Worst-case bounds for the logarithmic loss of predictors

We investigate on-line prediction of individual sequences. Given a class of predictors, the goal is to predict as well as the best predictor in the class, where the loss is measured by the self information (logarithmic) loss function. The excess loss (regret) is closely related to the redundancy of the associated lossless universal code. Using Shtarkov's theorem and tools from empirical process theory, we prove a general upper bound on the best possible (minimax) regret. The bound depends on certain metric properties of the class of predictors. We apply the bound to both parametric and nonparametric classes ofpredictors. Finally, we point out a suboptimal behavior of the popular Bayesian weighted average algorithm.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the Baker-Akhiezer function in the AKNS scheme

Expressions for the Baker-Akhiezer function and their logarithmic space and time derivatives are derived in terms of the matrix elements of U - V matrices and 'squared basis functions'. These expressions generalize the well known formulas for the KdV equation case and establish links between different forms of the Whitham averaging procedure.

Geometrical logarithmic and trigonometric hypercomplex functions of quaternionic type

Quaternionic theory has greatly been developed in recent years [1-12]. Thus, in our view, the study of trigonometric and logarithmic type quaternionic functions is important for the determination and realization of a hyper complex theory. In this paper, we intend to give a geometrical foundation for both logarithmic and trigonometric hyper complex functions based on the exponential function of quaternionic type recently introduced by Borges, Marão and Machado in their paper entitled Geometrical octonions II: Hyper regularity and hyper periodicity of the exponential function appearing. © 2011 Pushpa Publishing House.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

Structure-function Relationships Using the Cirrus Spectral Domain Optical Coherence Tomograph and Standard Automated Perimetry

Purpose: To evaluate the relationship between glaucomatous structural damage assessed by the Cirrus Spectral Domain OCT (SDOCT) and functional loss as measured by standard automated perimetry (SAP). Methods: Four hundred twenty-two eyes (78 healthy, 210 suspects, 134 glaucomatous) of 250 patients were recruited from the longitudinal Diagnostic Innovations in Glaucoma Study and from the African Descent and Glaucoma Evaluation Study. All eyes underwent testing with the Cirrus SDOCT and SAP within a 6-month period. The relationship between parapapillary retinal nerve fiber layer thickness (RNFL) sectors and corresponding topographic SAP locations was evaluated using locally weighted scatterplot smoothing and regression analysis. SAP sensitivity values were evaluated using both linear as well as logarithmic scales. We also tested the fit of a model (Hood) for structure-function relationship in glaucoma. Results: Structure was significantly related to function for all but the nasal thickness sector. The relationship was strongest for superotemporal RNFL thickness and inferonasal sensitivity (R(2) = 0.314, P < 0.001). The Hood model fitted the data relatively well with 88% of the eyes inside the 95% confidence interval predicted by the model. Conclusions: RNFL thinning measured by the Cirrus SDOCT was associated with correspondent visual field loss in glaucoma.

Method of Detecting System Function by Measuring Frequency Response

Methods of rapidly measuring an impedance spectrum of an energy storage device in-situ over a limited number of logarithmically distributed frequencies are described. An energy storage device is excited with a known input signal, and aresponse is measured to ascertain the impedance spectrum. An excitation signal is a limited time duration sum-of-sines consisting of a select number offrequencies. In one embodiment, magnitude and phase of each frequency ofinterest within the sum-of-sines is identified when the selected frequencies and sample rate are logarithmic integer steps greater than two. This technique requires a measurement with a duration of one period of the lowest frequency. In another embodiment, where selected frequencies are distributed in octave steps, the impedance spectrum can be determined using a captured time record that is reduced to a half-period of the lowest frequency.

Applicative theories for logarithmic complexity classes

We present applicative theories of words corresponding to weak, and especially logarithmic, complexity classes. The theories for the logarithmic hierarchy and alternating logarithmic time formalise function algebras with concatenation recursion as main principle. We present two theories for logarithmic space where the first formalises a new two-sorted algebra which is very similar to Cook and Bellantoni's famous two-sorted algebra B for polynomial time [4]. The second theory describes logarithmic space by formalising concatenation- and sharply bounded recursion. All theories contain the predicates WW representing words, and VV representing temporary inaccessible words. They are inspired by Cantini's theories [6] formalising B.

