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Dear authors, Thank you very much for your contribution to Chinese Physics B. Your paper has been published in Chinese Physics B, 2014, Vol.23, No.7. Attached is the PDF offprint of your published article, which will be convenient and helpful for your communication with peers and coworkers. Readers can download your published article through our website http://www.iop.org/cpb or http://cpb.iphy.ac.cn What follows is a list of related articles published recently in Chinese Physics B.
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Chin. Phys. B Vol. 23, No. 7 (2014) 078702 TOPICAL REVIEW — Statistical physics and complex systems
Collective behaviors of suprachiasm nucleus neurons under different light–dark cycles∗ Gu Chang-Gui(顾长贵) a) , Zhang Xin-Hua(张新华) b) , and Liu Zong-Hua(刘宗华) a)† a) Department of Physics, East China Normal University, Shanghai 200062, China b) Jinhua Middle School, Shanghai 200333, China (Received 25 November 2013; revised manuscript received 20 January 2014; published online 8 May 2014)
The principal circadian clock in the suprachiasm nucleus (SCN) regulates the circadian rhythm of physiological and behavioral activities of mammals. Except for the normal function of the circadian rhythm, the ensemble of SCN neurons may show two collective behaviors, i.e., a free running period in the absence of a light–dark cycle and an entrainment ability to an external T cycle. Experiments show that both the free running periods and the entrainment ranges may vary from one species to another and can be seriously influenced by the coupling among the SCN neurons. We here review the recent progress on how the heterogeneous couplings influence these two collective behaviors. We will show that in the case of homogeneous coupling, the free running period increases monotonically while the entrainment range decreases monotonically with the increase of the coupling strength. While in the case of heterogenous coupling, the dispersion of the coupling strength plays a crucial role. It has been found that the free running period decreases with the increase of the dispersion while the entrainment ability is enhanced by the dispersion. These findings provide new insights into the mechanism of the circadian clock in the SCN.
Keywords: suprachiasm nucleus, light–dark cycle, free running period, entrainment range PACS: 87.18.Yt, 05.45.Xt, 87.18.Sn
DOI: 10.1088/1674-1056/23/7/078702
1. Introduction In mammals, the circadian rhythm of physiological and behavioral activities is regulated by a principal circadian clock located in the suprachiasm nucleus (SCN) of the hypothalamus. [1–4] The SCN is bilaterally situated above the optic chiasm, composed of right SCN and left SCN. [5,6] In the condition of sunlight, the SCN controls the circadian rhythm of mammals. In addition, the SCN has two main features, as follows. In the absence of a light–dark cycle (typically under constant darkness or under constant light), the SCN keeps the free running period close to but not exactly 24 h, [7–9] i.e., maintaining a rhythmic cycle of approximately 24 h in the absence of the light–dark cycle. When there is an external light– dark cycle named the T cycle (the period T is not necessary 24 h), the SCN is able to be entrained to the T cycle, [10,11] i.e., the ability to entrain to the external light–dark cycle. Experiments have shown that both the free running period and the entrainment range are different from one species to another. For instance, the free running period is around 24.1 h for a Sudanian grass rat, 23.8 h for a southern flying squirrel, 22.9 h for a deer mouse, and 24.2 h for the human being. The entrainment range is from 22.9 h to 25.3 h for a Sudanian grass rat, from 23.5 h to 24.9 h for a southern flying squirrel, from 22.5 h to 25.1 h for a deer mouse, and from 21.5 h to 28.6 h for the human being. [3] An interesting question is how the en-
semble of neurons within the SCN produces the wide range of collective behaviors. [4,12,13] The SCN neurons have an intrinsic property of selfoscillation with periods ranging from 22 h to 28 h, which is the key to maintaining the circadian rhythm. [14,15] The molecular mechanism of the self-oscillation is based on the feedback loop of transcriptional and translational control. There are several key genes involved in the feedback loop, i.e., Per, Cry, Clock, and Bmal1. [16,17] This feedback loop can be simply described as follows. A clock gene mRNA upregulates the clock protein, and the clock protein upregulates the clock inhibitor, then the clock inhibitor downregulates the clock gene mRNA. Thus, the clock gene mRNA, the clock protein, and the clock inhibitor in a neuron constitute a negative feedback loop. [16] The individual neurons in SCN run with different intrinsic periods, but the output period of the SCN is uniform. This implies that the neurons are coupled to form a network, and synchronize to produce a common period. Many works have focused on the coupling mechanism between neurons within the SCN. Experiments revealed that the neurons are coupled mainly through transmitters, e.g., Gamma aminobutyric acid (GABA), vasoactive intestinal polypeptide (VIP), arginine vasopressin (AVP), and so on. [18–21] These neurons are functionally and physically coupled into two subgroups within each side of the SCN (right/left SCN), [22–25] i.e., a ventrolateral part
∗ Project
supported by the National Natural Science Foundation of China (Grant Nos. 11135001 and 11375066), the Joriss Project, China (Grant No. 78230050), and the National Basic Research Program of China (Grant No. 2013CB834100). † Corresponding author. E-mail:
[email protected] © 2014 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn
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Chin. Phys. B Vol. 23, No. 7 (2014) 078702 (VL) containing 25% SCN neurons and a dorsomedial part (DM) possessing the remaining neurons. The VL charges for receiving light information from the retinohypothalamic tract (RHT), and relays the light information to the DM. The neurons located in the VL mainly produce VIP, and the neurons situated in the DM mostly express AVP. [18–20] The communication between the VL and the DM is relied on GABA. [19] However, the coupling mechanism of left SCN and right SCN is still unclear. [26] Figure 1 shows the schematic diagram of the interaction within the SCN and the input/output of the SCN.
2. Experimental findings under different light– dark cycles
Left SCN g1 DM
VL g2
gs
RHT
Activity
L
ga
Light
g1 DM
and the entrainment ability of the SCN. [27,29] In the following sections, we will review the effect of the heterogenous coupling on the collective behaviors of the SCN in detail. The rest of the paper is organized as follows. In Section 2, we will summarize the experimental findings under four kinds of light–dark cycles, i.e., constant darkness, constant light, the 24 h light–dark cycle, and the T cycle. Then, in Section 3, we will discuss the theoretical explanations of the experiment findings by a modified Goodwin model. Finally, we provide a discussion and give a conclusion in Section 4.
VL g2
Right SCN Fig. 1. Interaction within SCN and intput/output of SCN. Here L denotes the strength of light information, and g represents the coupling strength. The light information from RHT is received by the VL containing 25% SCN neurons, and then the VL relays this information to the DM composed of 75% SCN neurons. Both the VL and the DM take part in the regulation of the circadian rhythm of activity. The arrows represent the directed couplings, and the thickness denotes the coupling strength. The coupling strength g1 from the VL to the DM is much stronger than the coupling strength g2 from the DM to the VL, while the coupling between the left SCN and the right SCN is still unclear. The coupling strength gs from the SCN to the behavioral activity is larger than the feedback strength ga .
