Analogues of Kahan's method for higher order equations of higher degree

Kahan introduced an explicit method of discretization for systems of first order differential equations with nonlinearities of degree at most two (quadratic vector fields). Kahan's method has attracted much interest due to the fact that it preserves many of the geometrical properties of the original continuous system. In particular, a large number of Hamiltonian systems of quadratic vector fields are known for which their Kahan discretization is a discrete integrable system. In this note, we introduce a special class of explicit order-preserving discretization schemes that are appropriate for certain systems of ordinary differential equations of higher order and higher degree

Resection of the liver for colorectal carcinoma metastases - A multi-institutional study of long-term survivors

In this review of a collected series of patients undergoing hepatic resection for colorectal metastases, 100 patients were found to have survived greater than five years from the time of resection. Of these 100 long-term survivors, 71 remain disease-free through the last follow-up, 19 recurred prior to five years, and ten recurred after five years. Patient characteristics that may have contributed to survival were examined. Procedures performed included five trisegmentectomies, 32 lobectomies, 16 left lateral segmentectomies, and 45 wedge resections. The margin of resection was recorded in 27 patients, one of whom had a positive margin, nine of whom had a less than or equal to 1-cm margin, and 17 of whom had a greater than 1-cm margin. Eighty-one patients had a solitary metastasis to the liver, 11 patients had two metastases, one patient had three metastases, and four patients had four metastases. Thirty patients had Stage C primary carcinoma, 40 had Stage B primary carcinoma, and one had Stage A primarycarcinoma. The disease-free interval from the time of colon resection to the time of liver resection was less than one year in 65 patients, and greater than one year in 34 patients. Three patients had bilobar metastases. Four of the patients had extrahepatic disease resected simultaneously with the liver resection. Though several contraindications to hepatic resection have been proposed in the past, five-year survival has been found in patients with extrahepatic disease resected simultaneously, patients with bilobar metastases, patients with multiple metastases, and patients with positive margins. Five-year disease-free survivors are also present in each of these subsets. It is concluded that five-year survival is possible in the presence of reported contraindications to resection, and therefore that the decision to resect the liver must be individualized. © 1988 American Society of Colon and Rectal Surgeons

No effect of auditory–visual spatial disparity on temporal recalibration

It is known that the brain adaptively recalibrates itself to small (∼100 ms) auditory–visual (AV) temporal asynchronies so as to maintain intersensory temporal coherence. Here we explored whether spatial disparity between a sound and light affects AV temporal recalibration. Participants were exposed to a train of asynchronous AV stimulus pairs (sound-first or light-first) with sounds and lights emanating from either the same or a different location. Following a short exposure phase, participants were tested on an AV temporal order judgement (TOJ) task. Temporal recalibration manifested itself as a shift of subjective simultaneity in the direction of the adapted audiovisual lag. The shift was equally big when exposure and test stimuli were presented from the same or different locations. These results provide strong evidence for the idea that spatial co-localisation is not a necessary constraint for intersensory pairing to occur

Protein disulfide-isomerase interacts with a substrate protein at all stages along its folding pathway

In contrast to molecular chaperones that couple protein folding to ATP hydrolysis, protein disulfide-isomerase (PDI) catalyzes protein folding coupled to formation of disulfide bonds (oxidative folding). However, we do not know how PDI distinguishes folded, partly-folded and unfolded protein substrates. As a model intermediate in an oxidative folding pathway, we prepared a two-disulfide mutant of basic pancreatic trypsin inhibitor (BPTI) and showed by NMR that it is partly-folded and highly dynamic. NMR studies show that it binds to PDI at the same site that binds peptide ligands, with rapid binding and dissociation kinetics; surface plasmon resonance shows its interaction with PDI has a Kd of ca. 10−5 M. For comparison, we characterized the interactions of PDI with native BPTI and fully-unfolded BPTI. Interestingly, PDI does bind native BPTI, but binding is quantitatively weaker than with partly-folded and unfolded BPTI. Hence PDI recognizes and binds substrates via permanently or transiently unfolded regions. This is the first study of PDI's interaction with a partly-folded protein, and the first to analyze this folding catalyst's changing interactions with substrates along an oxidative folding pathway. We have identified key features that make PDI an effective catalyst of oxidative protein folding – differential affinity, rapid ligand exchange and conformational flexibility

Probing electron-phonon interactions away from the Fermi level with resonant inelastic x-ray scattering

