Intermittent Chaotic Neural Firing Characterized by ...

ISSN: 0256 - 307 X

中国物理快报

Chinese Physics Letters

A Series Journal of the Chinese Physical Society Distributed by IOP Publishing Online: http://www.iop.org/journals/cpl http://cpl.iphy.ac.cn

CHINESE PHYSICAL SOCIETY

CHIN. PHYS. LETT. Vol. 27, No. 7 (2010) 070503

Intermittent Chaotic Neural Firing Characterized by Non-Smooth Features

*

WANG Dong(王栋)1 , MO Juan(莫娟)1 , ZHAO Xiao-Yan(赵小燕)1 , GU Hua-Guang(古华光)1** , QU Shi-Xian(屈世显)2 , REN Wei(任维)1 1

2

College of Life Science, Shaanxi Normal University, Xi’an 710062 College of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062

(Received 24 February 2010) A chaotic firing pattern, characterized by non-smooth features and generated through the routine of intermittency from period 3, is observed in biological experiments on a neural firing pacemaker and reproduced in simulations by using a theoretical neuronal model with multiple time scales. This chaotic activity exhibits a scale law very similar to those of both the type-I intermittency generated in smooth systems and the type-V intermittency in non-smooth systems.

PACS: 05. 45. −a, 87. 19. L−

DOI: 10.1088/0256-307X/27/7/070503

Since chaotic activities have been widely observed in fields ranging from engineering, physics, chemistry, biology, economy to sociology,[1] identification of their distinct routines has become critical. Period doubling bifurcation, intermittency, and quasiperiodicity collapse were identified as three classical routines to chaos in smooth nonlinear systems.[2,3] In fact, the theory of chaos has played an important role in the development of neuroscience since the 1980s.[4] Chaotic firing patterns and the three routines to chaos were discovered in the nervous systems stimulated by an external signal first,[5] and then, chaos and period doubling bifurcation to chaos were discovered in autonomous experimental neural pacemakers.[6] The functional significance of chaotic firing patterns in neuronal information processing has also been widely implied.[5,7,8] Previous studies on non-smooth systems or quasi-discontinuous systems revealed that chaos can arise directly from fixed points and corner-collision bifurcations,[9,10] for example, from type-V intermittency, which is generated in non-smooth systems and is very different to the type-I intermittency in smooth systems. Recently, a special type of intermittency, whose scale law is similar to that of not only typeI but also type-V intermittencies, was discovered in simulation with the Pikovsky circuit model and the Rose-Hindmarsh neuronal model, called the quasidiscontinuous system.[11−13] These models are continuous and smooth, showing quasi-discontinuous characteristics due to their multiple time scales. This novel intermittency is of great interest because it links the continuous and the discontinuous systems. To the best of our knowledge, experimental demonstration of this special intermittency has been seldom reported. In this Letter, we report experimental observation and theoretical reproduction of this special intermittent

chaos. Experiments were performed on experimental neural pacemakers formed at the injured site of adult male Sprague-Dawley (SD) rat (200–300 g) sciatic nerve subjected to chronic ligature. After 4–10 days of the surgical operation, the previously injured site was exposed and perfused continuously with 34∘ C Kreb’s solution. The spontaneous spike trains of individual fibers ending at the injured site were recorded with a Powerlab system (Australia) with the sampling frequency being 10.0 kHz. The time intervals between the maximal values of the successive spikes were recorded seriatim as inter-spike intervals (ISI) series. Our previous works studied periodic, chaotic and stochastic firing patterns, as well as the bifurcations between these patterns, observed in this experimental procedure.[6,14] Here we particularly report the intermittent chaotic patterns observed on 36 neural pacemakers. A typical example of the routine of this intermittent chaotic firing pattern is shown in Fig. 1. When the extracellular calcium concentration ([Ca2+ ]𝑜 ) is gradually increased from zero to 1.2 mmol/L, the original period-3 bursting changes into chaotic bursting first and then to period-2 bursting, as shown in Fig. 1(a). Within the regime of the chaotic bursting, it is of intermittent chaos near the period-3 bursting. The spike trains of the intermittent chaotic bursting exhibit continuous period-3 burst intermittently interrupted by other kinds of burst, as labeled by the titled arrows and shown in Fig. 1(b). The stable ISI series of the intermittent chaos exhibit three bands with a few scatter points, reflecting that most of the firing train is composed of period-3 burst, as shown in Fig. 1(c). The period-3 burst can also be reflected by the three peaks (ISI𝑝1 ≈ 0.115 sec, ISI𝑝2 ≈ 0.265 sec

* Supported by the National Natural Science Foundation of China under Grant Nos 10772101, 10774088, 30670533 and 10875076, the Fundamental Research Funds for the Central Universities under Grant No GK200902025, and partly by the National High Technology Research and Development Program of China under Grant No 2007AA02Z310. ** Email: [email protected] c 2010 Chinese Physical Society and IOP Publishing Ltd ○

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and ISI𝑝3 ≈ 0.855 sec) in the ISI histogram, as shown in Fig. 1(e). The first return map of the ISI series exhibits a single-hump-like deterministic structure. Most of the points in the map group into three clusters, labeled A(ISI𝑝1 , ISI𝑝2 ) and B(ISI𝑝2 , ISI𝑝3 ) and C(ISI𝑝3 , ISI𝑝1 ) and shown in Fig. 1(d). By summing the number of points of (ISI𝑘 , ISI𝑘+1 ) within every 0.012 sec × 0.012 sec area in the plane of the first return map, the point-density in the return map is represented with a grayscale image and shown in Fig. 1(f). It is clearly seen that period-3 burst is dominant in the intermittent chaos generated through the routing of intermittency from period 3. The first return map (Fig. 1(d)) is composed of four parts, from left to right, an upstroke branch, a branch with a positive slope, a down-stroke branch, and a branch with negative slope, demonstrating non-smooth like characteristics. The connection between the first and second parts and between the second and third parts are sharply non-smooth. The experimentally observed intermittent chaos can be reproduced with the following Chay model, a mathematical neuronal model whose dynamics was verified to be very close to the experimental neural pacemaker in a series of previous studies,[6,14−17] 𝑑𝑉 = 𝑔𝐼 𝑚3∞ ℎ∞ (𝑣𝐼 − 𝑉 ) + 𝑔𝑘𝑣 (𝑣𝑘 − 𝑉 )𝑛4 𝑑𝑡 𝐶 + 𝑔𝑘𝑐 (𝑣𝑘 − 𝑉 ) + 𝑔𝑙 (𝑣𝑙 − 𝑉 ), 1+𝐶

ISI

100

(a)

(1)

𝑛∞ − 𝑛 𝑑𝑛 = , 𝑑𝑡 𝜏𝑛

(2)

𝑑𝐶 𝑚3 ℎ∞ (𝑣𝑐 − 𝑉 ) − 𝑘𝑐 𝐶 = ∞ , 𝑑𝑡 𝜏𝑐

(3)

where 𝑉 is the membrane potential, 𝑛 is the probability of potassium channel activation and 𝐶 is the dimensionless intracellular concentration of the calcium ion ([Ca2+ ]𝑖 ). The summed ionic currents in Eq. (1) include mixed Na+ –Ca2+ , voltage-sensitive K+ , calcium dependent K+ , and leakage currents. 𝑔𝐼 , 𝑔𝑘𝑐 , 𝑔𝑘𝑣 and 𝑔𝑙 are, respectively, the maximum conductance of the corresponding current; 𝑣𝑐 is the reversal potential of the calcium ion, chosen as the bifurcation parameter, corresponding to adjustment of [Ca2+ ]𝑜 in experiment; 𝜏𝑛 = 1/(𝜆𝑛 (𝛼𝑛 + 𝛽𝑛 )) and the expression of 𝑚∞ , ℎ∞ , 𝑛∞ , 𝛼𝑛 and 𝛽𝑛 were described Refs. [17,18]. In this study, the parameters are taken as 𝑔𝐼 = 1800 mS/cm2 , 𝑔𝑘𝑐 = 1700 mS/cm2 , 𝑔𝑘𝑣 = 20 mS/cm2 , 𝑔𝑙 = 7 mS/cm2 , 𝑔𝑘𝑣 = 20 mS/cm2 , 𝑣𝐼 = 100 mV, 𝑣𝑘 = −75 mV, 𝑣𝑙 = 40 mV, 𝜆𝑛 = 228, 𝜏𝑐 = 100/27, 𝑘𝑐 = 3.3/18. The time scale in this model is taken as 103 (𝑔𝐼 = 1800 and 𝑔𝑘𝑣 = 1700), 102 (𝜆𝑛 = 228) and 10−1 (1/𝜏𝑐 = 0.27) for the three equations, respectively. The model was solved by the fourth Runge–Kutta numerical integration method with an integration time step of 10−4 sec. The amplitude of −25.0 mV of the voltage upstrokes was counted as the threshold of the spike. (b)

