Lerdahl's Surface Tension Rule: Validation or Modification

Lerdahls Tonal Pitch Space (2001) combines music theory with current understanding of music perception and cognition creating of model of tonal pitch space. Lerdahls goals include quantification of areas of tension and relaxation perceived by listeners experienced in Western tonal music. Tension is associated with instability, distance, uncommon tones, and weak attractional force; relaxation with stability, proximity, common tones, and strong attractional force. Quantification requires creation of a time-span segmentation derived from the metrical grid and grouping analysis of the score. The time-span segmentation is necessary for creating the time-span reduction. The time-span reduction removes structurally less significant elements from the musical surface through a series of steps not unlike the layers of Schenkerian analysis. The ultimate goal is the prolongational reduction accompanied by prolongational tree. Global tension is quantified by summing values obtained when considering the region in which an event occurs, distance between successive chords revealed by their position on the chordal circle-of-fifths, number of distinct pitch classes between successive chords, tension inherited by subordinate chords from superordinate chords, melodic and harmonic attraction, and surface dissonance. Lerdahls Surface Tension Rule assigns tension added values due to chord Inversion, chord note in the top voice (Melody), and nonharmonic chord tones. This study tested the validity of assigned tension added values for Inversion and Melody asking 82 participants familiar with Western tonal music to rate perceived tension of Major and minor four-note chords heard devoid of tonal and musical contexts. Results showed Lerdahls tension added values required modification. Root position chords and chords with the root in the Melody require a tension added value greater than 0. Tension due to First Inversion is not the same as tension due to Second Inversion. Tension due to First and Second Inversion is greater than tension due to the third or fifth of a chord in Melody. Tension due to Second Inversion is not different from tension due to root in Melody. A new category, chord Quality, needed to be added. Expertise did not play a role. Lerdahls model and these results provide insight for performers, teachers, listeners, and composers

Complex scheduling models and analyses for property-based real-time embedded systems

Modern multi core architectures and parallel applications pose a significant challenge to the worst-case centric real-time system verification and design efforts. The involved model and parameter uncertainty contest the fidelity of formal real-time analyses, which are mostly based on exact model assumptions. In this dissertation, various approaches that can accept parameter and model uncertainty are presented. In an attempt to improve predictability in worst-case centric analyses, the exploration of timing predictable protocols are examined for parallel task scheduling on multiprocessors and network-on-chip arbitration. A novel scheduling algorithm, called stationary rigid gang scheduling, for gang tasks on multiprocessors is proposed. In regard to fixed-priority wormhole-switched network-on-chips, a more restrictive family of transmission protocols called simultaneous progression switching protocols is proposed with predictability enhancing properties. Moreover, hierarchical scheduling for parallel DAG tasks under parameter uncertainty is studied to achieve temporal- and spatial isolation. Fault-tolerance as a supplementary reliability aspect of real-time systems is examined, in spite of dynamic external causes of fault. Using various job variants, which trade off increased execution time demand with increased error protection, a state-based policy selection strategy is proposed, which provably assures an acceptable quality-of-service (QoS). Lastly, the temporal misalignment of sensor data in sensor fusion applications in cyber-physical systems is examined. A modular analysis based on minimal properties to obtain an upper-bound for the maximal sensor data time-stamp difference is proposed

Quanta of Maths

The work of Alain Connes has cut a wide swath across several areas of math- ematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics

The Role of Arterial Spin Labelling (ASL) in Classification of Primary Adult Gliomas

Currently, the histological biopsy is the gold standard for classifying gliomas using the most recent histomolecular features. However, this process is both invasive and challenging, mainly when the lesion is in eloquent brain regions. Considering the complex interaction between the presence of the isocitrate dehydrogenase (IDH)-mutation, the upregulation of the hypoxia-induced factor (HIF), the neo-angiogenesis and the increased cellularity, perfusion MRI may be used indirectly for gliomas staging and further to predict the presence of key mutations, such as IDH. Recently, several studies have reported the subsidiary role of perfusion MRI in the prediction of gliomas histomolecular class. The three most common perfusion MRI methods are dynamic susceptibility contrast (DSC), dynamic contrast enhancement (DCE) and arterial spin labelling (ASL). Both DSC and DCE use exogenous contrast agent (CA) while ASL uses magnetically labelled blood water as an inherently diffusible tracer. ASL has begun to feature more prominently in clinical settings, as this method eliminates the need for CA and facilitates quantification of absolute cerebral blood flow (CBF). As a non-invasive, CA-free test, it can also be performed repeatedly where necessary. This makes it ideal for vulnerable patients, e.g. post-treatment oncological patients, who have reduced tolerance for high rate contrast injections and those suffering from renal insufficiency. This thesis performed a systematic review and critical appraisal of the existing ASL techniques for brain perfusion estimation, followed by a further systematic review and meta-analysis of the published studies, which have quantitatively assessed the diagnostic performance of ASL for grading preoperative adult gliomas. The repeatability of absolute tumour blood flow (aTBF) and relative TBF (rTBF) ASL-derived measurements were estimated to investigate the reliability of these ASL biomarkers in the clinical routine. Finally, utilising the radiomics pipeline analysis, the added diagnostic performance of ASL compared with CA-based MRI perfusion techniques, including DSC and DCE, and diffusion-weighted imaging (DWI) was investigated for glioma class prediction according to the WHO-2016 classification

Algebraic methods in randomness and pseudorandomness

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 183-188).Algebra and randomness come together rather nicely in computation. A central example of this relationship in action is the Schwartz-Zippel lemma and its application to the fast randomized checking of polynomial identities. In this thesis, we further this relationship in two ways: (1) by compiling new algebraic techniques that are of potential computational interest, and (2) demonstrating the relevance of these techniques by making progress on several questions in randomness and pseudorandomness. The technical ingredients we introduce include: " Multiplicity-enhanced versions of the Schwartz-Zippel lenina and the "polynomial method", extending their applicability to "higher-degree" polynomials. " Conditions for polynomials to have an unusually small number of roots. " Conditions for polynomials to have an unusually structured set of roots, e.g., containing a large linear space. Our applications include: * Explicit constructions of randomness extractors with logarithmic seed and vanishing "entropy loss". " Limit laws for first-order logic augmented with the parity quantifier on random graphs (extending the classical 0-1 law). " Explicit dispersers for affine sources of imperfect randomness with sublinear entropy.by Swastik Kopparty.Ph.D

Quanta of Maths

The work of Alain Connes has cut a wide swath across several areas of math- ematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics