Analysis of the rate of convergence of an over-parametrized deep neural network estimate learned by gradient descent

Estimation of a regression function from independent and identically distributed random variables is considered. The $L_2$ error with integration with respect to the design measure is used as an error criterion. Over-parametrized deep neural network estimates are defined where all the weights are learned by the gradient descent. It is shown that the expected $L_2$ error of these estimates converges to zero with the rate close to $n^{-1/(1+d)}$ in case that the regression function is H\"older smooth with H\"older exponent $p \in [1/2,1]$. In case of an interaction model where the regression function is assumed to be a sum of H\"older smooth functions where each of the functions depends only on $d^*$ many of $d$ components of the design variable, it is shown that these estimates achieve the corresponding $d^*$-dimensional rate of convergence

Acute Appendicitis Review: Background, Epidemiology, Diagnosis, and Treatment.

Appendicitis is a common occurrence in both the adult and pediatric populations. The condition most commonly occurs between the ages of 10 and 20 years with a lifetime risk of 8.6% and 6.7% for males and females respectively. Its diagnosis focuses on clinical presentation and imaging modalities classified according to scoring systems such as the Alvarado scoring system. A number of imaging modalities can be used, with CT being the most common one. For acute appendicitis, surgical intervention is considered to be the gold standard of treatment. However, recent research has focused on other modalities of treatment including antibiotics and endoscopic retrograde appendicitis therapy (ERAT) to avoid surgical complications

Adult Onset Morgagni Hernia: Medical vs. Surgical Management.

Morgagni hernia is a type of diaphragmatic hernia where bowel content herniates through an irregular opening into the thoracic cavity. Herein, we present the case of an 84-year-old female patient with multiple hospital admissions for abdominal symptoms. Radiological studies confirmed Morgagni hernia. She underwent a laparoscopic intervention with mesh placement. She was discharged in stable condition and was doing well on follow-up

Mesalamine Associated Bradycardia.

A 38-year-old female presented with an acute flare of ulcerative colitis. She was started on prednisone and mesalamine. Within 24 hours of initiating mesalamine, she developed sinus bradycardia. After holding mesalamine, the heart rate returned to normal within five days. Our case illustrates the third described case, to our knowledge, of severe sinus bradycardia secondary to mesalamine

Streptococcus Intermedius Brain and Diverticular Abscesses After Dental Manipulation: A Case Report.

A brain abscess is defined as a focal intracerebral infection consisting of an encapsulated collection of pus, which can be a life-threatening complication of infections, trauma, or surgery. While immunocompromised patients can have a wide array of causative organisms, bacterial species represent the most common etiology in immunocompetent individuals. The incidence of brain abscesses ranges from 0.4 to 0.9 per 100,000, with a high predisposition among immunocompromised patients and in those with disruption of the blood-brain barrier. The most common causative organisms found were Streptococcus species, particularly S. viridians and S. pneumonia, Enterococcus, and Staphylococcus species, mainly S. aurieus and S. epidermidis. Microorganism can invade the brain through different mechanisms, either directly by contiguous spread and odontogenic infections, which usually cause a single brain abscess, or indirectly through hematogenous spread which can cause multiple brain abscesses. Both surgical and conservative dental procedures contribute to hematogenous spreading of oral microorganisms. Although most of those organisms are eliminated shortly after they gain access to the bloodstream, some can persist and contribute to the pathogenesis of abscesses in the appropriate environment. Odontogenic origins are rarely implicated in the formation of brain abscesses, and oral foci comprise approximately 5% of identified cases. We report a case of brain and diverticular abscesses due to S. intermidius occurring two months after dental extraction. This case highlights the fact that even usual dental workup can result in the development of bacteremia and disseminated abscesses including but not restricted to the brain. Consequently, in addition to identifying the possible source of bacteremia with an extensive history and physical exam, the diagnosis of Streptococcus milleri organisms should prompt the physicians to screen for sites of possible metastatic infection spread