The SCN is a heterogeneous network where the VL neurons are sensitive to light information but the DM neurons are not. Physically, the size of the VL neurons is smaller than that of the DM neurons, and the VL neurons are positioned denser than the DM neurons. [4] Since the sensitive ability to VIP (or AVP) varies between the VL neurons and the DM neurons, and the influence of the VL neurons to the DM neurons is more than that of the DM neurons to the VL neurons, these factors result in heterogenous coupling strengths. The influence of this heterogenous coupling has been recently addressed by Gu et al. from two aspects, i.e., the mean coupling strength and its dispersion. [27–29] It is found that the homogeneous coupling between the neurons plays a key role in determining the free running period and the entrainment ability of the SCN. The free running period increases as the coupling strength increases. [30–32] While the entrainment range is negatively related to the coupling strength. [11,33] Recently, Gu et al. considered the heterogeneous coupling and found that in addition to the mean value of coupling strengths, the dispersion of coupling strengths also plays an important role in determining the free running period
Owing to the multiple recording methods, experiments can investigate the circadian rhythm from three levels: tissue level, organismal level, and supra-organismal level. The research at the tissue level is mainly focused on the concentration of gene expression in vitro, for example Per mNRA of a single neuron measured by bioluminescence. [5,34,35] At the organismal level, the animal behavior is often used as the recording marker, including wheel running, movements, and drinks. [36,37] Another marker used at the organismal level is the multi neuronal unit activity (MUA), which plants an electrode into the brain and records the neuronal activity within the SCN in vivo. [38,39] At the supra-organismal level, the social interaction between animals is considered, where the animal behavior is often recorded as a marker of the circadian rhythm. [40] With these recording methods, in order to explore the network structure of the SCN, the multiple light conditions are applied. Compared to other operations, e.g., anatomy or drug application, there is little physical damage on the SCN exposed to light. Furthermore, there are several kinds of light conditions in nature. For example, there is perpetual day (perpetual night) at the poles, which corresponds to the constant light (constant darkness) in experiments. The photoperiod varies among seasons, especially in the regions of high latitudes. Jet lag happens to travelers across time zones and in shift works. We introduce here the experimental results on the SCN under four kinds of light–dark cycles as follows. 2.1. Constant darkness It has been reported that there is a circadian rhythm in mammals even in the absence of a light–dark cycle, [7–9] indicating that there is an endogenous clock in mammals. Under constant darkness, it is interesting to find that the free running period changes from one species to another. Recently, studies revealed that this diversity also exists in age, ethnicity, and so on. [41,42] To show the changing process in activity patterns, this locomotor activity is usually displayed in the double-plot actogram (double means 24 h times 2) in the field of circadian
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Chin. Phys. B Vol. 23, No. 7 (2014) 078702 rhythm. As an example, figure 2 shows a schematic illustration of the double-plot actogram under constant darkness, where the x axis represents the external time, the y axis denotes the number of continuous days, and the red dots indicate the activity onset. It is visible that the activity onset is not shifted in Fig. 2(a), but delayed in Fig. 2(b) every day. Thus, the free running period is 24 h in Fig. 2(a) while it is larger than 24 h in Fig. 2(b).
Days
0
EXT/h 24
0
0
Days
5
Free running
10
20
Transition
Splitting
48 25
(a)
Fig. 3. Locomotor activity of one hamster under constant light in a double-plot actogram, where the x axis represents the external time, and the y axis denotes the number of continuous days. In the first 10 days, the animal shows the free running behavior with a period larger than 24 h. Then in the next 5 days, there emerge two activity bouts within one day, which depart from each other gradually. In the last 10 days, the phase difference between the two bouts is stable and equals to 12 h. This figure is made from artificial data.
20 30
Days
48
15
10
0
EXT/h 24
0
(b)
10 20 30
Fig. 2. Locomotor activity of one mouse under constant darkness in a double-plot actogram, where the x axis represents the external time, the y axis denotes the number of continuous days, and the red dots indicate the activity onset. (a) The free running period is 24 h and the external time of activity onset is a constant 11 h. (b) The free running period is larger than 24 h and the activity onset is delayed every day. This figure is made from artificial data.
In MUA studies in vivo, the SCN shows a strong rhythm under constant darkness, as found in the 24 h light–dark cycle (light 12 h and dark 12 h in one cycle). [43] There is a high synchronization between the neurons and the strong rhythm in a single neuron oscillation under both constant darkness and 24 h light–dark cycle conditions. [44,45] These studies suggest that the neurons are coupled very well under constant darkness. 2.2. Constant light Another form of absence of a light–dark cycle is in constant light conditions, such as the arctic ground squirrels. Exposed to constant light, animals may show three kinds of behavioral activities recorded by wheel running. [1,5,46,47] In the first one, animals keep free running with a period larger than 24 h. In the second one, the 24 h activity dissociates into two 12 h activity components which are 12 hs apart or in anti-phase (this phenomenon is called phase-splitting), thus the total activity exhibits a 12 h rhythm. In the third one, animals lose their activity rhythm. The free running and the phase-splitting behaviors under constant light are shown in Fig. 3. To further understand the rhythm regulation of the SCN to behavior activities, researchers investigated the circadian rhythm of the SCN tissue in vitro.
In the case of phase-splitting, researchers found that the behavioral activity shows a 12 h rhythm because of the antiphase between the left SCN and the right SCN. Within each side of the SCN from the same animal, the concentration of Per mRNA is recorded in one slice. Within each slice, the neurons are in-phase and high synchrony, thus the whole slice shows a high amplitude oscillation with a period equal to 24 h. Between the slices of right and left SCNs, the phase difference is 12 h, i.e., anti-phase. Furthermore, the ablation of one side of the SCN causes the disappearance of one activity component, and the animal activity restores the 24 h circadian rhythm. [6] Thus, one activity component is regulated by one side of the SCN. In the case of maintaining a 24 h circadian rhythm, there is no phase difference between the left SCN and the right SCN. Within the left or right SCN, the presence of high synchrony between the neurons leads to a large amplitude of the slice. Thus, the output of the whole SCN shows a pronounced 24 h rhythm, as found under constant darkness. In the case of disappearance of the rhythm, there are two alternative explanations. One is that the rhythm of a single neuron oscillator vanishes, [1] and the other is that the synchrony between the neurons is lost. [46] 2.3. 24 h light–dark cycle For mammals, the most crucial function of the SCN is to maintain synchronization to the external 24 h light–dark cycle. Most mammals have evolved to exhibit a stable phase difference to the external 24 h light–dark cycle. For instance, mice are active during the night-time, and human beings are active during the daytime. The difference between the free running period and 24 h contributes to the stable phase difference, i.e., animals with a free running period of less than 24 h are active during the night-time (they are called nocturnal animals)
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Chin. Phys. B Vol. 23, No. 7 (2014) 078702
The stable phase difference between the internal circadian clock and the external 24 h cycle may be disturbed by jet-lag across different time zones or in factory or hospital shift work that many people have suffered. After traveling to a new time zone, the VL will be quickly adjusted to the new 24 h cycle, while the DM will remain in the phase of the previous 24 h cycle at the beginning and then be gradually adjusted to the new 24 h cycle. The amount of adjusting time depends on the difference between the time zones, i.e., roughly 1 h time difference takes 1 day to be adjusted. [23,52,53] Moreover, the process of adjustment also proves that the VL directly receives the light information and relays it to the DM.
If the external T cycle is in the entrainment range, the SCN will remain synchronized. If the T cycle is out of the entrainment range, the SCN will lose the synchronization and its ability of being entrained to the T cycle partially or fully. [55,56] For example, under the T cycle of 22 h, the behavioral activity of a rat shows two components, see Fig. 4. One component shows a 22 h period, which is the same as the period of the external T cycle, and the other shows a 24 h period, which is close to the free running period under constant darkness. Recently, experiments found that the 22 h component is regulated by the VL, and the 24 h component is controlled by the DM. [56] Thus, under the external T cycle of 22 h, there is a desynchronization between the VL and the DM.
