Paraconformal geometry of nnth order ODEs, and exotic holonomy in dimension four

We characterise $n$th order ODEs for which the space of solutions $M$ is equipped with a particular paraconformal structure in the sense of \cite{BE}, that is a splitting of the tangent bundle as a symmetric tensor product of rank-two vector bundles. This leads to the vanishing of $(n-2)$ quantities constructed from of the ODE. If $n=4$ the paraconformal structure is shown to be equivalent to the exotic ${\cal G}_3$ holonomy of Bryant. If $n=4$, or $n\geq 6$ and $M$ admits a torsion--free connection compatible with the paraconformal structure then the ODE is trivialisable by point or contact transformations respectively. If $n=2$ or 3 $M$ admits an affine paraconformal connection with no torsion. In these cases additional constraints can be imposed on the ODE so that $M$ admits a projective structure if $n=2$, or an Einstein--Weyl structure if $n=3$. The third order ODE can in this case be reconstructed from the Einstein--Weyl data.Comment: Theorem 1.2 strengthened and its proof clarified. Theorem 1.3 generalised to all dimensions, updated references, an example of 5th order ODE on the space of conics in $CP^2$ added, connection with Doubrov-Wilczynski invariants clarified. Final version, to appear in Journal of Geometry and Physic

Imaging of the stroke-related changes in the vascular system of the mouse brain with the use of extended focus Optical Coherence Microscopy

We used Optical Coherence Microscopy (OCM) to monitor structural and functional changes due to ischemic stroke in small animals brains in vivo. To obtain lateral resolution of 2.2 μm over the range of 600 μm we used extended focus configuration of OCM instrument involving Bessel beam. It provided access to detailed 3D information about the changes in brain vascular system up to the level of capillaries across I and II/III layers of neocortex. We used photothrombotic stroke model involving photoactive application of rose bengal to assure minimal invasiveness of the procedure and precise localization of the clot distribution center. We present the comparative analysis involving structural and angiographic maps of the stroke-affected brain enabling in-depth insight to the process of development of the disorder

Clinical Study Complex Assessment of the Incidence and Risk Factors of Delirium in a Large Cohort of Cardiac Surgery Patients: A Single-Center 6-Year Experience

Background. Previous reports provided inconsistent data on the occurrence of postoperative delirium and emphasized its considerable impact on outcome. This study sought to evaluate the incidence and predictors of delirium, together with its relation to cerebral ischemia in a large cohort of cardiac surgery patients in a tertiary high-volume center. Methods and Results. Consecutive patients (n = 8792) were prospectively enrolled from 2003 to 2008. Exclusion criteria were history of psychiatric disorders, use of psychoactive drugs, alcohol abuse, and data incompleteness. Finally, 5781 patients were analyzed in terms of 100 perioperative patient-specific and treatment variables. The incidence of postoperative delirium (DSM IV criteria) was 4.1% and it coexisted with cerebral ischemia in 1.1% of patients. In bivariate analysis, 49 variables were significantly linked to postoperative delirium. Multivariate analysis confirmed that delirium was independently associated with postoperative stroke (logistic odds ratio (logOR) = 2.862, P = 0.004), any blood transfusions (logOR = 4.178, < 0.0001), age > 65 years (logOR = 2.417, P = 0.002), carotid artery stenosis (logOR = 2.15, P = 0.01), urgent/emergent surgery (logOR = 1.982, P = 0.02), fasting glucose level, intraoperative oxygen partial pressure fluctuations, and hematocrit. Area under ROC curve for the model was 0.8933. Conclusions. Early identification of nonpsychiatric perioperative determinants of delirium facilitates its diagnosis and might help develop preventive strategies to improve long-term outcome after cardiac surgery procedures

Statins Impair Antitumor Effects of Rituximab by Inducing Conformational Changes of CD20

Jakub Golab and colleagues found that statins significantly decrease rituximab-mediated complement-dependent cytotoxicity and antibody-dependent cellular cytotoxicity against B cell lymphoma cells

Experience-Dependent Plasticity and Modulation of Growth Regulatory Molecules at Central Synapses

