Mathematical Computing

More than 1,300 Austin Moore hemiarthroplasties have been reviewed in the literature, with no reports of fracture of the stem. Many patients with these hip implants had good function. The lack of stem fractures in patients with good function has not been explained and contrasts with stem fractures that have occurred in patients with cemented prostheses of other designs during the same time. We used three-dimensional finite-element analysis and free-body diagrams to explain the lack of fractures for this device by a description of the probable load-transfer mechanisms between the prosthesis and the bone. Results from our finite-element analysis indicate that, with good calcar-collar support, the stresses in the stem are small because the stem portion of the prosthesis and the bone are uncoupled and, consequently, do not share the resultant bending moment of the head and abductor forces. If the stem is coupled to the bone so that the resultant bending moment is shared, high stresses in the stem are predicted; such stresses are inconsistent with the complete absence of fractures of these prostheses. The results of the finite-element analysis further showed that loss of calcar-collar support with proximal fixation through the fenestrations resulted in high stresses in the stem and stress shielding of the proximal medial cortex. The uncoupled prosthesis also may be modeled with a free-body diagram as a three-force member loaded at the head, stem tip, and in the proximal region. With this model, it can be shown that the reaction force of the stem tip, and thus the peak bending stress in the stem, increases as calcar-collar support is decreased. If there is no calcar-collar support, proximal support must be provided by some combination of integration of bone in the fenestrations and wedging due to the lateral-medial taper of the device. Stresses in the stem are largest when there is no wedging, but high stresses develop in the cancellous bone in the fenestrations. When there is wedging, stresses in the stem can be low, but stresses in the supporting cancellous bone can be high; additional proximal support through the fenestrations substantially reduces these bone stresses. If reduced stresses in the cancellous bone are indicative of a stable device, these mechanisms indicate that fractures of the Austin Moore prosthesis have not occurred in normally loaded hips because load was transferred primarily either through the collar or by wedging, with additional support at the fenestrations.

This study examines the associations, and possible causal relationship, between mothers' authoritarian attitudes to discipline and child behaviour using cross-sectional and prospective data from a large population sample surveyed in the 1970 British Cohort Study. Results show a clear linear relationship between the degree of maternal approval of authoritarian child-rearing attitudes and the rates of conduct problems at age 5 and age 10. This association is independent of the confounding effects of socio-economic status and maternal psychological distress. Maternal authoritarian attitudes independently predicted the development of conduct problems 5 years later at age 10. The results of this longitudinal study suggest that authoritarian parenting attitudes expressed by mothers may be of significance in the development of conduct problems.

(PhD Dissertation, Stanford Mathematics 2001)
What sort of geometric creation and performance can or cannot be supported in a writing technology that spans freehand sketching, manipulable graphics, text, symbolic computation and simulation? How do we work with and gain intuitions about supposedly abstract things like a Riemannian manifold or an infinite-dimensional function space by manipulating material marks using chalk, pencil or computer? How do we exteriorize thought using the technologies of writing and sketching when it is about processes or objects that could not be embedded in a naive space-time?

I analyze in detail what differential geometric work can or cannot be performed easily in a hybrid medium provided by a generalized multi-modal writing and sketching technology. The critical part of this project is informed by insights from literary and performance studies as well as the mathematical sciences. Focusing on differential geometry through the lens of practice, I examine a-linguistic semiotic usage, and through the lens of phenomenological investigation, I examine how geometers work with continuous, smooth, or infinite structures and processes.

This investigation promises both pragmatic as well as conceptual results. Concretely, this study provides a design for future technologies of mathematical writing that will better augment the working practices of differential geometers.  Conceptually, my proposed materialized phenomenological view of mathematics as a performance practice eliminates three problems in philosophy and in critical studies of symbolic systems: (1) how do we represent continuity and smoothness using discrete symbolic systems? (2) how do we represent infinite things or processes? (3) why do symbolic systems have explanatory or generative power? These conundrums have occupied philosophers of mathematics, and have driven some to propose strict finitist or radically fictionalist theories of mathematics. Moreover, approaches to their resolution underwrite all the technologies that serve mathematical practice today, so these problems fundamentally affect the design of technologies for the working mathematician as well.

Mohd. Rohani, Jafri and Mohd. Yusof, Sha'ri and Mohamad, Ismail (2007) Application of statistical process control in manufacturing company to understand variability. In: 2nd International Conference on Mathematical Sciences 2007 (ICoMS 2007), 2007, Johor Bahru.

The aim of the present study was to examine somatotopy in the cerebellar cortex and a possible differential role of the cerebellar cortex and nuclei in functional outcome. Clinical findings and 3D MRI-based cerebellar lesions site were compared in a group of 90 patients with focal cerebellar lesion using International Cooperative Ataxia Rating Scale (ICARS) and voxel-based lesion–symptom mapping (VLSM). Separate analysis was performed in patients with acute and chronic ischemic lesions (n = 43) and patients with acute and chronic surgical lesions (n = 47). Thirty-eight patients were included after resection of a cerebellar tumor in childhood or adolescence.The most significant lesion symptom correlations were observed in the subgroup with acute ischemic lesions. Limb ataxia was significantly correlated with lesions of the interposed (NI) and part of the dentate nuclei (ND), ataxia of posture and gait with lesions of the fastigial nuclei (NF) including NI. Correlations with cortical lesions were less significant and present in the superior cerebellum only. Upper limb ataxia was correlated with lesions of vermal, paravermal and hemispheral lobules IV–V and VI, lower limb ataxia with lesions of vermal, paravermal and hemispheral lobules III and VI, dysarthria with lesions of paravermal and hemispheral lobules V and VI and ataxia of posture and gait with lesions of vermal and paravermal lobules II, III and IV. In the subgroups with chronic focal lesions, similar correlations were observed with lesions of the cerebellar nuclei, but significantly less correlations with lesions of the cerebellar cortex.Functional localization based on VLSM backs findings in previous animal and functional brain images studies in healthy human subjects. The lesion site appears to be critical for motor recovery. Lesions affecting the cerebellar nuclei are not fully compensated at any age and independent of the pathology in humans.

Despite being recognized as an important prognostic factor for the outcome in gender identity disorder (GID), psychiatric comorbidity has rarely been assessed by means of standardized diagnostic instruments. The aim of this study was to assess current and lifetime psychiatric comorbidity in patients with GID. A cross-sectional sample of 31 patients who were treated for GID was assessed by the structured clinical interview for Axis I and II (SCID-I/II) and the Hospital Anxiety and Depression Scale (HADS). Twenty-nine percent of the patients had no current or lifetime Axis I disorder; 39% fulfilled the criteria for current and 71% for current and/or lifetime Axis I diagnosis. Forty-two percent of the patients were diagnosed with one or more personality disorders. Lifetime psychiatric comorbidity in GID patients is high, and this should be taken into account in the assessment and treatment planning of GID patients.