Formalizing Moessner's theorem and generalizations in Nuprl

Moessner's theorem describes a procedure for generating a sequence of n integer sequences that lead unexpectedly to the sequence of nth powers 1^{n}, 2^{n}, 3^{n},...Several generalizations of Moessner's theorem exist. Recently, Kozen and Silva gave an algebraic proof of a general theorem that subsumes Moessner's original theorem and its known generalizations. In this note, we describe the formalization of this theorem that the first author did in Nuprl. On the one hand, the formalization remains remarkably close to the original proof. On the other hand, it leads to new insights in the proof, pointing to small gaps and ambiguities that would never raise any objections in pen and pencil proofs, but which must be resolved in machine formalization

Orbit transfer rocket engine integrated control and health monitoring system technology readiness assessment

The objectives of this task were to: (1) estimate the technology readiness of an integrated control and health monitoring (ICHM) system for the Aerojet 7500 lbF Orbit Transfer Vehicle engine preliminary design assuming space based operations; and (2) estimate the remaining cost to advance this technology to a NASA defined 'readiness level 6' by 1996 wherein the technology has been demonstrated with a system validation model in a simulated environment. The work was accomplished through the conduct of four subtasks. In subtask 1 the minimally required functions for the control and monitoring system was specified. The elements required to perform these functions were specified in Subtask 2. In Subtask 3, the technology readiness level of each element was assessed. Finally, in Subtask 4, the development cost and schedule requirements were estimated for bringing each element to 'readiness level 6'

CX3CL1 reduces neurotoxicity and microglial activation in a rat model of Parkinson\u27s disease

BACKGROUND: Parkinson\u27s disease is characterized by a progressive loss of dopaminergic neurons in the substantia nigra. The cause of the neurodegeneration is unknown. Neuroinflammation has been clearly shown in Parkinson\u27s disease and may be involved in the progressive nature of the disease. Microglia are capable of producing neuronal damage through the production of bioactive molecules such as cytokines, as well as reactive oxygen species (ROS), and nitric oxide (NO). The inflammatory response in the brain is tightly regulated at multiple levels. One form of immune regulation occurs via neurons. Fractalkine (CX3CL1), produced by neurons, suppresses the activation of microglia. CX3CL1 is constitutively expressed. It is not known if addition of exogenous CX3CL1 beyond otherwise physiologically normal levels could decrease microglia activation and thereby minimize the secondary neurodegeneration following a neurotoxic insult. METHODS: The intrastriatal 6-hydroxydopamine (6-OHDA) rat model of Parkinson disease, was used to test the hypothesis that exogenous CX3CL1 could be neuroprotective. Treatment with recombinant CX3CL1 was delivered to the striatum by an osmotic minipump for 28 days beginning 7 days after the initial insult. Unbiased stereological methods were used to quantify the lesion size in the striatum, the amount of neuronal loss in the substantia nigra, and the amount of microglia activation. RESULTS: As hypothesized, CX3CL1 was able to suppress this microglia activation. The reduced microglia activation was found to be neuroprotective as the CX3CL1 treated rats had a smaller lesion volume in the striatum and importantly significantly fewer neurons were lost in the CX3CL1 treated rats. CONCLUSION: These findings demonstrated that CX3CL1 plays a neuroprotective role in 6-OHDA-induced dopaminergic lesion and it might be an effective therapeutic target for many neurodegenerative diseases, including Parkinson disease and Alzheimer disease, where inflammation plays an important role

CX3CL1 reduces neurotoxicity and microglial activation in a rat model of Parkinson\u27s disease

BACKGROUND: Parkinson\u27s disease is characterized by a progressive loss of dopaminergic neurons in the substantia nigra. The cause of the neurodegeneration is unknown. Neuroinflammation has been clearly shown in Parkinson\u27s disease and may be involved in the progressive nature of the disease. Microglia are capable of producing neuronal damage through the production of bioactive molecules such as cytokines, as well as reactive oxygen species (ROS), and nitric oxide (NO). The inflammatory response in the brain is tightly regulated at multiple levels. One form of immune regulation occurs via neurons. Fractalkine (CX3CL1), produced by neurons, suppresses the activation of microglia. CX3CL1 is constitutively expressed. It is not known if addition of exogenous CX3CL1 beyond otherwise physiologically normal levels could decrease microglia activation and thereby minimize the secondary neurodegeneration following a neurotoxic insult. METHODS: The intrastriatal 6-hydroxydopamine (6-OHDA) rat model of Parkinson disease, was used to test the hypothesis that exogenous CX3CL1 could be neuroprotective. Treatment with recombinant CX3CL1 was delivered to the striatum by an osmotic minipump for 28 days beginning 7 days after the initial insult. Unbiased stereological methods were used to quantify the lesion size in the striatum, the amount of neuronal loss in the substantia nigra, and the amount of microglia activation. RESULTS: As hypothesized, CX3CL1 was able to suppress this microglia activation. The reduced microglia activation was found to be neuroprotective as the CX3CL1 treated rats had a smaller lesion volume in the striatum and importantly significantly fewer neurons were lost in the CX3CL1 treated rats. CONCLUSION: These findings demonstrated that CX3CL1 plays a neuroprotective role in 6-OHDA-induced dopaminergic lesion and it might be an effective therapeutic target for many neurodegenerative diseases, including Parkinson disease and Alzheimer disease, where inflammation plays an important role