A novel colourimetric technique to assess chewing function using two-coloured specimens: Validation and application

OBJECTIVES Chewing efficiency may be evaluated using cohesive specimen, especially in elderly or dysphagic patients. The aim of this study was to evaluate three two-coloured chewing gums for a colour-mixing ability test and to validate a new purpose built software (ViewGum©). METHODS Dentate participants (dentate-group) and edentulous patients with mandibular two-implant overdentures (IOD-group) were recruited. First, the dentate-group chewed three different types of two-coloured gum (gum1-gum3) for 5, 10, 20, 30 and 50 chewing cycles. Subsequently the number of chewing cycles with the highest intra- and inter-rater agreement was determined visually by applying a scale (SA) and opto-electronically (ViewGum©, Bland-Altman analysis). The ViewGum© software determines semi-automatically the variance of hue (VOH); inadequate mixing presents with larger VOH than complete mixing. Secondly, the dentate-group and the IOD-group were compared. RESULTS The dentate-group comprised 20 participants (10 female, 30.3±6.7 years); the IOD-group 15 participants (10 female, 74.6±8.3 years). Intra-rater and inter-rater agreement (SA) was very high at 20 chewing cycles (95.00-98.75%). Gums 1-3 showed different colour-mixing characteristics as a function of chewing cycles, gum1 showed a logarithmic association; gum2 and gum3 demonstrated more linear behaviours. However, the number of chewing cycles could be predicted in all specimens from VOH (all p<0.0001, mixed linear regression models). Both analyses proved discriminative to the dental state. CONCLUSION ViewGum© proved to be a reliable and discriminative tool to opto-electronically assess chewing efficiency, given an elastic specimen is chewed for 20 cycles and could be recommended for the evaluation of chewing efficiency in a clinical and research setting. CLINICAL SIGNIFICANCE Chewing is a complex function of the oro-facial structures and the central nervous system. The application of the proposed assessments of the chewing function in geriatrics or special care dentistry could help visualising oro-functional or dental comorbidities in dysphagic patients or those suffering from protein-energy malnutrition.

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.

Relationship Between Orofacial Function, Dentofacial Morphology, And Bite Force In Young Subjects.

The aim was to evaluate the relationship between orofacial function, dentofacial morphology, and bite force in young subjects. Three hundred and sixteen subjects were divided according to dentition stage (early, intermediate, and late mixed and permanent dentition). Orofacial function was screened using the Nordic Orofacial Test-Screening (NOT-S). Orthodontic treatment need, bite force, lateral and frontal craniofacial dimensions and presence of sleep bruxism were also assessed. The results were submitted to descriptive statistics, normality and correlation tests, analysis of variance, and multiple linear regression to test the relationship between NOT-S scores and the studied independent variables. The variance of NOT-S scores between groups was not significant. The evaluation of the variables that significantly contributed to NOT-S scores variation showed that age and presence of bruxism related to higher NOT-S total scores, while the increase in overbite measurement and presence of closed lip posture related to lower scores. Bite force did not show a significant relationship with scores of orofacial dysfunction. No significant correlations between craniofacial dimensions and NOT-S scores were observed. Age and sleep bruxism were related to higher NOT-S scores, while the increase in overbite measurement and closed lip posture contributed to lower scores of orofacial dysfunction.

Impaired Compensatory Beta-cell Function And Growth In Response To High-fat Diet In Ldl Receptor Knockout Mice.

