Zeros of random trigonometric polynomials with dependent coefficients

It is well known that the expected number of real zeros of a random cosine polynomial (of degree $n$)\begin{equation*} V_n(x) = \sum_ {j=0} ^{n} a_j \cos (j x) , \quad x \in (0,2\pi) , \end{equation*} where the coefficients $a_j$ are independent and identically distributed (i.i.d.) real-valued standard Gaussian random variables, is asymptotically $2n / \sqrt{3}$. To the best of our knowledge, the above asymptotic relation has always been the lower bound for the expected number of real zeros of $V_n$ when the $a_j$ employ different settings. However, this inequality is sharp for most of the cases that have been considered so far. Moreover, out of various ways to establish a set of dependent coefficients, one is to sort out the coefficients in the blocks of the same length, and then identify certain blocks. As one may expect, the expected number of real zeros of these polynomials is subject to the way we identify the blocks, yet it might be independent of the size of the blocks. In this manuscript, we investigate four cases of random cosine polynomials where the blocks of the coefficients are identified in different fashions. The cases we study include the adjacent, palindromic, and periodic blocks as well as the case involving only two blocks, each of which possesses a different expected number of real zeros from one another

On Computing Optimal Repairs for Conditional Independence

This thesis focuses on the concept of Conditional Independence (CI) and its testing, which holds immense significance across various fields, including economics, social sciences, and biomedical research. Notably, within computer science, CI has become an integral part of building probabilistic and causal models. It aids efficient inference and plays a key role in uncovering causal relationships. The primary aim of this thesis is to broaden the scope of CI beyond its testing aspect. We introduce the pioneering problem of data repair, designed to adhere to particular CI constraints. The value and pertinence of this problem are highlighted through two contrasting applications. The first application is debiasing data and developing fair machine learning (ML) models. As fairness becomes a central issue in machine learning, exploring techniques for debiasing data to construct more equitable models is crucial. The proposed data repair methodology supports this, assisting in creating fairer models. The second application is about improving data quality and cleaning processes. Maintaining data quality is a continuous challenge across various fields, and our repair methods present a novel way to address this, enhancing the overall quality and reliability of the data. The proposed repairs use optimal transport (OT) and Earth Mover’s distance as dissimilarity measures. This approach ensures the preservation of the underlying probability distribution’s geometry. In the context of fairness, this contributes to increased downstream model accuracy. In the realm of data cleaning, it offers a robust method for error detection. To facilitate the efficient generation of the repairs, we present novel techniques, including relaxed OT and block coordinate descent methods. The effectiveness of the repair methodologies is validated through experiments conducted on synthetic and real-world datasets. This comprehensive exploration highlights the potential of data repair in addressing critical issues in machine learning and data quality, offering a new perspective on using CI in these fields

日本文学の内と外 : 曽野綾子『哀歌』、前田河広一郎「三等船客」、川端康成『雪国』を中心に

関西大

Evaluating the Repeatability and Effect of Sex and Age on Corneal Biomechanical Parameters Measured Using Corvis ST

AbstractPurpose: To evaluate the repeatability of biomechanical readings by Corvis ST  (Wetzlar, Germany)  in healthy eyes and its relation with age and sex.Methods: Three consecutive measurements were performed on 100 eyes of 100 patients using the Corvis ST. Various parameters including first and second applanation length, first and second applanation velocity, first and second applanation time, peak distance, radius, deformation amplitude, corrected and non-corrected intraocular pressure (IOP), central corneal thickness (CCT), Corvis ST biomechanical index (CBI), and tomography and biomechanical index (TBI) were derived from the Corvis ST readings. Repeatability of each parameter and their correlation with age and sex were evaluated.Results: The mean IOP, CCT, CBI and TBI were 15.47 ± 2.24 mm Hg, 541.24 ± 38.90 μm, 0.048 ± 0.13 and 0.138 ± 0.17 respectively. Intra class correlation coefficient (ICC) for CCT, second applanation velocity and deformation amplitude were 0.985, 0.809 and 0.825 respectively. ICC was less than 0.8 for all other parameters. The device-specific readings showed no significant relationship with age and sex.Conclusion: The Corvis ST showed high repeatability for CCT, second applanation velocity, and deformation amplitude parameters. No relation between Corvis ST readings and age or sex was observed. Keywords: Cornea; Biomechanical; Age; Sex; Iran

The Therapeutic Effect of Honey on Dexamethasone-Induced Osteoporosis in Rats

Background: The effect of glucocorticoids on calcium balance and bone growth may lead to osteoporosis and currently glucocorticoid induced osteoporosis is one of the recognized types of osteoporosis. The present study aimed at evaluating the therapeutic effect of honey on dexamethasone-induced osteoporosis in rat model.Methods: Thirty-two male rats were randomly divided into four groups including dexamethasone receiving group, physiological serum receiving group, dexamethasone and honey receiving group, and dexamethasone and alendronate group. All rats were treated for 4 weeks. At the end of the treatment period, blood was collected and the changes in blood phosphorus, calcium and alkaline phosphatase (ALP) levels were compared on the first day. Animals were sacrificed and femurs were separated for histological evaluation, while specimens were obtained from the epiphysis and metaphysis.Results: The positive effect of honey on prevention of osteoporosis was demonstrated, although there were no significant differences between groups regarding serum calcium. Histomorphometric parameters revealed the effective role of honey in prevention of dexamethasone-induced osteoporosis.Conclusion: Prescription of dexamethasone was illustrated to reduce the histomorphometric parameters of rat femur that caused osteoporosis. On the other hand, the administration of honey with dexamethasone could largely prevent more reduction for osteoporosis. Therefore, honey is suggested as a potential treatment for glucocorticoid-induced osteoporosis

