How Noisy Data Affects Geometric Semantic Genetic Programming

Noise is a consequence of acquiring and pre-processing data from the environment, and shows fluctuations from different sources---e.g., from sensors, signal processing technology or even human error. As a machine learning technique, Genetic Programming (GP) is not immune to this problem, which the field has frequently addressed. Recently, Geometric Semantic Genetic Programming (GSGP), a semantic-aware branch of GP, has shown robustness and high generalization capability. Researchers believe these characteristics may be associated with a lower sensibility to noisy data. However, there is no systematic study on this matter. This paper performs a deep analysis of the GSGP performance over the presence of noise. Using 15 synthetic datasets where noise can be controlled, we added different ratios of noise to the data and compared the results obtained with those of a canonical GP. The results show that, as we increase the percentage of noisy instances, the generalization performance degradation is more pronounced in GSGP than GP. However, in general, GSGP is more robust to noise than GP in the presence of up to 10% of noise, and presents no statistical difference for values higher than that in the test bed.Comment: 8 pages, In proceedings of Genetic and Evolutionary Computation Conference (GECCO 2017), Berlin, German

Fractal dimension of transport coefficients in a deterministic dynamical system

In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $\gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2, corrected typos, etc.

Using intelligent optimization methods to improve the group method of data handling in time series prediction

In this paper we show how the performance of the basic algorithm of the Group Method of Data Handling (GMDH) can be improved using Genetic Algorithms (GA) and Particle Swarm Optimization (PSO). The new improved GMDH is then used to predict currency exchange rates: the US Dollar to the Euros. The performance of the hybrid GMDHs are compared with that of the conventional GMDH. Two performance measures, the root mean squared error and the mean absolute percentage errors show that the hybrid GMDH algorithm gives more accurate predictions than the conventional GMDH algorithm

Muon spin rotation and neutron scattering study of the non-centrosymmetric tetragonal compound CeAuAl3

We have investigated the non-centrosymmetric tetragonal heavy-fermion compound CeAuAl3 using muon spin rotation (muSR), neutron diffraction (ND) and inelastic neutron scattering (INS) measurements. We have also revisited the magnetic, transport and thermal properties. The magnetic susceptibility reveals an antiferromagnetic transition at 1.1 K with a possibility of another magnetic transition near 0.18 K. The heat capacity shows a sharp lambda-type anomaly at 1.1 K in zero-filed, which broadens and moves to higher temperature in applied magnetic field. Our zero-field muSR and ND measurements confirm the existence of a long-range magnetic ground state below 1.2 K. Further the ND study reveals an incommensurate magnetic ordering with a magnetic propagation vector k = (0, 0, 0.52) and a spiral structure of Ce moments coupled ferromagnetically within the ab-plane. Our INS study reveals the presence of two well-defined crystal electric field (CEF) excitations at 5.1 meV and 24.6 meV in the paramagnetic phase of CeAuAl3 which can be explained on the basis of the CEF theory. Furthermore, low energy quasi-elastic excitations show a Gaussian line shape below 30 K compared to a Lorentzian line shape above 30 K, indicating a slowdown of spin fluctuation below 30 K. We have estimated a Kondo temperature of TK=3.5 K from the quasi-elastic linewidth, which is in good agreement with that estimated from the heat capacity. This study also indicates the absence of any CEF-phonon coupling unlike that observed in isostructural CeCuAl3. The CEF parameters, energy level scheme and their wave functions obtained from the analysis of INS data explain satisfactorily the single crystal susceptibility in the presence of two-ion anisotropic exchange interaction in CeAuAl3.Comment: 28 pages and 17 figure

Investment Opportunities Forecasting: Extending the Grammar of a GP-based Tool

In this paper we present a new version of a GP financial forecasting tool, called EDDIE 8. The novelty of this version is that it allows the GP to search in the space of indicators, instead of using pre-specified ones. We compare EDDIE 8 with its predecessor, EDDIE 7, and find that new and improved solutions can be found. Analysis also shows that, on average, EDDIE 8's best tree performs better than the one of EDDIE 7. The above allows us to characterize EDDIE 8 as a valuable forecasting tool

Dynamics of the peripheral membrane protein P2 from human myelin measured by neutron scattering - a comparison between wild-type protein and a hinge mutant