0
0
EXT/h 24
48
20 Days
and animals with a free running period of larger than 24 h are active during the daytime (they are called diurnal animals). [48] For the human being, the free running period is around 24 h. [8] Thus, people with a free running period of less than 24 h wake up early, and prefer to work in the morning. These people are called “morning types”. On the other hand, people with a free running period of larger than 24 h sleep late, and prefer to work in the evening. These people are called “evening types”. [49] Unfortunately, some people are in lack of a stable phase difference to the 24 h light–dark cycle on account of their free running period being far from 24 h. [50,51]
40
60
2.4. T cycle
80
The SCN can be entrained not only to the 24 h light–dark cycle, but also to an artificial T cycle, where T denotes the period of the cycle. The artificial T cycle can provide some realistic significance. First, the rotation periods reflected by the light–dark cycle of other planets are not 24 h. For instance, the rotation period of Mars is 24.7 h. Second, the rotation period of Earth is gradually increased during its evolution. Third, mathematically, the free running period (τ) of one species is 0 = 24/τ. Due to the variation set as 1, and 24 h is set as T24 of the free running periods among species, the normalized pe0 will also vary among species. Thus, the T 0 is not a riod T24 24 constant among species. Most animals are able to be entrained to the 24 h cycle. While for the T cycle, an animal may perform two kinds of behavioral activities. One is that the animal may display the same period as the T cycle. This phenomenon is called the entrainment to the T cycle. [10,11,54] The other is that the period of the animal remains different from the T cycle, thus the animal loses the entrainment to the T cycle. [55,56] The range of T cycle for an animal to be entrained is called the entrainment range. In mice, the SCN can be entrained in the range from a 22 h cycle to a 28 h cycle. The entrainment range varies among species. The entrainment range can be also influenced by external conditions such as the light intensity and the wave form of the light–dark cycle ( e.g., square wave, sine wave). [57,58]
Fig. 4. Locomotor activity under the T cycle of 22 h in doubleplot actogram, where the x axis represents the external time, the y axis denotes the number of continuous days, and the grey region corresponds to darkness. There are two activity components which are represented by red solid and green dash lines, respectively. The period of the red solid lines is close to 24 h, while the period of the green dash lines equals to 22 h. This figure is made from artificial data.
3. Theoretical explanations based on heterogeneous couplings To explain the above experimental findings, much attention has been paid to the phenomena of collective behaviors of the SCN, such as the free running periods under constant darkness, phase-splitting under constant light, and entrainment to a T cycle, which emerge from the ensemble of neurons with different intrinsic periods. An SCN neuron may be regarded as a limit cycle oscillator, which is based on the gene translationtranscriptional feedback loop. Such behavior of the limit cycle has been well described by the Goodwin model for individual SCN neurons, which has three variables. [27–29,31,59–64] For simplicity, the Kuramoto model and the Poincar´e model have also been included for analysis. [11,27,28,30,65] Previously, the coupling between the neurons was assumed to be homogeneous and calculated by the mean-field method. However, the above experiment findings have revealed that the coupling between neurons is heterogeneous. For example, it was pointed
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Chin. Phys. B Vol. 23, No. 7 (2014) 078702 out that the coupling from the VL to the DM is dominant, and the inverse coupling from the DM to the VL is relatively weak. In addition, the sensitive abilities of the neurons to transmitters are non-identical. The neurons located in the VL are sensitive to VIP, while the neurons situated in the DM are sensitive to AVP. Therefore, recent works have focused on the influence of the heterogeneous coupling. In this section, we will briefly introduce these theoretical works. 3.1. A modified Goodwin model The Goodwin model has been widely used in studying the circadian rhythm of mammals. [27–29,31,59–64] In this model, a single SCN neuron is represented by three variables, i.e., a clock gene mRNA, a clock protein, and a transcriptional inhibitor. This Goodwin model is usually used for the case of homogeneous coupling. To consider the case of heterogeneous coupling, a modified Goodwin model has been provided for N coupled neurons and can be written as x˙i = y˙i = z˙i = V˙i = F =
light term Li can be represented by Li = Kf ,
mod(t, T ) < T /2,
i = 1, 2, . . . , pN,
Li = 0,
mod(t, T ) ≥ T /2,
Li = 0,
i = pN + 1, pN + 2, . . . , N,
i = 1, 2, . . . , pN,
(2) (3)
where p represents the ratio of the number of neurons sensitive to light information to the total number of SCN neurons, thus pN is the number of SCN neurons in the VL which are sensitive to light information, and Kf is the light intensity. We will mainly use this modified Goodwin model to explain the experiment findings in the following subsections. F x
z
V
y
V
x
z
y
k1n
xi gi F α1 n n − α2 + Li , + αc k1 + zi k2 + xi kc + gi F yi k3 xi − α4 , k4 + yi zi k5 yi − α6 , k6 + zi Vi k7 xi − α8 , i = 1, 2, . . . , N, k8 +Vi 1 N ∑ Vi , N i=1
Fig. 5. Schematic diagram of the Goodwin model composed of two neuron oscillators under constant darkness, where x, y, and z constitute a negative feedback loop in one clock cell, and x, y, and z represents a clock gene mRNA, a clock protein, and a transcriptional inhibitor, respectively. The oscillators are coupled through the mean field F, and F is defined as the mean value of the transmitters which are induced by the clock gene mRNA x.
3.2. Free running under constant darkness (1)
where xi , yi , and zi constitute a negative feedback loop in the clock cell i, x, y, and z indicate a clock gene mRNA, a clock protein, and a transcriptional inhibitor, respectively, F performs as a mean field, Li denotes the light information strength from RHT, and gi is regarded as the coupling strength and describes the sensitivity of neuron i to one transmitter (for instance VIP). Note that both the coupling strength gi and the light term Li is heterogenous based on the findings from experiments. When we set gi = gc and Li = Lc , model (1) will return to the original Goodwin model. The schematic diagram of the modified Goodwin model is illustrated in Fig. 5 under constant darkness. In Eq. (1), the main differences among the non-identical neurons are represented by the heterogenous coupling strength gi . This kind of heterogenous coupling strength can be characterized by the mean value hgi of the coupling strength and its standard deviation δ (named dispersion). In addition, the heterogenous light term Li is also taken into account. Experiments show that only the SCN neurons situated in the VL are sensitive to light information, while the neurons in the DM are not sensitive to light information. The DM will obtain the light information through the transmitter, i.e., coupling. Thus, the
Under constant darkness, the free running period of mammals changes from one species to another. This variation may come from two aspects. One is the different distributions of the intrinsic periods of individual neurons for different species, the other is the different couplings for different species. For the first aspect, a recent work shows that the standard deviation (dispersion) of the distribution of the intrinsic periods has little effect on the free running periods. [30] For the second aspect, several theoretical works have proved that the free running period increases as the coupling strength increases. [27,31] In addition, the amplitude of the SCN network goes up with the increase of the coupling strength. [31] Figure 6(a) shows the relationship between free running period τ and coupling strength hgi when the dispersion δ = 0, which is a monotonously increasing relationship. Except for the coupling strength, it is found that the distribution of the coupling strength among neurons will also influence the free running period. Figure 6(b) shows how the dispersion (standard deviation) of the coupling strength influences the free running period. [27] It is easy to see that the free running period τ monotonically decreases with the increase of the dispersion δ . Noticing that we have Li = 0, i = 1, 2, . . . , N in Eq. (2) under constant darkness, there is no difference between the VL and the DM. Thus, the results in
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Chin. Phys. B Vol. 23, No. 7 (2014) 078702 Figs. 6(a) and 6(b) work for both the neurons in the VL and the DM. 26 (a)
(b)
δ=0.0
25
=1.0
0.12
23.5 V
τ/h
τ/h
24.0
and amplitude death of the SCN, respectively. In fact, these three kinds of behaviors correspond to the free running, phasesplitting, and loss of rhythm found in animals, respectively. Furthermore, the feedback term also influences the period of the in-phase synchronization, which is consistent with the influence of exercise on the SCN period in mice. [66]
0.08
(a)
0.04 24
0 0.12 V
23.0
0.8
1.0 1.2
1.4
0
0.1
0.2
0 0.12 V
Fig. 6. Dependence of free running period τ on the mean coupling strength hgi and its dispersion δ . (a) The free running period τ versus the mean coupling strength hgi for δ = 0; (b) the free running period τ versus the dispersion δ for hgi = 1.0. This figure is reproduced from Figs. 1 and 2 in Ref. [27], the parameters are set as those used in Ref. [27].
