Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

MLDB: macromolecule ligand database

MLDB (macromolecule ligand database) is a knowledge base containing ligands co-crystallized with the three-dimensional structures available in the Protein Data Bank. The proposed knowledge base serves as an open resource for the analysis and visualization of all ligands and their interactions with macromolecular structures. MLDB can be used to search ligands, and their interactions can be visualized both in text and graphical formats. MLDB will be updated at regular intervals (weekly) with automated Perl scripts. The knowledge base is intended to serve the scientific community working in the areas of molecular and structural biology. It is available free to users around the clock and can be accessed at http://dicsoft2.physics.iisc.ernet.in/mldb/.

Analysis of the MAP/G(a,b)/1/N queue with multiple vacations

This paper deals with a batch service queue and multiple vacations. The system consists of a single server and a waiting room of finite capacity. Arrival of customers follows a Markovian arrival process (MAP). The server is unavailable for occasional intervals of time called vacations, and when it is available, customers are served in batches of maximum size ‘b’ with a minimum threshold value ‘a’. We obtain the queue length distributions at various epochs along with some key performance measures. Finally, some numerical results have been presented.

Total Hip and Knee Arthoplasty for Osteoarthritis : Factors Related to the Early Outcome of Surgery

Some perioperative clinical factors related to the primary cemented arthroplasty operation for osteoarthritis of the hip or knee joint are studied and discussed in this thesis. In a randomized, double-blind study, 39 patients were divided into two groups: one receiving tranexamic acid and the other not receiving it. Tranexamic acid was given in a dose of 10 mg/kg before the operation and twice thereafter, at 8-hour intervals. Total blood loss was smaller in the tranexamic acid group than in the control group. No thromboembolic complications were noticed. In a prospective, randomized study, 58 patients with hip arthroplasty and 39 patients with knee arthroplasty were divided into groups with postoperative closed-suction drainage and without drainage. There was no difference in healing of the wounds, postoperative blood transfusions, complications or range of motion. As a result of this study, the use of drains is no longer recommended. In a randomised study the effectiveness of a femoral nerve block (25 patients) was compared with other methods of pain control (24 patients) on the first postoperative day after total knee arthroplasty. The femoral block consisted of a single injection administered at patients´ bedside during the surgeon´s hospital rounds. Femoral block patients reported less pain and required half of the amount of oxycodone. Additional femoral block or continued epidural analgesia was required more frequently by the control group patients. Pain management with femoral blocks resulted in less work for nursing staff. In a retrospective study of 422 total hip and knee arthroplasty cases the C-reactive protein levels and clinical course were examined. After hip and knee arthroplasty the maximal C-reactive protein values are seen on the second and third postoperative days, after which the level decreases rapidly. There is no difference between patients with cemented or uncemented prostheses. Major postoperative complications may cause a further increase in C-reactive protein levels at one and two weeks. In-hospital and outpatient postoperative control radiographs of 200 hip and knee arthroplasties were reviewed retrospectively. If postoperative radiographs are of good quality, there seems to be no need for early repetitive radiographs. The quality and safety of follow-up is not compromised by limiting follow-up radiographs to those with clinical indications. Exposure of the patients and the staff to radiation is reduced. Reading of the radiographs by only the treating orthopaedic surgeon is enough. These factors may seem separate from each other, but linking them together may help the treating orthopaedic surgeon to adequate patient care strategy. Notable savings can be achieved.

Boxicity and maximum degree

A d-dimensional box is a Cartesian product of d closed intervals on the real line. The boxicity of a graph is the minimum dimension d such that it is representable as the intersection graph of d-dimensional boxes. We give a short constructive proof that every graph with maximum degree D has boxicity at most 2D2. We also conjecture that the best upper bound is linear in D.

