scholarly journals On the Controllability of a System Modeling Cell Dynamics Related to Leukemia

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1867
Author(s):  
Ioan Ştefan Haplea ◽  
Lorand Gabriel Parajdi ◽  
Radu Precup
Keyword(s):  
System Modeling ◽  
Leukemic Cells ◽  
Control Problems ◽  
Symmetric Model ◽  
Multiplication Rate ◽  
Cell Dynamics ◽  
Death Rates ◽  
Control Objective ◽  
Theoretical Results ◽  
General Method

In this paper, two control problems for a symmetric model of cell dynamics related to leukemia are considered. The first one, in connection with classical chemotherapy, is that the evolution of the disease under treatment should follow a prescribed trajectory assuming that the drug works by increasing the cell death rates of both malignant and normal cells. In the case of the second control problem, as for targeted therapies, the drug is assumed to work by decreasing the multiplication rate of leukemic cells only, and the control objective is that the disease state reaches a desired endpoint. The solvability of the two problems as well as their stability are proved by using a general method of analysis. Some numerical simulations are included to illustrate the theoretical results and prove their applicability. The results can possibly be used to design therapeutic scenarios such that an expected clinical evolution can be achieved.

Formation-containment control of sampled-data second-order multi-agent systems with sampling delay

2018 ◽  
Vol 40 (16) ◽  
pp. 4369-4381 ◽  
Author(s):  
Baojie Zheng ◽  
Xiaowu Mu
Keyword(s):  
Matrix Theory ◽  
Sufficient Conditions ◽  
Second Order ◽  
Control Problems ◽  
Sampled Data ◽  
Multi Agent Systems ◽  
Containment Control ◽  
Agent Systems ◽  
Multi Agent ◽  
Theoretical Results

The formation-containment control problems of sampled-data second-order multi-agent systems with sampling delay are studied. In this paper, we assume that there exist interactions among leaders and that the leader’s neighbours are only leaders. Firstly, two different control protocols with sampling delay are presented for followers and leaders, respectively. Then, by utilizing the algebraic graph theory and matrix theory, several sufficient conditions are obtained to ensure that the leaders achieve a desired formation and that the states of the followers converge to the convex hull formed by the states of the leaders, i.e. the multi-agent systems achieve formation containment. Furthermore, an explicit expression of the formation position function is derived for each leader. An algorithm is provided to design the gain parameters in the protocols. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.

scholarly journals Replicative cellular age distributions in compartmentalized tissues

2018 ◽  
Vol 15 (145) ◽  
pp. 20180272 ◽  
Author(s):  
Marvin A. Böttcher ◽  
David Dingli ◽  
Benjamin Werner ◽  
Arne Traulsen
Keyword(s):  
Stem Cell ◽  
Age Distribution ◽  
Cancer Risks ◽  
Cell Compartment ◽  
Cell Dynamics ◽  
Self Renewal ◽  
Long Tail ◽  
Stem Cell Compartment ◽  
Limiting Case ◽  
Theoretical Results

The cellular age distribution of hierarchically organized tissues can reveal important insights into the dynamics of cell differentiation and self-renewal and associated cancer risks. Here, we examine the effect of progenitor compartments with varying differentiation and self-renewal capacities on the resulting observable distributions of replicative cellular ages. We find that strongly amplifying progenitor compartments, i.e. compartments with high self-renewal capacities, substantially broaden the age distributions which become skewed towards younger cells with a long tail of few old cells. For several of these strongly amplifying compartments, the age distribution becomes virtually independent of the influx from the stem cell compartment. By contrast, if tissues are organized into many downstream compartments with low self-renewal capacity, the shape of the replicative cell distribution in more differentiated compartments is dominated by stem cell dynamics with little added variation. In the limiting case of a strict binary differentiation tree without self-renewal, the shape of the output distribution becomes indistinguishable from that of the input distribution. Our results suggest that a comparison of cellular age distributions between healthy and cancerous tissues may inform about dynamical changes within the hierarchical tissue structure, i.e. an acquired increased self-renewal capacity in certain tumours. Furthermore, we compare our theoretical results to telomere length distributions in granulocyte populations of 10 healthy individuals across different ages, highlighting that our theoretical expectations agree with experimental observations.

