An Efficient Solution to Systems of Multivariate Polynomial Using Expression Trees

In recent years, several quite successful attempts have been made to solve systems of polynomial constraints, using geometric design tools, exploiting the availability of subdivision-based solvers [7], [11], [12], [15]. This broad range of methods includes both binary domain subdivision as well as the projected polyhedron method of Sherbrooke and Patrikalakis [15]. A prime obstacle in using subdivision solvers is their scalability. When the given constraint is represented as a tensor product of all its independent variables, it grows exponentially in size as a function of the number of variables. In this work, we show that for many applications, especially geometric ones, the exponential complexity of the constraints can be reduced to a polynomial by representing the underlying structure of the problem in the form of expression trees that represent the constraints. We demonstrate the applicability and scalability of this representation and compare its performance to that of tensor product constraint representation through several examples.     

Static output-feedback of state-multiplicative systems with application to altitude control

A linear parameter dependent approach for designing a constant output-feedback controller for a linear time-invariant system with stochastic multiplicative Wiener-type noise, that achieves a minimum bound on either the stochastic H ₂ or the H _∞ performance level is introduced. A solution is achieved also for the case where in addition to the stochastic parameters, the system matrices reside in a given polytope. In this case, a parameter dependent Lyapunov function is introduced which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that corresponds to the vertices of the uncertainty polytope.

The stochastic uncertainties appear in both the dynamic and the measurement matrices of the system. The problems are solved using the expected value of the standard performance index over the stochastic parameters. The theory developed is applied to an altitude control example.     

Volume-preserving FFD for programmable graphics hardware

Free-Form Deformation (FFD) is a well established technique for deforming arbitrary object shapes in space. Although more recent deformation techniques have been introduced, among them skeleton-based deformation and cage-based deformation, the simple and versatile nature of FFD is a strong advantage, and justifies its presence in nowadays leading commercial geometric modeling and animation software systems. Since its introduction in the late 1980s, many improvements have been proposed to the FFD paradigm, including control lattices of arbitrary topology, direct shape manipulation and GPU implementation. Several authors have addressed the problem of volume-preserving FFD. These previous approaches either make use of expensive nonlinear optimization techniques, or resort to first order approximation suitable only for small-scale deformations. In this paper we take advantage of the multi-linear nature of the volume constraint in order to derive a simple, exact and explicit solution to the problem of volume-preserving FFD. Two variants of the algorithm are given, without and with direct shape manipulation. Moreover, the linearity of our solution enables to implement it efficiently on GPU.     

H∞ tracking of linear continuous‐time systems with stochastic uncertainties and preview

The problem of finite‐horizon H_∞ tracking for linear continuous time‐invariant systems with stochastic parameter uncertainties is investigated for both, the state‐feedback and the output‐feedback control problems. We consider three tracking patterns depending on the nature of the reference signal i.e. whether it is perfectly known in advance, measured on line or previewed in a fixed time‐interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices of the system. In the state‐feedback case, for each of the above three cases a game theory approach is applied where, given a specific reference signal, the controller plays against nature which chooses the initial condition and the energy‐bounded disturbance. The problems are solved using the expected value of the standard performance index over the stochastic parameters, where, in the state‐feedback case, necessary and sufficient conditions are found for the existence of a saddle‐point equilibrium. The corresponding infinite‐horizon time‐invariant tracking problem is also solved for the latter case, where a dissipativity approach is considered. The output‐feedback control problem is solved as a max–min problem for the three tracking patterns, where necessary and sufficient condition are obtained for the solution. The theory developed is demonstrated by a simple example where we compare our solution with an alternative solution which models the tracking signal as a disturbance. Copyright © 2004 John Wiley & Sons, Ltd.     

Robotic manipulators based on inflatable structures

This paper deals with a new kind of mechanical structure for the robotic arm based on elements made of thin, inflatable shells. This approach offers an increase of the payload-to-weight ratio of the robot. Moreover, it allows compact packaging and easier robot deployment, which is critical in hard-to-reach spaces and where volume and weight are of utmost importance. An inflatable link was constructed and tested statically and dynamically as part of the robot structure. To overcome the flexibility effects, an end-point sensor was installed that enables closing the control loop on the tip location. Path tracking performances of the experimental system, which consists of a SCARA type robot arm with an inflatable forearm, an end-effector position sensor and a digital controller, are presented.     

