Periodic oscillations in feedback systems with combined pulse modulation

This paper presents a systematic method of investigating the existence of limit cycle oscillations in feedback systems with combined integral pulse frequency-pulse width (IPF-P/V) modulation. The method is based on the non-linear discrete equivalence of the continuous feedback system containing the IPF-PW modulator.

Random vibration of a second order non-linear elastic system

A method is presented for obtaining, approximately, the response covariance and probability distribution of a non-linear oscillator under a Gaussian excitation. The method has similarities with the hierarchy closure and the equivalent linearization approaches, but is different. A Gaussianization technique is used to arrive at the output autocorrelation and the input-output cross-correlation. This along with an energy equivalence criterion is used to estimate the response distribution function. The method is applicable in both the transient and steady state response analysis under either stationary or non-stationary excitations. Good comparison has been observed between the predicted and the exact steady state probability distribution of a Duffing oscillator under a white noise input.

A differential transformation technique for the analysis of a class of non-linear time varying systems

The scope of the differential transformation technique, developed earlier for the study of non-linear, time invariant systems, has been extended to the domain of time-varying systems by modifications to the differential transformation laws proposed therein. Equivalence of a class of second-order, non-linear, non-autonomous systems with a linear autonomous model of second order is established through these transformation laws. The feasibility of application of this technique in obtaining the response of such non-linear time-varying systems is discussed.

Strategic Information Acquisition: Applications to Herding and Auctions

The information that the economic agents have and regard relevant to their decision making is often assumed to be exogenous in economics. It is assumed that the agents either poses or can observe the payoff relevant information without having to exert any effort to acquire it. In this thesis we relax the assumption of ex-ante fixed information structure and study what happens to the equilibrium behavior when the agents must also decide what information to acquire and when to acquire it. This thesis addresses this question in the two essays on herding and two essays on auction theory. In the first two essays, that are joint work with Klaus Kultti, we study herding models where it is costly to acquire information on the actions that the preceding agents have taken. In our model the agents have to decide both the action that they take and additionally the information that they want to acquire by observing their predecessors. We characterize the equilibrium behavior when the decision to observe preceding agents' actions is endogenous and show how the equilibrium outcome may differ from the standard model, where all preceding agents actions are assumed to be observable. In the latter part of this thesis we study two dynamic auctions: the English and the Dutch auction. We consider a situation where bidder(s) are uninformed about their valuations for the object that is put up for sale and they may acquire this information for a small cost at any point during the auction. We study the case of independent private valuations. In the third essay of the thesis we characterize the equilibrium behavior in an English auction when there are informed and uninformed bidders. We show that the informed bidder may jump bid and signal to the uninformed that he has a high valuation, thus deterring the uninformed from acquiring information and staying in the auction. The uninformed optimally acquires information once the price has passed a particular threshold and the informed has not signalled that his valuation is high. In addition, we provide an example of an information structure where the informed bidder initially waits and then makes multiple jumps. In the fourth essay of this thesis we study the Dutch auction. We consider two cases where all bidders are all initially uninformed. In the first case the information acquisition cost is the same across all bidders and in the second also the cost of information acquisition is independently distributed and private information to the bidders. We characterize a mixed strategy equilibrium in the first and a pure strategy equilibrium in the second case. In addition we provide a conjecture of an equilibrium in an asymmetric situation where there is one informed and one uninformed bidder. We compare the revenues that the first price auction and the Dutch auction generate and we find that under some circumstances the Dutch auction outperforms the first price sealed bid auction. The usual first price sealed bid auction and the Dutch auction are strategically equivalent. However, this equivalence breaks down in case information is acquired during the auction.

Decoupling in non-linear systems with two degrees of freedom

The problem of decoupling a class of non-linear two degrees of freedom systems is studied. The coupled non-linear differential equations of motion of the system are shown to be equivalent to a pair of uncoupled equations. This equivalence is established through transformation techniques involving the transformation of both the dependent and independent variables. The sufficient conditions on the form of the non-linearity, for the case wherein the transformed equations are linear, are presented. Several particular cases of interest are also illustrated.

Non-linear systems with quadratic and cubic damping - an analytical approach

The possible equivalence of second-order non-linear systems having quadratic and cubic damping with third-order linear systems is studied in this paper. It is shown that this equivalence can be established through transformation techniques under certain constraints on the form of the non-linearity of the given system.

On the expressive power of behavioral profiles

Behavioral profiles have been proposed as a behavioral abstraction of dynamic systems, specifically in the context of business process modeling. A behavioral profile can be seen as a complete graph over a set of task labels, where each edge is annotated with one relation from a given set of binary behavioral relations. Since their introduction, behavioral profiles were argued to provide a convenient way for comparing pairs of process models with respect to their behavior or computing behavioral similarity between process models. Still, as of today, there is little understanding of the expressive power of behavioral profiles. Via counter-examples, several authors have shown that behavioral profiles over various sets of behavioral relations cannot distinguish certain systems up to trace equivalence, even for restricted classes of systems represented as safe workflow nets. This paper studies the expressive power of behavioral profiles from two angles. Firstly, the paper investigates the expressive power of behavioral profiles and systems captured as acyclic workflow nets. It is shown that for unlabeled acyclic workflow net systems, behavioral profiles over a simple set of behavioral relations are expressive up to configuration equivalence. When systems are labeled, this result does not hold for any of several previously proposed sets of behavioral relations. Secondly, the paper compares the expressive power of behavioral profiles and regular languages. It is shown that for any set of behavioral relations, behavioral profiles are strictly less expressive than regular languages, entailing that behavioral profiles cannot be used to decide trace equivalence of finite automata and thus Petri nets.

Unitary Processes with Independent Increments and Representations of Hilbert Tensor Algebras

The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.

