Graph Orientation and Flows Over Time

Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems -- streets, tracks, etc. -- are inherently undirected and directions are only imposed on them to reduce the danger of colliding vehicles and similar problems. Thus the question arises, what influence the orientation of the network has on the network flow over time problem that is being solved on the oriented network. In the literature, this is also referred to as the contraflow or lane reversal problem. We introduce and analyze the price of orientation: How much flow is lost in any orientation of the network if the time horizon remains fixed? We prove that there is always an orientation where we can still send $\frac{1}{3}$ of the flow and this bound is tight. For the special case of networks with a single source or sink, this fraction is $\frac12$ which is again tight. We present more results of similar flavor and also show non-approximability results for finding the best orientation for single and multicommodity maximum flows over time

Fuzzy Riemann Surfaces

We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras

Application of ventriculoperitoneal shunt as a treatment for hydrocephalus in a dog with syringomyelia and Chiari I malformation

A twenty-month-old Chihuahua male dog was presented to us suffering with ataxia. Based on the physical examination, X-ray and magnetic resonance imaging (MRI) examinations, we diagnosed the dog with hydrocephalus, Chiari I malformation and syringomyelia. Treatment consisted of internal medical treatment and the placement of a ventriculoperitoneal (VP) shunt. The ventricular dilatation was relieved and the dog improved neurologically; however, the Chiari I malformation and syringomyelia remained after surgically positioning the VP shunt

Outcome of fetuses with prenatal diagnosis of isolated severe bilateral ventriculomegaly: A systematic review and meta-analysis.

Objective To quantify from the published literature survival and neurodevelopmental outcome of fetuses with prenatally detected isolated severe bilateral ventriculomegaly. Methods MEDLINE, EMBASE and the Cochrane Library were searched electronically. Only cases with a prenatal diagnosis of apparently isolated severe ventriculomegaly and postnatal neurodevelopmental assessment were selected and included. Severe ventriculomegaly was defined as enlargement of the ventricular atria, with a diameter of greater than 15 mm in the transventricular plane. All cases in which the investigators were unable to detect associated structural abnormality, chromosomal abnormality or fetal infection, and in which the ventriculomegaly was therefore regarded as apparently isolated, were included. Those for which the etiology was identified prenatally were excluded, whereas those with postnatal identification of the underlying cause were not excluded, since this information was not available prenatally. The quality of the included studies was assessed using the Newcastle–Ottawa Scale (NOS) for cohort studies. Pregnancy outcomes such as termination, stillbirth, neonatal survival and developmental outcome of the baby, were recorded. The degree of disability was classified as no, mild or severe disability. Statistical assessment was performed by meta‐analysis of proportions to combine data, weighting the studies using the inverse variance method and a random‐effects model. Proportions and CIs were reported. Results Eleven studies including 137 fetuses were found. Twenty‐seven pregnancies underwent termination and were excluded. The remaining 110 fetuses with apparently isolated severe ventriculomegaly for which continuation of pregnancy was intended, form the study population. Overall quality assessed using NOS for cohort studies was good. Survival was reported in 95/110 (pooled proportion 87.9% (95% CI, 75.6–96.2%)) cases. In 15/110 (pooled proportion 12.1% (95% CI, 3.8–24.4%)), either stillbirth or neonatal demise was reported. No disability was reported in 41/95 survivors (pooled proportion 42.2% (95% CI, 27.5–57.6%)). However, 17/95 showed mild/moderate disability (pooled proportion 18.6% (95% CI, 7.2–33.8%)) and 37/95 were reported to have severe disability (pooled proportion 39.6% (95% CI, 30.0–50.0%)). Conclusions Four‐fifths of fetuses with severe ventriculomegaly survive and, of these, just over two‐fifths show normal neurodevelopment. The overall survivors without disability account for more than one third of the total. Given that many cases undergo termination of pregnancy and require longer follow‐up in order to detect subtle abnormalities, mortality and prevalence of developmental delay may be even higher than that reported in this paper

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

In vivo study of experimental pneumococcal meningitis using magnetic resonance imaging

