A Purely Functional Computer Algebra System Embedded in Haskell

We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded domain-specific language in Haskell, a purely functional programming language. Utilising methods in functional programming and prominent features of Haskell, this library achieves safety, composability, and correctness at the same time. To demonstrate the advantages of our approach, we have implemented advanced Gr\"{o}bner basis algorithms, such as Faug\`{e}re's $F_4$ and $F_5$, in a composable way.Comment: 16 pages, Accepted to CASC 201

Sustained inflation and incremental mean airway pressure trial during conventional and high-frequency oscillatory ventilation in a large porcine model of acute respiratory distress syndrome

BACKGROUND: To compare the effect of a sustained inflation followed by an incremental mean airway pressure trial during conventional and high-frequency oscillatory ventilation on oxygenation and hemodynamics in a large porcine model of early acute respiratory distress syndrome. METHODS: Severe lung injury (Ali) was induced in 18 healthy pigs (55.3 ± 3.9 kg, mean ± SD) by repeated saline lung lavage until PaO(2 )decreased to less than 60 mmHg. After a stabilisation period of 60 minutes, the animals were randomly assigned to two groups: Group 1 (Pressure controlled ventilation; PCV): FIO(2 )= 1.0, PEEP = 5 cmH(2)O, V(T )= 6 ml/kg, respiratory rate = 30/min, I:E = 1:1; group 2 (High-frequency oscillatory ventilation; HFOV): FIO(2 )= 1.0, Bias flow = 30 l/min, Amplitude = 60 cmH(2)O, Frequency = 6 Hz, I:E = 1:1. A sustained inflation (SI; 50 cmH(2)O for 60s) followed by an incremental mean airway pressure (mPaw) trial (steps of 3 cmH(2)O every 15 minutes) were performed in both groups until PaO(2 )no longer increased. This was regarded as full lung inflation. The mPaw was decreased by 3 cmH(2)O and the animals reached the end of the study protocol. Gas exchange and hemodynamic data were collected at each step. RESULTS: The SI led to a significant improvement of the PaO(2)/FiO(2)-Index (HFOV: 200 ± 100 vs. PCV: 58 ± 15 and T(Ali): 57 ± 12; p < 0.001) and PaCO(2)-reduction (HFOV: 42 ± 5 vs. PCV: 62 ± 13 and T(Ali): 55 ± 9; p < 0.001) during HFOV compared to lung injury and PCV. Augmentation of mPaw improved gas exchange and pulmonary shunt fraction in both groups, but at a significant lower mPaw in the HFOV treated animals. Cardiac output was continuously deteriorating during the recruitment manoeuvre in both study groups (HFOV: T(Ali): 6.1 ± 1 vs. T(75): 3.4 ± 0.4; PCV: T(Ali): 6.7 ± 2.4 vs. T(75): 4 ± 0.5; p < 0.001). CONCLUSION: A sustained inflation followed by an incremental mean airway pressure trial in HFOV improved oxygenation at a lower mPaw than during conventional lung protective ventilation. HFOV but not PCV resulted in normocapnia, suggesting that during HFOV there are alternatives to tidal ventilation to achieve CO(2)-elimination in an "open lung" approach

Involution and Constrained Dynamics I: The Dirac Approach

We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an involutive system. We discuss the implications of this identification for field theories and argue that the involution analysis is more general and flexible than the Dirac approach. We also derive intrinsic expressions for the number of degrees of freedom.Comment: 28 pages, latex, no figure

Advanced optical imaging in living embryos

Developmental biology investigations have evolved from static studies of embryo anatomy and into dynamic studies of the genetic and cellular mechanisms responsible for shaping the embryo anatomy. With the advancement of fluorescent protein fusions, the ability to visualize and comprehend how thousands to millions of cells interact with one another to form tissues and organs in three dimensions (xyz) over time (t) is just beginning to be realized and exploited. In this review, we explore recent advances utilizing confocal and multi-photon time-lapse microscopy to capture gene expression, cell behavior, and embryo development. From choosing the appropriate fluorophore, to labeling strategy, to experimental set-up, and data pipeline handling, this review covers the various aspects related to acquiring and analyzing multi-dimensional data sets. These innovative techniques in multi-dimensional imaging and analysis can be applied across a number of fields in time and space including protein dynamics to cell biology to morphogenesis

Clinical Study Routine Follow-Up Cranial Computed Tomography for Deeply Sedated, Intubated, and Ventilated Multiple Trauma Patients with Suspected Severe Head Injury

Background. Missed or delayed detection of progressive neuronal damage after traumatic brain injury (TBI) may have negative impact on the outcome. We investigated whether routine follow-up CT is beneficial in sedated and mechanically ventilated trauma patients. Methods. The study design is a retrospective chart review. A routine follow-up cCT was performed 6 hours after the admission scan. We defined 2 groups of patients, group I: patients with equal or recurrent pathologies and group II: patients with new findings or progression of known pathologies. Results. A progression of intracranial injury was found in 63 patients (42%) and 18 patients (12%) had new findings in cCT 2 (group II). In group II a change in therapy was found in 44 out of 81 patients (54%). 55 patients with progression or new findings on the second cCT had no clinical signs of neurological deterioration. Of those 24 patients (44%) had therapeutic consequences due to the results of the follow-up cCT. Conclusion. We found new diagnosis or progression of intracranial pathology in 54% of the patients. In 54% of patients with new findings and progression of pathology, therapy was changed due to the results of follow-up cCT. In trauma patients who are sedated and ventilated for different reasons a routine follow-up CT is beneficial

How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A

We show how cyclic (f,σ,δ)-codes over finite rings canonically induce a Z-lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f. This construction generalizes the one using certain σ-constacyclic codes by Ducoat and Oggier, which used quotients of orders in non-commutative associative division algebras defined by f, and can be viewed as a generalization of the classical Construction A for lattices from linear codes. It has the potential to be applied to coset coding, in particular to wire-tap coding. Previous results by Ducoat and Oggier are obtained as special cases

High frequency oscillatory ventilation and prone positioning in a porcine model of lavage-induced acute lung injury

BACKGROUND: This animal study was conducted to assess the combined effects of high frequency oscillatory ventilation (HFOV) and prone positioning on pulmonary gas exchange and hemodynamics. METHODS: Saline lung lavage was performed in 14 healthy pigs (54 ± 3.1 kg, mean ± SD) until the arterial oxygen partial pressure (PaO(2)) decreased to 55 ± 7 mmHg. The animals were ventilated in the pressure controlled mode (PCV) with a positive endexpiratory pressure (PEEP) of 5 cmH(2)O and a tidal volume (V(T)) of 6 ml/kg body weight. After a stabilisation period of 60 minutes, the animals were randomly assigned to 2 groups. Group 1: HFOV in supine position; group 2: HFOV in prone position. After evaluation of prone positioning in group 2, the mean airway pressure (P(mean)) was increased by 3 cmH(2)O from 16 to 34 cmH(2)O every 20 minutes in both groups accompanied by measurements of respiratory and hemodynamic variables. Finally all animals were ventilated supine with PCV, PEEP = 5 cm H(2)O, V(T )= 6 ml/kg. RESULTS: Combination of HFOV with prone positioning improves oxygenation and results in normalisation of cardiac output and considerable reduction of pulmonary shunt fraction at a significant (p < 0.05) lower P(mean )than HFOV and supine positioning. CONCLUSION: If ventilator induced lung injury is ameliorated by a lower P(mean), a combined treatment approach using HFOV and prone positioning might result in further lung protection