The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Measuring the expressed emotion in Chinese family caregivers of persons with dementia: Validation of a Chinese version of the Family Attitude Scale

- Background Expressed emotion (EE) captures the affective quality of the relationship between family caregivers and their care recipients and is known to increase the risk of poor health outcomes for caregiving dyads. Little is known about expressed emotion in the context of caregiving for persons with dementia, especially in non-Western cultures. The Family Attitude Scale (FAS) is a psychometrically sound self-reporting measure for EE. Its use in the examination of caregiving for patients with dementia has not yet been explored. - Objectives This study was performed to examine the psychometric properties of the Chinese version of the FAS (FAS-C) in Chinese caregivers of relatives with dementia, and its validity in predicting severe depressive symptoms among the caregivers. - Methods The FAS was translated into Chinese using Brislin's model. Two expert panels evaluated the semantic equivalence and content validity of this Chinese version (FAS-C), respectively. A total of 123 Chinese primary caregivers of relatives with dementia were recruited from three elderly community care centers in Hong Kong. The FAS-C was administered with the Chinese versions of the 5-item Mental Health Inventory (MHI-5), the Zarit Burden Interview (ZBI) and the Revised Memory and Behavioral Problem Checklist (RMBPC). - Results The FAS-C had excellent semantic equivalence with the original version and a content validity index of 0.92. Exploratory factor analysis identified a three-factor structure for the FAS-C (hostile acts, criticism and distancing). Cronbach's alpha of the FAS-C was 0.92. Pearson's correlation indicated that there were significant associations between a higher score on the FAS-C and greater caregiver burden (r = 0.66, p < 0.001), poorer mental health of the caregivers (r = −0.65, p < 0.001) and a higher level of dementia-related symptoms (frequency of symptoms: r = 0.45, p < 0.001; symptom disturbance: r = 0.51, p < 0.001), which serves to suggest its construct validity. For detecting severe depressive symptoms of the family caregivers, the receiving operating characteristics (ROC) curve had an area under curve of 0.78 (95% confidence interval (CI) = 0.69–0.87, p < 0.0001). The optimal cut-off score was >47 with a sensitivity of 0.720 (95% CI = 0.506–0.879) and specificity of 0.742 (95% CI = 0.643–0.826). - Conclusions The FAS-C is a reliable and valid measure to assess the affective quality of the relationship between Chinese caregivers and their relatives with dementia. It also has acceptable predictability in identifying family caregivers with severe depressive symptoms.

Singular value decomposition based computationally efficient algorithm for rapid dynamic near-infrared diffuse optical tomography

Purpose: A computationally efficient algorithm (linear iterative type) based on singular value decomposition (SVD) of the Jacobian has been developed that can be used in rapid dynamic near-infrared (NIR) diffuse optical tomography. Methods: Numerical and experimental studies have been conducted to prove the computational efficacy of this SVD-based algorithm over conventional optical image reconstruction algorithms. Results: These studies indicate that the performance of linear iterative algorithms in terms of contrast recovery (quantitation of optical images) is better compared to nonlinear iterative (conventional) algorithms, provided the initial guess is close to the actual solution. The nonlinear algorithms can provide better quality images compared to the linear iterative type algorithms. Moreover, the analytical and numerical equivalence of the SVD-based algorithm to linear iterative algorithms was also established as a part of this work. It is also demonstrated that the SVD-based image reconstruction typically requires O(NN2) operations per iteration, as contrasted with linear and nonlinear iterative methods that, respectively, requir O(NN3) and O(NN6) operations, with ``NN'' being the number of unknown parameters in the optical image reconstruction procedure. Conclusions: This SVD-based computationally efficient algorithm can make the integration of image reconstruction procedure with the data acquisition feasible, in turn making the rapid dynamic NIR tomography viable in the clinic to continuously monitor hemodynamic changes in the tissue pathophysiology.

Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

Design of an optimal auction for sponsored search auctions

In this paper we first describe a framework to model the sponsored search auction on the web as a mechanism design problem. Using this framework, we design a novel auction which we call the OPT (optimal) auction. The OPT mechanism maximizes the search engine's expected revenue while achieving Bayesian incentive compatibility and individual rationality of the advertisers. We show that the OPT mechanism is superior to two of the most commonly used mechanisms for sponsored search namely (1) GSP (Generalized Second Price) and (2) VCG (Vickrey-Clarke-Groves). We then show an important revenue equivalence result that the expected revenue earned by the search engine is the same for all the three mechanisms provided the advertisers are symmetric and the number of sponsored slots is strictly less than the number of advertisers.

A systematic design of high-rate full-diversity space-frequency codes for MIMO-OFDM systems

This paper presents a systematic construction of high-rate and full-diversity space-frequency block codes for MIMO-OFDM systems. While all prior constructions offer only a maximum rate of one complex symbol per channel use, our construction yields rate equal to the number of transmit antennas and simultaneously achieves full-diversity. The proposed construction works for arbitrary number of transmit antennas and arbitrary channel power delay profile. A key step in this construction is the generalization of the stacked matrix code design criteria given by Bolcskei et.al., (IEEE WCNC 2000). Explicit equivalence of our generalized code design criteria with the Hadamard-product based criteria of W. Su et.al., (lEEE Trans. Sig. Proc. Nov 2003) is established and new high-rate codes are constructed using our criteria.

On the study of a third-order mechanical oscillator

In this paper, the study of a third-order mechanical oscillator is presented by demonstrating its equivalence to the well-known R.C. multivibrator with two additional reactive elements. The conditions for the oscillator's possession of periodic solutions are presented. It is also shown that under certain conditions, the study of the given third-order autonomous system can be reduced to the study of an equivalent second-order, non-autonomous system.