Pulvinar Projections to the Striatum and Amygdala in the Tree Shrew

Visually guided movement is possible in the absence of conscious visual perception, a phenomenon referred to as “blindsight.” Similarly, fearful images can elicit emotional responses in the absence of their conscious perception. Both capabilities are thought to be mediated by pathways from the retina through the superior colliculus (SC) and pulvinar nucleus. To define potential pathways that underlie behavioral responses to unperceived visual stimuli, we examined the projections from the pulvinar nucleus to the striatum and amygdala in the tree shrew (Tupaia belangeri), a species considered to be a prototypical primate. The tree shrew brain has a large pulvinar nucleus that contains two SC-recipient subdivisions; the dorsal (Pd) and central (Pc) pulvinar both receive topographic (“specific”) projections from SC, and Pd receives an additional non-topographic (“diffuse”) projection from SC (Chomsung et al., 2008). Anterograde and retrograde tract tracing revealed that both Pd and Pc project to the caudate and putamen, and Pd, but not Pc, additionally projects to the lateral amygdala. Using immunocytochemical staining for substance P (SP) and parvalbumin (PV) to reveal the patch/matrix organization of tree shrew striatum, we found that SP-rich/PV-poor patches interlock with a PV-rich/SP-poor matrix. Confocal microscopy revealed that tracer-labeled pulvino-striatal terminals preferentially innervate the matrix. Electron microscopy revealed that the postsynaptic targets of tracer-labeled pulvino-striatal and pulvino-amygdala terminals are spines, demonstrating that the pulvinar nucleus projects to the spiny output cells of the striatum matrix and the lateral amygdala, potentially relaying: (1) topographic visual information from SC to striatum to aid in guiding precise movements, and (2) non-topographic visual information from SC to the amygdala alerting the animal to potentially dangerous visual images

Oak Ridge National Laboratory West End Treatment Facility simulated sludge vitrification demonstration, Revision 1

Technologies are being developed by the US Department of Energy`s (DOE) Nuclear Facility sites to convert hazardous and mixed wastes to a form suitable for permanent disposal. Vitrification, which has been declared the Best Demonstrated Available Technology for high-level radioactive waste disposal by the EPA, is capable of producing a highly durable wasteform that minimizes disposal volumes through organic destruction, moisture evaporation, and porosity reduction. However, this technology must be demonstrated over a range of waste characteristics, including compositions, chemistries, moistures, and physical characteristics to ensure that it is suitable for hazardous and mixed waste treatment. These wastes are typically wastewater treatment sludges that are categorized as listed wastes due to the process origin or organic solvent content, and usually contain only small amounts of hazardous constituents. The Oak Ridge National Laboratory`s (ORNL) West End Treatment Facility`s (WETF) sludge is considered on of these representative wastes. The WETF is a liquid waste processing plant that generates sludge from the biodenitrification and precipitation processes. An alternative wasteform is needed since the waste is currently stored in epoxy coated carbon steel tanks, which have a limited life. Since this waste has characteristics that make it suitable for vitrification with a high likelihood of success, it was identified as a suitable candidate by the Mixed Waste Integrated Program (MWIP) for testing at CU. The areas of special interest with this sludge are (1) minimum nitrates, (2) organic destruction, and (3) waste water treatment sludges containing little or no filter aid

Implementation of outpatient total joint arthroplasty in canada: Where we are and where we need to go

© 2020 Zomar et al. Total joint arthroplasties (TJA) are successful procedures for the treatment of end-stage hip and knee arthritis. Length of stay in hospitals after these procedures has been steadily decreasing over time, with outpatient procedures (discharge on the same day as surgery) introduced in the US within the last 20 years. Reducing length of stay after TJA can provide cost savings. Centres in Canada have started to utilize outpatient TJA procedures, but we have identified some barriers that may have limited their implementation. We have summarized the current literature for outpatient TJA and discussed potential solutions for the current barriers

Peripheral injection of human umbilical cord blood stimulates neurogenesis in the aged rat brain

<p>Abstract</p> <p>Background</p> <p>Neurogenesis continues to occur throughout life but dramatically decreases with increasing age. This decrease is mostly related to a decline in proliferative activity as a result of an impoverishment of the microenvironment of the aged brain, including a reduction in trophic factors and increased inflammation.</p> <p>Results</p> <p>We determined that human umbilical cord blood mononuclear cells (UCBMC) given peripherally, by an intravenous injection, could rejuvenate the proliferative activity of the aged neural stem/progenitor cells. This increase in proliferation lasted for at least 15 days after the delivery of the UCBMC. Along with the increase in proliferation following UCBMC treatment, an increase in neurogenesis was also found in the aged animals. The increase in neurogenesis as a result of UCBMC treatment seemed to be due to a decrease in inflammation, as a decrease in the number of activated microglia was found and this decrease correlated with the increase in neurogenesis.</p> <p>Conclusion</p> <p>The results demonstrate that a single intravenous injection of UCBMC in aged rats can significantly improve the microenvironment of the aged hippocampus and rejuvenate the aged neural stem/progenitor cells. Our results raise the possibility of a peripherally administered cell therapy as an effective approach to improve the microenvironment of the aged brain.</p

Four patients with a history of acute exacerbations of COPD: implementing the CHEST/Canadian Thoracic Society guidelines for preventing exacerbations

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Factor Varieties and Symbolic Computation

We propose an algebraization of classical and non-classical logics, based on factor varieties and decomposition operators. In particular, we provide a new method for determining whether a propositional formula is a tautology or a contradiction. This method can be autom-atized by defining a term rewriting system that enjoys confluence and strong normalization. This also suggests an original notion of logical gate and circuit, where propositional variables becomes logical gates and logical operations are implemented by substitution. Concerning formulas with quantifiers, we present a simple algorithm based on factor varieties for reducing first-order classical logic to equational logic. We achieve a completeness result for first-order classical logic without requiring any additional structure