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Case: A 50 year old African-American woman with diabetes, hypertension, and hyperlipidemia presented with progressively worsening retro-sternal chest pain, exacerbated by activity and relieved by rest. She also endorsed a thirty-pound unintentional weight loss, and dysphagia. She was dysarthric with left-sided Bell's Palsy and a palpable left axillary lymph node. She had been evaluated at several hospitals in the previous months for similar typical chest pain. Her troponin values were normal, and an EKG showed T-wave inversions in leads I and aVL. On echocardiography, her ejection fraction was 45 percent with anterolateral hypokinesis. She was treated for NSTEMI, and an angiogram showed 95 percent stenosis of the right coronary artery. A modified barium swallow study revealed weakened swallowing with aspiration of thin liquids. An MRI Brain demonstrated scattered T2/ FLAIR hyper-intense foci in the subcortical white matter and focal meningeal thickening. ANA, dsDNA, ANCA, and Lyme antibodies were all negative, and a chest CT showed hilar lymphadenopathy. Cardiac MRI demonstrated scattered foci of delayed enhancement in the mid-myocardium and sub-epicardium without infarction. An endobronchial biopsy of hilar lymph nodes showed two small epithelioid granulomas, consistent with Sarcoidosis. She was started on high-dose corticosteroids with rapid improvement. A repeat modified barium swallow study was normal and a repeat echocardiogram demonstrated recovered ejection fraction of 55 percent with improved wall motion in the septum and apex. Additionally, her left-sided Bell's Palsy and dysarthria improved after several days of therapy., Discussion: To our knowledge, this report is the third case of multi-organ Sarcoidosis presenting as ACS. This case depicts the simultaneous presentation of neurologic, pharyngeal, pulmonary, and cardiac Sarcoidosis. Myocardial involvement in Sarcoidosis is rare and usually presents as conduction abnormalities with arrhythmia rather than ACS. Though her symptoms were consistent with Sarcoidosis, she had multiple risk factors for coronary atherosclerosis including diabetes, hypertension, and hyperlipidemia. This case highlights the importance of including Sarcoidosis in the differential diagnosis for patients with recurrent typical chest pain of uncertain etiology.

We study the polygons governing the convex hull of a point set created by the steps of n independent two-dimensional random walkers. Each such walk consists of T discrete time steps, where x and y increments are independent and identically distributed Gaussian. We analyze area A and perimeter L of the convex hulls. We obtain probability densities for these two quantities over a large range of the support by using a large-deviation approach allowing us to study densities below 10^{-900}. We find that the densities exhibit in the limit T→∞ a time-independent scaling behavior as a function of A/T and L/sqrt[T], respectively. As in the case of one walker (n=1), the densities follow Gaussian distributions for L and sqrt[A], respectively. We also obtained the rate functions for the area and perimeter, rescaled with the scaling behavior of their maximum possible values, and found limiting functions for T→∞, revealing that the densities follow the large-deviation principle. These rate functions can be described by a power law for n→∞ as found in the n=1 case. We also investigated the behavior of the averages as a function of the number of walks n and found good agreement with the predicted behavior.

A 37- year-old man with human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS) was admitted to the intensive care unit following a four month history of progressive shortness of breath, productive cough, and flu-like symptoms. His HIV/AIDS was diagnosed at the age of 19 (CD4 count =15; viral load = 294,436 copies/ mL) and was complicated by hemodialysis-dependent, HIV-associated nephropathy, prior Pneumocystis pneumonia and known noncompliance with prescribed antiretroviral therapy. Chest film at admission was interpreted as diffuse bilateral interstitial and airspace opacities with a right sided layering density representative of laminar pleural effusion. Bacterial blood cultures were subsequently negative. A bronchoalveolar lavage was performed and an image from the cytologic cell block is seen above in Figure 1. The patient's respiratory status continued to deteriorate and he was converted to comfort care. Following death, an unlimited autopsy examination was requested by the family and authorized by the coroner. At autopsy, additional gross pathologic findings included 350ml of chylous appearing pleural fluid and serous ascites (700ml). Histopathology revealed intra-alveolar acute fibrinopurulent exudate, chronic pericarditis and end-stage nephropathy. Similar cells to those shown above in Figure 1 were identified in lung epithelium and in pancreatic acinar cells. Special stain for Pneumocystis was negative.