b N1 a N c N Vi + Vi + ∑ Vi,−τ , ∑ ∑ N i=1 N i=N1 +1 N i=1
(c)
0 3800
3850
3900
t/h
Under constant light, the presence of phase-splitting between the left SCN and the right SCN inspires the theoretical research on its mechanism. The article [65] assumed that the feedback of the behavioral activity is crucially involved in phase-splitting based on the modified Kuramoto model. Recently, experiments [38,39] found that the activity indeed has a feedback to the SCN, while the feedback delay is unclear. There are three coupling interaction terms to one neuron oscillator in Ref. [65], i.e., the interactions from the same side of the SCN neurons, from the other side of the SCN, and the feedback of the behavioral activity. The feedback is assumed to have a time delay of several hours. We apply these assumptions to the modified Goodwin model, [28] where the mean field F of Eq. (1) is modified into
F2 =
0.08 0.04
Fig. 7. Three kinds of collective behaviors of the SCN neurons: [28] (a) in-phase synchronization between the left SCN and the right SCN; (b) phase-splitting (anti-phase) between the left SCN and the right SCN; (c) amplitude death of the SCN neurons. The parameters are a = 1.64, b = 0.32, and c = 0.02 in panel (a); a = 1.64, b = 0.16, and c = 0.1 in panel (b); and a = 1.16, b = 0.28, and c = 0.28 in panel (c). The parameters are set as those used in Ref. [28].
3.3. Phase-splitting under constant light
b N c N a N1 V + V + i i ∑ N ∑ ∑ Vi,−τ , N i=1 N i=1 i=N1 +1
(b)
0.04
0.3
δ
F1 =
0.08
(4)
where indices ‘1’ and ‘2’ represent the right SCN and the left SCN, respectively. The parameters a, b, and c represent the coupling weights from the same group, a different group, and the part due to the time delay, respectively, and satisfy the relationship (a + b)/2 + c = 1. τ represents the time delay of the behavioral activity feedback. We find that there are three kinds of collective behaviors of SCN neurons in Eq. (4), including phase-splitting (anti-phase) between the right SCN and the left SCN, in-phase synchronization between the right SCN and the left SCN, and the amplitude death of the SCN neurons. Figure 7 shows the results, where panels (a), (b), and (c) represent the cases of in-phase synchronization, phase-splitting,
In addition, the dispersion δ of the coupling strength distribution has been investigated in Ref. [28]. It was found that the dispersion δ has little effect on the three kinds of collective behaviors of the SCN neurons, but that it does have an influence on the SCN period. 3.4. Entrainment to T cycle The entrainment ability of the SCN neurons to an external T cycle can be influenced by several intrinsic parameters such as the coupling strength g, [11,33] the dispersion δ of the coupling strength distribution, [29] the ratio p of the number of light-sensitive neurons to the total number of SCN neurons, [29,67] and the dispersion µ of the distribution of single neuron intrinsic periods. [30] To check how these parameters influence the entrainment, we first consider the case of the SCN under a special T cycle condition T = 22 h (11 h light alternating with 11 h darkness) and focus on the effect of p. We find that both the periods of the VL and the DM can be easily entrained to T = 22 h, i.e., the external T cycle. [29] Then, we consider the case of T = 26 h (13 h light alternating with 13 h darkness). Surprisingly, we find that with the increase of p, the period of the DM is not entrained to T = 26 h but separated away from it. Figure 8(a) shows the result where the diamonds and circles represent the periods of the VL and the DM, respectively. From Fig. 8(a), we see that the period of the VL can be easily frequency-locked to the external period when p is small, whereas the period of the
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Chin. Phys. B Vol. 23, No. 7 (2014) 078702 DM will linearly decrease with the increase of p until a critical pc . There is a jumping transition at p = pc where the period of the DM jumps from 20.8 h to 26 h. The period of the DM will be entrained to the external period once p > pc . Then, an interesting question arises: what is the mechanism for this jumping transition? To understand the jumping transition better, we check how the oscillation amplitudes of the DM oscillators change with p. By checking the behaviors of xi in Eq. (1), we find that the oscillators in the DM are almost 1 synchronized. Thus, we let hXi = (1−p)N ∑Ni=1+pN xi represent the oscillations in the DM. Figures 8(b)–8(e) show the oscillations for p = 0.02, 0.2, 0.408, 0.42, respectively. It is easy to see that the amplitude of hXi is significantly reduced with the increase of p and reaches its minimum at the transition point of pc ≈ 0.408. This reduction of amplitude makes the neurons of the DM lose their intrinsic property and thus they can be entrained to the external 26 h cycle. 27
0.4
(a)
DM
VL
Period/h
25 24 23 22 21 0
0.1
0.2 0.3 p
0.4
0.5
a circadian clock to a T cycle. In Refs. [11] and [33], the external signal was temperature, and the entrainment ranges of the SCN (master clock) and the lung (peripheral clock) were compared in the case of a homogeneous coupling strength. The experiment results showed that the wider entrainment range exists in the peripheral clock, and the narrower entrainment range exists in the master clock. [11] Since the coupling strength of the SCN neurons is stronger than that of the lung cells, it was concluded that the entrainment range decreases with the increase of the coupling strength. This conclusion has been confirmed by the simulations and theoretical results based on the Poincar´e model. [11] An interesting question is, besides the temperature signal, what about other external signals for the SCN, such as the light signal? Based on the Poincar´e model and the Goodwin model, Gu
(b)
et al. recently found that the dependence of the entrainment
0 0.4 (c) 0.2
range on the coupling strength can be influenced by the pa-
0.2
26
The coupling is found to be crucial in the entrainment of
rameter p. [30,67] The Poincar´e model has the following form:
0 0.4 (d) 0.2 0 0.4 (e) 0.2 0 0
2yi π + gF + Li , τσi 2xi π y˙i = γyi (A0 − ri ) + , i = 1, 2, . . . , N, τσi x˙i = γxi (A0 − ri ) −
250 500 Time/h
F =
Fig. 8. The evolution of VL and DM subgroups for different parameter p during a 26 h cycle, where the parameters are taken as N = 500 and Kf = 0.02. (a) Periods of VL and DM versus p, where the diamonds and circles represent the periods of VL and DM, respectively. (b)–(e) The oscillations of hXi for p = 0.02, 0.2, 0.408, 0.42, respectively.
