Folding a Paper Strip to Minimize Thickness

In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to two metrics: minimizing the total number of layers in the folded state (so that a "flat folding" is indeed close to flat), and minimizing the total amount of paper required to execute the folding (where "thicker" creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove the first problem fixed-parameter tractable in 1D with respect to the number of layers.Comment: 9 pages, 7 figure

Single-Player and Two-Player Buttons & Scissors Games

We study the computational complexity of the Buttons \& Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for $C = 2$ colors but polytime solvable for $C = 1$. Similarly the game is NP-complete if every color is used by at most $F = 4$ buttons but polytime solvable for $F \leq 3$. We also consider restrictions on the board size, cut directions, and cut sizes. Finally, we introduce several natural two-player versions of the game and show that they are PSPACE-complete.Comment: 21 pages, 15 figures. Presented at JCDCG2 2015, Kyoto University, Kyoto, Japan, September 14 - 16, 201

Significant response of sunitinib for RCC

Introduction: A case of multiple liver metastases of clear cell RCC with a significant response to sunitinib as the fifth line after nivolumab is reported. Case presentation: The patient was a 65-year-old man who underwent open nephrectomy for RCC. After the nephrectomy, he had recurrences several times, and metastasectomy had been performed for each recurrence. At 13 years after the nephrectomy, multiple liver, and lung metastases appeared. The treatment was switched to axitinib, followed by cabozantinib, then nivolumab. The best response was PR, SD, and PD for these three drugs, and treatment duration was 14, 3, and 3 months, respectively. As the fifth line, sunitinib was administered, with significant shrinkage of the multiple liver metastases, and PR has been maintained for 34 months. Conclusion: Sunitinib after an IO-drug showed a significant effect in spite of only slight efficacy with other VEGFR-TKIs, which may have occurred through the alteration of the immunological microenvironment

Granulomatosis with Polyangiitis Localized in the Greater Omentum

Granulomatosis with polyangiitis (GPA) is known as anti-neutrophil cytoplasmic antibody- (ANCA-) associated small vessel vasculitis and typically manifests as pulmonary-renal syndrome, but the disease is not limited to pulmonary or renal systems. The inflammation can involve whole body organs. In addition, the ANCA titer does not always become positive. Here, we describe the case of a 91-year-old man who presented with umbilical pain and fever of unknown origin. Only the increased computed tomography value of the greater omentum suggested intra-abdominal inflammation; however, serological examinations, including the ANCA level, could not reveal the focus or cause of symptoms. Finally, the histopathological examination of specimens surgically excised from the greater omentum demonstrated GPA limited to the greater omentum. This report reminds physicians to consider GPA in the differential diagnosis of acute abdominal pain or fever of unknown origin

Critical roles of DDX31-mutp53-EGFR axis in MIBC progression

The p53 and EGFR pathways are frequently altered in bladder cancers, yet their contributions to its progression remain elusive. Here we report that DEAD box polypeptide 31 (DDX31) plays a critical role in the multistep progression of muscle invasive bladder cancer (MIBC) through its sequential interactions with mutant p53 (mutp53) and EGFR. In early MIBC cells, nuclear DDX31 bound mutp53/SP1 and enhanced mutp53 transcriptional activation, leading to migration and invasion of MIBC. Cytoplasmic DDX31 also bound EGFR and phospho-nucleolin (p-NCL) in advanced MIBC, leading to EGFR-Akt signaling activation. High expression of both cytoplasmic DDX31 and p53 proteins correlated with poor prognosis in patients with MIBC, and blocking the DDX31-NCL interaction resulted in downregulation of EGFR-Akt signaling, eliciting an in vivo anti-tumor effect against bladder cancer. These findings reveal that DDX31 cooperates with mutp53 and EGFR to promote progression of MIBC, and inhibition of DDX31-NCL formation may lead to potential treatment strategies for advanced MIBC

Folding a Paper Strip to Minimize Thickness

In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to twometrics:minimizing the total number of layers in the folded state (so that a “flat folding” is indeed close toflat), andminimizing the total amount of paper required to execute the folding (where “thicker” creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove the first problem fixed-parameter tractable in 1D with respect to the number of layers.National Science Foundation (U.S.). Origami Design for Integration of Self-assembling Systems for Engineering Innovation (grant EFRI- 124038)National Science Foundation (U.S.). Expedition grant (CCF-1138967)United States. Department of Defense. National Defense Science and Engineering Graduate (NDSEG) Fellowship (32 CFR 168a

Bumpy Pyramid Folding

We investigate folding problems for a class of petal polygons P, which have an n-polygonal base B surrounded by a sequence of triangles. We give linear time algorithms using constant precision to determine if P can fold to a pyramid with flat base B, and to determine a triangulation of B (crease pattern) that allows folding into a convex (triangulated) polyhedron. By Alexandrov's theorem, the crease pattern is unique if it exists, but the general algorithm known for this theorem is pseudo-polynomial, with very large running time; ours is the first efficient algorithm for Alexandrov's theorem for a special class of polyhedra. We also give a polynomial time algorithm that finds the crease pattern to produce the maximum volume triangulated polyhedron