Intersections of homogeneous Cantor sets and beta-expansions

Let $\Gamma_{\beta,N}$ be the $N$-part homogeneous Cantor set with $\beta\in(1/(2N-1),1/N)$. Any string $(j_\ell)_{\ell=1}^\N$ with $j_\ell\in\{0,\pm 1,...,\pm(N-1)\}$ such that $t=\sum_{\ell=1}^\N j_\ell\beta^{\ell-1}(1-\beta)/(N-1)$ is called a code of $t$. Let $\mathcal{U}_{\beta,\pm N}$ be the set of $t\in[-1,1]$ having a unique code, and let $\mathcal{S}_{\beta,\pm N}$ be the set of $t\in\mathcal{U}_{\beta,\pm N}$ which make the intersection $\Gamma_{\beta,N}\cap(\Gamma_{\beta,N}+t)$ a self-similar set. We characterize the set $\mathcal{U}_{\beta,\pm N}$ in a geometrical and algebraical way, and give a sufficient and necessary condition for $t\in\mathcal{S}_{\beta,\pm N}$. Using techniques from beta-expansions, we show that there is a critical point $\beta_c\in(1/(2N-1),1/N)$, which is a transcendental number, such that $\mathcal{U}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\beta_c)$, and contains countably infinite many elements if $\beta\in(\beta_c,1/N)$. Moreover, there exists a second critical point $\alpha_c=\big[N+1-\sqrt{(N-1)(N+3)}\,\big]/2\in(1/(2N-1),\beta_c)$ such that $\mathcal{S}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\alpha_c)$, and contains countably infinite many elements if $\beta\in[\alpha_c,1/N)$.Comment: 23 pages, 4 figure

Soft-tissue evidence for homeothermy and crypsis in a Jurassic ichthyosaur

Ichthyosaurs are extinct marine reptiles that display a notable external similarity to modern toothed whales. Here we show that this resemblance is more than skin deep. We apply a multidisciplinary experimental approach to characterize the cellular and molecular composition of integumental tissues in an exceptionally preserved specimen of the Early Jurassic ichthyosaur Stenopterygius. Our analyses recovered still-flexible remnants of the original scaleless skin, which comprises morphologically distinct epidermal and dermal layers. These are underlain by insulating blubber that would have augmented streamlining, buoyancy and homeothermy. Additionally, we identify endogenous proteinaceous and lipid constituents, together with keratinocytes and branched melanophores that contain eumelanin pigment. Distributional variation of melanophores across the body suggests countershading, possibly enhanced by physiological adjustments of colour to enable photoprotection, concealment and/or thermoregulation. Convergence of ichthyosaurs with extant marine amniotes thus extends to the ultrastructural and molecular levels, reflecting the omnipresent constraints of their shared adaptation to pelagic life

Downregulation of TGF-beta receptor types II and III in oral squamous cell carcinoma and oral carcinoma-associated fibroblasts

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to assess the expression levels for TβRI, TβRII, and TβRIII in epithelial layers of oral premalignant lesions (oral leukoplakia, OLK) and oral squamous cell carcinoma (OSCC), as well as in oral carcinoma-associated fibroblasts (CAFs), with the final goal of exploring the roles of various types of TβRs in carcinogenesis of oral mucosa.</p> <p>Methods</p> <p>Normal oral tissues, OLK, and OSCC were obtained from 138 previously untreated patients. Seven primary human oral CAF lines and six primary normal fibroblast (NF) lines were established successfully via cell culture. The three receptors were detected using immunohistochemical (IHC), quantitative RT-PCR, and Western blot approaches.</p> <p>Results</p> <p>IHC signals for TβRII and TβRIII in the epithelial layer decreased in tissue samples with increasing disease aggressiveness (P < 0.05); no expression differences were observed for TβRI, in OLK and OSCC (P > 0.05); and TβRII and TβRIII were significantly downregulated in CAFs compared with NFs, at the mRNA and protein levels (P < 0.05). Exogenous expression of TGF-β1 led to a remarkable decrease in the expression of TβRII and TβRIII in CAFs (P < 0.05).</p> <p>Conclusion</p> <p>This study provides the first evidence that the loss of TβRII and TβRIII expression in oral epithelium and stroma is a common event in OSCC. The restoration of the expression of TβRII and TβRIII in oral cancerous tissues may represent a novel strategy for the treatment of oral carcinoma.</p

