We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This first part introduces the main conceps and philosophies anddiscu...

We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This second part continues to study the question of catecoricitytrans...

Analysis of tides and internal waves from model studies in the South China Sea is done using three techniques. We summarize results from standard Fourier methods, continuous wavelet analysis and the direct scattering transform. Because the Fourier and wavelet analysis are inherently linear methods their utility in application to nonlinear dynamics is often questioned. Nevertheless, they have sh...

This paper presents theory, algorithms, and validation results for system identification of continuous-time statespace models from finite input–output sequences. The algorithms developed are methods of subspace model identification and stochastic realization adapted to the continuous-time context. The resulting model can be decomposed into an input–output model and a stochastic innovations mode...

We propose an algebraic model for hybrid systems and illustrate its usefulness by proving theorems in realization theory using this viewpoint. By a hybrid system, we mean a collection of continuous nonlinear control systems associated with a discrete finite state automaton. The automaton switches between the continuous control systems, and this switching is a function of the discrete input symb...

background: in medical research, dichotomisation of continuous variables is a widespread use approach. however, it has been argued that dichotomisation might be waste of information. the aim of this paper is to review the main methods to dichotomise continuous data, to address practical issues around dichotomisation methods, and to investigate whether dichotomisation is always a bad idea. metho...

This paper discusses the relative merits of discrete vs. continuous perspectives on innovation, technical change, and economic growth. It discusses the innovation time series liteature in some detail to extract the continuous and clustering properties of the historical record on innovation. It then proposes a mosaic/avalanche model based on percolation theory and selforganized criticality to ad...

Proposed in this paper is extended continuous logic (ECL), a generalization of continuous logic based on the introduction of variable degree of conjunction and disjunction in complex conjunctive and disjunctive statements. The properties of ECL, as an algebraic structure, are analysed and various ECL functions are defined and classified. The apparatus of sentential algebra in ECL is defined wit...