Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Equivalence Between the Lagrangian and Hamiltonian Formalisms for Constrained Systems

The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints that are first class with respect to the Hamiltonian constraints produce Lagrangian constraints that are FL-projectable.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.

Hamilton-Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Model-Free Reconstruction of Excitatory Neuronal Connectivity from Calcium Imaging Signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Computation of arbitrarily constrained synthetic discriminant functions

An algorithm for computing correlation filters based on synthetic discriminant functions that can be displayed on current spatial light modulators is presented. The procedure is nondivergent, computationally feasible, and capable of producing multiple solutions, thus overcoming some of the pitfalls of previous methods.

3D reconstruction and comparison of shapes of DNA minicircles observed by cryo-electron microscopy.

We use cryo-electron microscopy to compare 3D shapes of 158 bp long DNA minicircles that differ only in the sequence within an 18 bp block containing either a TATA box or a catabolite activator protein binding site. We present a sorting algorithm that correlates the reconstructed shapes and groups them into distinct categories. We conclude that the presence of the TATA box sequence, which is believed to be easily bent, does not significantly affect the observed shapes.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.

Cost limitation through constrained oviposition site in a plant-pollinator/seed predator mutualism

Mutualism often involves reciprocal exploitation due to individual selection for increased benefits even at the expense of the partner. Therefore, stability and outcomes of such interactions crucially depend on cost limitation mechanisms. In the plant, pollinator /seed predator interaction between Silene latifolia (Caryophyllaceae) and Hadena bicruris (Lepidoptera: Noctuidae), moths generate pollination benefits as adults but impose seed predation costs as larvae. We examined whether floral morphology limits over-exploitation by constraining oviposition site. Oviposition site varies naturally inside vs. outside the corolla tube, but neither its determinants nor its effect on the interaction have been investigated. In a common garden with plants originating from eight populations, corolla tube length predicted oviposition site, but not egg presence or pollination efficiency, suggesting that long corolla tubes constrain the moth to lay eggs on petals. Egg position was also predicted by the combined effect of corolla tube and moth ovipositor lengths, with shorter ovipositor than corolla tube resulting in higher probability for eggs outside. Egg position on a given plant was repeatable over different exposure nights. When egg position was experimentally manipulated, eggs placed on the petal resulted in significantly fewer successful fruit attacks compared with eggs placed inside the corolla tube, suggesting differences in egg/larval mortality. Egg position also differently affected larval mass, fruit mass and fruit development. Our results indicate that constraining oviposition site through a long corolla tube reduces seed predation costs suffered by the plant without negatively affecting pollination efficiency and, hence may act to limit over-exploitation. However, the net effects of corolla tube depth variation on this interaction may fluctuate with extrinsic factors affecting egg mortality, and with patterns of gene flow affecting trait matching between the interacting species. The intermediate fitness costs incurred by both plant and insect associated with the different egg positions may reduce selective pressures for this interaction to evolve towards antagonism, favouring instead a mutualistic outcome. While a role for oviposition site variation in cost limitation is a novel finding in this system, it may apply more generally also to other mutualisms involving pollinating seed predators.

Evidence of a critical time in constrained Kinetic Ising models

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile glasses.

Neutron structure of type-III antifreeze protein allows the reconstruction of AFP-ice interface.

Antifreeze proteins (AFPs) inhibit ice growth at sub-zero temperatures. The prototypical type-III AFPs have been extensively studied, notably by X-ray crystallography, solid-state and solution NMR, and mutagenesis, leading to the identification of a compound ice-binding surface (IBS) composed of two adjacent ice-binding sections, each which binds to particular lattice planes of ice crystals, poisoning their growth. This surface, including many hydrophobic and some hydrophilic residues, has been extensively used to model the interaction of AFP with ice. Experimentally observed water molecules facing the IBS have been used in an attempt to validate these models. However, these trials have been hindered by the limited capability of X-ray crystallography to reliably identify all water molecules of the hydration layer. Due to the strong diffraction signal from both the oxygen and deuterium atoms, neutron diffraction provides a more effective way to determine the water molecule positions (as D(2) O). Here we report the successful structure determination at 293 K of fully perdeuterated type-III AFP by joint X-ray and neutron diffraction providing a very detailed description of the protein and its solvent structure. X-ray data were collected to a resolution of 1.05 Å, and neutron Laue data to a resolution of 1.85 Å with a "radically small" crystal volume of 0.13 mm(3). The identification of a tetrahedral water cluster in nuclear scattering density maps has allowed the reconstruction of the IBS-bound ice crystal primary prismatic face. Analysis of the interactions between the IBS and the bound ice crystal primary prismatic face indicates the role of the hydrophobic residues, which are found to bind inside the holes of the ice surface, thus explaining the specificity of AFPs for ice versus water.

