An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota variously called 'Grassmann-Cayley algebra', or 'Peano spaces', to the Whitney algebra of a matroid, and finally to a resolution of the question "What, really, was Grassmann's regressive product?". This final question is the subject of ongoing joint work with Andrea Brini, Francesco Regonati, and William Schmitt. The present paper was presented at the conference "The Digital Footprint of Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It will appear in proceedings of that conference, to be published by Springer Verlag.Comment: 28 page

Children’s level of word knowledge predicts their exclusion of familiar objects as referents of novel words

When children are learning a novel object label, they tend to exclude as possible referents familiar objects for which they already have a name. In the current study, we wanted to know if children would behave in this same way regardless of how well they knew the name of potential referent objects, specifically, whether they could only comprehend it or they could both comprehend and produce it. Sixty-six monolingual German-speaking 2-, 3-, and 4-year-old children participated in two experimental sessions. In one session the familiar objects were chosen such that their labels were in the children’s productive vocabularies, and in the other session the familiar objects were chosen such that their labels were only in the children’s receptive vocabularies. Results indicated that children at all three ages were more likely to exclude a familiar object as the potential referent of the novel word if they could comprehend and produce its name rather than comprehend its name only. Indeed, level of word knowledge as operationalized in this way was a better predictor than was age. These results are discussed in the context of current theories of word learning by exclusion

Recombinant haplotypes narrow the ARMS2/HTRA1 association signal for age-related macular degeneration

Age-related macular degeneration (AMD) is the leading cause of blindness in ageing societies, triggered by both environmental and genetic factors. The strongest genetic signal for AMD with odds ratios of up to 2.8 per adverse allele was found previously over a chromosomal region in 10q26 harboring two genes, ARMS2 and HTRA1, although with little knowledge as to which gene or genetic variation is functionally relevant to AMD pathology. In this study, we analyzed rare recombinant haplotypes in 16,144 AMD cases and 17,832 controls from the International AMD Genomics Consortium and identified variants in ARMS2 but not HTRA1 to exclusively carry the AMD risk with P-values between 10 × 10-773 and 6.7 × 10-5. This now allows prioritization of the gene of interest for subsequent functional studies.</p

Genetic pleiotropy between age-related macular degeneration and 16 complex diseases and traits

Contains fulltext : 175039.pdf (publisher's version ) (Open Access)BACKGROUND: Age-related macular degeneration (AMD) is a common condition of vision loss with disease development strongly influenced by environmental and genetic factors. Recently, 34 loci were associated with AMD at genome-wide significance. So far, little is known about a genetic overlap between AMD and other complex diseases or disease-relevant traits. METHODS: For each of 60 complex diseases/traits with publicly available genome-wide significant association data, the lead genetic variant per independent locus was extracted and a genetic score was calculated for each disease/trait as the weighted sum of risk alleles. The association with AMD was estimated based on 16,144 AMD cases and 17,832 controls using logistic regression. RESULTS: Of the respective disease/trait variance, the 60 genetic scores explained on average 4.8% (0.27-20.69%) and 16 of them were found to be significantly associated with AMD (Q-values < 0.01, p values from < 1.0 x 10-16 to 1.9 x 10-3). Notably, an increased risk for AMD was associated with reduced risk for cardiovascular diseases, increased risk for autoimmune diseases, higher HDL and lower LDL levels in serum, lower bone-mineral density as well as an increased risk for skin cancer. By restricting the analysis to 1824 variants initially used to compute the 60 genetic scores, we identified 28 novel AMD risk variants (Q-values < 0.01, p values from 1.1 x 10-7 to 3.0 x 10-4), known to be involved in cardiovascular disorders, lipid metabolism, autoimmune diseases, anthropomorphic traits, ocular disorders, and neurological diseases. The latter variants represent 20 novel AMD-associated, pleiotropic loci. Genes in the novel loci reinforce previous findings strongly implicating the complement system in AMD pathogenesis. CONCLUSIONS: We demonstrate a substantial overlap of the genetics of several complex diseases/traits with AMD and provide statistically significant evidence for an additional 20 loci associated with AMD. This highlights the possibility that so far unrelated pathologies may have disease pathways in common

Corrigendum: Reduced mu power in response to unusual actions is context-dependent in 1-year-olds

