Uniqueness of the embedding continuous convolution semigroup of a Gaussian probability measure on the affine group and an application in mathematical finance

Let {mu((i))(t)}(t >= 0) (i = 1, 2) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that mu((1))(1) = mu((2))(1). Assume furthermore that {mu((1))(t)}(t >= 0) is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then mu((1))(1) = mu((2))(1) for all t >= 0. We end up with a possible application in mathematical finance

A small-molecule antagonist of the β-catenin/TCF4 interaction blocks the self-renewal of cancer stem cells and suppresses tumorigenesis

Wnt/beta-catenin signaling is a highly conserved pathway essential for embryogenesis and tissue homeostasis. However, deregulation of this pathway can initiate and promote human malignancies, especially of the colon and head and neck. Therefore, Wnt/beta-catenin signaling represents an attractive target for cancer therapy. We performed high-throughput screening (HTS) using AlphaScreen and ELISA techniques to identify small molecules that disrupt the critical interaction between beta-catenin and the transcription factor TCF4 required for signal transduction. We found that compound LF3, a 4-thioureido-benzenesulfonamide derivative, robustly inhibited this interaction. Biochemical assays revealed clues that the core structure of LF3 was essential for inhibition. LF3 inhibited Wnt/beta-catenin signals in cells with exogenous reporters and in colon cancer cells with endogenously high Wnt activity. LF3 also suppressed features of cancer cells related to Wnt signaling, including high cell motility, cell cycle progression, and the overexpression of Wnt target genes. However, LF3 did not cause cell death or interfere with cadherin-mediated cell-cell adhesion. Remarkably, the self-renewal capacity of cancer stem cells was blocked by LF3 in concentration-dependent manners, as examined by sphere formation of colon and head and neck cancer stem cells under non-adherent conditions. Finally, LF3 reduced tumor growth and induced differentiation in a mouse xenograft model of colon cancer. Collectively, our results strongly suggest that LF3 is a specific inhibitor of canonical Wnt signaling with anticancer activity that warrants further development for preclinical and clinical studies as a novel cancer therapy

Machining metals and silicon with GHz bursts: Surprising tremendous reduction of the specific removal rate for surface texturing applications

Bursts of 230 fs pulses with up to 25 pulses having a time spacing of 180 ps were applied to steel AISI304, copper DHP, brass and silicon in real surface texturing (milling) application by machining squares. The previously reported very high removal rates for GHz bursts could not be confirmed, on the contrary, the specific removal rate tremendously drops down to less than 10% for the metals and 25% for silicon when the number of pulses per burst is increased. This drop is fully in line with shielding effects already observed in case of MHz pulses and double pulse experiments. The increase of the number of pulses per burst directly goes with strongly increased melting effects which are assumed to additionally re-fill the already machined areas in this milling application. Calorimetric experiments show an increasing residual heat with higher number of pulses per burst. Further the removal rates of the GHz bursts directly follow the tendency of single pulses of identical duration. This fosters the hypothesis that in case of metals and silicon only melting and melt ejection lead to the high reported removal rates for GHz bursts in punching applications and that no additional "ablation cooling" effect is taking place

The decline of water hyacinth on Lake Victoria was due to biological control by Neochetina spp

There has been some debate recently about the cause of the decline of water hyacinth on Lake Victoria. While much of this evidence points to classical biological control as the major factor, the El Niño associated weather pattern of the last quarter of 1997 and the first half of 1998 has confused the issue. We argue first that the reductions in water hyacinth on Lake Victoria were ultimately caused by the widespread and significant damage to plants by Neochetina spp., although this process was increased by the stormy weather associated with the El Niño event; second that increased waves and current on Lake Victoria caused by El Niño redistributed water hyacinth plants around the lake; and third that a major lake-wide resurgence of water hyacinth plants on Lake Victoria has not occurred and will not occur unless the weevil populations are disrupted. We conclude that the population crash of water hyacinth on Lake Victoria would not have occurred in the absence of the weevils, but that it may have been hastened by stormy weather associated with the El Niño event