scholarly journals Restoration of superconductivity in high magnetic fields in UTe2

2020 ◽  
Vol 34 (32) ◽  
pp. 2030007
Author(s):  
Andrei G. Lebed
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Superconducting State ◽  
Critical Magnetic Field ◽  
High Magnetic Fields ◽  
Two Dimensional ◽  
Upper Critical Magnetic Field ◽  
Reentrant Superconductivity ◽  
Theoretical Results ◽  
General Method

It was theoretically predicted more than 20 years ago [A. G. Lebed and K. Yamaji, Phys. Rev. Lett. 80, 2697 (1998)], that a triplet quasi-two-dimensional (Q2D) superconductor could restore its superconducting state in parallel magnetic fields, which are higher than its upper critical magnetic field, [Formula: see text]. It is very likely that, recently, such phenomenon has been experimentally discovered in the Q2D superconductor UTe2 by Nicholas Butch, Sheng Ran, and their colleagues and has been confirmed by Japanese–French team. We review our previous theoretical results using such a general method that it describes the reentrant superconductivity in the abovementioned compound and will hopefully describes the similar phenomena, which can be discovered in other Q2D superconductors.

Triple-Stage Track-Following Servo Design for Hard Disk Drives

2016 ◽  
Author(s):  
Jinwen Pan ◽  
Omid Bagherieh ◽  
Behrooz Shahsavari ◽  
Roberto Horowitz
Keyword(s):  
Controller Design ◽  
System Modeling ◽  
Hard Disk Drives ◽  
Low Frequency ◽  
Stability Margin ◽  
Disturbance Attenuation ◽  
Stability Margins ◽  
Control Objective ◽  
Robust Control Design ◽  
Actuation Systems

This paper studies possible robust control design methods in triple-stage actuation settings for achieving minimum position error signal (PES) while maintaining enough stability margins. Firstly, the sensitivity-decoupling design technique, is utilized to estimate the resulting increase in low frequency disturbance attenuation and servo bandwidth. A systematic tuning methodology based on μ-synthesis is then proposed for track-following servo design of triple-stage actuation systems. In this approach, the objective is to minimize the PES, by considering all constraints and uncertainties explicitly in the design. We describe a step by step Multi-Input Single-Output (MISO) controller design methodology which includes system modeling, noise characterization, control objective determination and controller synthesis and verification. In this methodology, servo bandwidth is not the only performance metric. Rather, the control objective will be to minimize the closed-loop system H∞ norm directly, while all stroke and control constraints are satisfied and enough stability margin is ensured. The proposed method is applied to design track-following feedback controllers for single-, dual- and triple-stage actuation systems. Simulation results show that compared to dual-stage actuation, triple-stage actuation enhances low frequency disturbance rejection by 6 dB at around 100Hz and increases servo bandwidth from ∼3kHz to ∼5kHz.

Stability Conditions for a System Modeling Cell Dynamics in Leukemia

2010 ◽  
Vol 43 (2) ◽  
pp. 99-102 ◽  
Author(s):  
Hitay Özbay ◽  
Houda Benjelloun ◽  
Catherine Bonnet ◽  
Jean Clairambault
Keyword(s):  
System Modeling ◽  
Stability Conditions ◽  
Cell Dynamics

scholarly journals A Four-Dimensional Hyperchaotic Finance System and Its Control Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Lin Cao
Keyword(s):  
Qualitative Analysis ◽  
Phase Portraits ◽  
Control Problems ◽  
Complete Synchronization ◽  
Adaptive Controllers ◽  
Finance System ◽  
Single Input ◽  
Theoretical Results ◽  
Setting Parameters ◽  
New System

