Generalized Theorems for Nonlinear State Space Reconstruction

Takens' theorem (1981) shows how lagged variables of a single time series can be used as proxy variables to reconstruct an attractor for an underlying dynamic process. State space reconstruction (SSR) from single time series has been a powerful approach for the analysis of the complex, non-linear systems that appear ubiquitous in the natural and human world. The main shortcoming of these methods is the phenomenological nature of attractor reconstructions. Moreover, applied studies show that these single time series reconstructions can often be improved ad hoc by including multiple dynamically coupled time series in the reconstructions, to provide a more mechanistic model. Here we provide three analytical proofs that add to the growing literature to generalize Takens' work and that demonstrate how multiple time series can be used in attractor reconstructions. These expanded results (Takens' theorem is a special case) apply to a wide variety of natural systems having parallel time series observations for variables believed to be related to the same dynamic manifold. The potential information leverage provided by multiple embeddings created from different combinations of variables (and their lags) can pave the way for new applied techniques to exploit the time-limited, but parallel observations of natural systems, such as coupled ecological systems, geophysical systems, and financial systems. This paper aims to justify and help open this potential growth area for SSR applications in the natural sciences

Sprouty4 Is a Negative Regulator of Erk/Mapk Signaling in Breast Cancer and Plays a Role in the Transition from in situ to Invasive Disease

Breast ductal carcinoma in situ (DCIS) is a non-obligate precursor of invasive ductal carcinoma (IDC). It is still unclear which DCIS will become invasive and which will remain indolent. Previous data by our group found that Sprouty4 transcript was differentially expressed between three DCIS cell lines and a non-transformed breast epithelial cell line. Sprouty proteins are important regulators of ERK/MAPK signaling, and have been studied in various cancers. We hypothesized that Sprouty4 is an endogenous inhibitor of ERK/MAPK signaling and that its loss/reduced expression is a mechanism by which DCIS lesions progress toward IDC, including triple-negative disease. Using immunohistochemistry we found that Sprouty4 expression was reduced in IDC patient samples compared to DCIS, and that ERK/MAPK phosphorylation had an inverse relationship to Sprouty4 expression. These observations were reproduced using a 3D culture model of disease progression. Knockdown of Sprouty4 in MCF10.DCIS cells increased ERK/MAPK phosphorylation as well as their invasive capability, and overexpression of Sprouty4 in MCF10.CA1d IDC cells reduced ERK/MAPK phosphorylation and the aggressive phenotype exhibited by these cells. Immunofluorescence experiments revealed dynamic changes in the actin cytoskeleton and data consistent with the relocation of E-cadherin back to the cell surface and the restoration of adherens junctions. To determine whether these effects were due to changes in ERK/MAPK signaling, MEK1/2 was pharmacologically inhibited in IDC cells. Nanomolar concentrations of drug restored an epithelial-like phenotype and reduced pericellular proteolysis, similar to Sprouty4 overexpression. From these data we conclude that Sprouty4 acts to control ERK/MAPK signaling in DCIS, thus limiting the progression of these premalignant breast lesions

Probe-based fluorescence dosimetry of an antibody-dye conjugate to identify head and neck cancer as a first step to fluorescence-guided tissue preselection for pathological assessment

Background: Despite the rapid growth of fluorescence imaging, accurate sampling of tissue sections remains challenging. Development of novel technologies to improve intraoperative assessment of tissue is needed. Methods: A novel contact probe-based fluorescence dosimeter device, optimized for IRDye800CW quantification, was developed. After evaluation of the device in a phantom setup, its clinical value was defined ex vivo in patients with head and neck squamous cell carcinoma who received panitumumab-IRDye800CW. Results: Ten patients were enrolled with a total of 216 data points obtained. Final histopathology showed tumor in 119 spots and normal tissue in 97 spots. Fluorescence-to-excitation ratios in tumor tissue were more than three times higher than those in normal tissue. The area under the curve was 0.86 (95% CI: 0.81-0.91) for tumor detection. Conclusions: Fluorescence-guided tissue preselection using a fluorescence dosimeter could have substantial impact on tissue sampling for frozen section analysis and potentially reduce sampling errors

Drosophila muller f elements maintain a distinct set of genomic properties over 40 million years of evolution.

