Exact Algorithms for 0-1 Integer Programs with Linear Equality Constraints

In this paper, we show $O(1.415^n)$-time and $O(1.190^n)$-space exact algorithms for 0-1 integer programs where constraints are linear equalities and coefficients are arbitrary real numbers. Our algorithms are quadratically faster than exhaustive search and almost quadratically faster than an algorithm for an inequality version of the problem by Impagliazzo, Lovett, Paturi and Schneider (arXiv:1401.5512), which motivated our work. Rather than improving the time and space complexity, we advance to a simple direction as inclusion of many NP-hard problems in terms of exact exponential algorithms. Specifically, we extend our algorithms to linear optimization problems

A Stronger LP Bound for Formula Size Lower Bounds via Clique Constraints

We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan (1995) and the theory of stable set polytope. We apply it to majority functions and prove their formula size lower bounds improved from the classical result of Khrapchenko (1971). Moreover, we introduce a notion of unbalanced recursive ternary majority functions motivated by a decomposition theory of monotone self-dual functions and give integrally matching upper and lower bounds of their formula size. We also show monotone formula size lower bounds of balanced recursive ternary majority functions improved from the quantum adversary bound of Laplante, Lee and Szegedy (2006)

J wave due to diagonal branch ischemia

The culprit lesion of acute myocardial infarction could be predicted by electrocardiogram findings. However, we experienced some cases with coronary angiographic finding in the area of ST-T elevation that was different from that predicted. The lambda-like J wave could be caused by ischemia although the mechanism has not been fully elucidated. We report a case of acute myocardial infarction that showed discrepancy between ST-T elevation with lambda-like ischemic J wave in a broad area and coronary angiographical finding of diagonal branch occlusion

Regression of LV hypertrophy by tafamidis

Transthyretin amyloidosis (ATTR) variant is a life-threatening hereditary disease predominantly affecting the peripheral nervous system and heart. Tafamidis, which prevents the deposition of amyloid by stabilizing transthyretin, is available for the treatment of neuropathy and cardiomyopathy of ATTR. However, whether tafamidis could eliminate established amyloid deposits and improve cardiac function remains unknown. We reported a case of regression of left ventricular hypertrophy after tafamidis therapy in a patient with an ATTR variant

A Case of Chronic Thromboembolic Pulmonary Hypertension Secondary to Myeloproliferative Disease

A woman in her ６０s presented with shortness of breath on exertion and was admitted to a nearby hospital in March ２００X. Contrast-enhanced computer tomography scan showed contrast defect images in the pulmonary artery and lower extremity vein. She was diagnosed with pulmonary embolism and deep venous thrombosis and anticoagulant therapy was started. At the same time, a blood test revealed an abnormal increased platelet count（７４０，０００/μl）, and she was diagnosed as myeloproliferative disease（primary myelofibrosis, JAK２ mutation +）. We follow up with oral administration of a steroid because she had a low risk of primary myelofibrosis. However, the symptom had been lasting, she was admitted into our hospital for examining the origin of symptom and treatment. Cardiac echocardiography suggested the presence of pulmonary hypertension, and lung ventilation perfusion scintigraphy showed widespread wedge accumulation defect, depressed area in bilateral lungs, and ventilator blood flow mismatch. In cardiac catheterization, the mean pulmonary artery pressure was as high as ３７mmHg. Per the test results, she was diagnosed chronic thromboembolic pulmonary hypertension（CTEPH）secondary to primary myelofibrosis. We proposed invasive treatment（pulmonary artery endarterectomy, balloon pulmonary arterioplasty）, but she desired just oxygen administration and medication therapy. It is reported that CTEPH develops in an organized thrombus after acute pulmonary embolism, but the mechanism of that development has not been revealed. In this case with primary myelofibrosis, we consider that the decrease of pulmonary vascular bed is due to a blood cell disorder and vascular remodeling is due to an increase of vascular endothelial growth factor and platelet derived growth factor secreted by abnormal increased platelet contributed to elevation of pulmonary artery pressure

OMI-VT stormに対するカテーテルアブレーション

A ６８-year-old woman with VT storm and frequent appropriate ICD therapy was referred for catheter ablation. Her past history was notable for aortic valve replacement by mechanical valve due to infectious endocarditis １７ years prior to presentation and left ventricular apical old myocardial infarction with unknown onset. At ６７ years old, She admitted to the prior hospital due to ventricular tachycardia with LBBB and superior axis at heart rate of ２１０ per minutes. Administration of amiodarone and magnesium sulfate was ineffective and cardioversion of ２００J was successfully terminated the tachycardia. Intra-cardiac defibrillator was implanted and the administration of amiodarone and mexiletine was started. ５ months after, she admitted to the hospital due to the frequent appropriate shock against the same ventricular tachycardia. Administration of lidocaine, sotalol, pilsicainide, and magnesium sulfate could not control the tachycardia and she was referred to our hospital for catheter ablation. During the first session, ventricular tachycardia was easily induced and electroanatomical mapping was performed both during tachycardia and during sinus rhythm. Late diastolic potential preceding the onset of QRS wave by ４５ms was detected at the infero-septal side of the apical aneurysm. ７．５s of the RF energy application at this site could terminate the tachycardia and thereafter no ventricular tachycardia was induced. But after dose-reduction or cessation of some anti-arrhythmic drugs, ventricular tachycardia was recurred and second session was performed. This time, no ventricular tachycardia was induced, then we performed isthmus transection and core isolation against the apical aneurysm. Thereafter no ventricular tachycardia was occurred in spite of dose-reduction or cessation of some anti-arrhythmic drugs

A stronger LP bound for formula size lower bounds via clique constraints

We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan and the theory of stable set polytopes. We apply it to majority functions and prove their formula size lower bounds improved from the classical result of Khrapchenko. Moreover, we introduce a notion of unbalanced recursive ternary majority functions motivated by a decomposition theory of monotone self-dual functions and give matching upper and lower bounds of their formula size. We also show monotone formula size lower bounds of balanced recursive ternary majority functions improved from the quantum adversary bound of Laplante, Lee and Szegedy