The biomechanics of the locust ovipositor valves: a unique digging apparatus

The female locust has a unique mechanism for digging in order to deposit its eggs deep in the ground. It uses two pairs of sclerotized valves to displace the granular matter, while extending its abdomen as it propagates underground. This ensures optimal conditions for the eggs to incubate and provides them with protection from predators. Here, the direction-dependent biomechanics of the locust''s major, dorsal digging valves are quantified and analysed under forces in the physiological range and beyond, considering the hydration level as well as the females'' sexual maturation state. Our findings reveal that the responses of the valves to compression forces in the digging and propagation directions change upon sexual maturation to follow their function and depend on environmental conditions. In addition, mature females, which lay eggs, have stiffer valves, up to approximately 19 times the stiffness of the pre-mature locusts. The valves are stiffer in the major working direction, corresponding to soil shuffling and compression, compared with the direction of propagation. Hydration of the valves reduces their stiffness but increases their resilience against failure. These findings provide mechanical and materials guidelines for the design of novel non-drilling burrowing tools, including three-dimensionally printed anisotropic materials based on composites     

Cheating on Complementarity and Interference by Translational – Internal Entanglement

We show that if internal and momentum states of an interfering particle are entangled, then by measuring its internal state we may infer both path (corpuscular) and phase (wavelike) information with practically any precision, without the complementarity constraints of which-path detection. This holds also for multipath–multistate configurations, allowing large amounts of information to be stored in a single particle. We further show that highly complex particles (e.g., molecules or macroscopic bodies) subject to fields that couple (entangle) their internal and translational (momentum) states may undergo an irresversible randomization (diffusion), manifest by the disappearance of the interference pattern, as if they are subject to decoherence. Thus, translational-internal entanglement can give rise to anomalies in quantum wavepacket propagation.     

Relation of visual perception and visual-motor integration for clumsy children

Rac1 small GTPase plays pivotal roles in various cell functions such as cell morphology, cell polarity, and cell proliferation. We have previously identified IQGAP1 from bovine brain cytosol as a target for Rac1 by an affinity purification method. By using the same method, we purified a specifically Rac1-associated protein with a molecular mass of about 140 kDa (p140) from bovine brain cytosol. This protein interacted with guanosine 5'-(3-O-thio)triphosphate (GTPgammaS).glutathione S-transferase (GST)-Rac1 but not with the GDP.GST-Rac1, GTPgammaS.GST-Cdc42, or GTPgammaS.GST-RhoA. The amino acid sequences of this protein revealed that p140 is identified as a product of KIAA0068 gene. We denoted this protein as Sra-1 (Specifically Rac1-associated protein). Recombinant Sra-1 interacted with GTPgammaS.GST-Rac1 and weakly with GDP.Rac1 but not with GST-Cdc42 or GST-RhoA. The N-terminal domain of Sra-1 (1-407 amino acids) was responsible for the interaction with Rac1. Myc-tagged Sra-1 and the deletion mutant capable of interacting with Rac1, but not the mutants unable to bind Rac1, were colocalized with dominant active Rac1(Val-12) and cortical actin filament at the Rac1(Val-12)-induced membrane ruffling area in KB cells. Sra-1 was cosedimented with filamentous actin (F-actin), indicating that Sra-1 directly interacts with F-actin. These results suggest that Sra-1 is a novel and specific target for Rac1.     

CAT administration of language placement examinations

This article describes the development of a computerized adaptive test for Cegep de Jonquiere, a community college located in Quebec, Canada. Computerized language proficiency testing allows the simultaneous presentation of sound stimuli as the question is being presented to the test-taker. With a properly calibrated bank of items, the language proficiency test can be offered in an adaptive framework. By adapting the test to the test-taker's level of ability, an assessment can be made with significantly fewer items. We also describe our initial attempt to detect instances in which "cheating low" is occurring. In the "cheating low" situation, test-takers deliberately answer questions incorrectly, questions that they are fully capable of answering correctly had they been taking the test honestly.