147 research outputs found

    Checkerboard Julia Sets for Rational Maps

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    In this paper, we consider the family of rational maps \F(z) = z^n + \frac{\la}{z^d}, where n2n \geq 2, d1d\geq 1, and\la \in \bbC. We consider the case where \la lies in the main cardioid of one of the n1n-1 principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic. However, two such maps \F and FμF_\mu are conjugate on these Julia sets only if the parameters at the centers of the given cardioids satisfy \mu = \nu^{j(d+1)}\la or \mu = \nu^{j(d+1)}\bar{\la} where j \in \bbZ and ν\nu is an n1stn-1^{\rm st} root of unity. We define a dynamical invariant, which we call the minimal rotation number. It determines which of these maps are are conjugate on their Julia sets, and we obtain an exact count of the number of distinct conjugacy classes of maps drawn from these main cardioids.Comment: 25 pages, 14 figures; Changes since March 19 version: added nine figures, fixed one proof, added a section on a group actio

    Які соціально-економічні наслідки матиме скасування мораторію на продаж земель сільськогосподарського призначення в Україні?

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    This study investigated the long-term effects of total and partial replacement of dietary fish meal (FM) by a mixture of agricultural products on sperm quality of African catfish Clarias gariepinus. Four isonitrogenous and isoenergetic diets were formulated containing graded levels of either 50% FM and maize meal (diet 1); 25% FM mixed with crude sunflower oil cake (SFOC) and bean meal (BM) (diet 2); 12.5% FM mixed with sunflower oil cake, BM and ground nut oil cake (GOC) (diet 3) and 0% FM mixed with de-hulled sunflower oil cake (SFOCD), BM and ground nut oil cake (diet 4). Gonadosomatic index (GSI), sperm quality, plasma sex steroids (11-keto testosterone [11-KT]; testosterone [T]; estradiol-17beta [E2]) were evaluated on 10 to 24 fish fed on each diet. Sperm quality was assessed using computer-assisted sperm analysis (CASA). Total replacement of fish meal by plant products markedly increased sperm volume, spermatocrit, spermatozoa integrity, and sperm motility. Fish fed diet 3 (12.5% fish meal) provided intermediate results on sperm quality whereas the lowest values were obtained in fish fed diets 1 and 2. In fish fed 0% fish meal (diet 4), androgen levels were higher and estrogen levels were lower than in fish fed fish meal diets. Based on dietary lipid and fatty acid analyses, these results suggest a positive impact of short chain n-6 fatty acids on androgen synthesis and sperm quality. In conclusion, a combination of ground nut oil cake, bean meal and sunflower oil cake (preferably when the sunflower is dehulled) in African catfish diet improves the sperm quality

    The Maine Annex, vol. 2, no. 3

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    The Maine Annex covered a campus visit and presentation by Comander Donald B. MacMillan featuring his Kodachrome motion pictures

    The Maine Annex, vol. 2, no. 7

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    The Maine Annex, covers pre-holiday celebrations and events including the Maine Masque production of the play State of the Union featuring Carol Besse, Bob Townsend, Beatrice Hanson, George Morse, Emile Genest, and George Phocas

    Alzheimer\u27s Therapeutics Targeting Amyloid Beta 1–42 Oligomers II: Sigma-2/PGRMC1 Receptors Mediate Abeta 42 Oligomer Binding and Synaptotoxicity

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    Amyloid beta (Abeta) 1-42 oligomers accumulate in brains of patients with Mild Cognitive Impairment (MCI) and disrupt synaptic plasticity processes that underlie memory formation. Synaptic binding of Abeta oligomers to several putative receptor proteins is reported to inhibit long-term potentiation, affect membrane trafficking and induce reversible spine loss in neurons, leading to impaired cognitive performance and ultimately to anterograde amnesia in the early stages of Alzheimer\u27s disease (AD). We have identified a receptor not previously associated with AD that mediates the binding of Abeta oligomers to neurons, and describe novel therapeutic antagonists of this receptor capable of blocking Abeta toxic effects on synapses in vitro and cognitive deficits in vivo. Knockdown of sigma-2/PGRMC1 (progesterone receptor membrane component 1) protein expression in vitro using siRNA results in a highly correlated reduction in binding of exogenous Abeta oligomers to neurons of more than 90%. Expression of sigma-2/PGRMC1 is upregulated in vitro by treatment with Abeta oligomers, and is dysregulated in Alzheimer\u27s disease patients\u27 brain compared to age-matched, normal individuals. Specific, high affinity small molecule receptor antagonists and antibodies raised against specific regions on this receptor can displace synthetic Abeta oligomer binding to synaptic puncta in vitro and displace endogenous human AD patient oligomers from brain tissue sections in a dose-dependent manner. These receptor antagonists prevent and reverse the effects of Abeta oligomers on membrane trafficking and synapse loss in vitro and cognitive deficits in AD mouse models. These findings suggest sigma-2/PGRMC1 receptors mediate saturable oligomer binding to synaptic puncta on neurons and that brain penetrant, small molecules can displace endogenous and synthetic oligomers and improve cognitive deficits in AD models. We propose that sigma-2/PGRMC1 is a key mediator of the pathological effects of Abeta oligomers in AD and is a tractable target for small molecule disease-modifying therapeutics

    On systems and control approaches to therapeutic gain

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    BACKGROUND: Mathematical models of cancer relevant processes are being developed at an increasing rate. Conceptual frameworks are needed to support new treatment designs based on such models. METHODS: A modern control perspective is used to formulate two therapeutic gain strategies. RESULTS: Two conceptually distinct therapeutic gain strategies are provided. The first is direct in that its goal is to kill cancer cells more so than normal cells, the second is indirect in that its goal is to achieve implicit therapeutic gains by transferring states of cancer cells of non-curable cases to a target state defined by the cancer cells of curable cases. The direct strategy requires models that connect anti-cancer agents to an endpoint that is modulated by the cause of the cancer and that correlates with cell death. It is an abstraction of a strategy for treating mismatch repair (MMR) deficient cancers with iodinated uridine (IUdR); IU-DNA correlates with radiation induced cell killing and MMR modulates the relationship between IUdR and IU-DNA because loss of MMR decreases the removal of IU from the DNA. The second strategy is indirect. It assumes that non-curable patient outcomes will improve if the states of their malignant cells are first transferred toward a state that is similar to that of a curable patient. This strategy is difficult to employ because it requires a model that relates drugs to determinants of differences in patient survival times. It is an abstraction of a strategy for treating BCR-ABL pro-B cell childhood leukemia patients using curable cases as the guides. CONCLUSION: Cancer therapeutic gain problem formulations define the purpose, and thus the scope, of cancer process modeling. Their abstractions facilitate considerations of alternative treatment strategies and support syntheses of learning experiences across different cancers
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