Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page

Synthesis, Characterization of Nano MnO2 and its Adsorption Characteristics Over an Azo Dye

ABSTRACT Nano MnO2 powder was synthesized by low temperature solution combustion method using oxalyl dihydrazide (ODH) fuel. The final product was well characterized by Powder X-ray diffraction (PXRD), Fourier Transform Infrared Spectroscopy (FTIR) and Scanning electron microscopy (SEM) for crystallographic purity, phase formation and surface morphology respectively. PXRD results show that pure MnO2 was synthesized at 300 0 C with no other impurities. SEM micrograph shows the product has highly porous structure with large voids, typical of combustion derived material. An adsorption characteristic of the porous MnO2 was studied over direct green dye (DG). The optimum dose of MnO2 for removal of 10 ppm DG azo dye was found to be 0.4 g L -1

Effunet-spagen: An efficient and spatial generative approach to glaucoma detection

Current research in automated disease detection focuses on making algorithms “slimmer” reducing the need for large training datasets and accelerating recalibration for new data while achieving high accuracy. The development of slimmer models has become a hot research topic in medical imaging. In this work, we develop a two-phase model for glaucoma detection, identifying and exploiting a redundancy in fundus image data relating particularly to the geometry. We propose a novel algorithm for the cup and disc segmentation “EffUnet” with an efficient convolution block and combine this with an extended spatial generative approach for geometry modelling and classification, termed “SpaGen” We demonstrate the high accuracy achievable by EffUnet in detecting the optic disc and cup boundaries and show how our algorithm can be quickly trained with new data by recalibrating the EffUnet layer only. Our resulting glaucoma detection algorithm, “EffUnet-SpaGen”, is optimized to significantly reduce the computational burden while at the same time surpassing the current state-of-art in glaucoma detection algorithms with AUROC 0.997 and 0.969 in the benchmark online datasets ORIGA and DRISHTI, respectively. Our algorithm also allows deformed areas of the optic rim to be displayed and investigated, providing explainability, which is crucial to successful adoption and implementation in clinical settings

Midgut Barrier Imparts Selective Resistance to Filarial Worm Infection in Culex pipiens pipiens

Mosquitoes in the Culex pipiens complex thrive in temperate and tropical regions worldwide, and serve as efficient vectors of Bancroftian lymphatic filariasis (LF) caused by Wuchereria bancrofti in Asia, Africa, the West Indies, South America, and Micronesia. However, members of this mosquito complex do not act as natural vectors for Brugian LF caused by Brugia malayi, or for the cat parasite B. pahangi, despite their presence in South Asia where these parasites are endemic. Previous work with the Iowa strain of Culex pipiens pipiens demonstrates that it is equally susceptible to W. bancrofti as is the natural Cx. p. pipiens vector in the Nile Delta, however it is refractory to infection with Brugia spp. Here we report that the infectivity barrier for Brugia spp. in Cx. p. pipiens is the mosquito midgut, which inflicts internal and lethal damage to ingested microfilariae. Following per os Brugia exposures, the prevalence of infection is significantly lower in Cx. p. pipiens compared to susceptible mosquito controls, and differs between parasite species with <50% and <5% of Cx. p. pipiens becoming infected with B. pahangi and B. malayi, respectively. When Brugia spp. mf were inoculated intrathoracically to bypass the midgut, larvae developed equally well as in controls, indicating that, beyond the midgut, Cx. p. pipiens is physiologically compatible with Brugia spp. Mf isolated from Cx. p. pipiens midguts exhibited compromised motility, and unlike mf derived from blood or isolated from the midguts of Ae. aegypti, failed to develop when inoculated intrathoracically into susceptible mosquitoes. Together these data strongly support the role of the midgut as the primary infection barrier for Brugia spp. in Cx. p. pipiens. Examination of parasites recovered from the Cx. p. pipiens midgut by vital staining, and those exsheathed with papain, suggest that the damage inflicted by the midgut is subcuticular and disrupts internal tissues. Microscopic studies of these worms reveal compromised motility and sharp bends in the body; and ultrastructurally the presence of many fluid or carbohydrate-filled vacuoles in the hypodermis, body wall, and nuclear column. Incubation of Brugia mf with Cx. p. pipiens midgut extracts produces similar internal damage phenotypes; indicating that the Cx. p. pipiens midgut factor(s) that damage mf in vivo are soluble and stable in physiological buffer, and inflict damage on mf in vitro