Ultrasound-Triggered Controlled Drug Delivery and Biosensing Using Silica Nanotubes

Silica nanotubes (SNTs) have been demonstrated here as a versatile host for controlled drug delivery and biosensing. The sol-gel template synthesized SNTs have a slow rate of drug release. Application of an external stimulus in the form of ultrasound to or chemical functionalization of synthesized SNT results in higher yield of drug release as well as yield of drug release varying linearly with time. In case of controlled drug delivery triggered by ultrasound, drug yield as function of time is found to be heavily dependent on the ultrasound impulse protocol. Impulses of shorter duration (similar to 0.5 min) and shorter time intervals between successive impulses resulted in higher drug yields. Confinement of hemoglobin (Hb) inside nanometer sized channels of SNT does not have any detrimental effect on the native protein structure and function. Observance of significant enhancement in direct electron transfer of Hb makes the SNTs also promising for application in biosensors.

Ventricular repolarization during cardiovascular autonomic function testing

The autonomic nervous system is an important modulator of ventricular repolarization and arrhythmia vulnerability. This study explored the effects of cardiovascular autonomic function tests on repolarization and its heterogeneity, with a special reference to congenital arrhythmogenic disorders typically associated with stress-induced fatal ventricular arrhythmias. The first part explored the effects of standardized autonomic tests on QT intervals in a 12-lead electrocardiogram and in multichannel magnetocardiography in 10 healthy adults. The second part studied the effects of deep breathing, Valsalva manouvre, mental stress, sustained handgrip and mild exercise on QT intervals in asymptomatic patients with LQT1 subtype of the hereditary long QT syndrome (n=9) and in patients with arrhythmogenic right ventricular dysplasia (ARVD, n=9). Even strong sympathetic activation had no effects on spatial QT interval dispersion in healthy subjects, but deep respiratory efforts and Valsalva influenced it in ways that were opposite in electrocardiographic and magnetocardiographic recordings. LQT1 patients showed blunted QT interval and sinus nodal responses to sympathetic challenge, as well as an exaggerated QT prolongation during the recovery phases. LQT1 patients showed a QT interval recovery overshoot in 2.4 ± 1.7 tests compared with 0.8 ± 0.7 in healthy controls (P = 0.02). Valsalva strain prolonged the T wave peak to T wave end interval only in the LQT1 patients, considered to reflect the arrhythmogenic substrate in this syndrome. ARVD patients showed signs of abnormal repolarization in the right ventricle, modulated by abrupt sympathetic activation. An electrocardiographic marker reflecting interventricular dispersion of repolarization was introduced. It showed that LQT1 patients exhibit a repolarization gradient from the left ventricle towards the right ventricle, significantly larger than in controls. In contrast, ARVD patients showed a repolarization gradient from the right ventricle towards the left. Valsalva strain amplified the repolarization gradient in LQT1 patients whereas it transiently reversed it in patients with ARVD. In conclusion, intrathoracic volume and pressure changes influence regional electrocardiographic and magnetocardiographic QT interval measurements differently. Especially recovery phases of standard cardiovascular autonomic functions tests and Valsalva manoeuvre reveal the abnormal repolarization in asymptomatic LQT1 patients. Both LQT1 and ARVD patients have abnormal interventricular repolarization gradients, modulated by abrupt sympathetic activation. Autonomic testing and in particular the Valsalva manoeuvre are potentially useful in unmasking abnormal repolarization in these syndromes.

Neck length and mean arterial pressure in the sauropod dinosaurs

How blood was able to reach the heads of the long-necked sauropod dinosaurs has long been a matter of debate and several hypotheses have been presented. For example, it has been proposed that sauropods had exceptionally large hearts, multiple ‘normal’ sized hearts spaced at regular intervals up the neck or held their necks horizontal, or that the siphon effect was in operation. By means of an experimental model, we demonstrate that the siphon principle is able to explain how blood was able to adequately perfuse the sauropod brain. The return venous circulation may have been protected from complete collapse by a structure akin to the vertebral venous plexus. We derive an equation relating neck height and mean arterial pressure, which indicates that with a mean arterial pressure similar to that of the giraffe, the maximum safe vertical distance between heart and head would have been about 12 m. A hypothesis is presented that the maximum neck length in the fossil record is due to the siphon height limit. The equation indicates that to migrate over high ground, sauropods would have had to either significantly increase their mean arterial pressure or keep their necks below a certain height dependent on altitude.

