Provable Bounds for Learning Some Deep Representations

We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an $n$ node multilayer neural net that has degree at most $n^{\gamma}$ for some $\gamma <1$ and each edge has a random edge weight in $[-1,1]$. Our algorithm learns {\em almost all} networks in this class with polynomial running time. The sample complexity is quadratic or cubic depending upon the details of the model. The algorithm uses layerwise learning. It is based upon a novel idea of observing correlations among features and using these to infer the underlying edge structure via a global graph recovery procedure. The analysis of the algorithm reveals interesting structure of neural networks with random edge weights.Comment: The first 18 pages serve as an extended abstract and a 36 pages long technical appendix follow

Acquired Acrodermatitis Enteropathica Secondary to Nutritional Deficiency from Alcoholism

History A 30-year-old white male with history of alcoholism complicated by cirrhosis who presented to an outside hospital with loss of consciousness after being found down in excrement and urine for an unknown amount of time. Patient’s course was complicated by pancreatitis, urosepsis, spontaneous bacterial peritonitis, and hepatic encephalopathy. Patient was transferred to Henry Ford Hospital for further management, and dermatology was consulted for a one-year history of pruritic rash on the arms and legs with concern for scabies. Examination: Patient appeared thin and malnourished. He was intubated with 2+ pitting edema to his mid-thighs. On his scalp, lateral neck, right abdomen, bilateral dorsal hands extending onto the dorsal forearms, dorsal feet, bilateral inner thighs and the entirety of his scrotum, the patient had well-demarcated pink plaques with cracked riverbed-appearing scale. There was no involvement of the axillae, interdigital finger or toe web spaces, mons pubis, or umbilicus. Course and therapy: Zinc level was found to be markedly decreased at 35 mcg/dL [normal: 70-150 mcg/dL], confirming a diagnosis of acrodermatitis enteropathica (AE). HIV 4th generation Ag/Ab was found to be nonreactive. Alkaline phosphatase was found to be elevated at 735 IU/L [normal: 44-147 IU/L]. Patient was treated with oral zinc replacement at 1.5 mg/kg/day as well as topical petrolatum as needed. Patient had improvement of his zinc level from 35 mcg/dL to within normal limits at 80 mcg/dL within three weeks. Discussion: Acrodermatitis enteropathica is a condition resulting from zinc deficiency characterized by sharply demarcated, symmetric erythematous patches and plaques with erosions and scale-crust in a peri-oral, genital, and acral distribution. Severe deficiency may be accompanied by alopecia, diarrhea, depression, hypogonadism, and immunosuppression. AE may be inherited as an autosomal recessive gene mutation in SLC39A4 leading to deficiency in an intestinal zinc transporter protein. This process often presents in neonates when weaning from breast milk to formula or in cases of low maternal breast milk zinc concentrations. AE, however, may also be acquired secondary to decreased nutritional intake or increased excretion/malabsorption leading to zinc deficiency. Risk factors for decreased nutritional zinc intake include limited resources, alcoholism, anorexia nervosa, vegan diets, and diets high in mineral-binding phytates. Risk factors for increased excretion include intestinal malabsorption, liver disease, renal disease, Crohn’s disease, cystic fibrosis, and sickle cell disease. Diagnosis is made based on clinical features and serum zinc level \u3c 60 mcg/dL. In our patient, his zinc level was found to be significantly lower at 35 mcg/dL. Typically in AE, given that serum alkaline phosphatase (ALP) is a zinc-dependent enzyme, a decreased ALP is expected. Our patient’s ALP was found to be elevated, likely secondary to concomitant pancreatitis. Appropriate treatment is with oral zinc replacement at 1-2 mg/kg/day of elemental zinc with cutaneous improvement expected in weeks to months. Extracutaneous improvement often shows within 24 hours of beginning treatment. Our patient was treated with 1.5 mg/kg/day of oral elemental zinc, with improvement in his cutaneous lesions seen within 3 weeks.https://scholarlycommons.henryford.com/merf2019caserpt/1086/thumbnail.jp

Investigation of Solar Flare Classification to Identify Optimal Performance

When an intense brightness for a small amount of time is seen in the sun, then we can say that a solar flare emerged. As solar flares are made up of high energy photons and particles, thus causing the production of high electric fields and currents and therefore results in the disruption in space-borne or ground-based technological system. It also becomes a challenging task to extract its important features for prediction. Convolutional Neural Networks have gain a significant amount of popularity in the classification and localization tasks. This paper has given stress on the classification of the solar flares emerged on different years by stacking different convolutional layers followed by max pooling layers. From the reference of Alexnet, the pooling layer employed in this paper is the overlapping pooling. Also two different activation functions that are ELU and CReLU have been used to investigate how many number of convolutional layers with a particular activation function provides with the best results on this dataset as the size of the dataset in this domain is always small. The proposed investigation can be further used in a novel solar prediction systems

An anthropometric study of intercondylar femur notch with MRI analysis

Background: Anterior cruciate ligament is the most common ligament injury of knee. The bony anatomy of femur and tibia is responsible for normal knee kinematics and static stability. Intercondylar notch dimensions is considered as a significant predictive risk factor for ACL tear. Narrow femoral intercondylar notch width in either sex were major correlating factors. Aim was to evaluate the intercondylar femur notch dimensions in patients of knee injury using magnetic resonance imaging at RD Gardi Medical College, Ujjain, Madhya Pradesh. Methods: This is a prospective study consist of 400 patients carried out from October 2020 to August 2022 in the Department of Orthopaedics, RDGMC Ujjain. All the patients of knee injury including ACL tear and age 18 years to 60 years are included in the study. Patient less than 18 years and more than 60 years were excluded from the study. Dicom radiant software is used as statistical tool to analyse the data. Various intercondylar notch dimensions in different sections are measured using MRI in the dicom software. Results: The cut off values of axial NWI, NSI, NDI as 0.238, 0.662, 0.472 respectively. Conclusions: We conclude that narrow femoral intercondylar notch, lower notch width index increases the risk of an ACL tear in the given population. This would help in identification of people at risk for ACL injuries. Our study provides a comprehensive analysis on the risk factor of ACL tear, which would help in betterment of the patients at danger for anterior cruciate ligament injury. People with decreased notch dimensions should be educated on the high risk of ACL tear and be given proper prophylactic precautions