The construction and several control problems of a new hyperchaotic finance system are investigated in this paper. Firstly, a new four-dimensional hyperchaotic finance system is introduced, based on which a new hyperchaos is then generated by setting parameters. And the qualitative analysis is numerically studied to confirm the dynamical processes, for example, the bifurcation diagram, Poincaré sections, Lyapunov exponents, and phase portraits. Interestingly, the obtained results show that this new system can display complex characteristics: chaotic, hyperchaotic, and quasiperiodic phenomena occur alternately versus parameters. Secondly, three single input adaptive controllers are designed to realize the control problems of such system: stabilization, synchronization, and coexistence of antisynchronization and complete synchronization, respectively. It is noted that the designed controllers are simpler than the existing ones. Finally, numerical simulations are provided to demonstrate the validity and the effectiveness of the proposed theoretical results.

scholarly journals Feedback linearization-based vaccination control strategies for true-mass action type SEIR epidemic models

2011 ◽  
Vol 16 (3) ◽  
pp. 283-314 ◽  
Author(s):  
Manuel De la Sen ◽  
Asier Ibeas ◽  
Santiago Alonso-Quesada
Keyword(s):  
Feedback Linearization ◽  
Total Population ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Disease Model ◽  
Mass Action ◽  
Control Objective ◽  
Action Type ◽  
True Mass ◽  
General Method

This paper presents a feedback linearization-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The control objective is novel in the sense that the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously the remaining population (i.e. susceptible plus infected plus infectious) to asymptotically converge to zero. The vaccination policy is firstly designed on the above proposed tracking objective. Then, it is proven that identical vaccination rules might be found based on a general feedback linearization technique. Such a formal technique is very useful in control theory which provides a general method to generate families of vaccination policies with sound technical background which include those proposed in the former sections of the paper. The output zero dynamics of the normal canonical form in the theoretical feedback linearization analysis is identified with that of the removed-by-immunity population. The various proposed vaccination feedback rules involved one of more of the partial populations and there is a certain flexibility in their designs since some control parameters being multiplicative coefficients of the various populations may be zeroed. The basic properties of stability and positivity of the solutions are investigated in a joint way. The equilibrium points and their stability properties as well as the positivity of the solutions are also investigated.

Neimark–Sacker bifurcations in a non-standard numerical scheme for a class of positivity-preserving ODEs

2006 ◽  
Vol 462 (2074) ◽  
pp. 3167-3184 ◽  
Author(s):  
Murray E Alexander ◽  
Arthur R Summers ◽  
Seyed M Moghadas
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Scheme ◽  
Integration Time ◽  
Bifurcation Parameter ◽  
Two Dimensional ◽  
Time Step ◽  
Positivity Preserving ◽  
Lyapunov Coefficient ◽  
Theoretical Results ◽  
General Method

We discuss the nature of Neimark–Sacker bifurcations occurring in a non-standard numerical scheme, for a class of positivity-preserving systems of ordinary differential equations (ODEs) which undergoes a corresponding Hopf bifurcation. Extending previous work (Alexander & Moghadas 2005 a Electron. J. Diff. Eqn. Conf . 12 , 9–19), it is shown that the type of Neimark–Sacker bifurcation (supercritical or subcritical) may be affected by the integration time-step . The general form of the scheme in the vicinity of a fixed point is given, from which the expression for the first Lyapunov coefficient for two-dimensional systems, valid for arbitrary time-step, is explicitly derived. The analysis shows that this coefficient undergoes an shift with respect to the corresponding coefficient of the original ODE. This could lead to a type of bifurcation which differs from the corresponding Hopf bifurcation in the ODE, due to changes in the sign of the first Lyapunov coefficient as varies. This is especially problematic in the vicinity of certain types of degenerate Hopf bifurcation, at which this coefficient may vanish. We also present a general method to eliminate the possible shift in the bifurcation parameter of the scheme; however, the first Lyapunov coefficient may still be subjected to an shift, leading to a possibly erroneous type of bifurcation. Examples are given to illustrate the theoretical results of the paper with applications to mathematical biology.

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