185 resultados para k-Uniformly Convex Function


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The molecular structure of the mineral archerite ((K,NH4)H2PO4) has been determined and compared with that of biphosphammite ((NH4,K)H2PO4). Raman spectroscopy and infrared spectroscopy has been used to characterise these ‘cave’ minerals. Both minerals originated from the Murra-el-elevyn Cave, Eucla, Western Australia. The mineral is formed by the reaction of the chemicals in bat guano with calcite substrates. Raman and infrared bands are assigned to H2PO4-, OH and NH stretching vibrations. The Raman band at 981 cm-1 is assigned to the HOP stretching vibration. Bands in the 1200 to 1800 cm-1 region are associated with NH4+ bending modes. The molecular structure of the two minerals appear to be very similar, and it is therefore concluded that the two minerals are identical.

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Purpose: Age-related macular degeneration (AMD) is the leading cause of irreversible visual impairment among older adults. This study explored the relationship between AMD, falls risk and other injuries and identified visual risk factors for these adverse events. Methods: Participants included 76 community-dwelling individuals with a range of severity of AMD (mean age, 77.0±6.9 years). Baseline assessment included binocular visual acuity, contrast sensitivity and merged visual fields. Participants completed monthly falls and injury diaries for one year following the baseline assessment. Results: Overall, 74% of participants reported having either a fall, injurious fall or other injury. Fifty-four percent of participants reported a fall and 30% reported more than one fall; of the 102 falls reported, 63% resulted in an injury. Most occurred outdoors (52%), between late morning and late afternoon (61%) and when navigating on level ground (62%). The most common non-fall injuries were lacerations (36%) and collisions with an object (35%). Reduced contrast sensitivity and visual acuity were associated with increased fall rate, after controlling for age, gender, cognitive function, cataract severity and self-reported physical function. Reduced contrast sensitivity was the only significant predictor of falls and other injuries. Conclusion: Among older adults with AMD, increased visual impairment was significantly associated with an increased incidence of falls and other injuries. Reduced contrast sensitivity was significantly associated with increased rates of falls, injurious falls and injuries, while reduced visual acuity was only associated with increased falls risk. These findings have important implications for the assessment of visually impaired older adults.

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Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise, and show that in this case, strictly convex loss functions lead to faster rates of convergence of the risk than would be implied by standard uniform convergence arguments. Finally, we present applications of our results to the estimation of convergence rates in function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions.

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Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive semidefinite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space - classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -using the labeled part of the data one can learn an embedding also for the unlabeled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method for learning the 2-norm soft margin parameter in support vector machines, solving an important open problem.

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We consider the problem of binary classification where the classifier can, for a particular cost, choose not to classify an observation. Just as in the conventional classification problem, minimization of the sample average of the cost is a difficult optimization problem. As an alternative, we propose the optimization of a certain convex loss function φ, analogous to the hinge loss used in support vector machines (SVMs). Its convexity ensures that the sample average of this surrogate loss can be efficiently minimized. We study its statistical properties. We show that minimizing the expected surrogate loss—the φ-risk—also minimizes the risk. We also study the rate at which the φ-risk approaches its minimum value. We show that fast rates are possible when the conditional probability P(Y=1|X) is unlikely to be close to certain critical values.

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Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space -- classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -- using the labelled part of the data one can learn an embedding also for the unlabelled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method to learn the 2-norm soft margin parameter in support vector machines, solving another important open problem. Finally, the novel approach presented in the paper is supported by positive empirical results.

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We report that 10% of melanoma tumors and cell lines harbor mutations in the fibroblast growth factor receptor 2 (FGFR2) gene. These novel mutations include three truncating mutations and 20 missense mutations occurring at evolutionary conserved residues in FGFR2 as well as among all four FGFRs. The mutation spectrum is characteristic of those induced by UV radiation. Mapping of these mutations onto the known crystal structures of FGFR2 followed by in vitro and in vivo studies show that these mutations result in receptor loss of function through several distinct mechanisms, including loss of ligand binding affinity, impaired receptor dimerization, destabilization of the extracellular domains, and reduced kinase activity. To our knowledge, this is the first demonstration of loss-of-function mutations in a class IV receptor tyrosine kinase in cancer. Taken into account with our recent discovery of activating FGFR2 mutations in endometrial cancer, we suggest that FGFR2 may join the list of genes that play context-dependent opposing roles in cancer.