Myelin protein P2 is a fatty acid-binding structural component of the myelin sheath in the peripheral nervous system, and its function is related to its membrane binding capacity. Here, the link between P2 protein dynamics and structure and function was studied using elastic incoherent neutron scattering (EINS). The P38G mutation, at the hinge between the β barrel and the α-helical lid, increased the lipid stacking capacity of human P2 in vitro, and the mutated protein was also functional in cultured cells. The P38G mutation did not change the overall structure of the protein. For a deeper insight into P2 structure-function relationships, information on protein dynamics in the 10 ps to 1 ns time scale was obtained using EINS. Values of mean square displacements mainly from protein H atoms were extracted for wild-type P2 and the P38G mutant and compared. Our results show that at physiological temperatures, the P38G mutant is more dynamic than the wild-type P2 protein, especially on a slow 1-ns time scale. Molecular dynamics simulations confirmed the enhanced dynamics of the mutant variant, especially within the portal region in the presence of bound fatty acid. The increased softness of the hinge mutant of human myelin P2 protein is likely related to an enhanced flexibility of the portal region of this fatty acid-binding protein, as well as to its interactions with the lipid bilayer surface requiring conformational adaptations

Optimization by Quantum Annealing: Lessons from hard 3-SAT cases

The Path Integral Monte Carlo simulated Quantum Annealing algorithm is applied to the optimization of a large hard instance of the Random 3-SAT Problem (N=10000). The dynamical behavior of the quantum and the classical annealing are compared, showing important qualitative differences in the way of exploring the complex energy landscape of the combinatorial optimization problem. At variance with the results obtained for the Ising spin glass and for the Traveling Salesman Problem, in the present case the linear-schedule Quantum Annealing performance is definitely worse than Classical Annealing. Nevertheless, a quantum cooling protocol based on field-cycling and able to outperform standard classical simulated annealing over short time scales is introduced.Comment: 10 pages, 6 figures, submitted to PR

Hopping motion of lattice gases through nonsymmetric potentials under strong bias conditions

The hopping motion of lattice gases through potentials without mirror-reflection symmetry is investigated under various bias conditions. The model of 2 particles on a ring with 4 sites is solved explicitly; the resulting current in a sawtooth potential is discussed. The current of lattice gases in extended systems consisting of periodic repetitions of segments with sawtooth potentials is studied for different concentrations and values of the bias. Rectification effects are observed, similar to the single-particle case. A mean-field approximation for the current in the case of strong bias acting against the highest barriers in the system is made and compared with numerical simulations. The particle-vacancy symmetry of the model is discussed.Comment: 8 pages (incl. 6 eps figures); RevTeX 3.

Magnetic structures and excitations in CePd2(Al, Ga)2 series: Development of the "vibron" states

CePd2Al2-xGax compounds crystallizing in the tetragonal CaBe2Ge2-type structure (space group P4/nmm) and undergoing a structural phase transition to an orthorhombic structure (Cmme) at low temperatures were studied by means of neutron scattering. The amplitude-modulated magnetic structure of CePd2Al2 is described by an incommensurate propagation vector k - =(dx, 12+dy, 0) with dx=0.06 and dy=0.04. The magnetic moments order antiferromagnetically within the ab planes stacked along the c axis and are arranged along the direction close to the orthorhombic a axis with a maximum value of 1.5(1) µB/Ce3+. CePd2Ga2 reveals a magnetic structure composed of two components: the first is described by the propagation vector k1 - =(12, 12, 0), and the second one propagates with k2 - =(0, 12, 0). The magnetic moments of both components are aligned along the same direction - the orthorhombic 100] direction - and their total amplitude varies depending on the mutual phase of magnetic moment components on each Ce site. The propagation vectors k1 - and k2 - describe also the magnetic structure of substituted CePd2Al2-xGax compounds, except the one with x=0.1.CePd2Al1.9Ga0.1 with magnetic structure described by k - and k1 - stays on the border between pure CePd2Al2 and the rest of the series. Determined magnetic structures are compared with other Ce 112 compounds. Inelastic neutron scattering experiments disclosed three nondispersive magnetic excitations in the paramagnetic state of CePd2Al2, while only two crystal field (CF) excitations are expected from the splitting of ground state J=52 of the Ce3+ ion in a tetragonal/orthorhombic point symmetry. Three magnetic excitations at 1.4, 7.8, and 15.9 meV are observed in the tetragonal phase of CePd2Al2. A structural phase transition to an orthorhombic structure shifts the first excitation up to 3.7 meV, while the other two excitations remain at almost the same energy. The presence of an additional magnetic peak is discussed and described within the Thalmeier-Fulde CF-phonon coupling (i.e., magnetoelastic coupling) model generalized to the tetragonal point symmetry. The second parent compound CePd2Ga2 does not display any sign of additional magnetic excitation. The expected two CF excitations were observed. The development of magnetic excitations in the CePd2Al2-xGax series is discussed and crystal field parameters determined