Regional projection of climate warming effects on coastal seas in east China

The coastal region in east China experiences massive anthropogenic eutrophication, and the bottom water off the Changjiang River Estuary in the East China Sea faces the threat of severe seasonal hypoxia. We find that projected future climate changes will work in parallel with anthropogenic eutrophication to exacerbate current hypoxia and increase shelf vulnerability to bottom hypoxia. We use a coupled physical-biogeochemical regional model to investigate the differences of shelf hydrography and oxygen dynamics between present and future projected states. Model results indicate that the Yellow Sea Cold Water Mass which plays essential roles in nekton migration and shellfish farming practically disappears by the end of the 21st century, and shelf vertical stratification strengthens by an average of 12.7%. Hypoxia off the Changjiang River Estuary is exacerbated with increased (by one month) hypoxia duration, lower dissolved oxygen minima, and significant lateral (202%) and vertical (60%) expansions of hypoxic water. Reduced oxygen solubility, and accelerated oxygen consumption under increased primary production and rising water temperature contribute 42% and 58%, respectively, of bottom dissolved oxygen decrease in the East China Sea. Model results also show increased vertical diffusion of oxygen, despite vertical stratification strengthening, due to increased surface-bottom oxygen concentration gradient associated with increased oxygen release in surface water and exacerbated oxygen consumption in subsurface water

Paleoproteomics of Mesozoic Dinosaurs and Other Mesozoic Fossils

Molecular studies have contributed greatly to our understanding of evolutionary processes that act upon virtually every aspect of living organisms. However, these studies are limited with regard to extinct organisms, particularly those from the Mesozoic because fossils pose unique challenges to molecular workflows, and because prevailing wisdom suggests no endogenous molecular components can persist into deep time. Here, the power and potential of a molecular approach to Mesozoic fossils is discussed. Molecular methods that have been applied to Mesozoic fossils—including iconic, non-avian dinosaurs— and the challenges inherent in such analyses, are compared and evaluated. Taphonomic processes resulting in the transition of living organisms from the biosphere into the fossil record are reviewed, and the possible effects of taphonomic alteration on downstream analyses that can be problematic for very old material (e.g., molecular modifications, limitations of on comparative databases) are addressed. Molecular studies applied to ancient remains are placed in historical context, and past and current studies are evaluated with respect to producing phylogenetically and/or evolutionarily significant data. Finally, some criteria for assessing the presence of endogenous biomolecules in very ancient fossil remains are suggested as a starting framework for such studies

A novel allosteric inhibitor of the uridine diphosphate N-acetylglucosamine pyrophosphorylase from Trypanosoma brucei.

Uridine diphosphate N-acetylglucosamine pyrophosphorylase (UAP) catalyzes the final reaction in the biosynthesis of UDP-GlcNAc, an essential metabolite in many organisms including Trypanosoma brucei, the etiological agent of Human African Trypanosomiasis. High-throughput screening of recombinant T. brucei UAP identified a UTP-competitive inhibitor with selectivity over the human counterpart despite the high level of conservation of active site residues. Biophysical characterization of the UAP enzyme kinetics revealed that the human and trypanosome enzymes both display a strictly ordered bi−bi mechanism, but with the order of substrate binding reversed. Structural characterization of the T. brucei UAP−inhibitor complex revealed that the inhibitor binds at an allosteric site absent in the human homologue that prevents the conformational rearrangement required to bind UTP. The identification of a selective inhibitory allosteric binding site in the parasite enzyme has therapeutic potential