The Geometric Algebra Lift of Qubits and Beyond

The Geometric Algebra formalism opens the door to developing a theory upgrading conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions; unambiguous definition of states, observables, measurements bring into reality clear explanations of conventional weird quantum mechanical features, particularly the results of double split experiments where particles create diffraction patterns inherent to wave diffraction. This weirdness of the double split experiment is milestone of all further difficulties in interpretation of quantum mechanics.

Clifford Fuzzy Support Vector Machine for Regression and Its Application in Electric Load Forecasting of Energy System

Electric load forecasting is a prominent topic in energy research. Support vector regression (SVR) has extensively and successfully achieved good performance in electric load forecasting. Clifford support vector regression (CSVR) realizes multiple outputs by the Clifford geometric algebra which can be used in multistep forecasting of electric load. However, the effect of input is different from the forecasting value. Since the load forecasting value affects the energy reserve and distribution in the energy system, the accuracy is important in electric load forecasting. In this study, a fuzzy support vector machine is proposed based on geometric algebra named Clifford fuzzy support vector machine for regression (CFSVR). Through fuzzy membership, different input points have different contributions to deciding the optimal regression hyperplane. We evaluate the performance of the proposed CFSVR in fitting tasks on numerical simulation, UCI data set and signal data set, and forecasting tasks on electric load data set and NN3 data set. The result of the experiment indicates that Clifford fuzzy support vector machine for regression has better performance than CSVR and SVR of other algorithms which can improve the accuracy of electric load forecasting and achieve multistep forecasting.

Self calibration method of binocular vision based on Conformal geometric algebra

We will study binocular vision for 6-DOF robotic manipulator in conformal geometric algebra approach. We will focus on the case where some information as relative cameras positions, has been lost. In particular, we will use the construction of the manipulator to infer a self calibration method for cameras position based in binocular vision with incomplete information.

Note on geometric algebras and control problems with SO(3)-symmetries

We study the role of symmetries in control systems by means of geometric algebra approach. We discuss two specific control problems on Carnot group of step 2 invariant with respect to the action of$SO(3). We understand geodesics as curves in suitable geometric algebras which allows us to asses an efficient algorithm for local control.

A Spinor Model for Cascading Two-port Scattering Matrices In Conformal Geometric Algebra

Building on the work in [1], this paper shows how Conformal Geometric Algebra (CGA) can be used to model an arbitrary two-port scattering matrix as a rotation in four dimensional Minkowski space, known as a spinor. This spinor model plays the role of the wave-cascading matrix in conventional microwave network theory. Techniques to translate two-port scattering matrix in and out of spinor form are given. Once the translation is laid out, geometric interpretations are given to the physical properties of reciprocity, loss, and symmetry and some mathe- matical groups are identified. Methods to decompose a network into various sub-networks, are given. An example application of interpolating a 2-port network is provided demonstrating an advantage of the spinor model. Since rotations in four dimensional Minkowski space are Lorentz transformations, this model opens up the field of network theory to physicists familiar with relativity, and vice versa.

Geometric Algebra Framework Applied to Circuits with Non-sinusoidal Voltages and Currents

We apply a well known technique of theoretical physics, known as Geometric Algebra or Clifford algebra, to linear electrical circuits with non-sinusoidal voltages and currents. We rederive from the first principles the Geometric Algebra approach to the apparent power decomposition. The important new point consists in a choice of a natural convenient basis in the Clifford vector space which simplifies considerably the presentation. Thus we are able to derive a number of general results which are missing in the former papers. In particular, a natural correspondence with the Current Physical Components approach is shown.