An Open Inflationary Model for Dimensional Reduction and its Effects on the Observable Parameters of the Universe

Assuming that higher dimensions existed in the early stages of the universe where the evolution was inflationary, we construct an open, singularity-free, spatially homogeneous and isotropic cosmological model to study the effects of dimensional reduction that may have taken place during the early stages of the universe. We consider dimensional reduction to take place in a stepwise manner and interpret each step as a phase transition. By imposing suitable boundary conditions we trace their effects on the present day parameters of the universe.Comment: 5 pages, accepted for publication in Int. J. of Mod. Phys.

Magnetic resonance imaging of the quadriceps fat pad oedema pattern in relation to patellofemoral joint pathologies

Purpose: Quadriceps fat pad is located posterior to the quadriceps tendon. Increased signal intensity of this fat pad is seen on routine knee magnetic resonance imaging (MRI) examinations, but the exact mechanism and related pathologies are not clear. In this study we aimed to evaluate the relationship between MRI signal intensity and morphological features of quadriceps fat pad, as well as various pathologies of the patellofemoral joint. Material and methods: Sixty-one knees with quadriceps fat pad oedema out of 457 knee MRI examinations were included. Quadriceps fat pad signal intensity, dimensions, posterior indentation, and various parameters related to patellofemoral joint such as trochlear facet asymmetry, trochlear depth and sulcus angle, and the Insall-Salvati ratio were evaluated. Results: There was no statistically significant correlation between quadriceps fat pad oedema intensity and its dimensions, but it was significant when compared to posterior indentation. There was no correlation between fat pad oedema and each of the pathologies. However, there was a significant correlation between the presence of fat pad oedema and the presence of at least one of the pathologies related to patellofemoral joint. Conclusions: Quadriceps fat pad oedema detected in MRI examinations should warn the radiologist against the presence of various pathologies related to the patellofemoral joint

On the Consistency of the Solutions of the Space Fractional Schr\"odinger Equation

Recently it was pointed out that the solutions found in literature for the space fractional Schr\"odinger equation in a piecewise manner are wrong, except the case with the delta potential. We reanalyze this problem and show that an exact and a proper treatment of the relevant integral proves otherwise. We also discuss effective potential approach and present a free particle solution for the space and time fractional Schr\"odinger equation in general coordinates in terms of Fox's H-functions

Comparison of HCV core antigen and anti-HCV with HCV RNA results

Background: The measurement of anti-HCV antibodies using immunological methods and the confirmation of viral nuclear acid based on molecular methods is important in diagnosis and follow-up of the HCV infection.Objectives: In this study, we aimed to analyse HCV core Antigen positivity among anti-HCV antibody positive sera to determine the significance of testing of HCV core Ag for the laboratory diagnosis of HCV infection, by considering the correlation between serum HCV core Ag and HCV RNA levels.Methods: 115 patients suspected of having hepatitis C and who were positive for anti-HCV antibody were investigated using chemiluminescent and molecular methods. Anti-HCV antibody, HCV core Ag and HCV RNA levels were detected by the Vitros ECiQ immunodiagnostic system, Architect i2000 system and RT-PCR, respectively.Results: The sensitivity, specificity, positive and negative predictive values and accuracy rate of HCV core Antigen assay were detected as 86.5%(83/96), 100%(19/19), 100%(83/83), 59.4%(19/32), 88.7%(102/115) respectively.Conclusion: HCV core Ag assay could be used for diagnosis of HCV infection as it is easy to perform, cost-effective, has high specificity and positive predictive value. However, it should be kept in mind that it may have lack of sensitivity and negative predictive value.Key Words: HCV, anti-HCV antibody, HCV core Ag, HCV RN

Robust threshold schemes based on the Chinese remainder theorem

Recently, Chinese Remainder Theorem (CRT) based function sharing schemes are proposed in the literature. In this paper, we investigate how a CRT-based threshold scheme can be enhanced with the robustness property. To the best of our knowledge, these are the first robust threshold cryptosystems based on a CRT-based secret sharing. © 2008 Springer-Verlag Berlin Heidelberg

Domain Generalization -- A Causal Perspective

Machine learning models rely on various assumptions to attain high accuracy. One of the preliminary assumptions of these models is the independent and identical distribution, which suggests that the train and test data are sampled from the same distribution. However, this assumption seldom holds in the real world due to distribution shifts. As a result models that rely on this assumption exhibit poor generalization capabilities. Over the recent years, dedicated efforts have been made to improve the generalization capabilities of these models collectively known as -- \textit{domain generalization methods}. The primary idea behind these methods is to identify stable features or mechanisms that remain invariant across the different distributions. Many generalization approaches employ causal theories to describe invariance since causality and invariance are inextricably intertwined. However, current surveys deal with the causality-aware domain generalization methods on a very high-level. Furthermore, we argue that it is possible to categorize the methods based on how causality is leveraged in that method and in which part of the model pipeline is it used. To this end, we categorize the causal domain generalization methods into three categories, namely, (i) Invariance via Causal Data Augmentation methods which are applied during the data pre-processing stage, (ii) Invariance via Causal representation learning methods that are utilized during the representation learning stage, and (iii) Invariance via Transferring Causal mechanisms methods that are applied during the classification stage of the pipeline. Furthermore, this survey includes in-depth insights into benchmark datasets and code repositories for domain generalization methods. We conclude the survey with insights and discussions on future directions