High-precision measurement of hyperfine structure in the D lines of alkali atoms

We have measured hyperfine structure in the first-excited P state (D lines) of all the naturally occurring alkali atoms. We use high-resolution laser spectroscopy to resolve hyperfine transitions, and measure intervals by locking the frequency shift produced by an acousto-optic modulator to the difference between two transitions. In most cases, the hyperfine coupling constants derived from our measurements improve previous values significantly.

Circulating Glucocorticoid Bioactivity and Serum Glucocorticoid-Responsive Biomarkers during Steroid Therapy in Children and Adolescents with Inflammatory Bowel Disease

Objective: Glucocorticoid therapy is used worldwide to treat various inflammatory and immune conditions, including inflammatory bowel disease (IBD). In IBD, 80% of the patients obtain a positive response to the therapy; however the development of glucocorticoid-related side-effects is common. Our aim was therefore to study the possibility of optimizing glucocorticoid therapy in children and adolescents with IBD by measuring circulating glucocorticoid bioactivity (GBA) and serum glucocorticoid-responsive biomarkers in patients receiving steroid treatment for active disease. Methods: A total of sixty-nine paediatric IBD patients from the Paediatric Outpatient Clinics of the University Hospitals of Helsinki and Tampere participated in the studies. Control patients included 101 non-IBD patients and 41 disease controls in remission. In patients with active disease, blood samples were withdrawn before the glucocorticoid therapy was started, at 2-4 weeks after the initiation of the steroid and at 1-month intervals thereafter. Clinical response to glucocorticoid treatment and the development of steroid adverse events was carefully registered. GBA was analyzed with a COS-1 cell bioassay. The measured glucocorticoid therapy-responsive biomarkers included adipocyte-derived adiponectin and leptin, bone turnover-related collagen markers amino-terminal type I procollagen propeptide (PINP) and carboxyterminal telopeptide of type I collagen (ICTP) as well as insulin-like growth factor 1 (IGF-1) and sex hormone-binding globulin (SHBG), and inflammatory marker high-sensitivity C-reactive protein (hs-CRP). Results: The most promising marker for glucocorticoid sensitivity was serum adiponectin that associated with steroid therapy–related adverse events. Serum leptin indicated a similar trend. In contrast, circulating GBA rose in all subjects receiving glucocorticoid treatment but did not associate with the clinical response to steroids or with glucocorticoid therapy-related side-effects. Of notice, young patients (<10 years) showed similar GBA levels than older patients, despite receiving higher weight-adjusted doses of glucocorticoid. Markers of bone formation were lower in children with active IBD than in the control patients, probably reflecting the suppressive effect of the active inflammation. The onset of the glucocorticoid therapy further suppressed bone turnover. Inflammatory marker hs-CRP decreased readily after the initiation of the steroid, however the decrease did not associate with the clinical response to glucocorticoids. Conclusions: This is the first study to show that adipocyte-derived adiponectin associates with steroid therapy-induced side-effects. Further studies are needed, but it is possible that the adiponectin measurement could aid the recognition of glucocorticoid-sensitive patients in the future. GBA and the other markers reflecting glucocorticoid activity in different tissues changed during the treatment, however their change did not correlate with the therapeutic response to steroids or with the development of glucocorticoid-related side effects and therefore cannot guide the therapy in these patients. Studies such as as the present one that combine clinical data with newly developed biomolecular technology are needed to step-by-step build a general picture of the glucocorticoid actions in different tissues.

