Dynamic diabetes solutions: physiologic insulin resensitization

Diabetes is a disease currently affecting over 30 million Americans and is a leading cause of amputation, blindness, and chronic kidney disease. Treatment of diabetes with medications and lifestyle modifications alone have not eliminated these complications, because in part they lack the ability to restore the periodic cycles and rest periods of insulin that exist in healthy physiology. Insulin is excreted in a cyclical and oscillatory pattern by the pancreas, that is critical to maintain adequate insulin sensitivity at the insulin receptor level. Administration of exogenous insulin bio identically matching this physiologic profile is more effective at controlling blood glucose level and reducing complications of diabetes than standard drug therapy and lifestyle modifications alone. This matching of physiological insulin helps reduce inflammatory cascades responsible for a number of diabetic complications. In this article, we will review how insulin is secreted and functions physiologically and highlight a dynamic insulin delivery modality that mimics normal secretion profiles. This biomimicry reduces insulin exposure, which appears to reduce the progression to or worsening of insulin resistance. We will review how administration of insulin in this manner has been associated with reduction of diabetic complications.

Periodic Cycles of Eyewall Convection Limit the Rapid Intensification of Typhoon Hato (2017)

The ability to forecast tropical cyclone (TC) intensity has improved modestly in recent years, partly because of an inadequate understanding of eyewall convection processes. Short-term periodic convection activities (period: 3–5 h) have been identified in a number of TCs, but the effect of these activities on the evolution of TC intensity at the hourly scale is yet to be fully investigated. Using radar observations and a high-resolution numerical simulation based on the Weather Research and Forecasting model, we analyzed the periodic cycles of eyewall convection associated with the intensification of Typhoon Hato (2017). Results indicate the presence of four short-term periodic cycles (period: 3–5 h) in the eyewall convection, which correspond to TC intensification. We further divided each cycle into three stages. The periodic evolution of convection inhibited the rapid intensification of the TC. The highest and lowest intensification rates were associated with the first and third stages according to the virtual potential temperature tendency in the eyewall region, respectively. Heating was dominated by the vertical advection associated with sensible heat and latent heat, which were controlled by the eyewall convection and structure. Of the three stages in each cycle, the vertical transport released the largest amount of latent heat in the first stage; consequently, the highest intensification rate occurred in this stage. In the second stage, heating was reduced because of decreased latent heat and increased cooling of sensible heat associated with vertical advection as the eyewall intensified. Vertical transport was the weakest in the third stage; this resulted in the smallest amount of heating, which limited the rapid intensification of the TC.

Further Discussions of the Complex Dynamics of a 2D Logistic Map: Basins of Attraction and Fractal Dimensions

In this paper, we study the complex dynamic characteristics of a simple nonlinear logistic map. The map contains two parameters that have complex influences on the map’s dynamics. Assuming different values for those parameters gives rise to strange attractors with fractal dimensions. Furthermore, some of these chaotic attractors have heteroclinic cycles due to saddle-fixed points. The basins of attraction for some periodic cycles in the phase plane are divided into three regions of rank-1 preimages. We analyze those regions and show that the map is noninvertible and includes Z0,Z2 and Z4 regions.

Perturbative norm for associated spreading of diseases

The mathematical modelling of a pandemic with prevention, mutation and infection parameters to justify the natural properties of the diseases with a view in controlling it. Strength of the virus strain, population density gradient, cyclic healthcare potentials (with vaccination and cure) along with 2 WAVES (generalized upto ‘n’ waves with dual and anti-dual factors) interpreted over periodic cycles of odd and even permutations to illuminate the necessary conditions for natural and artificial immunization thereby emanating the potential for cures over (−3, ±1, +3) instigation factors as interpreted over a Bell curve.

4:10 Cycles of Very Low Calories Protect Against Tumor Xenografts, but Not Metastases in the Absence of Chemotherapy

Cancer is a leading cause of mortality, with its incidence only expected to rise with an increasingly aging population. Dietary interventions, primarily caloric restriction (CR), lower cellular energy metabolism and have long been utilized to slow the aging process and protect against age-related diseases, including cancer. However, due to the stringency of CR, dietary alternatives that offer the same beneficial outcomes in cancer prevention and longevity have become increasingly attractive. Periodic cycles (4 days twice a month) of low caloric intake followed by a standard ad libitum (AL) diet was previously shown to promote health-span in mice and humans and protect against primary tumorigenesis and enhanced the effects of chemotherapy. The aim of our study was to compare the tumorigenic potential of 4T1 cells, a murine model of stage IV breast cancer, in young and aged female BALB/c mice fed either periodic cycles of low caloric diets versus chronic 20% CR. Compared to AL controls, we found a significant delay in primary tumor growth in mice regardless of diet composition by the 4:10 cycles of very low caloric intake. However, unlike in CR, CR-alternative diets were not protective against lung metastases in the absence of chemotherapy. Our study sheds light into the underlying differences of calorie-based interventions in the absence of chemotherapy.

Degree gaps for multipliers and the dynamical André–Oort conjecture

We demonstrate how recent work of Favre and Gauthier, together with a modification of a result of the author, shows that a family of polynomials with infinitely many post-critically finite specializations cannot have any periodic cycles with multiplier of very low degree, except those that vanish, generalizing results of Baker and DeMarco, and Favre and Gauthier.

A Remanufacturing Duopoly Game Based on a Piecewise Nonlinear Map: Analysis and Investigations

A remanufacturing Cournot duopoly game is introduced based on a nonlinear utility function in this paper. What we mean by remanufacturing here is that the second firm in this game receives used products and remanufacture them and then sell them again in the market. The bounded rationality mechanism is used to form a piecewise system that describes this game in discrete time periods. This piecewise system depends on five parameters and is defined on two regions separated by a border curve. The fixed points of this system in each region are calculated and their stability is discussed. Numerical simulations for this system exhibit the occurrence of different types of multiple attractors. We also give examples of different stable periodic cycles and chaotic attractors that are separated by the border curve or passing through it.

Geometric mixing

Mixing fluids often involves a periodic action, like stirring one’s tea. But reciprocating motions in fluids at low Reynolds number, in Stokes flows where inertia is negligible, lead to periodic cycles of mixing and unmixing, because the physics, molecular diffusion excepted, is time reversible. So how can fluid be mixed in such circumstances? The answer involves a geometric phase. Geometric phases are found everywhere in physics as anholonomies, where after a closed circuit in the parameters, some system variables do not return to their original values. We discuss the geometric phase in fluid mixing: geometric mixing. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game

We investigate the complex dynamic characteristics of a duopoly game whose players adopt a gradient-based mechanism to update their outputs and one of them possesses in some way certain information about his/her opponent. We show that knowing such asymmetric information does not give any advantages but affects the stability of the game’s equilibrium points. Theoretically, we prove that the equilibrium points can be destabilized through Neimark-Sacker followed by flip bifurcation. Numerically, we prove that the map describing the game is noninvertible and gives rise to several stable attractors (multistability). Furthermore, the dynamics of the map give different shapes of quite complicated attraction basins of periodic cycles.