The Muller F element (4.2 Mb, ~80 protein-coding genes) is an unusual autosome of Drosophila melanogaster; it is mostly heterochromatic with a low recombination rate. To investigate how these properties impact the evolution of repeats and genes, we manually improved the sequence and annotated the genes on the D. erecta, D. mojavensis, and D. grimshawi F elements and euchromatic domains from the Muller D element. We find that F elements have greater transposon density (25-50%) than euchromatic reference regions (3-11%). Among the F elements, D. grimshawi has the lowest transposon density (particularly DINE-1: 2% vs. 11-27%). F element genes have larger coding spans, more coding exons, larger introns, and lower codon bias. Comparison of the Effective Number of Codons with the Codon Adaptation Index shows that, in contrast to the other species, codon bias in D. grimshawi F element genes can be attributed primarily to selection instead of mutational biases, suggesting that density and types of transposons affect the degree of local heterochromatin formation. F element genes have lower estimated DNA melting temperatures than D element genes, potentially facilitating transcription through heterochromatin. Most F element genes (~90%) have remained on that element, but the F element has smaller syntenic blocks than genome averages (3.4-3.6 vs. 8.4-8.8 genes per block), indicating greater rates of inversion despite lower rates of recombination. Overall, the F element has maintained characteristics that are distinct from other autosomes in the Drosophila lineage, illuminating the constraints imposed by a heterochromatic milieu

Identification of seven new prostate cancer susceptibility loci through a genome-wide association study

Prostate cancer (PrCa) is the most frequently diagnosed male cancer in developed countries. To identify common PrCa susceptibility alleles, we have previously conducted a genome-wide association study in which 541, 129 SNPs were genotyped in 1,854 PrCa cases with clinically detected disease and 1,894 controls. We have now evaluated promising associations in a second stage, in which we genotyped 43,671 SNPs in 3,650 PrCa cases and 3,940 controls, and a third stage, involving an additional 16,229 cases and 14,821 controls from 21 studies. In addition to previously identified loci, we identified a further seven new prostate cancer susceptibility loci on chromosomes 2, 4, 8, 11, and 22 (P=1.6×10−8 to P=2.7×10−33)

\u3ci\u3eDrosophila\u3c/i\u3e Muller F Elements Maintain a Distinct Set of Genomic Properties Over 40 Million Years of Evolution

The Muller F element (4.2 Mb, ~80 protein-coding genes) is an unusual autosome of Drosophila melanogaster; it is mostly heterochromatic with a low recombination rate. To investigate how these properties impact the evolution of repeats and genes, we manually improved the sequence and annotated the genes on the D. erecta, D. mojavensis, and D. grimshawi F elements and euchromatic domains from the Muller D element. We find that F elements have greater transposon density (25–50%) than euchromatic reference regions (3–11%). Among the F elements, D. grimshawi has the lowest transposon density (particularly DINE-1: 2% vs. 11–27%). F element genes have larger coding spans, more coding exons, larger introns, and lower codon bias. Comparison of the Effective Number of Codons with the Codon Adaptation Index shows that, in contrast to the other species, codon bias in D. grimshawi F element genes can be attributed primarily to selection instead of mutational biases, suggesting that density and types of transposons affect the degree of local heterochromatin formation. F element genes have lower estimated DNA melting temperatures than D element genes, potentially facilitating transcription through heterochromatin. Most F element genes (~90%) have remained on that element, but the F element has smaller syntenic blocks than genome averages (3.4–3.6 vs. 8.4–8.8 genes per block), indicating greater rates of inversion despite lower rates of recombination. Overall, the F element has maintained characteristics that are distinct from other autosomes in the Drosophila lineage, illuminating the constraints imposed by a heterochromatic milieu