Rationality, Irrationality and Escalating Behavior in Lowest Unique Bid Auctions

Information technology has revolutionized the traditional structure of markets. The removal of geographical and time constraints has fostered the growth of online auction markets, which now include millions of economic agents worldwide and annual transaction volumes in the billions of dollars. Here, we analyze bid histories of a little studied type of online auctions – lowest unique bid auctions. Similarly to what has been reported for foraging animals searching for scarce food, we find that agents adopt Lévy flight search strategies in their exploration of “bid space”. The Lévy regime, which is characterized by a power-law decaying probability distribution of step lengths, holds over nearly three orders of magnitude. We develop a quantitative model for lowest unique bid online auctions that reveals that agents use nearly optimal bidding strategies. However, agents participating in these auctions do not optimize their financial gain. Indeed, as long as there are many auction participants, a rational profit optimizing agent would choose not to participate in these auction markets

Plasmodial sugar transporters as anti-malarial drug targets and comparisons with other protozoa

Glucose is the primary source of energy and a key substrate for most cells. Inhibition of cellular glucose uptake (the first step in its utilization) has, therefore, received attention as a potential therapeutic strategy to treat various unrelated diseases including malaria and cancers. For malaria, blood forms of parasites rely almost entirely on glycolysis for energy production and, without energy stores, they are dependent on the constant uptake of glucose. Plasmodium falciparum is the most dangerous human malarial parasite and its hexose transporter has been identified as being the major glucose transporter. In this review, recent progress regarding the validation and development of the P. falciparum hexose transporter as a drug target is described, highlighting the importance of robust target validation through both chemical and genetic methods. Therapeutic targeting potential of hexose transporters of other protozoan pathogens is also reviewed and discussed

Batch effect correction for genome-wide methylation data with Illumina Infinium platform

<p>Abstract</p> <p>Background</p> <p>Genome-wide methylation profiling has led to more comprehensive insights into gene regulation mechanisms and potential therapeutic targets. Illumina Human Methylation BeadChip is one of the most commonly used genome-wide methylation platforms. Similar to other microarray experiments, methylation data is susceptible to various technical artifacts, particularly batch effects. To date, little attention has been given to issues related to normalization and batch effect correction for this kind of data.</p> <p>Methods</p> <p>We evaluated three common normalization approaches and investigated their performance in batch effect removal using three datasets with different degrees of batch effects generated from HumanMethylation27 platform: quantile normalization at average β value (QNβ); two step quantile normalization at probe signals implemented in "lumi" package of R (lumi); and quantile normalization of A and B signal separately (ABnorm). Subsequent Empirical Bayes (EB) batch adjustment was also evaluated.</p> <p>Results</p> <p>Each normalization could remove a portion of batch effects and their effectiveness differed depending on the severity of batch effects in a dataset. For the dataset with minor batch effects (Dataset 1), normalization alone appeared adequate and "lumi" showed the best performance. However, all methods left substantial batch effects intact in the datasets with obvious batch effects and further correction was necessary. Without any correction, 50 and 66 percent of CpGs were associated with batch effects in Dataset 2 and 3, respectively. After QNβ, lumi or ABnorm, the number of CpGs associated with batch effects were reduced to 24, 32, and 26 percent for Dataset 2; and 37, 46, and 35 percent for Dataset 3, respectively. Additional EB correction effectively removed such remaining non-biological effects. More importantly, the two-step procedure almost tripled the numbers of CpGs associated with the outcome of interest for the two datasets.</p> <p>Conclusion</p> <p>Genome-wide methylation data from Infinium Methylation BeadChip can be susceptible to batch effects with profound impacts on downstream analyses and conclusions. Normalization can reduce part but not all batch effects. EB correction along with normalization is recommended for effective batch effect removal.</p