SummaryA 25 -year-old Egyptian man presented to our unit for the evaluation of a large pericardial effusion. At 1 month before presentation he suffered from daily bouts of fever. Chest x-ray revealed cardiomegaly, echocardiography showed large pericardial effusion and multiple pericardial masses. Needle pericardiocentesis revealed a bloody exudate with no malignant cells. Chest CT showed a well-circumscribed anterior mediastinal cystic mass with a central fat component and foci of calcification. MRI of the chest similarly showed no intracardiac extension. A cystic mass 7×9 cm was removed via a median sternotomy with uneventful postoperative course. Pathological evaluation revealed a benign cystic teratoma and a thymic cyst. Most cystic teratomas are accidentally discovered, large ones can cause symptoms through the compression of mediastinal structures or rupture in pericardial sac.
BACKGROUND
In this paper, we propose a new set representation for binary vectors called logical zonotopes. A logical zonotope is constructed by XOR-ing a binary vector with a combination of binary vectors called generators. A logical zonotope can efficiently represent up to 2 𝛾 binary vectors using only 𝛾 generators. Instead of the explicit enumeration of the zonotopes' members, logical operations over sets of binary vectors are applied directly to a zonotopes' generators. Thus, logical zonotopes can be used to greatly reduce the computational complexity of a variety of operations over sets of binary vectors, including logical operations (e.g. XOR, NAND, AND, OR) and semi-tensor products. Additionally, we show that, similar to the role classical zonotopes play for formally verifying dynamical systems defined over real vector spaces, logical zonotopes can be used to efficiently analyze the forward reachability of dynamical systems defined over binary vector spaces (e.g. logical circuits or Boolean networks). To showcase the utility of logical zonotopes, we illustrate three use cases: (1) discovering the key of a linearfeedback shift register with a linear time complexity, (2) verifying the safety of a logical vehicle intersection crossing protocol, and (3) performing reachability analysis for a high-dimensional Boolean function.
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