1 N ∑ xi , N i=1
(5)
where γ is the relaxation parameter, A0 and τσi represent the amplitude and the intrinsic period of anq individual oscillator in the absence of a light–dark cycle, ri =
In summary, the entrainment abilities for T = 22 < 24 and T = 26 > 24 are different. For a fixed p, an interesting quantity will be the range between the lower limit of entrainment (T < 24) and the higher limit of entrainment (T > 24), called the entrainment range. When the external light–dark cycle is outside this entrainment range, the SCN neurons will lose their synchronization and thus the T cycle cannot be successfully entrained to the DM. For simplicity, either the lower limit of entrainment (LLE) or the higher limit of entrainment (HLE) is often used to represent the entrainment range, provided that the LLE and the HLE are symmetrically distant from the freerunning period. [11,30] For example, the entrainment range is from 23.5 h (LLE) to 24.9 h (HLE) for Peromyscus leucopus, from 22.8 h to 26.5 h for Mus musculus, from 21.5 h to 28.6 h for Homo sapiens, and from 14.9 h to 32.4 h for Eutamias sibiricus. We may use the LLE 23.5 h to represent the entrainment range from 23.5 h to 24.9 h for Peromyscus leucopus and the same way for other animals.
xi2 + y2i , and σi satis-
fies a normal distribution with mean value 1 and deviation µ. The Li represents the light signal and is defined as Li =
Kf sin(Ωt), i = 1, 2, . . . , pN, 0, i = pN + 1, pN + 2, . . . , N,
(6)
where Kf and Ω represent the light intensity and the angular frequency of the light–dark cycle, respectively. Figure 9 shows the results of Eqs. (5) and (6). From Fig. 9, we see that for p = 1, the LLE decreases with the increase of the coupling strength. For p < 1, the relationship between the LLE and the coupling strength is represented by a unimodal curve with a maxima at gc ≈ 0.08, indicating that there is an optimal coupling for the entrainment. In the situation of g ≥ gc , the relationship is positive, while in the situation of g < gc , the relationship is negative.
078702-7
Chin. Phys. B Vol. 23, No. 7 (2014) 078702 p=1 p=0.75 p=0.5 p=0.25 p=0.1
21 LLE/h
Entrainment range
20
22
23
24 0.05
0
0.10 g
0.15
0.20
Fig. 9. The entrainment range of the SCN versus coupling strength under different ratios p in the case of homogeneous coupling strength. It is noticed that the entrainment range decreases with the increase of the coupling strength when p = 1. When p < 1, there is an optimal entrainment range at gc ≈ 0.08. In the situation of g ≥ gc , the relationship is positive, while in the situation of g < gc , the relationship is negative. This figure is reproduced from Fig. 1 in Ref. [67]. The light intensity is Kf = 0.01, and the other parameters are chosen as those used in Ref. [67].
In addition to the coupling strength, it is found that the dispersion µ also influences the entrainment range LLE. Figure 10 shows the results where all neurons are sensitive to light (p = 1). From Fig. 10, we see that the entrainment range LLE increases with the increase of dispersion µ, indicating that increasing µ is beneficial for the entrainment range. This result also works for the case of p < 1 and has been confirmed by the theoretical analysis in Ref. [30]. Thus, it may provide a new clue to explain the variation of entrainment ranges between species. 20 Kf=0.15 Kf=0.20
LLE/h
entrainment range
Kf=0.10
22
24 0
0.05
0.10 µ
0.15
0.20
Fig. 10. The influence of dispersion µ on the lower limit of entrainment of the SCN, where all neurons are sensitive to light (p = 1). This figure is reproduced from Fig. 2 in Ref. [30]. Three kinds of light intensities Kf are considered, and the other parameters are chosen as those used in Ref. [30].
constant light, and different T cycles including the 24 h cycle. These three aspects are mainly focused on the diversity of the free-running periods, phase-splitting, and entrainment ability, respectively. Then, we discussed how the modified Goodwin model can be applied to all three aspects. We revealed that these collective behaviors of the SCN neurons can be influenced not only by the heterogenous intrinsic properties of the neurons but also by the heterogenous couplings through transmitters among the neurons, in contrast to the previous theoretical works only on the effect of the homogenous coupling strength. For the case of constant darkness, the neurons in the VL and the DM are treated as the same. The free-running period τ is influenced by both the mean coupling strength hgi and the dispersion δ . The τ increases with increasing hgi but decreases with the increase of δ . For the case of constant light, the left SCN and the right SCN neurons show an anti-phase synchronization and thus can be used to explain the phasesplitting phenomenon observed in mammals. Interestingly, this phase-splitting behavior is not influenced by the dispersion δ . For the case of different T cycles, the main concern is focused on the entrainment ability. All the animals are used to a 24 h cycle of circadian rhythm. When the T cycle is not a 24 h cycle, the entrainment abilities for T > 24 and T < 24 will be different and can be described by the lower limit of entrainment and the higher limit of entrainment, respectively. Similar to the case of constant darkness, the entrainment range can also be influenced by both the mean coupling strength hgi and the dispersion δ or µ. However, there are two differences between these two cases. The first one is that τ monotonously increases with increasing hgi while there is an optimal hgi for the LLE. The second one is that τ decreases with the increase of δ but the LLE increases with increasing δ or µ. In addition to the heterogenous couplings, the effect of the heterogenous intrinsic properties of the neurons on the SCN behaviors are also discussed here. We considered the effect of the ratio of the number of light-sensitive neurons to the total number of SCN neurons. On one hand, the ratio influences the entrainment range, i.e., it increases with the ratio. On the other hand, the ratio also affects the relationship between the entrainment range and the coupling strength, i.e., the relationship remains negative when ratio = 1 but becomes a unimodal curve when ratio < 1. These results may shed light on the field of circadian rhythm.
