From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression

This paper studies, under the setting of spline regression, the connection between finite-sample properties of selection criteria and their asymptotic counterparts, focusing on bridging the gap between the two. We introduce a bias-variance decomposition of the prediction error, using which it is shown that in the asymptotics the bias term dominates the variability term, providing an explanation of the gap. A geometric exposition is provided for intuitive understanding. The theoretical and geometric results are illustrated through a numerical example.Comment: Published at http://dx.doi.org/10.1214/009053604000000841 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins

Advances in nanotechnology have allowed scientists to study biological processes on an unprecedented nanoscale molecule-by-molecule basis, opening the door to addressing many important biological problems. A phenomenon observed in recent nanoscale single-molecule biophysics experiments is subdiffusion, which largely departs from the classical Brownian diffusion theory. In this paper, by incorporating fractional Gaussian noise into the generalized Langevin equation, we formulate a model to describe subdiffusion. We conduct a detailed analysis of the model, including (i) a spectral analysis of the stochastic integro-differential equations introduced in the model and (ii) a microscopic derivation of the model from a system of interacting particles. In addition to its analytical tractability and clear physical underpinning, the model is capable of explaining data collected in fluorescence studies on single protein molecules. Excellent agreement between the model prediction and the single-molecule experimental data is seen.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS149 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonparametric inference of doubly stochastic Poisson process data via the kernel method

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS352 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Equi-energy sampler with applications in statistical inference and statistical mechanics

We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperature-domain methods, the equi-energy sampler, utilizing the temperature--energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and microcanonical averages in statistical mechanics. The equi-energy sampler is applied to a variety of problems, including exponential regression in statistics, motif sampling in computational biology and protein folding in biophysics.Comment: This paper discussed in: [math.ST/0611217], [math.ST/0611219], [math.ST/0611221], [math.ST/0611222]. Rejoinder in [math.ST/0611224]. Published at http://dx.doi.org/10.1214/009053606000000515 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

AAA gunnermodel based on observer theory

The Luenberger observer theory is used to develop a predictive model of a gunner's tracking response in antiaircraft artillery systems. This model is composed of an observer, a feedback controller and a remnant element. An important feature of the model is that the structure is simple, hence a computer simulation requires only a short execution time. A parameter identification program based on the least squares curve fitting method and the Gauss Newton gradient algorithm is developed to determine the parameter values of the gunner model. Thus, a systematic procedure exists for identifying model parameters for a given antiaircraft tracking task. Model predictions of tracking errors are compared with human tracking data obtained from manned simulation experiments. Model predictions are in excellent agreement with the empirical data for several flyby and maneuvering target trajectories

Collective Engagement in Creative Tasks: The Role of Evaluation in the Creative Process in Groups

Research on group creativity has concentrated on explaining how the group context influences idea generation and has conceptualized the evaluation of creative ideas as a process of convergent decision making that takes place after ideas are generated to improve the quality of the group’s creative output. We challenge this view by exploring the situated nature of evaluations that occur throughout the creative process. We present an inductive qualitative process analysis of four U.S. healthcare policy groups tasked with producing creative output in the form of policy recommendations to a federal agency. Results show four modes of group interaction, each with a distinct form of evaluation: brainstorming without evaluation, sequential interactions in which one idea was generated and evaluated, parallel interactions in which several ideas were generated and evaluated, and iterative interactions in which the group evaluated several ideas in reference to the group’s goals. Two of the groups in our study followed an evaluation-centered sequence that began with evaluating a small set of ideas. Surprisingly, doing so did not impede the groups’ creativity. To explain this, we develop an alternative conceptualization of evaluation as a generative process that shapes and guides collective creativity

Computing A Glimpse of Randomness

A Chaitin Omega number is the halting probability of a universal Chaitin (self-delimiting Turing) machine. Every Omega number is both computably enumerable (the limit of a computable, increasing, converging sequence of rationals) and random (its binary expansion is an algorithmic random sequence). In particular, every Omega number is strongly non-computable. The aim of this paper is to describe a procedure, which combines Java programming and mathematical proofs, for computing the exact values of the first 64 bits of a Chaitin Omega: 0000001000000100000110001000011010001111110010111011101000010000. Full description of programs and proofs will be given elsewhere.Comment: 16 pages; Experimental Mathematics (accepted

Influence of chemical and magnetic interface properties of Co-Fe-B / MgO / Co-Fe-B tunnel junctions on the annealing temperature dependence of the magnetoresistance

The knowledge of chemical and magnetic conditions at the Co40Fe40B20 / MgO interface is important to interpret the strong annealing temperature dependence of tunnel magnetoresistance of Co-Fe-B / MgO / Co-Fe-B magnetic tunnel junctions, which increases with annealing temperature from 20% after annealing at 200C up to a maximum value of 112% after annealing at 350C. While the well defined nearest neighbor ordering indicating crystallinity of the MgO barrier does not change by the annealing, a small amount of interfacial Fe-O at the lower Co-Fe-B / MgO interface is found in the as grown samples, which is completely reduced after annealing at 275C. This is accompanied by a simultaneous increase of the Fe magnetic moment and the tunnel magnetoresistance. However, the TMR of the MgO based junctions increases further for higher annealing temperature which can not be caused by Fe-O reduction. The occurrence of an x-ray absorption near-edge structure above the Fe and Co L-edges after annealing at 350C indicates the recrystallization of the Co-Fe-B electrode. This is prerequisite for coherent tunneling and has been suggested to be responsible for the further increase of the TMR above 275C. Simultaneously, the B concentration in the Co-Fe-B decreases with increasing annealing temperature, at least some of the B diffuses towards or into the MgO barrier and forms a B2O3 oxide