Interactions between electrons and lattice vibrations are responsible for a wide range of material properties and applications. Recently, there has been considerable interest in the development of resonant inelastic x-ray scattering (RIXS) as a tool for measuring electron-phonon ( e -ph) interactions. Here, we demonstrate the ability of RIXS to probe the interaction between phonons and specific electronic states both near to, and away from, the Fermi level. We perform carbon K -edge RIXS measurements on graphite, tuning the incident x-ray energy to separately probe the interactions of the π ∗ and σ ∗ electronic states. Our high-resolution data reveal detailed structure in the multiphonon RIXS features that directly encodes the momentum dependence of the e -ph interaction strength. We develop a Green’s-function method to model this structure, which naturally accounts for the phonon and interaction-strength dispersions, as well as the mixing of phonon momenta in the intermediate state. This model shows that the differences between the spectra can be fully explained by contrasting trends of the e -ph interaction through the Brillouin zone, being concentrated at the Γ and K points for the π ∗ states while being significant at all momenta for the σ ∗ states. Our results advance the interpretation of phonon excitations in RIXS and extend its applicability as a probe of e -ph interactions to a new range of out-of-equilibrium situations

The Impact of Global Warming and Anoxia on Marine Benthic Community Dynamics: an Example from the Toarcian (Early Jurassic)

The Pliensbachian-Toarcian (Early Jurassic) fossil record is an archive of natural data of benthic community response to global warming and marine long-term hypoxia and anoxia. In the early Toarcian mean temperatures increased by the same order of magnitude as that predicted for the near future; laminated, organic-rich, black shales were deposited in many shallow water epicontinental basins; and a biotic crisis occurred in the marine realm, with the extinction of approximately 5% of families and 26% of genera. High-resolution quantitative abundance data of benthic invertebrates were collected from the Cleveland Basin (North Yorkshire, UK), and analysed with multivariate statistical methods to detect how the fauna responded to environmental changes during the early Toarcian. Twelve biofacies were identified. Their changes through time closely resemble the pattern of faunal degradation and recovery observed in modern habitats affected by anoxia. All four successional stages of community structure recorded in modern studies are recognised in the fossil data (i.e. Stage III: climax; II: transitional; I: pioneer; 0: highly disturbed). Two main faunal turnover events occurred: (i) at the onset of anoxia, with the extinction of most benthic species and the survival of a few adapted to thrive in low-oxygen conditions (Stages I to 0) and (ii) in the recovery, when newly evolved species colonized the re-oxygenated soft sediments and the path of recovery did not retrace of pattern of ecological degradation (Stages I to II). The ordination of samples coupled with sedimentological and palaeotemperature proxy data indicate that the onset of anoxia and the extinction horizon coincide with both a rise in temperature and sea level. Our study of how faunal associations co-vary with long and short term sea level and temperature changes has implications for predicting the long-term effects of “dead zones” in modern oceans

CD24 staining of mouse mammary gland cells defines luminal epithelial, myoepithelial/basal and non-epithelial cells

INTRODUCTION: Breast cancer is thought to arise in mammary epithelial stem cells. There is, therefore, a large amount of interest in identifying these cells. The breast is a complex tissue consisting of two epithelial layers (an outer myoepithelial/basal layer and an inner luminal epithelial layer) as well as a large non-epithelial component (fibroblasts, endothelial cells, lymphocytes, adipocytes, neurons and myocytes). The definitive identification of a mammary epithelial stem cell population is critically dependent on its purity. To date, this has been hampered by the lack of suitable markers to separate out the two epithelial layers, and to remove contaminating non-epithelial cells. METHODS: Mouse mammary glands were dissociated and stained with CD24. Cells were sorted into separate populations based on CD24 expression and assessed for luminal epithelial and myoepithelial/basal markers by direct fluorescent microscopy and real time PCR. The stem/progenitor potential of these cell populations was assessed in vivo by cleared mammary fat pad transplantation. RESULTS: Three populations of CD24 expressing cells were identified: CD24(Negative), CD24(Low )and CD24(High). Staining of these cells with cytokeratin markers revealed that these populations correspond to non-epithelial, myoepithelial/basal and luminal epithelial cells, respectively. Cell identities were confirmed by quantitative PCR. Cleared mammary fat pad transplantation of these cell populations revealed that extensive mammary fat pad repopulation capacity segregates with the CD24(Low )cells, whilst CD24(High )cells have limited repopulation capacity. CONCLUSION: Differential staining of mammary epithelial cells for CD24 can be used to simultaneously isolate pure populations of non-epithelial, myoepithelial/basal and luminal epithelial cells. Furthermore, mammary fat pad repopulation capacity is enriched in the CD24(Low )population. As separation is achieved using a single marker, it will be possible to incorporate additional markers to further subdivide these populations. This will considerably facilitate the further analysis of mammary epithelial subpopulations, whilst ensuring high purity, which is key for understanding mammary epithelial stem cells in normal tissue biology and carcinogenesis