Bicomplex quantum mechanics: I. The generalized Schr\"odinger equation

We introduce the set of bicomplex numbers $\mathbb{T}$ which is a commutative ring with zero divisors defined by $\mathbb{T}=\{w_0+w_1 \bold{i_1}+w_2\bold{i_2}+w_3 \bold{j}| w_0,w_1,w_2,w_3 \in \mathbb{R}\}$ where $\bold{i^{\text 2}_1}=-1, \bold{i^{\text 2}_2}=-1, \bold{j}^2=1,\ \bold{i_1}\bold{i_2}=\bold{j}=\bold{i_2}\bold{i_1}$. We present the conjugates and the moduli associated with the bicomplex numbers. Then we study the bicomplex Schr\"odinger equation and found the continuity equations. The discrete symmetries of the system of equations describing the bicomplex Schr\"odinger equation are obtained. Finally, we study the bicomplex Born formulas under the discrete symetries. We obtain the standard Born's formula for the class of bicomplex wave functions having a null hyperbolic angle

Lie symmetries of multidimensional difference equations

A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be used to perform symmetry reduction. The method generalizes one presented in a recent publication for the case of ordinary difference equations. In turn, it can easily be generalized to difference systems involving an arbitrary number of dependent and independent variables

Mitigation of Conflicts with Automation: Use of Cognitive Countermeasures

Objective: The aim of this study was to empirically assess the efficacy of cognitive countermeasures based on the technique of information removal to enhance human operator attentional disengagement abilities when facing attentional tunneling. Background: Lessons learned from human factors studies suggest that conflict with automation leads to the degradation of operators’ performance by promoting excessive focusing on a single task to the detriment of the supervision of other critical parameters. Method: An experimental setup composed of a real unmanned ground vehicle and a ground station was developed to test the efficiency of the cognitive countermeasures.The scenario (with and without countermeasure) involved an authority conflict between the participants and the robot induced by a battery failure.The effects of the conflict and, in particular, the impact of cognitive countermeasures on the participants’ cognition and arousal were assessed through heart rate measurement and eye tracking techniques. Results: In the control group (i.e., no countermeasure), 8 out of 12 participants experienced attentional tunneling when facing the conflict, leading them to neglect the visual alarms displayed that would have helped them to understand the evolution of the tactical situation. Participants in the countermeasure group showed lower heart rates and enhanced attentional abilities, and 10 out of 11 participants made appropriate decisions. Conclusions: The use of cognitive countermeasures appeared to be an efficient means to mitigate excessive focus issues in the unmanned ground vehicle environment. Applications: The principle of cognitive counter- measures can be applied to a large domain of applications involving human operators interacting with critical systems

Dehydration, deamination and enzymatic repair of cytosine glycols from oxidized poly(dG-dC) and poly(dI-dC)

Cytosine glycols (5,6-dihydroxy-5,6-dihydrocytosine) are initial products of cytosine oxidation. Because these products are not stable, virtually all biological studies have focused on the stable oxidation products of cytosine, including 5-hydroxycytosine, uracil glycols and 5-hydroxyuracil. Previously, we reported that the lifetime of cytosine glycols was greatly enhanced in double-stranded DNA, thus implicating these products in DNA repair and mutagenesis. In the present work, cytosine and uracil glycols were generated in double-stranded alternating co-polymers by oxidation with KMnO4. The half-life of cytosine glycols in poly(dG-dC) was 6.5 h giving a ratio of dehydration to deamination of 5:1. At high substrate concentrations, the excision of cytosine glycols from poly(dG-dC) by purified endonuclease III was comparable to that of uracil glycols, whereas the excision of these substrates was 5-fold greater than that of 5-hydroxycytosine. Kinetic studies revealed that the Vmax was several fold higher for the excision of cytosine glycols compared to 5-hydroxycytosine. In contrast to cytosine glycols, uracil glycols did not undergo detectable dehydration to 5-hydroxyuracil. Replacing poly(dG-dC) for poly(dI-dC) gave similar results with respect to the lifetime and excision of cytosine glycols. This work demonstrates the formation of cytosine glycols in DNA and their removal by base excision repair