Nonstandard Metrics Research Articles

New vector transport operators extending a Riemannian CG algorithm to generalized Stiefel manifold with low-rank applications

This paper proposes two innovative vector transport operators, leveraging the Cayley transform, for the generalized Stiefel manifold embedded with a non-standard metric. Specifically, it introduces the differentiated retraction and an approximation of the Cayley transform to the differentiated matrix exponential. These vector transports are demonstrated to satisfy the Ring–Wirth non-expansive condition under non-standard metrics, and one of them is also isometric. Building upon the novel vector transport operators, we extend the modified Polak–Ribière–Polyak (PRP) conjugate gradient method to the generalized Stiefel manifold. Under a non-monotone line search condition, we prove our algorithm globally converges to a stationary point. The efficiency of the proposed vector transport operators is empirically validated through numerical experiments involving generalized eigenvalue problems and canonical correlation analysis.

Assessing the efficacy of thyroid nodule radiofrequency ablation using patient-reported outcome measures

BackgroundRadiofrequency ablation has recently emerged as an alternative treatment for thyroid nodules. Most studies are centered on volume reduction, whereas a few have assessed symptom improvement mainly with nonstandardized metrics. As experience in the United States is growing, we aim to assess the efficacy of radiofrequency ablation in treating benign thyroid nodules using the validated Patient-Reported Outcomes Measurement for Parathyroid and Thyroid Disease. MethodsThis is a prospective study of a newly established radiofrequency ablation program at a single tertiary referral center in 2022. Patients who underwent radiofrequency ablation were evaluated using the Patient-Reported Outcomes Measurement for Parathyroid and Thyroid Disease, a validated metric ranging from 0 to 100 at baseline, 2 weeks, 3 months, and 6 months. In addition, a thyroid ultrasound was done at those intervals to assess size and volume reduction. Procedure complications were evaluated as well. ResultsA total of 25 patients underwent radiofrequency ablation during the study period for a total of 32 nodules treated; 84% were female with a mean age of 51 years. The baseline mean nodule volume and largest dimension were 13 ± 11 mL and 3.4 ± 1 cm, respectively. A significant change in the Patient-Reported Outcomes Measurement for Parathyroid and Thyroid Disease compressive score was seen at 3 months (38.9 ± 26.4 to 21.0 ± 21.4; P = .004) and 6 months (32.7 ± 19.9 to 17.5 ± 21.0; P = .02) but not at 2 weeks (41.0 ± 22.7 to 36.1 ± 21.9; P = .28). Significant volume and size reductions were seen at all 3-time points. Two complications occurred. ConclusionOur initial results of the thyroid radiofrequency ablation program find that it effectively alleviates symptoms by reducing nodule size in patients with symptomatic benign thyroid nodules.

Are performance-based payment structures more strongly correlated with better health outcomes compared to solely fee-for-service payment for surgeons?

For years, the healthcare industry has compensated its surgeons with a simple fee-for-service model. With more payment structures becoming prevalent, we decided to review one specific type of payment structure, pay-for-performance, and its impact on patient health outcomes. We hypothesized that, on average, across all specialties, performance-based contracts would yield better health outcomes compared to fee-for-service payments alone. We also hypothesized that performance-based contracts might pressure physicians to get results and could lead to mistakes and a worse quality of care. We reviewed nine papers from 2006-2014, of which the majority were conducted in the United States, with one each from Italy and Germany. Our review included three literary/systematic reviews, three before & after studies, and two cross-sectional analyses. Many papers did not provide strong evidence of the effect of pay-for-performance on health outcomes, although examined papers agree on certain things. A common theme we found was the pay-for-performance increased documentation and the number of procedures done, but with minimal conclusions about outcomes. This may result from poor or non-standardized metrics being used to measure and report “performance.” However, two studies found that pay-for-performance improved patient health outcomes, despite limitations. For example, Brosig-Koch et al., (2013) found that P4P was not cost-effective from a solely financial standpoint.

Comparisons of Modern United States and Canadian Malting Barley Cultivars with Those from Pre-Prohibition: IV. Malting Quality Assessments Using Standard and Nonstandard Measures

