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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.

A case of primary clear cell adenocarcinoma of the colon, a rare oncologic variant, was diagnosed in a 25-year-old man who presented with partial bowel obstruction. To understand better the pathology of this neoplasm, a retrospective review of Entrez PubMed entries describing primary clear cell adenocarcinoma of the colon and/or rectum was performed. Only 13 previous cases of primary clear cell adenocarcinoma of the colon and/or rectum have been reported, with an average presentation age of 57 years and generally afflicting the descending colon of men. Herein we present a case occurring in the distal ascending colon of the youngest patient in the literature to date. Our patient's diagnosis is rare in occurrence, location, and age of onset.

We study the vertex-cover problem, which is a nondeterministic polynomial-time hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, such as Erdős-Rényi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g., for the ER ensemble at connectivity c=e≈2.7183 from replica symmetric to replica-symmetry broken. For the vertex-cover problem, the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, also changes close to this phase transition from "easy" to "hard." In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach; hence the algorithm operates in a space outside the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an easy-hard transition around c=e, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.

Cardiac sarcoidosis should be suspected in young patients with cardiac symptoms, especially when there is concurrent personal or family history of sarcoidosis. While sarcoidosis is self-limiting in about 40% of cases, cardiac involvement portends a more ominous prognosis with higher mortality rates. The definitive diagnostic test for cardiac sarcoidosis is the endomyocardial biopsy, an invasive test with low sensitivity. The multiple clinical modalities, which comprise the Japanese Ministry of Health clinical diagnostic guidelines, and newer modalities, including MRI, are more sensitive and demonstrate reliable diagnostic efficacy when compared to endomyocardial biopsy. Management of cardiac sarcoidosis involves early initiation of corticosteroid therapy to limit progression and maintain the structural and electrical integrity of the heart. When necessary, more invasive modalities (e.g. ICD, pacemaker, and transplant) may improve outcomes in advanced disease.

We present a 10-year-old girl with a pure Bednar tumor (pigmented dermatofibrosarcoma protuberans) of the right shoulder. Cytogenetic analysis demonstrated 47 chromosomes with 2 copies of a derivative chromosome 22, der(22)t(17;22)(q22;q13). Fluorescence in situ hybridization (FISH) analysis demonstrated the COL1A1-PDGFB fusion on both der(22) chromosomes. By RT-PCR and sequencing, we observed a fusion of the COL1A1 exon 41 with PDGFB exon 2. This pure pediatric Bednar tumor in a child, like childhood dermatofibrosarcoma protuberans, had a linear structural abnormality rather than a ring chromosome that is more commonly encountered in adult Bednar and dermatofibrosarcoma protuberans tumors. The underlying molecular abnormality in this pediatric Bednar tumor is the same as in dermatofibrosarcoma protuberans.