In this study, we investigated the effect of low density lipoprotein receptor (LDLr) deficiency on gap junctional connexin 36 (Cx36) islet content and on the functional and growth response of pancreatic beta-cells in C57BL/6 mice fed a high-fat (HF) diet. After 60 days on regular or HF diet, the metabolic state and morphometric islet parameters of wild-type (WT) and LDLr-/- mice were assessed. HF diet-fed WT animals became obese and hypercholesterolaemic as well as hyperglycaemic, hyperinsulinaemic, glucose intolerant and insulin resistant, characterizing them as prediabetic. Also they showed a significant decrease in beta-cell secretory response to glucose. Overall, LDLr-/- mice displayed greater susceptibility to HF diet as judged by their marked cholesterolaemia, intolerance to glucose and pronounced decrease in glucose-stimulated insulin secretion. HF diet induced similarly in WT and LDLr-/- mice, a significant decrease in Cx36 beta-cell content as revealed by immunoblotting. Prediabetic WT mice displayed marked increase in beta-cell mass mainly due to beta-cell hypertrophy/replication. Nevertheless, HF diet-fed LDLr-/- mice showed no significant changes in beta-cell mass, but lower islet-duct association (neogenesis) and higher beta-cell apoptosis index were seen as compared to controls. The higher metabolic susceptibility to HF diet of LDLr-/- mice may be explained by a deficiency in insulin secretory response to glucose associated with lack of compensatory beta-cell expansion.

Long-term Postoperative Atrophy Of Contralateral Hippocampus And Cognitive Function In Unilateral Refractory Mtle With Unilateral Hippocampal Sclerosis.

This study aimed to evaluate long-term atrophy in contralateral hippocampal volume after surgery for unilateral MTLE, as well as the cognitive outcome for patients submitted to either selective transsylvian amygdalohippocampectomy (SelAH) or anterior temporal lobe resection (ATL). We performed a longitudinal study of 47 patients with MRI signs of unilateral hippocampal sclerosis (23 patients with right-sided hippocampal sclerosis) who underwent surgical treatment for MTLE. They underwent preoperative/postoperative high-resolution MRI as well as neuropsychological assessment for memory and estimated IQ. To investigate possible changes in the contralateral hippocampus of patients, we included 28 controls who underwent two MRIs at long-term intervals. The volumetry using preoperative MRI showed significant hippocampal atrophy ipsilateral to the side of surgery when compared with controls (p<0.0001) but no differences in contralateral hippocampal volumes. The mean postoperative follow-up was 8.7 years (± 2.5 SD; median=8.0). Our patients were classified as Engel I (80%), Engel II (18.2%), and Engel III (1.8%). We observed a small but significant reduction in the contralateral hippocampus of patients but no volume changes in controls. Most of the patients presented small declines in both estimated IQ and memory, which were more pronounced in patients with left TLE and in those with persistent seizures. Different surgical approaches did not impose differences in seizure control or in cognitive outcome. We observed small declines in cognitive scores with most of these patients, which were worse in patients with left-sided resection and in those who continued to suffer from postoperative seizures. We also demonstrated that manual volumetry can reveal a reduction in volume in the contralateral hippocampus, although this change was mild and could not be detected by visual analysis. These new findings suggest that dynamic processes continue to act after the removal of the hippocampus, and further studies with larger groups may help in understanding the underlying mechanisms.

Doehlert Design-desirability Function Multi-criteria Optimal Separation Of 17 Phenolic Compounds From Extra-virgin Olive Oil By Capillary Zone Electrophoresis.

In Brazil, the consumption of extra-virgin olive oil (EVOO) is increasing annually, but there are no experimental studies concerning the phenolic compound contents of commercial EVOO. The aim of this work was to optimise the separation of 17 phenolic compounds already detected in EVOO. A Doehlert matrix experimental design was used, evaluating the effects of pH and electrolyte concentration. Resolution, runtime and migration time relative standard deviation values were evaluated. Derringer's desirability function was used to simultaneously optimise all 37 responses. The 17 peaks were separated in 19min using a fused-silica capillary (50μm internal diameter, 72cm of effective length) with an extended light path and 101.3mmolL(-1) of boric acid electrolyte (pH 9.15, 30kV). The method was validated and applied to 15 EVOO samples found in Brazilian supermarkets.