Avian diversification patterns across the K-Pg boundary: Influence of calibrations, datasets, and model misspecification

Birds represent the most diverse extant tetrapod clade, with ca. 10,000 extant species, and the timing of the crown avian radiation remains hotly debated. The fossil record supports a primarily Cenozoic radiation of crown birds, whereas molecular divergence dating analyses generally imply that this radiation was well underway during the Cretaceous. Furthermore, substantial differences have been noted between published divergence estimates. These have been variously attributed to clock model, calibration regime, and gene type. One underappreciated phenomenon is that disparity between fossil ages and molecular dates tends to be proportionally greater for shallower nodes in the avian Tree of Life. Here, we explore potential drivers of disparity in avian divergence dates through a set of analyses applying various calibration strategies and coding methods to a mitochondrial genome dataset and an 18-gene nuclear dataset, both sampled across 72 taxa. Our analyses support the occurrence of two deep divergences (i.e., the Palaeognathae/Neognathae split and the Galloanserae/Neoaves split) well within the Cretaceous, followed by a rapid radiation of Neoaves near the K-Pg boundary. However, 95% highest posterior density intervals for most basal divergences in Neoaves cross the boundary, and we emphasize that, barring unreasonably strict prior distributions, distinguishing between a rapid Early Paleocene radiation and a Late Cretaceous radiation may be beyond the resolving power of currently favored divergence dating methods. In contrast to recent observations for placental mammals, constraining all divergences within Neoaves to occur in the Cenozoic does not result in unreasonably high inferred substitution rates. Comparisons of nuclear DNA (nDNA) versus mitochondrial DNA (mtDNA) datasets and NT- versus RY-coded mitochondrial data reveal patterns of disparity that are consistent with substitution model misspecifications that result in tree compression/tree extension artifacts, which may explain some discordance between previous divergence estimates based on different sequence types. Comparisons of fully calibrated and nominally calibrated trees support a correlation between body mass and apparent dating error. Overall, our results are consistent with (but do not require) a Paleogene radiation for most major clades of crown birds.

Asteroid identification using statistical orbital inversion methods

An efficient and statistically robust solution for the identification of asteroids among numerous sets of astrometry is presented. In particular, numerical methods have been developed for the short-term identification of asteroids at discovery, and for the long-term identification of scarcely observed asteroids over apparitions, a task which has been lacking a robust method until now. The methods are based on the solid foundation of statistical orbital inversion properly taking into account the observational uncertainties, which allows for the detection of practically all correct identifications. Through the use of dimensionality-reduction techniques and efficient data structures, the exact methods have a loglinear, that is, O(nlog(n)), computational complexity, where n is the number of included observation sets. The methods developed are thus suitable for future large-scale surveys which anticipate a substantial increase in the astrometric data rate. Due to the discontinuous nature of asteroid astrometry, separate sets of astrometry must be linked to a common asteroid from the very first discovery detections onwards. The reason for the discontinuity in the observed positions is the rotation of the observer with the Earth as well as the motion of the asteroid and the observer about the Sun. Therefore, the aim of identification is to find a set of orbital elements that reproduce the observed positions with residuals similar to the inevitable observational uncertainty. Unless the astrometric observation sets are linked, the corresponding asteroid is eventually lost as the uncertainty of the predicted positions grows too large to allow successful follow-up. Whereas the presented identification theory and the numerical comparison algorithm are generally applicable, that is, also in fields other than astronomy (e.g., in the identification of space debris), the numerical methods developed for asteroid identification can immediately be applied to all objects on heliocentric orbits with negligible effects due to non-gravitational forces in the time frame of the analysis. The methods developed have been successfully applied to various identification problems. Simulations have shown that the methods developed are able to find virtually all correct linkages despite challenges such as numerous scarce observation sets, astrometric uncertainty, numerous objects confined to a limited region on the celestial sphere, long linking intervals, and substantial parallaxes. Tens of previously unknown main-belt asteroids have been identified with the short-term method in a preliminary study to locate asteroids among numerous unidentified sets of single-night astrometry of moving objects, and scarce astrometry obtained nearly simultaneously with Earth-based and space-based telescopes has been successfully linked despite a substantial parallax. Using the long-term method, thousands of realistic 3-linkages typically spanning several apparitions have so far been found among designated observation sets each spanning less than 48 hours.