References
4. Discussion and conclusion In this review, we have summarized the collective behaviors of the heterogeneous SCN neurons based on the experimental findings and pointed out that they can be classified into three aspects by the light–dark cycles, i.e., constant darkness,
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078702-9
Chinese Physics B Volume 23
Number 7
July 2014
TOPICAL REVIEW — Magnetism, magnetic materials, and interdisciplinary research 077308
Exotic electronic states in the world of flat bands: From theory to material Liu Zheng, Liu Feng and Wu Yong-Shi
077501
Perpendicular magnetic tunnel junction and its application in magnetic random access memory Liu Hou-Fang, Syed Shahbaz Ali and Han Xiu-Feng
078704
Formation of multifunctional Fe3 O4 /Au composite nanoparticles for dual-mode MR/CT imaging applications Hu Yong, Li Jing-Chao, Shen Ming-Wu and Shi Xiang-Yang TOPICAL REVIEW — Statistical physics and complex systems
070501
Nonequilibrium thermodynamics and fluctuation relations for small systems Cao Liang, Ke Pu, Qiao Li-Yan and Zheng Zhi-Gang
070507
Level spacing statistics for two-dimensional massless Dirac billiards Huang Liang, Xu Hong-Ya, Lai Ying-Cheng and Celso Grebogi
070512
Nonequilibrium work equalities in isolated quantum systems Liu Fei and Ouyang Zhong-Can
070513
Equivalent formulations of “the equation of life” Ao Ping
070514
Sub-diffusive scaling with power-law trapping times Luo Liang and Tang Lei-Han
074501
Effective temperature and fluctuation-dissipation relation in athermal granular systems: A review Chen Qiong and Hou Mei-Ying
076402
Percolation on networks with dependence links Li Ming and Wang Bing-Hong
078701
RNA structure prediction: Progress and perspective Shi Ya-Zhou, Wu Yuan-Yan, Wang Feng-Hua and Tan Zhi-Jie
078702
Collective behaviors of suprachiasm nucleus neurons under different light–dark cycles Gu Chang-Gui, Zhang Xin-Hua and Liu Zong-Hua
078705
Proteins: From sequence to structure Zheng Wei-Mou
078901
Statistical physics of hard combinatorial optimization: Vertex cover problem
078902
Zhao Jin-Hua and Zhou Hai-Jun Statistical physics of human beings in games: Controlled experiments Liang Yuan and Huang Ji-Ping (Continued on the Bookbinding Inside Back Cover)
078903
A mini-review on econophysics: Comparative study of Chinese and western financial markets Zheng Bo, Jiang Xiong-Fei and Ni Peng-Yun
078905
Zero-determinant strategy: An underway revolution in game theory Hao Dong, Rong Zhi-Hai and Zhou Tao
078906
Attractive target wave patterns in complex networks consisting of excitable nodes Zhang Li-Sheng, Liao Xu-Hong, Mi Yuan-Yuan, Qian Yu and Hu Gang RAPID COMMUNICATION
073402
A double toroidal analyzer for scanning probe electron energy spectrometer Xu Chun-Kai, Zhang Pan-Ke, Li Meng and Chen Xiang-Jun
077505
Multiferroic properties in terbium orthoferrite Song Yu-Quan, Zhou Wei-Ping, Fang Yong, Yang Yan-Ting, Wang Liao-Yu, Wang Dun-Hui and Du You-Wei GENERAL
070201
Symmetries and variational calculation of discrete Hamiltonian systems Xia Li-Li, Chen Li-Qun, Fu Jing-Li and Wu Jing-He
070202
Non-autonomous discrete Boussinesq equation: Solutions and consistency Nong Li-Juan and Zhang Da-Juan
070203
Rogue-wave pair and dark-bright-rogue wave solutions of the coupled Hirota equations Wang Xin and Chen Yong
070204
Optimal switching policy for performance enhancement of distributed parameter systems based on event-driven control Mu Wen-Ying, Cui Bao-Tong, Lou Xu-Yang and Li Wen
070205
Impulsive effect on exponential synchronization of neural networks with leakage delay under sampleddata feedback control S. Lakshmanan, Ju H. Park, Fathalla A. Rihan and R. Rakkiyappan
070206
Co-evolution of the brand effect and competitiveness in evolving networks
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Guo Jin-Li An interpolating reproducing kernel particle method for two-dimensional scatter points Qin Yi-Xiao, Liu Ying-Ying, Li Zhong-Hua and Yang Ming
070208
Average vector field methods for the coupled Schr¨odinger KdV equations Zhang Hong, Song Song-He, Chen Xu-Dong and Zhou Wei-En
070301
Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states: Non-classical and non-Gaussian properties Xu Xue-Xiang, Yuan Hong-Chun and Wang Yan
070302
Global entanglement in ground state of {Cu3 } single-molecular magnet with magnetic field Li Ji-Qiang and Zhou Bin
070303
Rise of quantum correlations in non-Markovian environments in continuous-variable systems
070304
Liu Xin and Wu Wei Optimal 1 → 𝑀 phase-covariant cloning in three dimensions Zhang Wen-Hai, Yu Long-Bao, Cao Zhuo-Liang and Ye Liu
(Continued on the Bookbinding Inside Back Cover) 070305
Symmetric quantum discord for a two-qubit state Wang Zhong-Xiao and Wang Bo-Bo
070306
Quantum correlations in a two-qubit anisotropic Heisenberg XY Z chain with uniform magnetic field Li Lei and Yang Guo-Hui
070307
Adiabatic tunneling of Bose–Einstein condensates with modulated atom interaction in a double-well potential Xin Xiao-Tian, Huang Fang, Xu Zhi-Jun and Li Hai-Bin
070308
Ground state of rotating ultracold quantum gases with anisotropic spin orbit coupling and concentrically coupled annular potential Wang Xin, Tan Ren-Bing, Du Zhi-Jing, Zhao Wen-Yu, Zhang Xiao-Fei and Zhang Shou-Gang
070502
Delay-dependent asymptotic stability of mobile ad-hoc networks: A descriptor system approach Yang Juan, Yang Dan, Huang Bin, Zhang Xiao-Hong and Luo Jian-Lu
070503
Mapping equivalent approach to analysis and realization of memristor-based dynamical circuit Bao Bo-Cheng, Hu Feng-Wei, Liu Zhong and Xu Jian-Ping
070504
Signal reconstruction in wireless sensor networks based on a cubature Kalman particle filter Huang Jin-Wang and Feng Jiu-Chao
070505
Space time fractional KdV Burgers equation for dust acoustic shock waves in dusty plasma with nonthermal ions Emad K. El-Shewy, Abeer A. Mahmoud, Ashraf M. Tawfik, Essam M. Abulwafa and Ahmed Elgarayhi
070506
PC synchronization of a class of chaotic systems via event-triggered control Luo Run-Zi and He Long-Min
070508
Partial and complete periodic synchronization in coupled discontinuous map lattices Yang Ke-Li, Chen Hui-Yun, Du Wei-Wei, Jin Tao and Qu Shi-Xian
070509
Distributed formation control for a multi-agent system with dynamic and static obstacle avoidances Cao Jian-Fu, Ling Zhi-Hao, Yuan Yi-Feng and Gao Chong
070510
Fault-tolerant topology in the wireless sensor networks for energy depletion and random failure Liu Bin, Dong Ming-Ru, Yin Rong-Rong and Yin Wen-Xiao
070511
Nonequilibrium behavior of the kinetic metamagnetic spin-5/2 Blume–Capel model
070701
