Matrix Multiplication and Number on the Forehead Communication

Three-player Number On the Forehead communication may be thought of as a three-player Number In the Hand promise model, in which each player is given the inputs that are supposedly on the other two players\u27 heads, and promised that they are consistent with the inputs of the other players. The set of all allowed inputs under this promise may be thought of as an order-3 tensor. We surprisingly observe that this tensor is exactly the matrix multiplication tensor, which is widely studied in the design of fast matrix multiplication algorithms. Using this connection, we prove a number of results about both Number On the Forehead communication and matrix multiplication, each by using known results or techniques about the other. For example, we show how the Laser method, a key technique used to design the best matrix multiplication algorithms, can also be used to design communication protocols for a variety of problems. We also show how known lower bounds for Number On the Forehead communication can be used to bound properties of the matrix multiplication tensor such as its zeroing out subrank. Finally, we substantially generalize known methods based on slice-rank for studying communication, and show how they directly relate to the matrix multiplication exponent ?

Discrete Painlevé equations from Y-systems

We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free T-systems) were described in the work of Fordy and Marsh, who completely classified all such quivers in the case of period 1, and characterized them in terms of the skew-symmetric exchange matrix B that defines the quiver. A broader notion of periodicity in general cluster algebras was introduced by Nakanishi, who also described the corresponding Y-systems, and T-systems with coefficients. A result of Fomin and Zelevinsky says that the coefficient-free T-system provides a solution of the Y-system. In this paper, we show that in general there is a discrepancy between these two systems, in the sense that the solution of the former does not correspond to the general solution of the latter. This discrepancy is removed by introducing additional non-autonomous coefficients into the T-system. In particular, we focus on the period 1 case and show that, when the exchange matrix B is degenerate, discrete Painlev\'e equations can arise from this construction

Oxidation of alloys targeted for advanced steam turbines

Ultra supercritical (USC) power plants offer the promise of higher efficiencies and lower emissions. Current goals of the U.S. Department of Energy’s Advanced Power Systems Initiatives include coal generation at 60% efficiency, which would require steam temperatures of up to 760°C. This research examines the steamside oxidation of alloys for use in USC systems, with emphasis placed on applications in high- and intermediate-pressure turbines

Corrosion Performance of Ferritic Steel for SOFC Interconnect Applications

Ferritic stainless steels have been identified as potential candidates for interconnects in planar-type solid oxide fuel cells (SOFC) operating below 800ºC. Crofer 22 APU was selected for this study. It was studied under simulated SOFC-interconnect dual environment conditions with humidified air on one side of the sample and humidified hydrogen on the other side at 750ºC. The surfaces of the oxidized samples were studied by scanning electron microscopy (SEM) equipped with microanalytical capabilities. X-ray diffraction (XRD) analysis was also used in this study

Determination of Stromal Signatures in Breast Carcinoma

Many soft tissue tumors recapitulate features of normal connective tissue. We hypothesize that different types of fibroblastic tumors are representative of different populations of fibroblastic cells or different activation states of these cells. We examined two tumors with fibroblastic features, solitary fibrous tumor (SFT) and desmoid-type fibromatosis (DTF), by DNA microarray analysis and found that they have very different expression profiles, including significant differences in their patterns of expression of extracellular matrix genes and growth factors. Using immunohistochemistry and in situ hybridization on a tissue microarray, we found that genes specific for these two tumors have mutually specific expression in the stroma of nonneoplastic tissues. We defined a set of 786 gene spots whose pattern of expression distinguishes SFT from DTF. In an analysis of DNA microarray gene expression data from 295 previously published breast carcinomas, we found that expression of this gene set defined two groups of breast carcinomas with significant differences in overall survival. One of the groups had a favorable outcome and was defined by the expression of DTF genes. The other group of tumors had a poor prognosis and showed variable expression of genes enriched for SFT type. Our findings suggest that the host stromal response varies significantly among carcinomas and that gene expression patterns characteristic of soft tissue tumors can be used to discover new markers for normal connective tissue cells

Spina bifida-predisposing heterozygous mutations in Planar Cell Polarity genes and Zic2 reduce bone mass in young mice

