Parameter estimation of ODE's via nonparametric estimators

Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional sets of coupled nonlinear differential equations. In this setting, we propose a general method for estimating the parameters indexing ODE's from times series. Our method is able to alleviate the computational difficulties encountered by the classical parametric methods. These difficulties are due to the implicit definition of the model. We propose the use of a nonparametric estimator of regression functions as a first-step in the construction of an M-estimator, and we show the consistency of the derived estimator under general conditions. In the case of spline estimators, we prove asymptotic normality, and that the rate of convergence is the usual $\sqrt{n}$-rate for parametric estimators. Some perspectives of refinements of this new family of parametric estimators are given.Comment: Published in at http://dx.doi.org/10.1214/07-EJS132 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the creation of networks and knowledge

This paper examines the evolution of networks when innovation takes place as a result of agents bringing together their knowledge endowments. Agents freely form pairs creating a globally stable matching. paired agents combine their existing knowledge to create new knowledge. We study the properties of the dynamic network formed by these interactions, and the resultant knowledge dynamics. Each agent carries an amount of knowledge of a certain type, and the innovative output of a pair is a function of the partners'' endowments and types. We find evidence that the pattern of substitution between quantity and type of knowledge in the innovation function is vital in determining the growth of knowledge, the emergence of expertise and the stability of a number of network structures. Network structure itself exhibits a phase change when the relative importance of diversity compared to quantity increases beyond a threshold value.economics of technology ;

Can one see entanglement ?

The human eye can detect optical signals containing only a few photons. We investigate the possibility to demonstrate entanglement with such biological detectors. While one person could not detect entanglement by simply observing photons, we discuss the possibility for several observers to demonstrate entanglement in a Bell-type experiment, in which standard detectors are replaced by human eyes. Using a toy model for biological detectors that captures their main characteristic, namely a detection threshold, we show that Bell inequalities can be violated, thus demonstrating entanglement. Remarkably, when the response function of the detector is close to a step function, quantum non-locality can be demonstrated without any further assumptions. For smoother response functions, as for the human eye, post-selection is required.Comment: 5 pages, 5 figure

Networks as Emergent Structures from Bilateral Collaboration

In this paper we model the formation of innovation networks as they emerge from bilateral actions. The effectiveness of a bilateral collaboration is determined by cognitive, relational and structural embeddedness. Innovation results from the recombination of knowledge held by the partners to the collaboration, and the extent to which agents’ knowledge complement each others is an issue of cognitive embeddedness. Previous collaborations (relational embeddedness) increase the probability of a successful collaboration; as does information gained from common third parties (structural embeddedness). As a result of repeated alliance formation, a network emerges whose properties are studied, together with those of the process of knowledge creation. Two features are central to the innovation process: how agents pool their knowledge resources; and how agents derive information about potential partners. We focus on the interplay between these two dimensions, and find that they both matter. The networks that emerge are not random, but in certain parts of the parameter space have properties of small worlds. (JEL Classification: L14, Z13, O3 Keywords: Networks, Innovation, Network Formation, Knowledge)industrial organization ;

Impact of Diet and Quality Grade on Shelf Life of Beef Steaks

Steers were fed a diet containing dry rolled corn, steam flaked corn, dry rolled corn with 30% dried distillers grains, or steam flaked corn with 30% dried distillers grains. Strip loins from upper 2/3 Choice and Select- grade carcasses were obtained to evaluate the effects of diet and quality grade on shelf life characteristics. Strip loins were aged for 2, 9, 16, or 23 days. Results suggest that steaks from cattle fed steam flaked corn (with or without dried distillers grains) and from cattle fed dried distillers grains (regardless of corn type) had higher levels of many unsaturated fatty acids, more discoloration, and greater lipid oxidation compared to the dry rolled corn treatments or the no dried distillers grains treatments, respectively. Feeding of dry rolled corn or diets without dried distillers grains maintained red color better during retail display. Choice- grade steaks had significantly higher levels of unsaturated fatty acids like 18:2 and total polyunsaturated fatty acids than Select- grade steaks but did not diff er in color stability or oxidation. These data indicate the longest shelf life will occur when cattle are fed diets containing dry rolled corn (versus steam flaked corn) or without dried distillers grains (versus with dried distillers grains) and that both steam flaked corn and distillers grains have a negative impact on shelf life. Quality grade did not affect color stability

A quantum de Finetti theorem in phase space representation

The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, towards probabilistic mixtures of independent and identically distributed (i.i.d.) states. Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a new type of quantum de Finetti's theorem that is particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge towards a probabilistic mixture of i.i.d. Gaussian states (actually, n identical thermal states).Comment: 5 page

Constraints on Non-standard Top Quark Couplings

We study non-standard top quark couplings in the effective field theory approach. All nine dimension-six operators that generate anomalous couplings between the electroweak gauge bosons and the third-generation quarks are included. We calculate their contributions at tree level and one loop to all major precision electroweak observables. The calculations are compared with data to obtain constraints on eight of these operators.Comment: 26 pages, 2 figure