¨ ut Temizer Um¨ Ferromagnetic materials under high pressure in a diamond-anvil cell: A magnetic study Wang Xin, Hu Tian-Li, Han Bing, Jin Hui-Chao, Li Yan, Zhou Qiang and Zhang Tao
070702
Mutator for transferring a memristor emulator into meminductive and memcapacitive circuits Yu Dong-Sheng, Liang Yan, Herbert H. C. Iu and Hu Yi-Hua ATOMIC AND MOLECULAR PHYSICS
073101
2 3 A typical slow reaction H(2 S) + S2 (𝑋 3 Σ− g ) → SH(𝑋 Π) + S( P) on a new surface: Quantum dynamics
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073201
On-chip optical pulse shaper for arbitrary waveform generation Liao Sha-Sha, Yang Ting and Dong Jian-Ji
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Dynamical correlation between quantum entanglement and intramolecular energy in molecular vibrations: An algebraic approach Feng Hai-Ran, Meng Xiang-Jia, Li Peng and Zheng Yu-Jun
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Potential energy curves and spectroscopic properties of X2 Σ+ and A2 Π states of 13 C14 N Liao Jian-Wen and Yang Chuan-Lu ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS
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A progressive processing method for breast cancer detection via UWB based on an MRI-derived model Xiao Xia, Song Hang, Wang Zong-Jie and Wang Liang
074201
Solar-blind ultraviolet band-pass filter based on metal–dielectric multilayer structures Wang Tian-Jiao, Xu Wei-Zong, Lu Hai, Ren Fang-Fang, Chen Dun-Jun, Zhang Rong and Zheng You-Dou
074202
Scintillation of partially coherent Gaussian–Schell model beam propagation in slant atmospheric turbulence considering inner- and outer-scale effects Li Ya-Qing, Wu Zhen-Sen, Zhang Yuan-Yuan and Wang Ming-Jun
074203
Entropy squeezing and atomic inversion in the 𝑘-photon Jaynes–Cummings model in the presence of the Stark shift and a Kerr medium: A full nonlinear approach H R Baghshahi, M K Tavassoly and A Behjat
074204
Electromagnetically induced grating in a four-level tripod-type atomic system Dong Ya-Bin and Guo Yao-Hua
074205
Application of thermal stress model to paint removal by Q-switched Nd:YAG laser Zou Wan-Fang, Xie Ying-Mao, Xiao Xing, Zeng Xiang-Zhi and Luo Ying
074206
All optical method for measuring the carrier envelope phase from half-cycle cutoffs Li Qian-Guang, Chen Huan, Zhang Xiu and Yi Xu-Nong
074207
Spectral energetic properties of the X-ray-boosted photoionization by an intense few-cycle laser Ge Yu-Cheng and He Hai-Ping
074208
Transversal reverse transformation of anomalous hollow beams in strongly isotropic nonlocal media Dai Zhi-Ping, Yang Zhen-Jun, Zhang Shu-Min, Pang Zhao-Guang and You Kai-Min
074209
Phase transition model of water flow irradiated by high-energy laser in a chamber Wei Ji-Feng, Sun Li-Qun, Zhang Kai and Hu Xiao-Yang
074301
Nonlinear impedances of thermoacoustic stacks with ordered and disordered structures Ge Huan, Fan Li, Xia Jie, Zhang Shu-Yi, Tao Sha, Yang Yue-Tao and Zhang Hui
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Integrated physics package of a chip-scale atomic clock Li Shao-Liang, Xu Jing, Zhang Zhi-Qiang, Zhao Lu-Bing, Long Liang and Wu Ya-Ming
074401
Flow and heat transfer of a nanofluid over a hyperbolically stretching sheet A. Ahmad, S. Asghar and A. Alsaedi (Continued on the Bookbinding Inside Back Cover)
074701
Three-dimensional magnetohydrodynamics axisymmetric stagnation flow and heat transfer due to an axisymmetric shrinking/stretching sheet with viscous dissipation and heat source/sink Dinesh Rajotia and R. N. Jat
074702
Molecular dynamics simulations of the nano-droplet impact process on hydrophobic surfaces Hu Hai-Bao, Chen Li-Bin, Bao Lu-Yao and Huang Su-He
074703
Influence of limestone fillers on combustion characteristics of asphalt mortar for pavements Wu Ke, Zhu Kai, Wu Hao, Han Jun, Wang Jin-Chang, Huang Zhi-Yi and Liang Pei PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
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Balmer-alpha and Balmer-beta Stark line intensity profiles for high-power hydrogen inductively coupled plasmas Wang Song-Bai, Lei Guang-Jiu, Liu Dong-Ping and Yang Si-Ze
075202
Mitigation of energetic ion debris from Gd plasma using dual laser pulses and the combined effect with ambient gas Dou Yin-Ping, Sun Chang-Kai, Liu Chao-Zhi, Gao Jian, Hao Zuo-Qiang and Lin Jing-Quan
075203
Characteristics of wall sheath and secondary electron emission under different electron temperatures in a Hall thruster Duan Ping, Qin Hai-Juan, Zhou Xin-Wei, Cao An-Ning, Chen Long and Gao Hong
075204
Atmospheric pressure plasma jet utilizing Ar and Ar/H2 O mixtures and its applications to bacteria inactivation Cheng Cheng, Shen Jie, Xiao De-Zhi, Xie Hong-Bing, Lan Yan, Fang Shi-Dong, Meng Yue-Dong and Chu Paul K
075205
Effect of passive structure and toroidal rotation on resistive wall mode stability in the EAST tokamak Liu Guang-Jun, Wan Bao-Nian, Sun You-Wen, Liu Yue-Qiang, Guo Wen-Feng, Hao Guang-Zhou, Ding Si-Ye, Shen Biao, Xiao Bing-Jia and Qian Jin-Ping
075206
Toroidicity and shape dependence of peeling mode growth rates in axisymmetric toroidal plasmas Shi Bing-Ren
075207
DD proton spectrum for diagnosing the areal density of imploded capsules on Shenguang III prototype laser facility Teng Jian, Zhang Tian-Kui, Wu Bo, Pu Yu-Dong, Hong Wei, Shan Lian-Qiang, Zhu Bin, He Wei-Hua, Lu Feng, Wen Xian-Lun, Zhou Wei-Min, Cao Lei-Feng, Jiang Shao-En and Gu Yu-Qiu
075208
Efficiency and stability enhancement of a virtual cathode oscillator Fan Yu-Wei, Li Zhi-Qiang, Shu Ting and Liu Jing
075209
Mode transition in homogenous dielectric barrier discharge in argon at atmospheric pressure Liu Fu-Cheng, He Ya-Feng and Wang Xiao-Fei
075210
Shockwave–boundary layer interaction control by plasma aerodynamic actuation: An experimental investigation Sun Quan, Cui Wei, Li Ying-Hong, Cheng Bang-Qin, Jin Di and Li Jun (Continued on the Bookbinding Inside Back Cover)
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES 076101
Small-angle X-ray analysis of the effect of grain size on the thermal damage of octahydro-1, 3, 5, 7tetranitro-1, 3, 5, 7 tetrazocine-based plastic-bounded expolsives Yan Guan-Yun, Tian Qiang, Liu Jia-Hui, Chen Bo, Sun Guang-Ai, Huang Ming and Li Xiu-Hong
076102
Quantum confinement and surface chemistry of 0.8–1.6 nm hydrosilylated silicon nanocrystals Pi Xiao-Dong, Wang Rong and Yang De-Ren
076103
Spectroscopic and scanning probe analysis on large-area epitaxial graphene grown under pressure of 4 mbar on 4H-SiC (0001) substrates Wang Dang-Chao and Zhang Yu-Ming
076104
Ferromagnetism on a paramagnetic host background in cobalt-doped Bi2 Se3 topological insulator Zhang Min, L¨u Li, Wei Zhan-Tao, Yang Xin-Sheng and Zhao Yong
