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Suppose that G is a finite group and let H be a proper subgroup of G. Then the restriction map from the characters of G to the characters of H is never injective.
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We prove a normalized version of the restricted invertibility principle obtained by Spielman and Srivastava in [An elementary proof of the restricted invertibility theorem. Israel J. Math. 190 (2012), 83-91]. Applying this result,...
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We prove a normalized version of the restricted invertibility principle obtained by Spielman and Srivastava in [An elementary proof of the restricted invertibility theorem. Israel J. Math. 190 (2012), 83-91]. Applying this result, we get a new proof of the proportional Dvoretzky-Rogers factorization theorem recovering the best current estimate in the symmetric setting while we improve the best known result in the non-symmetric case. As a consequence, we slightly improve the estimate for the Banach-Mazur distance to the cube: the distance of every ndimensional normed space from ?_∞~n is at most (2n)~(5/6). Finally, using tools from the work of Batson et al in [Twice-Ramanujan sparsifiers. In STOC'09 - Proceedings of the 2009 ACM International Symposium on Theory of Computing, ACM (New York, 2009), 255-262], we give a new proof for a theorem of Kashin and Tzafriri [Some remarks on the restriction of operators to coordinate subspaces. Preprint, 1993] on the norm of restricted matrices.
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Almost exactly 100 years ago Osborne and colleagues demonstrated that restricting the food intake of a small number of female rats extended their lifespan. In the 1930s experiments on the impact of diet on lifespan were extended b...
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Almost exactly 100 years ago Osborne and colleagues demonstrated that restricting the food intake of a small number of female rats extended their lifespan. In the 1930s experiments on the impact of diet on lifespan were extended by Slonaker, and subsequently McCay. Slonaker concluded that there was a strong impact of protein intake on lifespan, while McCay concluded that calories are the main factor causing differences in lifespan when animals are restricted (Calorie restriction or CR). Hence from the very beginning the question of whether food restriction acts on lifespan via reduced calorie intake or reduced protein intake was disputed. Subsequent work supported the idea that calories were the dominant factor. More recently, however, this role has again been questioned, particularly in studies of insects. Here we review the data regarding previous studies of protein and calorie restriction in rodents. We show that increasing CR (with simultaneous protein restriction: PR) increases lifespan, and that CR with no PR generates an identical effect. None of the residual variation in the impact of CR (with PR) on lifespan could be traced to variation in macronutrient content of the diet. Other studies show that low protein content in the diet does increase median lifespan, but the effect is smaller than the CR effect. We conclude that CR is a valid phenomenon in rodents that cannot be explained by changes in protein intake, but that there is a separate phenomenon linking protein intake to lifespan, which acts over a different range of protein intakes than is typical in CR studies. This suggests there may be a fundamental difference in the responses of insects and rodents to CR. This may be traced to differences in the physiology of these groups, or reflect a major methodological difference between 'restriction' studies performed on rodents and insects. We suggest that studies where the diet is supplied ad libitum, but diluted with inert components, should perhaps be called dietary or caloric dilution, rather than dietary or caloric restriction, to distinguish these potentially important methodological differences. (C) 2016 Elsevier Inc. All rights reserved.
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Caloric restriction (CR), protein restriction (PR), and specific amino acid restriction (e.g., methionine restriction (MR)) are different dietary interventions that have been confirmed with regard to their comprehensive benefits t...
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Caloric restriction (CR), protein restriction (PR), and specific amino acid restriction (e.g., methionine restriction (MR)) are different dietary interventions that have been confirmed with regard to their comprehensive benefits to metabolism and health. Based on bone densitometric measurements, weight loss induced by dietary restriction is known to be accompanied by reduced areal bone mineral density, bone mass, and/or bone size, and it is considered harmful to bone health. However, because of technological advancements in bone densitometric instruments (e. g., high-resolution X-ray tomography), dietary restrictions have been found to cause a reduction in bone mass/size rather than volumetric bone mineral density. Furthermore, when considering bone quality, bone health consists of diverse indices that cannot be fully represented by densitometric measurements alone. Indeed, there is evidence that moderate dietary restrictions do not impair intrinsic bone material properties, despite the reduction in wholebone strength because of a smaller bone size. In the present review, we integrate research evidence from traditional densitometric measurements, metabolic status assays (e.g., energy metabolism, oxidative stresses, and inflammatory responses), and biomaterial analyses to provide revised conclusions regarding the effects of CR, PR, and MR on the skeleton.
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Dietary restriction (DR) without malnutrition is associated with longevity in various organisms. However, it has also been shown that reduced calorie intake is often ineffective in extending life span. Selecting optimal dietary re...
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Dietary restriction (DR) without malnutrition is associated with longevity in various organisms. However, it has also been shown that reduced calorie intake is often ineffective in extending life span. Selecting optimal dietary regimens for DR studies is complicated, as the same regimen may lead to different outcomes depending on genotype and environmental factors. Recent studies suggested that interventions such as moderate protein restriction with or without adequate nutrition (e.g., particular amino acids or carbohydrates) may have additional beneficial effects mediated by certain metabolic and hormonal factors implicated in the biology of aging, regardless of total calorie intake. In particular, it was shown that restriction of a single amino acid, methionine, can mimic the effects of DR and extend life span in various model organisms. We discuss the beneficial effects of a methionine-restricted diet, the molecular pathways involved, and the use of this regimen in longevity interventions.
