appropriate for capturing the complexity of certain data sets than either a simple HMM or a simple peristimulus time histogram model alone.     

Adaptive multi-scale segmentation of surface data using unsupervised learning of seed positions

This paper presents a method for multi-scale segmentation of surface data using scale-adaptive region growing. The proposed segmentation algorithm is initiated by an unsupervised learning of optimal seed positions through the surface attribute clustering with a two-criterion score function. The seeds are selected as consecutive local maxima of the clustering map, which is computed by an aggregation of the local isotropic contrast and local variance maps. The proposed method avoids typical segmentation errors caused by an inappropriate choice of seed points and thresholds used in the region-growing algorithm. The scale-adaptive threshold estimate is based on the image local statistics in the neighborhoods of seed points. The performance of this method was evaluated on LiDAR surface images.     

On the number of Dejean words over alphabets of 5, 6, 7, 8, 9 and 10 letters

We give lower bounds on the growth rate of Dejean words, i.e. minimally repetitive words, over a k-letter alphabet, for 5≤k≤10. Put together with the known upper bounds, we estimate these growth rates with the precision of 0.005. As a consequence, we establish the exponential growth of the number of Dejean words over a k-letter alphabet, for 5≤k≤10.     

Scheduling loops with partial loop-carried dependencies

This paper deals with task scheduling, where each task is one particular iteration of a DO loop with partial loop-carried dependencies. Independent iterations of such loops can be scheduled in an order different from the one of classical serial execution, so as to increase program performance.The approach that we present is based both on the use of a directive added to the High Performance Fortran (HPF2) language, which specifies the dependencies between iterations, and on inspector/executor support, implemented in the CoLUMBO library, which builds the task graph and schedules tasks associated with iterations. We validate our approach by showing results achieved on an IBM SP2 for a sparse Cholesky factorization algorithm applied to real problems.     

Network effects as drivers of individual technology adoption: Analyzing adoption and diffusion of mobile communication services

Adoption research has largely ignored the dynamic impact of network effects on technology adoption and diffusion. For example, some technologies become more attractive the more social peers use them as well. But adoption at the same time increases the value for the peers and thereby their adoption decisions as well. Unfortunately, interdependencies like these make adoption and diffusion patterns very complex. Drawing on network effect theory, we develop an adoption and diffusion model that explicitly considers the role of direct and indirect network effects for individual technology adoption, using mobile commerce adoption as application example. By applying a simulation approach we can exemplify and analyze the fundamental adoption dynamics given rise to by network effects. We thereby propose a way of how to incorporate network effects into adoption research and disclose the role of the technology diffusion lifecycle for individual adoption.     

Towards a continuous microfluidic rheometer

In a previous paper we presented a way to measure the rheological properties of complex fluids on a microfluidic chip (Guillot et al., Langmuir 22:6438, 2006). The principle of our method is to use parallel flows between two immiscible fluids as a pressure sensor. In fact, in a such flow, both fluids flow side by side and the size occupied by each fluid stream depends only on both flow rates and on both viscosities. We use this property to measure the viscosity of one fluid knowing the viscosity of the other one, both flow rates and the relative size of both streams in a cross-section. We showed that using a less viscous fluid as a reference fluid allows to define a mean shear rate with a low standard deviation in the other fluid. This method allows us to measure the flow curve of a fluid with less than 250 μL of fluid. In this paper we implement this principle in a fully automated set up which controls the flow rate, analyzes the picture and calculates the mean shear rate and the viscosity of the studied fluid. We present results obtained for Newtonian fluids and complex fluids using this set up and we compare our data with cone and plate rheometer measurements. By adding a mixing stage in the fluidic network we show how this set up can be used to characterize in a continuous way the evolution of the rheological properties as a function of the formulation composition. We illustrate this by measuring the rheological curve of four formulations of polyethylene oxide solution with only 1.3 mL of concentrated polyethylene oxide solution. This method could be very useful in screening processes where the viscosity range and the behavior of the fluid to an applied stress must be evaluated.