Existence Of Different Families Research Articles

Stochasticity and Drug Effects in Dynamical Model for Cancer Stem Cells.

The Cancer Stem Model allows for a dynamical description of cancer colonies which accounts for the existence of different families of cells, namely stem cells, highly proliferating and quasi-immortal, and differentiated cells, both undergoing cellular processes under numerous activated pathways. In the present work, we investigate a dynamical model numerically, as a system of coupled differential equations, and include a plasticity mechanism, of differentiated cells turning into a stem state if the stem concentration drops low. We are particularly interested in the stability of the model once we introduce stochastically evolving parameters, associated with environmental and cellular intrinsic variabilities, as well as the response of the model after introducing a drug therapy. As long as we stay within the characteristic time scale of the system, defined on the base of the needed time for the trajectories to converge on stable states, we observe that the system remains stable for the main parameters evolving stochastically according to white noise. As for the drug treatments, we discuss a model both for the kinetics and the dynamics of the substance in the organism, and then consider the impact of different types of therapies in a few particular examples, outlining some interesting mechanisms, such as the tumor growth paradox, that possibly impact the outcome of therapy significantly.

Breather propagation and arrest in a strongly nonlinear locally resonant lattice

Locally resonant metamaterials have recently drawn the attention of many researchers due to their capability in controlling low-frequency waves by forming a bandgap resulting from mode hybridization. Although linear acoustics of these metamaterials have been extensively explored, only a little is known about their nonlinear acoustics. This work investigates the nonlinear acoustics of a 1D discrete strongly nonlinear locally resonant metamaterial under impulsive force excitation. The metamaterial is modeled as a chain of linearly grounded masses connected by essential strong nonlinearity (purely cubic nonlinearity), and embedded by linear local resonators. Numerical investigations demonstrate the existence of different families of traveling breathers that depend on the coupling coefficient between the local resonator and its holding cell. One of these families is reported for the first time in the current work due to the existence of multiple fast frequencies in its profile. Although the investigated system is undamped, numerical simulations demonstrate that the breather arrest is controlled by certain parameters of the system. In the limit of small energy levels, the complexification averaging method (CX-A) is utilized with the help of numerical observations to demonstrate some aspects of the nonlinear acoustics of the system. Particularly, analytical analysis is used to determine the nonlinear band structure of the system. The outcome indicates the presence of two energy-dependent nonlinear propagation zones (PZs) (i.e., acoustics and optical) and three complementary attenuation zones (AZs) for the infinite lattice case. In addition, the different families of traveling breathers in the semi-infinite lattice are investigated analytically and compared to their corresponding numerical results.

Nonlinear localized gap modes in width-modulated Fibonacci lattices

We address the properties of nonlinear localized gap modes supported by the width-modulated Fibonacci lattices, including their existence and stability. Linear system with the width-modulated Fibonacci lattices has multiple gaps. We find the existence of different families of nonlinear localized modes in two relatively large gaps. One of the nonlinear localized gap modes originates from the upper band-edge linear mode. Such gap modes are mostly stable in their entire existence domain, except for a small region in the middle of their existence. The other two families of nonlinear modes localized in the relatively large gap are pure nonlinear modes, and they have a narrow stable region near their upper cutoff. The results of the linear stability analysis are in good agreement with that of the propagation simulations.

Chemical Composition of Essential Oil, Phenolic Compounds Content, and Antioxidant Activity of Cistus monspeliensis from Northern Morocco.

Currently, oxidative stress is one of the major problems that threatens human health. It is at the root of many diseases such as cancer. Despite the enormous efforts provided to combat this scourge, oxidative stress is still relevant and hence comes the need for research of new remedies especially from natural origin. For this purpose, the study of the antioxidant activity of extracts of Cistus monspeliensis from Morocco is a principal research objective. The phenolic extracts were obtained by maceration of the plant in a water/acetone mixture and then separated by liquid/liquid extraction with solvents of increasing polarity. The first phytochemical tests carried out on these extracts showed the existence of different families of phenolic compounds, such as flavonoids, tannins, and others. Assays for total polyphenols, flavonoids, hydrolysable, and condensed tannins were carried out by known colorimetric methods. The results of these assays have shown that the studied extracts are rich in phenolic compounds present in the plant in the form of flavonoids (69.81 ± 0.22 mg EQ/g DM), hydrolysable tannins (61.86 ± 0.89 mg ETA/g DM), and condensed tannins (70.05 ± 1.61 mg EC/g DM). The evaluation of the antioxidant activity is carried out by two different methods: the DPPH test (2,2-DiPhenyl-1-Picryl-Hydrazyl) and the FRAP test (Ferric Reducing Antioxidant Power). The results obtained show that the extracts of Cistus monspeliensis are active and have interesting antioxidant powers. In particular, the water/acetone (WAE) (IC50 = 0.079 mg/mL) and butanolic (BUE) (IC0.5 = 0.099 mg/mL) extracts are the most active with values comparable to that of ascorbic acid. The interesting results obtained in this study clearly show that Cistus monspeliensis originating from Morocco can be considered as a source of natural antioxidants. Therefore, the extracts of this plant deserve to be tested in the medicinal field, against cancer and cardiovascular diseases, and in food field as an additive and preservative.

