Stability of switched linear differential systems

We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching instants is specified by gluing conditions, i.e. algebraic conditions on the trajectories and their derivatives at the switching instant. We provide sufficient conditions for stability based on LMIs for systems with general gluing conditions. We also analyse the role of positive-realness in providing sufficient polynomial-algebraic conditions for stability of two-modes switched systems with special gluing conditions

The Maximal Positively Invariant Set: Polynomial Setting

This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating that the related preimage map preserves basic semialgebraic structure. In fact, this property propagates to underlying set--dynamics induced by the associated restricted preimage map in general and to its maximal trajectory in particular. The finite time convergence of the corresponding maximal trajectory to the maximal positively invariant set is verified under reasonably mild conditions. The analysis is complemented with a discussion of computational aspects and a prototype implementation based on existing toolboxes for polynomial optimization

Construction and analysis of causally dynamic hybrid bond graphs

Engineering systems are frequently abstracted to models with discontinuous behaviour (such as a switch or contact), and a hybrid model is one which contains continuous and discontinuous behaviours. Bond graphs are an established physical modelling method, but there are several methods for constructing switched or ‘hybrid’ bond graphs, developed for either qualitative ‘structural’ analysis or efficient numerical simulation of engineering systems. This article proposes a general hybrid bond graph suitable for both. The controlled junction is adopted as an intuitive way of modelling a discontinuity in the model structure. This element gives rise to ‘dynamic causality’ that is facilitated by a new bond graph notation. From this model, the junction structure and state equations are derived and compared to those obtained by existing methods. The proposed model includes all possible modes of operation and can be represented by a single set of equations. The controlled junctions manifest as Boolean variables in the matrices of coefficients. The method is more compact and intuitive than existing methods and dispenses with the need to derive various modes of operation from a given reference representation. Hence, a method has been developed, which can reach common usage and form a platform for further study

Up or Down? How Culture and Color Affect Judgments

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In the Mainland China stock market, an upmarket is represented by the color red, whereas a downmarket is represented by the color green. Elsewhere, including the Chinese Hong Kong stock market, the color representations are the opposite. Three studies were conducted to examine the red-up–green-down effect for Mainland Chinese as well as the green-up–red-down effect for Hong Kong people. Study 1 showed that Mainland Chinese tended to predict greater economic growth (study 1a) and higher growth in consumption trends (study 1b) when the experimental materials were presented in red than in green, whereas Hong Kong participants exhibited the opposite tendencies. Study 2 found that Mainland Chinese implicitly associated red and green with up and down, respectively; Hong Kong people, however, implicitly associated green and red with up and down, respectively. Study 3 further indicated that Mainland Chinese were more likely to predict good outcomes when scenarios were presented in red, whereas Hong Kong participants were more likely to predict good outcomes when scenarios were presented in green. These findings suggest that culturally specific environment cues could influence human prediction and judgment. Implications for judgment generally are discussed

A Combined Representation Learning Approach for Better Job and Skill Recommendation

Job recommendation is an important task for the modern recruitment industry. An excellent job recommender system not only enables to recommend a higher paying job which is maximally aligned with the skill-set of the current job, but also suggests to acquire few additional skills which are required to assume the new position. In this work, we created three types of information net- works from the historical job data: (i) job transition network, (ii) job-skill network, and (iii) skill co-occurrence network. We provide a representation learning model which can utilize the information from all three networks to jointly learn the representation of the jobs and skills in the shared k-dimensional latent space. In our experiments, we show that by jointly learning the representation for the jobs and skills, our model provides better recommendation for both jobs and skills. Additionally, we also show some case studies which validate our claims

Coupling different levels of resolution in molecular simulations

Simulation schemes that allow to change molecular representation in a subvolume of the simulation box while preserving the equilibrium with the surrounding introduce conceptual problems of thermodynamic consistency. In this work we present a general scheme based on thermodynamic arguments which ensures thermodynamic equilibrium among the molecules of different representation. The robustness of the algorithm is tested for two examples, namely an adaptive resolution simulation, atomistic/coarse-grained, for a liquid of tetrahedral molecules and an adaptive resolution simulation of a binary mixture of tetrahedral molecules and spherical solutes

The Role of Representations in Executive Function: Investigating a Developmental Link between Flexibility and Abstraction.

Young children often perseverate, engaging in previously correct, but no longer appropriate behaviors. One account posits that such perseveration results from the use of stimulus-specific representations of a situation, which are distinct from abstract, generalizable representations that support flexible behavior. Previous findings supported this account, demonstrating that only children who flexibly switch between rules could generalize their behavior to novel stimuli. However, this link between flexibility and generalization might reflect general cognitive abilities, or depend upon similarities across the measures or their temporal order. The current work examined these issues by testing the specificity and generality of this link. In two experiments with 3-year-old children, flexibility was measured in terms of switching between rules in a card-sorting task, while abstraction was measured in terms of selecting which stimulus did not belong in an odd-one-out task. The link between flexibility and abstraction was general across (1) abstraction dimensions similar to or different from those in the card-sorting task and (2) abstraction tasks that preceded or followed the switching task. Good performance on abstraction and flexibility measures did not extend to all cognitive tasks, including an IQ measure, and dissociated from children's ability to gaze at the correct stimulus in the odd-one-out task, suggesting that the link between flexibility and abstraction is specific to such measures, rather than reflecting general abilities that affect all tasks. We interpret these results in terms of the role that developing prefrontal cortical regions play in processes such as working memory, which can support both flexibility and abstraction

Approximations and their consequences for dynamic modelling of signal transduction pathways

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system and its approximations with respect to the transient and steady state behavior