Bell inequalities from variable elimination methods

Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here we present an alternative method based on a combination of algebraic results on extensions of measures and variable elimination methods, e.g., the Fourier-Motzkin method. Our method is shown to overcome some of the computational difficulties associated with the hull problem in some non-trivial cases. Moreover, it provides an explanation for the arising of only a finite number of families of Bell inequalities in measurement scenarios where one experimenter can choose between an arbitrary number of different measurements

Circuits And Methods For Artifact Elimination

Disclosed are apparatus and methods that provide the ability to electrical stimulate a physical system, and actively eliminate interference with signal acquisition (artifacts) that arises from the stimulation. The technique implemented in the circuits and methods for eliminating interference connects a discharge path to a physical interface to the system to remove charge that is built-up during stimulation. By placing the discharge path in a feedback loop that includes a recording preamplifier and AC-coupling circuitry, the physical interface is brought back to its pre-stimulation offset voltage. The disclosed apparatus and methods may be used with piezoelectric transducers, ultrasound devices, optical diodes, and polarizable and non-polarizable electrodes. The disclosed apparatus can be employed in implantable devices, in vitro or in vivo setups with vertebrate and invertebrate neural tissue, muscle fibers, pancreatic islet cells, osteoblasts, osteoclasts, bacteria, algae, fungi, protists, and plants.Georgia Tech Research Corporatio

Methods of power line interference elimination in EMG signals

Electromyogram (EMG) recordings are often corrupted by the wide range of artifacts, which one of them is power line interference (PLI). The study focuses on some of the well-known signal processing approaches used to eliminate or attenuate PLI from EMG signal. The results are compared using signal-to-noise ratio (SNR), correlation coefficients and Bland-Altman analysis for each tested method: notch filter, adaptive noise canceller (ANC) and wavelet transform (WT). Thus, the power of the remaining noise and shape of the output signal are analysed. The results show that the ANC method gives the best output SNR and lowest shape distortion compared to the other methods.Web of Science40706

Adapting Real Quantifier Elimination Methods for Conflict Set Computation

The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice

Quantifier Elimination over Finite Fields Using Gr\"obner Bases

We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite fields. We analyze the theoretical complexity of the algorithm and show its application in the formal analysis of a biological controller model.Comment: A shorter version is to appear in International Conference on Algebraic Informatics 201

Gr\"obner Bases and Generation of Difference Schemes for Partial Differential Equations

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gr\"obner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gr\"obner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

How can onchocerciasis elimination in Africa be accelerated? Modelling the impact of increased ivermectin treatment frequency and complementary vector control

Background: Great strides have been made toward onchocerciasis elimination by mass drug administration (MDA) of ivermectin. Focusing on MDA-eligible areas, we investigated where the elimination goal can be achieved by 2025 by continuation of current practice (annual MDA with ivermectin) and where intensification or additional vector control is required. We did not consider areas hypoendemic for onchocerciasis with loiasis coendemicity where MDA is contraindicated. Methods: We used 2 previously published mathematical models, ONCHOSIM and EPIONCHO, to simulate future trends in microfilarial prevalence for 80 different settings (defined by precontrol endemicity and past MDA frequency and coverage) under different future treatment scenarios (annual, biannual, or quarterly MDA with different treatment coverage through 2025, with or without vector control strategies), assessing for each strategy whether it eventually leads to elimination. Results: Areas with 40%–50% precontrol microfilarial prevalence and ≥10 years of annual MDA may achieve elimination with a further 7 years of annual MDA, if not achieved already, according to both models. For most areas with 70%–80% precontrol prevalence, ONCHOSIM predicts that either annual or biannual MDA is sufficient to achieve elimination by 2025, whereas EPIONCHO predicts that elimination will not be achieved even with complementary vector control. Conclusions: Whether elimination will be reached by 2025 depends on precontrol endemicity, control history, and strategies chosen from now until 2025. Biannual or quarterly MDA will accelerate progress toward elimination but cannot guarantee it by 2025 in high-endemicity areas. Long-term concomitant MDA and vector control for high-endemicity areas might be useful