The Relationship between Small for Gestational Age (SGA) at Birth and Developmental Delay in Children Aged 4 to 60 Months

Background Progress in medical science and success in increasing the survival rate of vulnerable infants have raised the issue of future development in these children. This study aimed to investigate the relationship between small for gestational age (SGA) status at birth and developmental delay in children aged 4 to 60 months. Materials and Methods This study was a correlation descriptive through a multistage sampling method on 419 Iranian children aged 4 to 60 months who attended healthcare centers affiliated to Isfahan University of Medical Sciences and Healthcare Services, Iran. Data collection tools included a data collection checklist and the Ages and Stages Questionnaires (ASG). The data obtained were analyzed using the SPSS software (version 18.0.( Results The results showed that 83 (19.8%) of 419 children in the study, had developmental delay and 336 (80.2%) had normal development. Comparison of developmental domains between the two groups of children based on birth weight, showed that there was a significant relationship between the birth weight of children and developmental delay in the domain of fine movements (p = 0.02, r=0.81), problem solving (p = 0.02, r= 0.73), and the total score (p =0.02, r= 0.87). In addition, the Chi-square test showed a significant relationship between small for gestational age (SGA) status at birth and developmental delay in children (p = 0.001). Conclusion Given the relationship between birth weight and developmental disorders, special attention to the birth weight of infants and performing regular care during pregnancy and afterwards for SGA children can prevent many developmental problems

Imidazopyridine hydrazone derivatives exert antiproliferative effect on lung and pancreatic cancer cells and potentially inhibit receptor tyrosine kinases including c-Met

Aberrant activation of c-Met signalling plays a prominent role in cancer development and progression. A series of 12 imidazo [1,2-α] pyridine derivatives bearing 1,2,3-triazole moiety were designed, synthesized and evaluated for c-Met inhibitory potential and anticancer effect. The inhibitory activity of all synthesized compounds against c-Met kinase was evaluated by a homogeneous time-resolved fluorescence (HTRF) assay at the concentration range of 5-25 µM. Derivatives 6d, 6e and 6f bearing methyl, tertiary butyl and dichloro-phenyl moieties on the triazole ring, respectively, were the compounds with the highest potential. They significantly inhibited c-Met by 55.3, 53.0 and 51.3%, respectively, at the concentration of 25 µM. Synthetic compounds showed antiproliferative effects against lung (EBC-1) and pancreatic cancer cells (AsPc-1, Suit-2 and Mia-PaCa-2) expressing different levels of c-Met, with IC50 values as low as 3.0 µM measured by sulforhodamine B assay. Active derivatives significantly blocked c-Met phosphorylation, inhibited cell growth in three-dimensional spheroid cultures and also induced apoptosis as revealed by Annexin V/propidium iodide flow cytometric assay in AsPc-1 cells. They also inhibited PDGFRA and FLT3 at 25 µM among a panel of 16 kinases. Molecular docking and dynamics simulation studies corroborated the experimental findings and revealed possible binding modes of the select derivatives with target receptor tyrosine kinases. The results of this study show that some imidazopyridine derivatives bearing 1,2,3-triazole moiety could be promising molecularly targeted anticancer agents against lung and pancreatic cancers

A Review of the Effects of Omega-3 and Omega-6 on Alcoholic and Non-Alcoholic Fatty Liver

Non-alcoholic fatty liver disease is a type of fatty fat that causes an increase in alcohol consumption. Excessive alcohol consumption causes inflammation, and liver damage. The certain fatty acids (FAs) may be involved in this liver damage. Anti-inflammatory and blood lipid lowering effects are the effects of omega-3 unsaturated fatty acids (n-3 PUFAs). NAFLD is the hepatic manifestation of metabolic syndrome because obesity and insulin resistance are the main pathogenic factors of both diseases. NAFLD is a disease associated with metabolic syndrome. Most patients with NAFLD are obese, although the disease can also affect non-obese people. Metabolic and genetic factors play an important role in the occurrence of this disease. Oxidative stress, lipotoxicity and inflammation play a key role in the development of NAFLD. There is a lot of evidence for the therapeutic potential of omega-3 PUFAs fatty acids (n-3 PUFA), mainly docosahexaenoic acid and eicosatetraenoic acid in the treatment of metabolic diseases due to their antioxidant and anti-inflammatory properties. Therefore, in this review article, we examined the effects of omega-3 and omega-6 on alcoholic and non-alcoholic fatty liver disease