Fractures are a common comorbidity in children with the neural tube defect (NTD) spina bifida. Mutations in the Wnt/planar cell polarity (PCP) pathway contribute to NTDs in humans and mice, but whether this pathway independently determines bone mass is poorly understood. Here, we first confirmed that core Wnt/PCP components are expressed in osteoblasts and osteoclasts in vitro. In vivo, we performed detailed µCT comparisons of bone structure in tibiae from young male mice heterozygous for NTD-associated mutations versus WT littermates. PCP signalling disruption caused by Vangl2 (Vangl2Lp/+) or Celsr1 (Celsr1Crsh/+) mutations significantly reduced trabecular bone mass and distal tibial cortical thickness. NTD-associated mutations in non-PCP transcription factors were also investigated. Pax3 mutation (Pax3Sp2H/+) had minimal effects on bone mass. Zic2 mutation (Zic2Ku/+) significantly altered the position of the tibia/fibula junction and diminished cortical bone in the proximal tibia. Beyond these genes, we bioinformatically documented the known extent of shared genetic networks between NTDs and bone properties. 46 genes involved in neural tube closure are annotated with bone-related ontologies. These findings document shared genetic networks between spina bifida risk and bone structure, including PCP components and Zic2. Genetic variants which predispose to spina bifida may therefore independently diminish bone mass

Invasion and MMP expression profile in desmoid tumours

Desmoid tumours are locally invasive soft tissue tumours in which beta-catenin mediated TCF-dependent transcription is activated. The role of soluble factors secreted by the myofibroblastic desmoid tumour, which could stimulate tumour invasiveness, was investigated. Using collagen gel invasion assays, the presence of factors stimulating invasion in desmoid conditioned media (CM) could be established. Since matrix metalloproteinases (MMPs) have been implicated in the process of tumoral invasion, the expression levels of the MMP family members were evaluated. Quantitative reverse transcription-PCR was used to determine the expression levels of MMP1, MMP2, MMP3, MMP7, MMP11, MMP12, MMP13, MMP14 and the inhibitors TIMP1, TIMP2 and TIMP3. Besides overexpression of MMP7, a known TCF-dependent target gene, a striking upregulation of the expression levels of MMP1, MMP3, MMP11, MMP12 and MMP13 in desmoid tumours, compared to unaffected fibroblasts from the same patients, was found. Treating the CM of desmoids with a synthetic and a physiologic MMP inhibitor reduced the invasion-stimulating capacity of the desmoid CM by approximately 50%. These results suggest the involvement of soluble factors, released by the desmoid cells, in stimulating invasion and implicate the MMPs as facilitators of invasion

Time Trends in the Incidence and Treatment of Extra-Abdominal and Abdominal Aggressive Fibromatosis: A Population-Based Study

BACKGROUND: Aggressive fibromatosis (AF) is a locally infiltrating soft-tissue tumor. In a population-based study in the Netherlands, we evaluated time trends for the incidence and treatment of AF. METHODS: In PALGA: Dutch Pathology Registry, all patients diagnosed between 1993 and 2013 as having extra-abdominal or abdominal wall aggressive fibromatosis were identified and available pathology data of the patients were evaluated. Epidemiological and treatment-related factors were analyzed with χ(2)and regression analysis. RESULTS: During the study period, 1134 patients were identified. The incidence increased from 2.10 to 5.36 per million people per year. Median age at the time of diagnosis increased annually by B 0.285 (P = 0.001). Female gender prevailed and increased over time [annual odds ratio (OR) 1.022; P = 0.058]. All anatomic localizations, but in particular truncal tumors, became more frequent. During the study period diagnostic histological biopsies were performed more often (annual OR 1.096; P < 0.001). The proportion of patients who underwent surgical treatment decreased (annual OR 0.928; P < 0.001). When resection was preceded by biopsy, 49.8 % of the patients had R0-resection versus 30.7 % in patients without biopsy (P < 0.001). CONCLUSIONS: In this population-based study, an increasing incidence of extra-abdominal and abdominal-wall aggressive fibromatosis was observed. The workup of patients improved and a trend towards a nonsurgical treatment policy was observed