<p>Abstract</p> <p>Background</p> <p>Magnetic Resonance Imaging (MRI) methods were evaluated as a tool for the study of experimental meningitis. The identification and characterisation of pathophysiological parameters that vary during the course of the disease could be used as markers for future studies of new treatment strategies.</p> <p>Methods</p> <p>Rats infected intracisternally with <it>S. pneumoniae </it>(n = 29) or saline (n = 13) were randomized for imaging at 6, 12, 24, 30, 36, 42 or 48 hours after infection. T1W, T2W, quantitative diffusion, and post contrast T1W images were acquired at 4.7 T. Dynamic MRI (dMRI) was used to evaluate blood-brain-barrier (BBB) permeability and to obtain a measure of cerebral and muscle perfusion. Clinical- and motor scores, bacterial counts in CSF and blood, and WBC counts in CSF were measured.</p> <p>Results</p> <p>MR images and dMRI revealed the development of a highly significant increase in BBB permeability (P < 0.002) and ventricle size (P < 0.0001) among infected rats. Clinical disease severity was closely related to ventricle expansion (P = 0.024).</p> <p>Changes in brain water distribution, assessed by ADC, and categorization of brain 'perfusion' by cortex ΔSI_(bolus)were subject to increased inter-rat variation as the disease progressed, but without overall differences compared to uninfected rats (P > 0.05). Areas of well-'perfused' muscle decreased with the progression of infection indicative of septicaemia (P = 0.05).</p> <p>Conclusion</p> <p>The evolution of bacterial meningitis was successfully followed <it>in-vivo </it>with MRI. Increasing BBB-breakdown and ventricle size was observed in rats with meningitis whereas changes in brain water distribution were heterogeneous. MRI will be a valuable technique for future studies aiming at evaluating or optimizing adjunctive treatments</p

Reduction of astrogliosis and microgliosis by cerebrospinal fluid shunting in experimental hydrocephalus

<p>Abstract</p> <p>Background</p> <p>Reactive gliosis has the potential to alter biomechanical properties of the brain, impede neuronal regeneration and affect plasticity. Determining the onset and progression of reactive astrogliosis and microgliosis due to hydrocephalus is important for designing better clinical treatments.</p> <p>Methods</p> <p>Reactive astrogliosis and microgliosis were evaluated as the severity of hydrocephalus increased with age in hydrocephalic H-Tx rats and control littermates. Previous studies have suggested that gliosis may persist after short-term drainage (shunt treatment) of the cerebrospinal fluid. Therefore shunts were placed in 15d hydrocephalic rats that were sacrificed after 6d (21d of age) or after 21d (36d of age). Tissue was processed for Western blot procedures and immunohistochemistry, and probed for the astrocytic protein, Glial Fibrillary Acidic Protein (GFAP) and for microglial protein, Isolectin B4 (ILB4).</p> <p>Results</p> <p>In the parietal cortex of untreated hydrocephalic animals, GFAP levels increased significantly at 5d and at 12d compared to age-matched control rats. There was a continued increase in GFAP levels over control at 21d and at 36d. Shunting prevented some of the increase in GFAP levels in the parietal cortex. In the occipital cortex of untreated hydrocephalic animals, there was a significant increase over control in levels of GFAP at 5d. This trend continued in the 12d animals, although not significantly. Significant increases in GFAP levels were present in 21d and in 36d animals. Shunting significantly reduced GFAP levels in the 36d shunted group. Quantitative grading of immuno-stained sections showed similar changes in GFAP stained astrocytes.</p> <p>Immuno-stained microglia were altered in shape in hydrocephalic animals. At 5d and 12d, they appeared to be developmentally delayed with a lack of processes. Older 21d and 36d hydrocephalic animals exhibited the characteristics of activated microglia, with thicker processes and enlarged cell bodies. Following shunting, fewer activated microglia were present.</p> <p>Histologic examination of the periventricular area and the periaqueductal area showed similar findings with the 21d and 36d animals having increased populations of both astrocytes and microglia which were reduced following shunting with a more dramatic reduction in the long term shunted animals.</p> <p>Conclusion</p> <p>Overall, these results suggest that reactive astrocytosis and microgliosis are associated with progressive untreated ventriculomegaly, but that shunt treatment can reduce the gliosis occurring with hydrocephalus.</p

Benign external hydrocephalus: a review, with emphasis on management

Benign external hydrocephalus in infants, characterized by macrocephaly and typical neuroimaging findings, is considered as a self-limiting condition and is therefore rarely treated. This review concerns all aspects of this condition: etiology, neuroimaging, symptoms and clinical findings, treatment, and outcome, with emphasis on management. The review is based on a systematic search in the Pubmed and Web of Science databases. The search covered various forms of hydrocephalus, extracerebral fluid, and macrocephaly. Studies reporting small children with idiopathic external hydrocephalus were included, mostly focusing on the studies reporting a long-term outcome. A total of 147 studies are included, the majority however with a limited methodological quality. Several theories regarding pathophysiology and various symptoms, signs, and clinical findings underscore the heterogeneity of the condition. Neuroimaging is important in the differentiation between external hydrocephalus and similar conditions. A transient delay of psychomotor development is commonly seen during childhood. A long-term outcome is scarcely reported, and the results are varying. Although most children with external hydrocephalus seem to do well both initially and in the long term, a substantial number of patients show temporary or permanent psychomotor delay. To verify that this truly is a benign condition, we suggest that future research on external hydrocephalus should focus on the long-term effects of surgical treatment as opposed to conservative management