076105
Physical properties of FePt nanocomposite doped with Ag atoms: First-principles study Jia Yong-Fei, Shu Xiao-Lin, Xie Yong and Chen Zi-Yu
076301
Effect of size polydispersity on the structural and vibrational characteristics of two-dimensional granular assemblies Zhang Guo-Hua, Sun Qi-Cheng, Shi Zhi-Ping, Feng Xu, Gu Qiang and Jin Feng
076401
Characteristics of phase transitions via intervention in random networks Jia Xiao, Hong Jin-Song, Yang Hong-Chun, Yang Chun, Shi Xiao-Hong and Hu Jian-Quan
076403
Electrical and optical properties of indium tin oxide/epoxy composite film Guo Xia, Guo Chun-Wei, Chen Yu and Su Zhi-Ping
076501
Dynamic thermo-mechanical coupled response of random particulate composites: A statistical two-scale method Yang Zi-Hao, Chen Yun, Yang Zhi-Qiang and Ma Qiang
076801
Fabrication of VO2 thin film by rapid thermal annealing in oxygen atmosphere and its metal–insulator phase transition properties Liang Ji-Ran, Wu Mai-Jun, Hu Ming, Liu Jian, Zhu Nai-Wei, Xia Xiao-Xu and Chen Hong-Da CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES
077101
Interaction and spin–orbit effects on a kagome lattice at 1/3 filling Liu Hai-Di, Chen Yao-Hua, Lin Heng-Fu, Tao Hong-Shuai and Wu Jian-Hua
077102
First-principles study of structural, electronic and optical properties of ZnF2 Wu Jian-Bang, Cheng Xin-Lu, Zhang Hong and Xiong Zheng-Wei
077103
Hybrid density functional studies of cadmium vacancy in CdTe Xu Run), Xu Hai-Tao, Tang Min-Yan and Wang Lin-Jun
077104
A theoretical investigation of the band alignment of type-I direct band gap dilute nitride phosphide alloy of GaNx Asy P1−x−y /GaP quantum wells on GaP substrates ¨ L Unsal, ¨ O B G¨on¨ul and M Temiz (Continued on the Bookbinding Inside Back Cover)
077105
Influence of temperature on strain-induced polarization Coulomb field scattering in AlN/GaN heterostructure field-effect transistors L¨u Yuan-Jie, Feng Zhi-Hong, Lin Zhao-Jun, Guo Hong-Yu, Gu Guo-Dong, Yin Jia-Yun, Wang Yuan-Gang, Xu Peng, Song Xu-Bo and Cai Shu-Jun
077201
Design consideration and fabrication of 1.2-kV 4H-SiC trenched-and-implanted vertical junction fieldeffect transistors Chen Si-Zhe and Sheng Kuang
077202
A novel solution-based self-assembly approach to preparing ultralong titanyl phthalocyanine sub-micron wires Zhu Zong-Peng, Wei Bin, Zhang Jian-Hua and Wang Jun
077301
Lattice structures and electronic properties of CIGS/CdS interface: First-principles calculations Tang Fu-Ling, Liu Ran, Xue Hong-Tao, Lu Wen-Jiang, Feng Yu-Dong, Rui Zhi-Yuan, and Huang Min
077302
Efficiency of electrical manipulation in two-dimensional topological insulators Pang Mi and Wu Xiao-Guang
077303
Effect of annealing on performance of PEDOT:PSS/n-GaN Schottky solar cells Feng Qian, Du Kai, Li Yu-Kun, Shi Peng and Feng Qing
077304
Non-recessed-gate quasi-E-mode double heterojunction AlGaN/GaN high electron mobility transistor with high breakdown voltage Mi Min-Han, Zhang Kai, Chen Xing, Zhao Sheng-Lei, Wang Chong, Zhang Jin-Cheng, Ma Xiao-Hua and Hao Yue
077305
Effect of alumina thickness on Al2 O3 /InP interface with post deposition annealing in oxygen ambient Yang Zhuo, Yang Jing-Zhi, Huang Yong, Zhang Kai and Hao Yue
077306
A low specific on-resistance SOI LDMOS with a novel junction field plate Luo Yin-Chun, Luo Xiao-Rong, Hu Gang-Yi, Fan Yuan-Hang, Li Peng-Cheng, Wei Jie, Tan Qiao and Zhang Bo
077307
High dV /dt immunity MOS controlled thyristor using a double variable lateral doping technique for capacitor discharge applications Chen Wan-Jun, Sun Rui-Ze, Peng Chao-Fei and Zhang Bo
077401
Formation of epitaxial Tl2 Ba2 Ca2 Cu3 O10 superconducting films by dc-magnetron sputtering and triple post-annealing method Xie Wei, Wang Pei, Ji Lu, Ge De-Yong, Du Jia-Nan, Gao Xiao-Xin, Liu Xin, Song Feng-Bin, Hu Lei, Zhang Xu, He Ming and Zhao Xin-Jie
077502
Modulation of magnetic properties and enhanced magnetoelectric effects in MnW1−𝑥 Mo𝑥 O4 compounds Fang Yong, Zhou Wei-Ping, Song Yu-Quan, L¨u Li-Ya, Wang Dun-Hui and Du Yu Wei
077503
Substituting Al for Fe in Pr(Al𝑥 Fe1−𝑥 )1.9 alloys: Effects on magnetic and magnetostrictive properties Tang Yan-Mei, Chen Le-Yi, Wei Jun, Tang Shao-Long and Du You-Wei
(Continued on the Bookbinding Inside Back Cover)
077504
Degradation of ferroelectric and weak ferromagnetic properties of BiFeO3 films due to the diffusion of silicon atoms Xiao Ren-Zheng, Zhang Zao-Di, Vasiliy O. Pelenovich, Wang Ze-Song, Zhang Rui, Li Hui, Liu Yong, Huang Zhi-Hong and Fu De-Jun
077601
An electron spin resonance study of Eu doping effect in La4/3 Sr5/3 Mn2 O7 single crystal He Li-Min, Ji Yu, Wu Hong-Ye, Xu Bao, Sun Yun-Bin, Zhang Xue-Feng, Lu Yi and Zhao Jian-Jun
077801
What has been measured by reflection magnetic circular dichroism in Ga1−𝑥 Mn𝑥 As/GaAs structures? He Zhen-Xin, Zheng Hou-Zhi, Huang Xue-Jiao, Wang Hai-Long and Zhao Jian-Hua
077802
Pure blue and white light electroluminescence in a multilayer organic light-emitting diode using a new blue emitter Wei Na, Guo Kun-Ping, Zhou Peng-Chao, Yu Jian-Ning, Wei Bin and Zhang Jian-Hua
077901
Self-organized voids revisited: Experimental verification of the formation mechanism Song Juan, Ye Jun-Yi, Qian Meng-Di, Luo Fang-Fang, Lin Xian, Bian Hua-Dong, Dai Ye, Ma Guo-Hong, Chen Qing-Xi, Jiang Yan, Zhao Quan-Zhong and Qiu Jian-Rong INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY
078101
Microwave absorption properties of a double-layer absorber based on nanocomposite BaFe12 O19 /α-Fe and nanocrystalline α-Fe microfibers Shen Xiang-Qian, Liu Hong-Bo, Wang Zhou, Qian Xin-Ye, Jing Mao-Xiang and Yang Xin-Chun
078102
Improved interfacial and electrical properties of GaSb metal oxide semiconductor devices passivated with acidic (NH4 )2 S solution Zhao Lian-Feng, Tan Zhen, Wang Jing and Xu Jun
078401
Hybrid phase-locked loop with fast locking time and low spur in a 0.18-µm CMOS process Zhu Si-Heng, Si Li-Ming, Guo Chao, Shi Jun-Yu and Zhu Wei-Ren
078402
Four-dimensional parameter estimation of plane waves using swarming intelligence Fawad Zaman, Ijaz Mansoor Qureshi, Fahad Munir and Zafar Ullah Khan
078703
Image reconstruction from few views by ℓ0 -norm optimization
078904
Sun Yu-Li and Tao Jin-Xu Row–column visibility graph approach to two-dimensional landscapes Xiao Qin, Pan Xue, Li Xin-Li, Mutua Stephen, Yang Hui-Jie, Jiang Yan, Wang Jian-Yong and Zhang Qing-Jun GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS
079401
Experimental verification of the parasitic bipolar amplification effect in PMOS single event transients He Yi-Bai and Chen Shu-Ming