This study was conducted to identify which traits or combination of traits associated with malting quality and mashing performance could best define the differences between and within a population of six pre-Prohibition malting barley varieties and a population of five modern elite malting barley cultivars. To accomplish this, standard and nonstandard metrics of malt quality and of performance during Congress mashing were analyzed by simple linear correlations and multivariate statistics. Analyses of the two populations combined revealed that activities of α-amylase at each time sampled during mashing were positively and significantly correlated with the concentrations of glucose at that same time, were not significantly correlated with maltose concentrations at any time, and were only significantly correlated with maltotriose concentrations for the first 30 min of mashing. Activities of β-amylase were not significantly correlated with concentrations of glucose, maltose, or maltotriose at any time during mashing. Analysis of α-glucosidase activities showed no consistent trends in correlations with either glucose or maltotriose and no significant correlation with maltose at any time. Analysis of limit dextrinase activities showed significant and positive correlations with glucose and maltotriose concentrations prior to the mash temperature reaching the starch conversion stage. Although no individual amylolytic enzyme activity was significantly correlated with maltose concentration, diastatic power was positively and significantly correlated with maltose at five of six times sampled during mashing. Diastatic power was not significantly correlated with glucose or maltotriose concentrations at any time. Malt extract values and osmolyte concentrations were positively and significantly correlated with mash glucose concentrations at all times sampled, with maltose concentrations at the first four times sampled, and with maltotriose for the first five times. Principal component analysis (PCA) of the traits analyzed in the two populations combined showed that the modern malting barleys were generally well separated from the pre-Prohibition barleys by three principal components that accounted for 75% of the variation among the 11 cultivars. The traits that collectively contributed the most to separation of the modern from the pre-Prohibition barleys were osmolyte concentrations, malt extract values and glucose concentration, which were higher in the modern cultivars, and α-glucosidase thermostability and concentrations of maltopentaose, maltohexaose and maltoheptaose, which were higher in the pre-Prohibition cultivars. PCA of the individual populations also separated Tradition from the other modern cultivars due to its lower levels of glucose, maltotriose, and α-amylase activity and by its higher levels of maltose and % plump. PCA of the pre-Prohibition population separated Hanna from the other pre-Prohibition cultivars primarily by its higher levels of maltopentaose through maltoheptaose and its low levels of osmolytes. Silver King was somewhat displaced from other pre-Prohibition cultivars due to its low levels of osmolytes and to its very high levels of α-glucosidase thermostability.

Evaluation and integration of cancer gene classifiers: identification and ranking of plausible drivers.

The number of mutated genes in cancer cells is far larger than the number of mutations that drive cancer. The difficulty this creates for identifying relevant alterations has stimulated the development of various computational approaches to distinguishing drivers from bystanders. We develop and apply an ensemble classifier (EC) machine learning method, which integrates 10 classifiers that are publically available, and apply it to breast and ovarian cancer. In particular we find the following: (1) Using both standard and non-standard metrics, EC almost always outperforms single method classifiers, often by wide margins. (2) Of the 50 highest ranked genes for breast (ovarian) cancer, 34 (30) are associated with other cancers in either the OMIM, CGC or NCG database (P < 10−22). (3) Another 10, for both breast and ovarian cancer, have been identified by GWAS studies. (4) Several of the remaining genes--including a protein kinase that regulates the Fra-1 transcription factor which is overexpressed in ER negative breast cancer cells; and Fyn, which is overexpressed in pancreatic and prostate cancer, among others--are biologically plausible. Biological implications are briefly discussed. Source codes and detailed results are available at http://www.visantnet.org/misi/driver_integration.zip.

Kernelized vector quantization in gradient-descent learning

Abstract Prototype based vector quantization is usually proceeded in the Euclidean data space. In the last years, also non-standard metrics became popular. For classification by support vector machines, Hilbert space representations, which are based on so-called kernel metrics, seem to be very successful. In this paper we show that gradient based learning in prototype-based vector quantization is possible by means of kernel metrics instead of the standard Euclidean distance. We will show that an appropriate handling requires differentiable universal kernels defining the feature space metric. This allows a prototype adaptation in the original data space but equipped with a metric determined by the kernel and, therefore, it is isomorphic to respective kernel Hilbert space. However, this approach avoids the Hilbert space representation as known for support vector machines. We give the mathematical justification for the isomorphism and demonstrate the abilities and the usefulness of this approach for several examples including both artificial and real world datasets.

Generating groups of isometries of the line using non-standard metrics

In this article, a simple exercise for finding groups isomorphic to the symmetry group of the real line is presented. A mechanism for producing metrics on the real line is used to construct the group elements, and these transformations, by construction, are isometries with respect to the generating metric.

Complex powers of degenerate differential operators connected with the Klein-Gordon-Fock operator

We develop a theory of complex powers of the generalized Klein-Gordon-Fock operator $$ m^2 - \square - i\lambda \frac{{\partial ^2 }} {{\partial x_1^2 }},\lambda > 0. $$ . The negative powers of this operator are realized as potential-type integrals with nonstandard metrics, while positive powers inverse to negative ones are realized as approximative inverse operators.

Sectional curvatures of nonstandard metrics on CP2n+1

Sectional curvatures of nonstandard metrics on CP2n+1