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Fig. 1. The intermittent chaotic bursting discovered in the experiment on the neural pacemaker. (a) Period-3 bursting is changed into chaotic bursting first and then to period-2 bursting when [Ca2+ ]𝑜 is changed from 0 mmol/L to 1.2 mmol/L; (b) the spike train; (c) ISI series discovered in another pacemaker; (d) the first return map of ISI series corresponding to (c); (e) ISI histogram of (c); (f) number of points of (ISI𝑘 , ISI𝑘+1 ) in the first return map.

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(a)

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Fig. 2. The intermittent chaos simulated in the Chay model. (a) Spike trains; (b) period-3 bursting is changed into chaos first and then to period-2 bursting when 𝜆𝑛 = 228; (c) the third return map of 𝐶𝑣 max ; (d) ISI series; (e) the first return map of the ISI series; (f) number of points of (ISI𝑘 , ISI𝑘+1 ) in the first return map when the bin of ISI is taken as 0.04 sec. Except for (b), the parameters are 𝜆𝑛 = 228 and 𝑣𝑐 = 54.3021130.

When 𝑣𝑐 is adjusted from 54.2 to 54.6, the firing pattern is changed from period 3 to chaos via intermittency first (the critical value 𝑣𝑐* = 54.3020900) and then to period-2 busting (𝑣𝑐 = 54.6), as shown in Fig. 2(a). As shown in Fig. 2(b), the intermittent chaos obtained with 𝑣𝑐 = 54.3021130 is mainly composed of period-3 bursts, randomly disrupted by some non-period-3 burst labeled by titled arrows. The third return map of 𝐶𝑣 max (𝐶 values when 𝑉 reaches the maximum), shown in Fig. 2(c), shows three narrow channels called “ghost tunnels” between the map trajectories and the diagonal.[19] The map iterates for many times in the channel, forming the “laminar phase” with continuous period-3 points, and then irregularly leaves the channel briefly, forming the “turbulent phase” with non-period-3 points. The first return map of ISI series exhibits non-smooth structures very similar to those of the experiment, as shown in Fig. 2(e). The density of points (ISI𝑘 , ISI𝑘+1 ) in the first return map is also similar to the experiment result, as shown in Fig. 2(f) (with bin= 0.04 sec). The third return map of 𝐶𝑣 max shows a non-smooth-like sharp corner (non-tangent) in the middle “ghost tunnel”, labeled by a titled arrow as shown in Fig. 2(c). This non-tangent or non-smooth-like characteristics will lead to the varied scale law of intermittent chaos. In order to quantitatively study the intermittent chaos, we compared the scale law of the averaged laminar length ⟨𝐿⟩ of the Chay model with those of type-I intermittency of the logistic map (𝑥𝑘+1 = 𝑎𝑥𝑘 (1−𝑥𝑘 ), 𝑥 ∈ [0, 1], 𝑎 ∈ [0, 4], 𝑘 = 0, 1, 2, 3, · · · ,) and typeV intermittency of a constructed map.[20] The intermittently chaotic iteration series of the logistic map