Effects of climate and morphology on temperature conditions of lakes

To a large extent, lakes can be described with a one-dimensional approach, as their main features can be characterized by the vertical temperature profile of the water. The development of the profiles during the year follows the seasonal climate variations. Depending on conditions, lakes become stratified during the warm summer. After cooling, overturn occurs, water cools and an ice cover forms. Typically, water is inversely stratified under the ice, and another overturn occurs in spring after the ice has melted. Features of this circulation have been used in studies to distinguish between lakes in different areas, as basis for observation systems and even as climate indicators. Numerical models can be used to calculate temperature in the lake, on the basis of the meteorological input at the surface. The simple form is to solve the surface temperature. The depth of the lake affects heat transfer, together with other morphological features, the shape and size of the lake. Also the surrounding landscape affects the formation of the meteorological fields over the lake and the energy input. For small lakes the shading by the shores affects both over the lake and inside the water body bringing limitations for the one-dimensional approach. A two-layer model gives an approximation for the basic stratification in the lake. A turbulence model can simulate vertical temperature profile in a more detailed way. If the shape of the temperature profile is very abrupt, vertical transfer is hindered, having many important consequences for lake biology. One-dimensional modelling approach was successfully studied comparing a one-layer model, a two-layer model and a turbulence model. The turbulence model was applied to lakes with different sizes, shapes and locations. Lake models need data from the lakes for model adjustment. The use of the meteorological input data on different scales was analysed, ranging from momentary turbulent changes over the lake to the use of the synoptical data with three hour intervals. Data over about 100 past years were used on the mesoscale at the range of about 100 km and climate change scenarios for future changes. Increasing air temperature typically increases water temperature in epilimnion and decreases ice cover. Lake ice data were used for modelling different kinds of lakes. They were also analyzed statistically in global context. The results were also compared with results of a hydrological watershed model and data from very small lakes for seasonal development.

Japanese encephalitis: pathogenesis, prophylactics and therapeutics

Japanese encephalitis (JE) is one of the most dreaded mosquito-borne viral encephalitis known to afflict humans. The Japanese encephalitis virus (JEV) is a neurotropic flavivirus that affects the CNS, causing extensive damage that may lead to fatality in about one third of bpatients. Half of the survivors suffer from severe neuropshychiatric sequelae. With nearly 3 billion people living under the current JE-endemic region, recurring incidents of epidemic are being reported at regular intervals. With no established antiviral therapies against JE available, vaccination has been the only way of preventing JE. Two types of JE vaccines are currently in vogue although the safety of administering them is questionable, in certain individuals. Thus, there is a need to develop a safe, affordable and potent JE vaccine and this review addresses the current efforts in this direction. This review also focuses on the pathophysiology of JE and efforts towards a possible breakthrough in anti-JEV therapy.

Hydrothermal synthesis and characterization of CaSO4 pseudomicrorods

Calcium sulphate (CaSO4) pseudomicrorods have been synthesized by alow-temperature hydrothermal method using CaSO4 powder as a precursor and hexadecylamine as a surfactant at 180 degrees C for at different intervals of time. The powder X-ray diffraction pattern indicates that the as-formed pseudomicrorods are of orthorhombic phase with lattice parameters a = 7.0023(4) angstrom, b = 6.9939(5) angstrom and c = 6.2434(4) angstrom. Scanning electron microscopy images show that the pseudomicrorods have diameters of about 0.2-2.5 mm and lengths of about 2-10 mm. Fourier transform infrared spectroscopy shows a strong doublet near 609 and 681 cm(-1) arising from nu(4) (SO42) bending vibrations. The strongest band observed at 1132 cm(-1) is associated with nu(3) (SO42-) stretching vibrations. The band near 420-450 cm(-1) is attributed to nu(2) (SO42-) bending vibrations. The Raman spectrum exhibits an intense peak at 1008 cm(-1) associated with the SO42- mode. The photoluminescence spectrum exhibits UV bands (330, 350 nm), strong green bands (402, 436 nm) and weak blue bands (503 nm). A widening of the optical band gap was observed as the particle size decreased.