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In rats immunized systemically with tetanus toxoid the concentration of specific anti-tetanus-toxoid-specific IgG in fluid from the rete testis and cauda epididymidis were respectively 0.6% and 1.4% the concentration in blood serum. The extratesticular duct system reabsorbed 97% of the IgG and 99% of the fluid leaving the rete, but estradiol administration affected the site of reabsorption. In untreated rats, the ductuli efferentes reabsorbed 94% of the IgG and 96% of the fluid leaving the rete, whereas estradiol-treated rats reabsorbed 83% of the IgG and 86% of the fluid, and the ductus epididymidis fully compensated for these different effects of estradiol on the ductuli efferentes. The concentrations of IgG in secretions of the seminal vesicles and prostate gland were lower (0.1% and 0.3% respectively of the titers in blood serum) than in fluids from the extratesticular ducts, and were not affected by the administration of estradiol. RT-PCR showed that Fcgrt (neonatal Fc receptor, also known as FcRn) is expressed in the reproductive ducts, where IgG is probably transported across epithelium, being particularly strong in the ductuli efferentes (where most IgG was reabsorbed) and distal caput epididymidis. It is concluded that IgG enters the rete testis and is concentrated only 2.5-fold along the extratesticular duct system, unlike spermatozoa, which are concentrated 95-fold. Further, the ductus epididymidis can recognize and compensate for changes in function of the ductuli efferentes.

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Diabetes is an increasingly prevalent disease worldwide. Providing early management of the complications can prevent morbidity and mortality in this population. Peripheral neuropathy, a significant complication of diabetes, is the major cause of foot ulceration and amputation in diabetes. Delay in attending to complication of the disease contributes to significant medical expenses for diabetic patients and the community. Early structural changes to the neural components of the retina have been demonstrated to occur prior to the clinically visible retinal vasculature complication of diabetic retinopathy. Additionally visual functionloss has been shown to exist before the ophthalmoscopic manifestations of vasculature damage. The purpose of this thesis was to evaluate the relationship between diabetic peripheral neuropathy and both retinal structure and visual function. The key question was whether diabetic peripheral neuropathy is the potential underlying factor responsible for retinal anatomical change and visual functional loss in people with diabetes. This study was conducted on a cohort with type 2 diabetes. Retinal nerve fibre layer thickness was assessed by means of Optical Coherence Tomography (OCT). Visual function was assessed using two different methods; Standard Automated Perimetry (SAP) and flicker perimetry were performed within the central 30 degrees of fixation. The level of diabetic peripheral neuropathy (DPN) was assessed using two techniques - Quantitative Sensory Testing and Neuropathy Disability Score (NDS). These techniques are known to be capable of detecting DPN at very early stages. NDS has also been shown as a gold standard for detecting 'risk of foot ulceration'. Findings reported in this thesis showed that RNFL thickness, particularly in the inferior quadrant, has a significant association with severity of DPN when the condition has been assessed using NDS. More specifically it was observed that inferior RNFL thickness has the ability to differentiate individuals who are at higher risk of foot ulceration from those who are at lower risk, indicating that RNFL thickness can predict late-staged DPN. Investigating the association between RNFL and QST did not show any meaningful interaction, which indicates that RNFL thickness for this cohort was not as predictive of neuropathy status as NDS. In both of these studies, control participants did not have different results from the type 2 cohort who did not DPN suggesting that RNFL thickness is not a marker for diagnosing DPN at early stages. The latter finding also indicated that diabetes per se, is unlikely to affect the RNFL thickness. Visual function as measured by SAP and flicker perimetry was found to be associated with severity of peripheral neuropathy as measured by NDS. These findings were also capable of differentiating individuals at higher risk of foot ulceration; however, visual function also proved not to be a maker for early diagnosis of DPN. It was found that neither SAP, nor flicker sensitivity have meaningful associations with DPN when neuropathy status was measured using QST. Importantly diabetic retinopathy did not explain any of the findings in these experiments. The work described here is valuable as no other research to date has investigated the association between diabetic peripheral neuropathy and either retinal structure or visual function.