Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

Sound Synthesis for Contact-Driven Musical Instruments via Discretisation of Hamilton's Equations

Physical modelling of musical instruments involves studying nonlinear interactions between parts of the instrument. These can pose several difficulties concerning the accuracy and stability of numerical algorithms. In particular, when the underlying forces are non-analytic functions of the phase-space variables, a stability proof can only be obtained in limited cases. An approach has been recently presented by the authors, leading to unconditionally stable simulations for lumped collision models. In that study, discretisation of Hamilton’s equations instead of the usual Newton’s equation of motion yields a numerical scheme that can be proven to be energy conserving. In this paper, the above approach is extended to collisions of distributed objects. Namely, the interaction of an ideal string with a flat barrier is considered. The problem is formulated within the Hamiltonian framework and subsequently discretised. The resulting nonlinearmatrix equation can be shown to possess a unique solution, that enables the update of the algorithm. Energy conservation and thus numerical stability follows in a way similar to the lumped collision model. The existence of an analytic description of this interaction allows the validation of the model’s accuracy. The proposed methodology can be used in sound synthesis applications involving musical instruments where collisions occur either in a confined (e.g. hammer-string interaction, mallet impact) or in a distributed region (e.g. string-bridge or reed-mouthpiece interaction).

Energy conserving schemes for the simulation of musical instrument contact dynamics

Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton׳s equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton׳s method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument.

Parent education and home-based behaviour analytic intervention: an examination of parents' perceptions of outcome

There is convincing evidence that applied behaviour analysis (ABA) offers a highly effective form of intervention for children with autistic spectrum disorder (ASD). There is less evidence, however, about how parents perceive and evaluate ABA programmes. In this paper an examination of parents’ perceptions of outcome is reported. Twenty-two questionnaires were completed by two groups of parents. The first group had just completed an introductory course in ABA and were in the early stages of implementing ABA programmes with their children. The second group had been involved in ABA education for more than 2 years. Overall, both groups of parents reported a positive impact of ABA on the lives of their children, their family life, and themselves. The long- term group reported that they had achieved complex goals with their children, whilst the short-term group reported an immediate positive impact on child and family functioning and parental self-esteem. Conclusions are drawn in the context of evidence-based practice.

Cognitive inhibition and interference in dissociative indentity disorder: the effects of anxiety on specific executive functions:The effects of anxiety on specific executive functions

Using an experimentally based, computer-presented task, this study assessed cognitive inhibition and interference in individuals from the dissociative identity disorder (DID; n=12), generalized anxiety disorder (GAD; n=12) and non-clinical (n=12) populations. Participants were assessed in a neutral and emotionally negative (anxiety provoking) context, manipulated by experimental instructions and word stimuli. The DID sample displayed effective cognitive inhibition in the neutral but not the anxious context. The GAD sample displayed the opposite findings. However, the interaction between group and context failed to reach significance. There was no indication of an attentional bias to non-schema specific negative words in any sample. Results are discussed in terms of the potential benefit of weakened cognitive inhibition during anxious arousal in dissociative individuals.

Linguistics and Information Theory: Analytic advantages

The analytic advantages of central concepts from linguistics and information theory, and the analogies demonstrated between them, for understanding patterns of retrieval from full-text indexes to documents are developed. The interaction between the syntagm and the paradigm in computational operations on written language in indexing, searching, and retrieval is used to account for transformations of the signified or meaning between documents and their representation and between queries and documents retrieved. Characteristics of the message, and messages for selection for written language, are brought to explain the relative frequency of occurrence of words and multiple word sequences in documents. The examples given in the companion article are revisited and a fuller example introduced. The signified of the sequence stood for, the term classically used in the definitions of the sign, as something standing for something else, can itself change rapidly according to its syntagm. A greater than ordinary discourse understanding of patterns in retrieval is obtained.

BRCA1 Functions as a Differential Modulator of Chemotherapy-induced Apoptosis

We have evaluated the role played by BRCA1 in mediating the phenotypic response to a range of chemotherapeutic agents commonly used in cancer treatment. Here we provide evidence that BRCA1 functions as a differential mediator of chemotherapy-induced apoptosis. Specifically, we demonstrate that BRCA1 mediates sensitivity to apoptosis induced by antimicrotubule agents but conversely induces resistance to DNA-damaging agents. These data are supported by a variety of experimental models including cells with inducible expression of BRCA1, siRNA-mediated inactivation of endogenous BRCA1, and reconstitution of BRCA1-deficient cells with wild-type BRCA1. Most notably we demonstrate that BRCA1 induces a 10–1000-fold increase in resistance to a range of DNA-damaging agents, in particular those that give rise to double-strand breaks such as etoposide or bleomycin. In contrast, BRCA1 induces a >1000-fold increase in sensitivity to the spindle poisons, paclitaxel and vinorelbine. Fluorescence-activated cell sorter analysis demonstrated that BRCA1 mediates G2/M arrest in response to both antimicrotubule and DNA-damaging agents. However, poly(ADP-ribose) polymerase and caspase-3 cleavage assays indicate that the differential effect mediated by BRCA1 in response to these agents occurs through the inhibition or induction of apoptosis. Therefore, our data suggest that BRCA1 acts as a differential modulator of apoptosis depending on the nature of the cellular insult.