Generalized probabilities taking values in non-Archimedean fields and topological groups

We develop an analogue of probability theory for probabilities taking values in topological groups. We generalize Kolmogorov's method of axiomatization of probability theory: main distinguishing features of frequency probabilities are taken as axioms in the measure-theoretic approach. We also present a review of non-Kolmogorovian probabilistic models including models with negative, complex, and $p$-adic valued probabilities. The latter model is discussed in details. The introduction of $p$-adic (as well as more general non-Archimedean) probabilities is one of the main motivations for consideration of generalized probabilities taking values in topological groups which are distinct from the field of real numbers. We discuss applications of non-Kolmogorovian models in physics and cognitive sciences. An important part of this paper is devoted to statistical interpretation of probabilities taking values in topological groups (and in particular in non-Archimedean fields)

Insights into the regulation of DMSP synthesis in the diatom Thalassiosira pseudonana through APR activity, proteomics and gene expression analyses on cells acclimating to changes in salinity, light and nitrogen

Despite the importance of dimethylsulphoniopropionate (DMSP) in the global sulphur cycle and climate regulation, the biological pathways underpinning its synthesis in marine phytoplankton remain poorly understood. The intracellular concentration of DMSP increases with increased salinity, increased light intensity and nitrogen starvation in the diatom Thalassiosira pseudonana. We used these conditions to investigate DMSP synthesis at the cellular level via analysis of enzyme activity, gene expression and proteome comparison. The activity of the key sulphur assimilatory enzyme, adenosine 5′- phosphosulphate reductase was not coordinated with increasing intracellular DMSP concentration. Under all three treatments coordination in the expression of sulphur assimilation genes was limited to increases in sulphite reductase transcripts. Similarly, proteomic 2D gel analysis only revealed an increase in phosphoenolpyruvate carboxylase following increases in DMSP concentration. Our findings suggest that increased sulphur assimilation might not be required for increased DMSP synthesis, instead the availability of carbon and nitrogen substrates may be important in the regulation of this pathway. This contrasts with the regulation of sulphur metabolism in higher plants, which generally involves upregulation of several sulphur assimilatory enzymes. In T. pseudonana changes relating to sulphur metabolism were specific to the individual treatments and, given that little coordination was seen in transcript and protein responses across the three growth conditions, different patterns of regulation might be responsible for the increase in DMSP concentration seen under each treatment

Loss-of-function uORF mutations in human malignancies

Ribosome profiling revealed widespread translational activity at upstream open reading frames (uORFs) and validated uORF-mediated translational control as a commonly repressive mechanism of gene expression. Translational activation of proto-oncogenes through loss-of-uORF mutations has been demonstrated, yet a systematic search for cancer-associated genetic alterations in uORFs is lacking. Here, we applied a PCR-based, multiplex identifier-tagged deep sequencing approach to screen 404 uORF translation initiation sites of 83 human tyrosine kinases and 49 other proto-oncogenes in 308 human malignancies. We identified loss-of-function uORF mutations in EPHB1 in two samples derived from breast and colon cancer, and in MAP2K6 in a sample of colon adenocarcinoma. Both mutations were associated with enhanced translation, suggesting that loss-of-uORF-mediated translational induction of the downstream main protein coding sequence may have contributed to carcinogenesis. Computational analysis of whole exome sequencing datasets of 464 colon adenocarcinomas subsequently revealed another 53 non-recurrent somatic mutations functionally deleting 22 uORF initiation and 31 uORF termination codons, respectively. These data provide evidence for somatic mutations affecting uORF initiation and termination codons in human cancer. The insufficient coverage of uORF regions in current whole exome sequencing datasets demands for future genome-wide analyses to ultimately define the contribution of uORF-mediated translational deregulation in oncogenesis