Palindromic polynomials, time-reversible systems, and conserved quantities

The roots of palindromic and antipalindromic polynomials appear in pairs (s,1/s). A polynomial with such roots is antipalindromic if and only if in addition, it has a root at 1 of an odd multiplicity. The result has applications in system theory: 1) any kernel representation of a discrete-time, time-reversible, scalar, autonomous LTI system is either palindromic or antipalindromic. (Similar statement holds for systems with inputs.) 2) LTI systems with palindromic or antipalindromic kernel representations have nontrivial conserved quantities

Autonomous linear lossless systems

We define a lossless autonomous system as one having a quadratic differential form associated with it called an energy function, which is positive and which is conserved. We define an oscillatory system as one which has all its trajectories bounded on the entire time axis. In this paper, we show that an autonomous system is lossless if and only if it is oscillatory. Next we discuss a few properties of energy functions of autonomous lossless systems and a suitable way of splitting a given energy function into its kinetic and potential energy components

A polynomial approach to the realization of J-lossless behaviors

We consider the problem of realizing lossless behaviours with respect to the supply rate equal to the scalar product of the input and of the derivative of the output variables. Using polynomial algebraic method we devise a realization procedure which, starting from an image representation, yields the same state representation used by van der Schaft and Oeloff in the context of model reduction. We also apply the insights derived from this realization procedure to the synthesis of lossless mechanical systems with given transfer functions using springs and masses

Stiffness and position control of a prosthetic wrist by means of an EMG interface

In this paper, we present a novel approach for decoding electromyographic signals from an amputee and for interfacing them with a prosthetic wrist. The model for the interface makes use of electromyographic signals from electrodes placed in agonistic and antagonistic sides of the forearm. The model decodes these signals in order to control both the position and the stiffness of the wrist

Stability analysis of the Michaelis-Menten approximation of a mixed mechanism of a phosphorylation system

In this paper, we consider a mixed mechanism of a n-site phosphorylation system in which the mechanism of phosphorylation is distributive and that of dephosphorylation is processive. It is assumed that the concentrations of the substrates are much higher than those of the enzymes and their intermediate complexes. This assumption enables us to reduce the system using the steady-state approach to a Michaelis-Menten approximation of the system. It is proved that the resulting system of nonlinear ordinary differential equations admits a unique positive equilibrium in every positive stoichiometric compatibility class using the theory of quadratic equations. We then consider two special cases. In the first case, we assume that the Michaelis constants associated with the different substrates in the phosphorylation reactions are equal and construct a Lyapunov function to prove asymptotic stability of the system. In the second case, we assume that there are just two sites of phosphorylation and dephoshorylation and prove that the resulting system is asymptotically stable using Poincare Bendixson theorem

A polynomial approach to the realization of J-lossless behaviours

In this paper, a class of behaviours known as J-lossless behaviours is introduced, where J is a symmetric two-variable polynomial matrix. For a certain J, it is shown that the resulting set of J-lossless behaviours are SISO behaviours such that for each of such behaviours, there exists a quadratic differential form which is positive for nonzero trajectories of the behaviour and whose derivative is equal to the product of the input variable and the derivative of the output variable. Earlier, Van der Schaft and Oeloff had considered a specific form of realization for such behaviours that plays an important role in their model reduction procedure. In our paper, we give a method of computation of a state space realization from a transfer function of such a behaviour in the same form as considered by Van der Schaft and Oeloff, using polynomial algebraic methods. Apart from being useful in enlarging the scope of the model reduction procedure of Van der Schaft and Oeloff, we show that our method of realization also has application in the synthesis of lossless mechanical systems with given transfer functions using springs and masses

Complex and detailed balancing of chemical reaction networks revisited

The characterization of the notions of complex and detailed balancing for mass action kinetics chemical reaction networks is revisited from the perspective of algebraic graph theory, in particular Kirchhoff's Matrix Tree theorem for directed weighted graphs. This yields an elucidation of previously obtained results, in particular with respect to the Wegscheider conditions, and a new necessary and sufficient condition for complex balancing, which can be verified constructively.Comment: arXiv admin note: substantial text overlap with arXiv:1502.0224

A network dynamics approach to chemical reaction networks

A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in chemical reaction network theory, and which directly relates to the thermodynamics of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This directly leads to the characterization of the set of equilibria and their stability. Both the form of the dynamics and the deduced dynamical behavior are very similar to consensus dynamics. The assumption of complex-balancedness is revisited from the point of view of Kirchhoff's Matrix Tree theorem, providing a new perspective. Finally, using the classical idea of extending the graph of chemical complexes by an extra 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action outflows is given.Comment: 18 page

Solid solubility of sulfur, selenium, and tellurium in molybdenum at 1100°C, lattice constants thermal expansion coefficients, and densities of molybdenum and the molybdenum-base alloys

With the ever increasing requirement for engineering materials having adequate mechanical properties at ever higher temperatures there has been, in quite recent years, a considerable increase in the study of molybdenum and molybdenum-rich alloys. Since 1945 extensive information on the engineering properties of molybdenum and molybdenum-base alloys has gradually become more available ... The present work involves the determination of solid solubility of elements with large atoms such as sulfur, selenium, and tellurium in molybdenum at 1100°C using the parametric method. Furthermore, the thermal expansion coefficients of pure molybdenum and of molybdenum-base solid solutions containing the elements just mentioned were of interest. In addition the densities of pure molybdenum and of some of the molybdenum-base chalcogenide alloys were also determined --Introduction, page 1-2

Retrograde Epidural Catheter Relieves Intractable Sacral Pain

Pain caused by tumor infiltration of the sacral area remains a major clinical challenge. Patients with poor pain control despite comprehensive medical management may be treated with neuraxial techniques such as continuous epidural or spinal anesthetic. We report a case in which a patient with metastatic breast cancer experienced inadequate pain relief after multiple intravenous pain management regimens as well as intrathecal (IT) drug delivery. The concentration of local anesthetics delivered via the IT catheter was limited due to the patient\u27s baseline motor weakness which would be exacerbated with higher concentrations of local anesthetics. Thus, a decision was made to insert an epidural catheter via a retrograde technique to provide the patient with a band of anesthesia which would provide profound sensory blockade without concomitant motor weakness. Pain refractory to other modalities of pain control was successfully treated with the epidural technique