Existence and Stability of Periodic Orbits for a Hamiltonian System with Homogeneous Potential of Degree Five

In this paper we consider the autonomous Hamiltonian system with two degrees of freedom associated to the function $$H=\dfrac{1}{2} (x^2+y^2)+ \frac{1}{2}(p_x^2+ p_y^2)+ V_5(x, y)$$, where $$V_5(x,y)=\Big (\dfrac{A}{5}x^5+Bx^3y^2+\dfrac{C}{5}xy^4\Big )$$ which is related to a homogeneous potential of degree five. We prove the existence of different families of periodic orbits and the type of stability is analyzed through the averaging theory which guarantee the existence of such orbits on adequate sets defined by the parameters A, B, C.

Existence of simple BIBDs from a prime power difference family with minimum index

We show that under certain technical conditions that simple [Formula: see text] balanced incomplete block designs (BIBDs) exist for all allowable values of [Formula: see text], where [Formula: see text] is an odd prime power. Our primary technique is to argue for the existence of difference families in finite fields, in the flavor of Wilson [J. Number Theory 4 (1972) 17–47]. We provide an extensive analysis in the cases, where [Formula: see text] and also for [Formula: see text].

Entrainment of a thalamocortical neuron to periodic sensorimotor signals

In this work we study the dynamics of a 3-dimensional conductance-based model of a single thalamocortical (TC) neuron in response to sensorimotor signals. In particular, we focus on the entrainment of the system to a periodic excitatory signal that alternates between ‘on’ and ‘off’ states lasting for time T1 and T2, respectively. By exploiting invariant sets of the system and their associated invariant fiber bundles that foliate the phase space, we reduce the dynamics to the composition of two 2-dimensional maps, with the two components of one of the maps being simply a uniform shift and a uniform decay. With this reduction in computational complexity, we are able to analyze the model’s response to the excitatory signal while varying T1 and T2 systematically. We find that for fixed T2 but different T1 there exist and in some cases co-exist entrained periodic oscillations with different number of spikes (see Figure ​Figure11 for the case with T2 = 60 milliseconds). For relatively large T2 (above 55 milliseconds) it is also possible that the model responds to the excitatory signal with delayed spikes. Furthermore, we find that the size of the T1 intervals that allow coexistence of different types of entrained oscillations becomes larger as T2 increases. Figure 1 The top panel shows the T1 intervals (with T2 = 60 milliseconds) for the existence of different families of entrained periodic oscillations (green for sub-threshold oscillations, red for 1-spike oscillations, dark blue for 2-spike oscillations, and light ...

The role of serotonin receptor subtypes in treating depression: a review of animal studies

Serotonin reuptake inhibitors (SSRIs) are effective in treating depression. Given the existence of different families and subtypes of 5-HT receptors, multiple 5-HT receptors may be involved in the antidepressant-like behavioral effects of SSRIs. Behavioral pharmacology studies investigating the role of 5-HT receptor subtypes in producing or blocking the effects of SSRIs were reviewed. Few animal behavior tests were available to support the original development of SSRIs. Since their development, a number of behavioral tests and models of depression have been developed that are sensitive to the effects of SSRIs, as well as to other types of antidepressant treatments. The rationale for the development and use of these tests is reviewed. Behavioral effects similar to those of SSRIs (antidepressant-like) have been produced by agonists at 5-HT(1A), 5-HT(1B), 5-HT(2C), 5-HT(4), and 5-HT(6) receptors. Also, antagonists at 5-HT(2A), 5-HT(2C), 5-HT(3), 5-HT(6), and 5-HT(7) receptors have been reported to produce antidepressant-like responses. Although it seems paradoxical that both agonists and antagonists at particular 5-HT receptors can produce antidepressant-like effects, they probably involve diverse neurochemical mechanisms. The behavioral effects of SSRIs and other antidepressants may also be augmented when 5-HT receptor agonists or antagonists are given in combination. The involvement of 5-HT receptors in the antidepressant-like effects of SSRIs is complex and involves the orchestration of stimulation and blockade at different 5-HT receptor subtypes. Individual 5-HT receptors provide opportunities for the development of a newer generation of antidepressants that may be more beneficial and effective than SSRIs.

Polariton effect in nonlinear pulse propagation

The joint influence of the polariton effect and Kerr-like nonlinearity on propagation of optical pulses is studied. The existence of different families of envelope solitary wave solutions in the vicinity of polariton gap is shown. The properties of solutions depend strongly on the carrier wave frequency. In particular, solitary waves inside and outside of the polariton gap exhibit different velocity and amplitude dependencies on their duration.

Structure maps for close-packed alloys by the Ising model

Abstract The one-dimensional Ising model can explain the different stackings of close-packed alloys by attractive (h 2 c 2) or repulsive (ch) interactions between metal atoms. A similar analysis explains the ordering in the hexagonal planes. The three-dimensional analysis of ordered hcp and ccp alloys shows the existence of different families of structures and the construction from structural units e.g. to long-range ordered alloys with antiphase boundaries or shearing.