Supraclavicular flap in head and neck reconstruction: experience in 50 consecutive patients.

The supraclavicular flap (SCF) is a fasciocutaneous flap used to cover head, oral, and neck region defects after tumor resection. Its main vascular supply is the supraclavicular artery and accompanying veins and it can be harvested as a vascularised pedicled flap. The SCF serves as an excellent outer skin cover as well as a good inner mucosal lining after oral cavity and head-neck tumor resections. The flap has a wide arc of rotation and matches the skin colour and texture of the face and neck. Between March 2006 and March 2011, the pedicled supraclavicular flap was used for reconstruction in 50 consecutive patients after head and neck tumor resections and certain benign conditions in a tertiary university hospital setting. The flaps were tunnelized under the neck skin to cover the external cervicofacial defects or passed medial to the mandible to give an inner epithelial lining after the oral cavity and oropharyngeal tumor excision. Forty-four of the 50 patients had 100% flap survival with excellent wound healing. All the flaps were harvested in less than 1 h. There were four cases of distal tip desquamation and two patients had complete flap necrosis. Distal flap desquamation was observed in SCFs used for resurfacing the external skin defects after oral cavity tumor ablation and needed only conservative treatment measures. Total flap failure was encountered in two patients who had failed in previous chemoradiotherapy for squamous cell cancer of the floor of mouth and tonsil, respectively, and the SCF was used in mucosal defect closure after tumor ablation. The benefits of a pedicled fasciocutaneous supraclavicular flap are clear; it is thin, reliable, easy, and quick to harvest. In head, face and neck reconstructions, it is a good alternative to free fasciocutaneous flaps, regional pedicled myocutaneous flaps, and the deltopectoral flap.

A simple bypass technique for superior vena cava reconstruction.

Superior vena cava (SVC) clamping can be required during thoracic surgery for SVC replacement or repair. In such cases, bypass techniques can be necessary to avoid hemodynamic instability, cerebral venous hypertension and hypoperfusion. Here, we report a novel and simple SVC bypass technique which does not require full systemic heparinization, specialized cannulation techniques or pumping devices and which can be applied percutaneously in the preoperative phase or intraoperatively. The preoperative shunt consisted in two Swan-Ganz catheters inserted in the jugular and femoral veins and connected by perfusion tubing with a three way stopcock. The intraoperative shunt consisted of a Pruitt(®)-catheter inserted in the left innominate vein and connected to a femoral Swan-Ganz catheter by perfusion tubing. We validated our system in seven patients undergoing SVC reconstruction. We monitored the systemic arterial blood pressures, the heart rate and vasoactive peptide requirements throughout the procedure. We also determined the neurological status and the in-hospital morbidity and mortality for each patient. Using this bypass, SVC clamping caused no hemodynamic instability, no neurological impairments and no in-hospital complications or deaths. This simple temporary SVC bypass procedure is safe and avoids hemodynamic instability and cerebral venous hypertension.

Dispersal routes reconstruction and the minimum cost arborescence problem.

We show that the dispersal routes reconstruction problem can be stated as an instance of a graph theoretical problem known as the minimum cost arborescence problem, for which there exist efficient algorithms. Furthermore, we derive some theoretical results, in a simplified setting, on the possible optimal values that can be obtained for this problem. With this, we place the dispersal routes reconstruction problem on solid theoretical grounds, establishing it as a tractable problem that also lends itself to formal mathematical and computational analysis. Finally, we present an insightful example of how this framework can be applied to real data. We propose that our computational method can be used to define the most parsimonious dispersal (or invasion) scenarios, which can then be tested using complementary methods such as genetic analysis.