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Restricted channels differ from ordinary channels because of their external environmental factors; they have many restrictions on vessel scheduling. In particular, for ports with restricted channels and harbor basins, these restri...
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Restricted channels differ from ordinary channels because of their external environmental factors; they have many restrictions on vessel scheduling. In particular, for ports with restricted channels and harbor basins, these restrictions affect the safety and efficiency of vessel scheduling, resulting in traffic congestion and causing long delays and waiting times for vessels. Therefore, in this study, we use a mathematical optimization model to optimize vessel scheduling in ports with restricted channel to reduce vessel waiting time, improve vessel transportation efficiency, and ensure transportation safety. We simultaneously considered constraints such as complex navigation rules of restricted channel and scheduling resources to develop the mathematical optimization model. An elite selection genetic algorithm (e-GA) with the vessel service sequence as the code is proposed to solve the optimization model. Finally, using the optimization model, a customized model of the Port of Huanghua was developed based on the actual layout and rules of the port and case studies were conducted. The research results prove the rationality and reliability of the proposed optimization model as well as the effectiveness of e-GA and provide basic theoretical support for expanding this research direction. The results show that compared with the traditional first come first service (FCFS) strategy, the optimization model and e-GA can yield better auxiliary decision making for vessel scheduling in restricted channel and have practical significance.
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Integration of dark- and photo-fermentation is a promising strategy to enhance saline wastewater treatment efficiency and biohydrogen production. In this study, dark-and photo-fermentative bacterial consortium was respectively enr...
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Integration of dark- and photo-fermentation is a promising strategy to enhance saline wastewater treatment efficiency and biohydrogen production. In this study, dark-and photo-fermentative bacterial consortium was respectively enriched and their communities were analyzed using polymerase chain reaction-denaturing gradient gel electrophoresis (PCR-DGGE). Both consortia were mainly composed of hydrogen-producing strains. After the first-stage dark-fermentation, the following conditions were applied prior to the second-stage fermentation: fermentative broth pH regulation (the pH group), glucose addition (the glucose group), glucose addition and pH regulation (the glucose+ pH group), photosynthetic bacteria addition (the photo group), and photosynthetic bacteria addition and pH regulation (the photo + pH group), respectively. Dark fermentative broth with no pretreatment was used as control (the control group). Then the second stage began. The results showed that pH restriction had more influence than substrate or products restriction on dark-fermentative hydrogen production. Addition of photo-fermentative bacteria after dark-fermentation increased the hydrogen yield (134%) and substrate utilization (67%). These findings indicated syntrophic interactions between dark- and photo-fermentative bacteria during the hydrogen production process.
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Background: Dietary restriction (DR), defined as reduced nutrient intake without malnutrition, is associated with longevity extension, improved glucose metabolism, and increased stress resistance, but also poor wound healing. Shor...
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Background: Dietary restriction (DR), defined as reduced nutrient intake without malnutrition, is associated with longevity extension, improved glucose metabolism, and increased stress resistance, but also poor wound healing. Short-term preoperative DR followed by a return to normal feeding after surgery results in improved surgical outcomes in preclinical models. However, the effect of preoperative DR on wound healing and perioperative glucose homeostasis is currently unknown. Here, we tested the effects of two different preoperative DR regimens-protein restriction (PR) and methionine restriction (MR)-on wound healing and perioperative glucose homeostasis using an established murine model of wound healing in both nondiabetic and diabetic mice.
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We improve the best known exponent for the restriction conjecture in R-6, improving the recent results of Bourgain and Guth. The proof is applicable to any dimension n satisfying n equivalent to 0 mod 3.
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Background: Dietary restriction (DR) is a widely used experimental intervention in aging research due to its consistent ability to extend lifespan in most species tested. DR is an all-encompassing term describing interventions tha...
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Background: Dietary restriction (DR) is a widely used experimental intervention in aging research due to its consistent ability to extend lifespan in most species tested. DR is an all-encompassing term describing interventions that restrict some aspect of nutrition - from calorie amount to calorie type to timing of food intake - and yet share common functional endpoints including extended longevity, but also improvements in healthspan, or the time spent in good health, as well as metabolic fitness and stress resistance. Recent studies highlight the preponderance of sexual dimorphisms in the response to DR and argue for the importance of inclusion of both sexes in preclinical research. OBJECTIVE: We set out to perform a comprehensive assessment of documented health and lifespan outcomes of interventional DR studies in mice that display sexual dimorphism. METHODS: A systematic literature search was conducted according to the PRISMA statement to identify mouse DR studies in which both sexes were included using PubMed. The specific DR interventions examined included calorie restriction (CR), intermittent fasting (IF), protein restriction (PR) and methionine restriction (MetR), with experimental endpoints focused on lifespan and healthspan. RESULTS: Sexual dimorphism in the lifespan and healthspan effects of various DR regimens is a common finding in mice, with the magnitude and direction of dimorphic responses influenced by the specific dietary intervention as well as the strain of mouse used in the study. CONCLUSIONS: Despite the fact that preclinical lifespan and healthspan analyses in mice reveal sexual dimorphism in the response to DR, there is still a large gap in our understanding of how sex affects dietary outcomes. More preclinical research comparing both sexes in the same study with better attention to reporting metrics during peer review and in easily searchable text including title and abstract is required to further our understanding of the impact of sex on health and lifespan in response to DR in rodent studies.
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