Structural remodeling or repair of neural circuits depends on the balance between intrinsic neuronal properties and regulatory cues present in the surrounding microenvironment. These processes are also influenced by experience, but it is still unclear how external stimuli modulate growth-regulatory mechanisms in the central nervous system. We asked whether environmental stimulation promotes neuronal plasticity by modifying the expression of growth-inhibitory molecules, specifically those of the extracellular matrix. We examined the effects of an enriched environment on neuritic remodeling and modulation of perineuronal nets in the deep cerebellar nuclei of adult mice. Perineuronal nets are meshworks of extracellular matrix that enwrap the neuronal perikaryon and restrict plasticity in the adult CNS. We found that exposure to an enriched environment induces significant morphological changes of Purkinje and precerebellar axon terminals in the cerebellar nuclei, accompanied by a conspicuous reduction of perineuronal nets. In the animals reared in an enriched environment, cerebellar nuclear neurons show decreased expression of mRNAs coding for key matrix components (as shown by real time PCR experiments), and enhanced activity of matrix degrading enzymes (matrix metalloproteinases 2 and 9), which was assessed by in situ zymography. Accordingly, we found that in mutant mice lacking a crucial perineuronal net component, cartilage link protein 1, perineuronal nets around cerebellar neurons are disrupted and plasticity of Purkinje cell terminal is enhanced. Moreover, all the effects of environmental stimulation are amplified if the afferent Purkinje axons are endowed with enhanced intrinsic growth capabilities, induced by overexpression of GAP-43. Our observations show that the maintenance and growth-inhibitory function of perineuronal nets are regulated by a dynamic interplay between pre- and postsynaptic neurons. External stimuli act on this interaction and shift the balance between synthesis and removal of matrix components in order to facilitate neuritic growth by locally dampening the activity of inhibitory cues

Conjugate priors for exponential-type processes

In the paper the family of proper conjugate priors for curved exponential families of stochastic processes is characterized.Conjugate prior exponential-type process curved exponential family stopping time

On Finding Optimal Partitions of a Measurable Space

We present an algorithm for nding almost optimal partitions of the unit interval [0; 1) according to given nonatomic measures 1; 2; : : : ; n. This algorithm is based on the idea of Riemann integral and the linear programming method. We also discuss the number of cuts needed for nding the optimal partitions

Extended-focus optical coherence microscopy for high-resolution imaging of the murine brain

We propose a new method and optical instrumentation for mouse brain imaging based on extended-focus optical coherence microscopy. This in vivo imaging technique allows the evaluation of the cytoarchitecture at cellular level and the circulation system dynamics in three dimensions. This minimally invasive and non-contact approach is performed without the application of contrasting agents. The optical design achieved a resolution of 2.2 mu m over a distance of 800 mu m, which was sufficient to obtain a detailed three-dimensional image of a wild-type mouse's brain down to the layer III of the cortex. Intrinsically contrasted microvessels and structures similar to the bodies of neurons were distinguishable. (C) 2016 Optical Society of Americ

Visualization 1: Extended-focus optical coherence microscopy for high-resolution imaging of the murine brain

Fly-through across the whole 3D structural data set from the mouse brain after spatio-temporal averaging. Originally published in Biomedical Optics Express on 01 November 2016 (boe-7-11-4400

The extracellular matrix glycoprotein tenascin-C and matrix metalloproteinases modify cerebellar structural plasticity by exposure to an enriched environment

The importance of the extracellular matrix (ECM) glycoprotein tenascin-C (TnC) and the ECM degrading enzymes, matrix metalloproteinases (MMPs) -2 and -9, in cerebellar histogenesis is well established. This study aimed to examine whether there is a functional relationship between these molecules in regulating structural plasticity of the lateral deep cerebellar nucleus. To this end, starting from postnatal day 21, TnC- or MMP-9-deficient mice were exposed to an enriched environment (EE). We show that 8 weeks of exposure to EE leads to reduced lectin-based staining of perineuronal nets (PNNs), reduction in the size of GABAergic and increase in the number and size of glutamatergic synaptic terminals in wild-type mice. Conversely, TnC-deficient mice showed reduced staining of PNNs compared to wild-type mice maintained under standard conditions, and exposure to EE did not further reduce, but even slightly increased PNN staining. EE did not affect the densities of the two types of synaptic terminals in TnC-deficient mice, while the size of inhibitory, but not excitatory synaptic terminals was increased. In the time frame of 4-8 weeks, MMP-9, but not MMP-2, was observed to influence PNN remodeling and cerebellar synaptic plasticity as revealed by measurement of MMP-9 activity and colocalization with PNNs and synaptic markers. These findings were supported by observations on MMP-9-deficient mice. The present study suggests that TnC contributes to the regulation of structural plasticity in the cerebellum and that interactions between TnC and MMP-9 are likely to be important for these processes to occur