During social interactions infants predict and evaluate other people’s actions. Previous behavioral research found that infants’ imitation of others’ actions depends on these evaluations and is context-dependent: 1-year-olds predominantly imitated an unusual action (turning on a lamp with one’s forehead) when the model’s hands were free compared to when the model’s hands were occupied or restrained. In the present study, we adapted this behavioral paradigm to a neurophysiological study measuring infants’ brain activity while observing usual and unusual actions via electroencephalography. In particular, we measured differences in mu power (6 – 8 Hz) associated with motor activation. In a between-subjects design, 12- to 14-month-old infants watched videos of adult models demonstrating that their hands were either free or restrained. Subsequent test frames showed the models turning on a lamp or a soundbox by using their head or their hand. Results in the hands-free condition revealed that 12- to 14-month-olds displayed a reduction of mu power in frontal regions in response to unusual and thus unexpected actions (head touch) compared to usual and expected actions (hand touch). This may be explained by increased motor activation required for updating prior action predictions in response to unusual actions though alternative explanations in terms of general attention or cognitive control processes may also be considered. In the hands-restrained condition, responses in mu frequency band did not differ between action outcomes. This implies that unusual head-touch actions compared to hand-touch actions do not necessarily evoke a reduction of mu power. Thus, we conclude that reduction of mu frequency power is context-dependent during infants’ action perception. Our results are interpreted in terms of motor system activity measured via changes in mu frequency band as being one important neural mechanism involved in action prediction and evaluation from early on

The agonistic TSPO ligand XBD173 attenuates the glial response thereby protecting inner retinal neurons in a murine model of retinal ischemia

Peer reviewedPublisher PD

Gram-negative and -positive bacteria differentiation in blood culture samples by headspace volatile compound analysis

BACKGROUND: Identification of microorganisms in positive blood cultures still relies on standard techniques such as Gram staining followed by culturing with definite microorganism identification. Alternatively, matrix-assisted laser desorption/ionization time-of-flight mass spectrometry or the analysis of headspace volatile compound (VC) composition produced by cultures can help to differentiate between microorganisms under experimental conditions. This study assessed the efficacy of volatile compound based microorganism differentiation into Gram-negatives and -positives in unselected positive blood culture samples from patients. METHODS: Headspace gas samples of positive blood culture samples were transferred to sterilized, sealed, and evacuated 20 ml glass vials and stored at −30 °C until batch analysis. Headspace gas VC content analysis was carried out via an auto sampler connected to an ion–molecule reaction mass spectrometer (IMR-MS). Measurements covered a mass range from 16 to 135 u including CO(2), H(2), N(2), and O(2). Prediction rules for microorganism identification based on VC composition were derived using a training data set and evaluated using a validation data set within a random split validation procedure. RESULTS: One-hundred-fifty-two aerobic samples growing 27 Gram-negatives, 106 Gram-positives, and 19 fungi and 130 anaerobic samples growing 37 Gram-negatives, 91 Gram-positives, and two fungi were analysed. In anaerobic samples, ten discriminators were identified by the random forest method allowing for bacteria differentiation into Gram-negative and -positive (error rate: 16.7 % in validation data set). For aerobic samples the error rate was not better than random. CONCLUSIONS: In anaerobic blood culture samples of patients IMR-MS based headspace VC composition analysis facilitates bacteria differentiation into Gram-negative and -positive. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s40709-016-0040-0) contains supplementary material, which is available to authorized users

Precise Critical Exponents for the Basic Contact Process

We calculated some of the critical exponents of the directed percolation universality class through exact numerical diagonalisations of the master operator of the one-dimensional basic contact process. Perusal of the power method together with finite-size scaling allowed us to achieve a high degree of accuracy in our estimates with relatively little computational effort. A simple reasoning leading to the appropriate choice of the microscopic time scale for time-dependent simulations of Markov chains within the so called quantum chain formulation is discussed. Our approach is applicable to any stochastic process with a finite number of absorbing states.Comment: LaTeX 2.09, 9 pages, 1 figur

On-the-fly Uniformization of Time-Inhomogeneous Infinite Markov Population Models

This paper presents an on-the-fly uniformization technique for the analysis of time-inhomogeneous Markov population models. This technique is applicable to models with infinite state spaces and unbounded rates, which are, for instance, encountered in the realm of biochemical reaction networks. To deal with the infinite state space, we dynamically maintain a finite subset of the states where most of the probability mass is located. This approach yields an underapproximation of the original, infinite system. We present experimental results to show the applicability of our technique

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics