Hopf bifurcation for a discontinuous HTLV-1 model

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6247-6267 ◽  
Author(s):  
Elham Shamsara ◽  
Zahra Afsharnezhad ◽  
Reihaneh Mostolizadeh
Keyword(s):  
Hopf Bifurcation ◽  
Sliding Mode ◽  
Early Stage ◽  
Time Lag ◽  
Discontinuous System ◽  
Steady State Condition ◽  
Ctl Response ◽  
Optimal Drug ◽  
Long Time ◽  
Immunosuppressive Diseases

Developing accurate mathematical models for host immune response in immunosuppressive diseases such as HIV and HTLV-1 are essential to achieve an optimal drug therapy regime. Since for HTLV-1 specific CTL response typically occurs after a time lag, we consider a discontinuous response function to better describe this lagged response during the early stage of the infectious, thus the system of HTLV-1 model will be a discontinuous system. For analyzing the dynamic of the system we use Filippov theory and find conditions in which the Filippov system undergoes a Hopf bifurcation. The Hopf bifurcation help us to find stable and unstable periodic oscillations and can be used to predict whether the CTL response can return to a steady state condition. Also, Hopf bifurcation in sliding mode is investigated. In this case the solutions will remain in the hyper-surface of discontinuity and as a consequence the disease cannot progress, at least for a long time. Finally we use numerical simulations to demonstrate the results by example.

Effects of Isothermal Aging on Clustering and Paint-Bake Hardening Behavior in an Al-Mg-Si Alloy

2014 ◽  
Vol 794-796 ◽  
pp. 897-902 ◽  
Author(s):  
Yasuhiro Aruga ◽  
Masaya Kozuka ◽  
Yasuo Takaki ◽  
Tatsuo Sato
Keyword(s):  
Early Stage ◽  
Natural Aging ◽  
Atom Probe ◽  
Bake Hardening ◽  
Subsequent Aging ◽  
Significant Drop ◽  
Β Phase ◽  
Long Time ◽  
Hardness Increase ◽  
Small Clusters

The relationship between the cluster morphology formed during natural or artificial aging and the paint-bake hardening response in an Al-0.62Mg-0.93Si (mass%) alloy have been investigated using atom probe tomography (APT). Increasing the subsequent aging time at 170 °C causes a gradual increase in hardness in the artificially aged materials, while the retardation period of the hardness increase appears in the naturally aged materials at the early stage of aging. The statistically-proved records in the APT analysis have shown that the artificially aged materials have some large clusters. It is revealed that the hardening at the early stage of the subsequent aging at 170 °C is not promoted in the long-time naturally aged material although the number density of small clusters increases approximately 1.3 times by prolonged natural aging.Hence, we believe that the small clusters are hard to transform continuously into the β'' phase during aging at 170 °C. As for the naturally aged materials, the long-time aging leads to a significant drop in hardness at the early stage of aging at 170 °C. It is speculated that the Mg-Si mixed clusters formed after long-time natural aging can be reversed during the subsequent heat treatment.

A “Natural” Proposal for Addressing Climate Change

2014 ◽  
Vol 28 (3) ◽  
pp. 359-363 ◽  
Author(s):  
Thomas E. Lovejoy
Keyword(s):  
Climate Change ◽  
Greenhouse Gases ◽  
Ethical Issues ◽  
Time Lag ◽  
Radiant Heat ◽  
Time Frame ◽  
Future Generations ◽  
Considerable Time ◽  
Long Time

One of the fundamental challenges of climate change is that we contribute to it increment by increment, and experience it increment by increment after a considerable time lag. As a consequence, it is very difficult to see what we are doing to ourselves, to future generations, and to the living planet as a whole. There are monumental ethical issues involved, but they are obscured by the incremental nature of the process and the long time frame before reaching the concentration of greenhouse gases and the ensuing accumulation of radiant heat—and consequent climate change—that ensues.

Downregulation of the vasopressin type 2 receptor after vasopressin-induced internalization: involvement of a lysosomal degradation pathway

2005 ◽  
Vol 288 (6) ◽  
pp. C1390-C1401 ◽  
Author(s):  
Richard Bouley ◽  
Herbert Y. Lin ◽  
Malay K. Raychowdhury ◽  
Vladimir Marshansky ◽  
Dennis Brown ◽  
...  
Keyword(s):  
Cell Surface ◽  
Fluorescent Protein ◽  
Collecting Duct ◽  
Time Lag ◽  
Renal Medulla ◽  
Degradation Pathway ◽  
Urinary Concentration ◽  
Long Time ◽  
Green Fluorescent ◽  
Golgi Network

Vasopressin (VP) increases urinary concentration by signaling through the vasopressin receptor (V2R) in collecting duct principal cells. After downregulation, V2R reappears at the cell surface via an unusually slow (several hours) “recycling” pathway. To examine this pathway, we expressed V2R-green fluorescent protein (GFP) in LLC-PK1a cells. V2R-GFP showed characteristics similar to those of wild-type V2R, including high affinity for VP and adenylyl cyclase stimulation. V2R-GFP was located mainly in the plasma membrane in unstimulated cells, but it colocalized with the lysosomal marker Lysotracker after VP-induced internalization. Western blot analysis of V2R-GFP showed a broad 57- to 68-kDa band and a doublet at 46 and 52 kDa before VP treatment. After 4-h VP exposure, the 57- to 68-kDa band lost 50% of its intensity, whereas the lower 46-kDa band increased by 200%. The lysosomal inhibitor chloroquine abolished this VP effect, whereas lactacystin, a proteasome inhibitor, had no effect. Incubating cells at 20°C to block trafficking from the trans-Golgi network reduced V2R membrane fluorescence, and a perinuclear patch developed. Cycloheximide reduced the intensity of this patch, showing that newly synthesized V2R-GFP contributed significantly to its appearance. Cycloheximide also inhibited the reappearance of cell surface V2R after downregulation. We conclude that after downregulation, V2R-GFP is delivered to lysosomes and degraded. Reappearance of V2R at the cell surface depends on new protein synthesis, partially explaining the long time lag needed to fully reestablish V2R at the cell surface after downregulation. This degradative pathway may be an adaptive response to allow receptor-ligand association in the hypertonic and acidic environment of the renal medulla.

Non-Gaussian probability distributions of solar wind fluctuations

1994 ◽  
Vol 12 (12) ◽  
pp. 1127-1138 ◽  
Author(s):  
E. Marsch ◽  
C. Y. Tu
Keyword(s):  
Solar Wind ◽  
Probability Distributions ◽  
Time Lag ◽  
Small Scale ◽  
Time Lags ◽  
Mhd Turbulence ◽  
Theoretical Concepts ◽  
Fluid Turbulence ◽  
Long Time ◽  
Non Gaussian

Abstract. The probability distributions of field differences ∆x(τ)=x(t+τ)-x(t), where the variable x(t) may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag τ, ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of ∆x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale τ by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of ∆x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD) turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.

scholarly journals Modelling HIV dynamics with cell-to-cell transmission and CTL response

2021 ◽  
Author(s):  
Zirui Zhu ◽  
Ranchao Wu ◽  
Yu Yang ◽  
Yancong Xu
Keyword(s):  
Hopf Bifurcation ◽  
Cell Interaction ◽  
Backward Bifurcation ◽  
Hiv Treatment ◽  
Hiv Model ◽  
Ctl Response ◽  
Hiv Dynamics ◽  
Subcritical Hopf Bifurcation ◽  
Cell Transmission ◽  
New Type

In most HIV models, the emergence of backward bifurcation means that the control for basic reproduction number less than one is no longer effective for HIV treatment. In this paper, we study an HIV model with CTL response and cell-to-cell transmission by using the dynamical approach. The local and global stability of equilibria is investigated, the relations of subcritical Hopf bifurcation and supercritical bifurcation points are revealed, especially, the so-called new type bifurcation is also found with two Hopf bifurcation curves meeting at the same Bogdanov-Takens bifurcation point. Forward and backward bifurcation, Hopf bifurcation, saddle-node bifurcation, Bogdanov-Takens bifurcation are investigated analytically and numerically. Two limit cycles are also found numerically, which indicates that the complex behavior of HIV dynamics. Interestingly, the role of cell-to-cell interaction is fully uncovered, it may cause the oscillations to disappear and keep the so-called new type bifurcation persist. Finally, some conclusions and discussions are also given.

scholarly journals Uwarunkowania procesu pojednania w Kambodży

2020 ◽  
Vol 14 ◽  
pp. 267-280
Author(s):  
Radosław Zarzecki
Keyword(s):  
Early Stage ◽  
Khmer Rouge ◽  
State Level ◽  
Political Life ◽  
Historical Background ◽  
Difficult Situation ◽  
Main Challenge ◽  
Long Time ◽  
History Of ◽  
Culture Of Silence

Determinants of Reconciliation in Cambodia Forty years after Cambodian genocide the reconciliation is still in early stage. Despite such long time there was almost nothing done, especially in 20th century, to make that process happened. The article discusses the determinants, reasons and factors that had impact on reconciliation. Determinants can be divided into different categories. First of all the socio-historical background. Circumstances in which Khmer Rouge come to power, their revolutionary approach to economy, implemented reforms, use of children, displacements of people and categorization of citizens had great impact on post-1979 Cambodia. Another determinant is a political one. Policy of post-Khmer Rouge Cambodia rulers stunted the reconciliation. There reason of such actions are multidimensional but the most important one is provenance of People’s Republic of Kampuchea leaders. The most important figures in Cambodia politics are ex-Khmer Rouge soldiers, accused by some of taking a part in genocide. What’s even more confusing, the most powerful opposition party in 1980s were perpetrators themselves and their allies. Even after signing Paris Peace Accords in 1991 until early 2000s there was no will to punish Khmer Rouge officials responsible for genocide. The Cambodian culture of silence, the third determinant, only exacerbates a difficult situation. Cambodians rarely speak about atrocities and harsh past because of fear, shame or trauma. Even in school textbooks until 2009 there was almost nothing said about tragic events which happened between 1975 and 1979. History of Democratic Kampuchea still affects the Cambodian society. Despite sentencing few Khmer Rouge officials in 2010s, there’s still lot to be done also on state-level. Reconciliation and coming back to the state of balance is the main challenge for Cambodia in the nearest future, crucially important to social and political life of this nation.

The Vanishing Gradient Problem During Learning Recurrent Neural Nets and Problem Solutions

1998 ◽  
Vol 06 (02) ◽  
pp. 107-116 ◽  
Author(s):  
Sepp Hochreiter
Keyword(s):  
Time Series ◽  
Time Series Prediction ◽  
Time Lag ◽  
Neural Nets ◽  
Alternative Methods ◽  
Reasonable Time ◽  
Practical Applications ◽  
Learning Time ◽  
Long Time ◽  
Gradient Based

Recurrent nets are in principle capable to store past inputs to produce the currently desired output. Because of this property recurrent nets are used in time series prediction and process control. Practical applications involve temporal dependencies spanning many time steps, e.g. between relevant inputs and desired outputs. In this case, however, gradient based learning methods take too much time. The extremely increased learning time arises because the error vanishes as it gets propagated back. In this article the de-caying error flow is theoretically analyzed. Then methods trying to overcome vanishing gradients are briefly discussed. Finally, experiments comparing conventional algorithms and alternative methods are presented. With advanced methods long time lag problems can be solved in reasonable time.

scholarly journals Planting and harvesting innovation - an analysis of Samsung Electronics

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Seung Hoon Jang ◽  
Sang M. Lee ◽  
Taewan Kim ◽  
Donghyun Choi
Keyword(s):  
Early Stage ◽  
New Products ◽  
Limited Resources ◽  
High Tech ◽  
Short Term ◽  
Entire Life ◽  
Entire Life Cycle ◽  
Time Period ◽  
Innovation Projects ◽  
Long Time

Abstract This study explores how firms manage the entire life cycle of innovation projects based on the framework of harvesting and planting innovation. While harvesting innovation seeks new products in the expectation of financial performance in the short term, planting innovation pursues creating value over a long time period. Without proper management of the process of planting and harvesting innovation, firms with limited resources may not be successful in launching innovative new products to seize a momentum in high tech industries. To examine this issue, the case of Samsung Electronics (SE), now an electronics giant originated from a former developing country, is analyzed. SE has shown to effectively utilize co-innovation to maintain numerous planting and harvesting innovation projects. Both researchers and practitioners would be interested in learning about how SE shared risks of innovation investment with external partners at the early stage of innovation cycles.

scholarly journals Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Kejun Zhuang ◽  
Gao Jia ◽  
Dezhi Liu
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Solution ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Time Behavior ◽  
Delayed Reaction ◽  
Constant Equilibrium ◽  
Homogeneous Neumann Boundary Condition ◽  
Long Time ◽  
The Stability

Due to the different roles that nontoxic phytoplankton and toxin-producing phytoplankton play in the whole aquatic system, a delayed reaction-diffusion planktonic model under homogeneous Neumann boundary condition is investigated theoretically and numerically. This model describes the interactions between the zooplankton and two kinds of phytoplanktons. The long-time behavior of the model and existence of positive constant equilibrium solution are first discussed. Then, the stability of constant equilibrium solution and occurrence of Hopf bifurcation are detailed and analyzed by using the bifurcation theory. Moreover, the formulas for determining the bifurcation direction and stability of spatially bifurcating solutions are derived. Finally, some numerical simulations are performed to verify the appearance of the spatially homogeneous and nonhomogeneous periodic solutions.

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