is obtained near the critical value of tangent bifurcation from period 3 to intermittent chaos, where 𝑎* = 3.8284270. The scale law of type-I intermittency in the logistic map is given as log10 ⟨𝐿⟩ ∝ −0.5 log10 (𝑎 − 𝑎* ), while that of the type-V intermittency is ⟨𝐿⟩ = log10 (𝑢)/log10 (𝑠) + 𝛽, where 𝑢 is the control parameter, 𝑠 is a fixed value being the “slope” at the point of discontinuity, and 𝛽 is a constant value. Three cases of intermittent chaos corresponding to different 𝜆𝑛 are studied. The critical values near which period-3 bursting is changed into intermittent chaos are 𝑣𝑐* = 44.1708535 for 𝜆𝑛 = 223, 𝑣𝑐* = 50.2768158 for 𝜆𝑛 = 225.8, and 𝑣𝑐* = 54.3020900 for 𝜆𝑛 = 228, respectively. In the double-logarithmic plane, the linear fitting equations of the scale law of the intermittent chaos are log10 ⟨𝐿⟩ = −0.450 log10 𝜀 + 0.777 for 𝜆𝑛 = 223 (squares), log10 ⟨𝐿⟩ = −0.448 log10 𝜀 + 0.595 for 𝜆𝑛 = 225.8 (circles), and log10 ⟨𝐿⟩ = −0.377 log10 𝜀 + 0.816 for 𝜆𝑛 = 228 (triangles), respectively, with the correlation coefficients being −0.996, −0.993 and −0.974, as shown in Fig. 3(a). The slopes of the equations of the intermittent chaos from the Chay model are different from those of the type-I intermittency; the latter is typically −0.5. In the single-logarithmic plane, the linear line can be fitted as ⟨𝐿⟩ = −3004.9 log10 𝜀 − 14845.4 for 𝜆𝑛 = 223, ⟨𝐿⟩ = −1915.8 log10 𝜀 − 9445.0 for 𝜆𝑛 = 225.8, and ⟨𝐿⟩ = −965.3 log10 𝜀 − 4535.4 for 𝜆𝑛 = 228, with correlation coefficients of −0.981, −0.984 and −0.987, respectively, as shown in Fig. 3(b). The results show that the intermittent chaos from the Chay model is a special intermittency similar to both type-I and typeV intermittencies.

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CHIN. PHYS. LETT. Vol. 27, No. 7 (2010) 070503 (a)

log10< >

3.6 3.3

time scales of the nonlinear system. The scale law of the observed intermittent chaos is similar to both type-I and type-V intermittent chaos, suggesting that intermittent chaos from a neuronal system with multiple time scales might be a special intermittency.

3.0

References

2.7 (b)

< >

4000

2000

-6.4

-6.0

log10

-5.6

Fig. 3. Scale law of intermittent chaos with different parameters 𝜆𝑛 = 223 (squares), 𝜆𝑛 = 225.8 (circles) and 𝜆𝑛 = 228 (triangles) in the Chay model, where 𝜀 = 𝑣𝑐 −𝑣𝑐* . (a) Double-logarithmic plane; (b) single-logarithmic plane.

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]

In summary, we have experimentally observed and theoretically simulated an intermittently chaotic firing pattern, which is generated via intermittency from period-3 bursting. In its return maps of both ISI and 𝐶𝑣 max series, the intermittent chaos manifests nonsmooth-like characteristics arising from the multiple

[17] [18] [19] [20]

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Stark J and Hardy K 2003 Science 301 1192 Eckmann J P 1981 Rev. Mod. Phys. 53 643 Mayer-Kress G and Haken H 1981 Phys. Lett. A 82 151 King C C 1991 Prog. Neurobiol. 36 279 Faure P and Korn H 2001 C. R. Acad. Sci. III 324 773 Ren W, Hu S J, Zhang B J, Wang F Z, Gong Y F and Xu J X 1997 Int. J. Bifur. Chaos 7 1867 Korn H and Faure P 2003 C. R. Biol. 326 787 Stam C J 2005 Clin. Neurophysiol. 116 2266 Tian L and Xu G 2007 Int. J. Bifur. Chaos 17 271 Qin Z Y and Lu Q S 2007 Chin. Phys. Lett. 24 886 Wu S G and He D R 2001 J. Phys. Soc. Jpn. 70 69 Wu S G and He D R 2000 Chin. Phys. Lett. 17 398 Wu S G and He D R 2001 Commun. Theor. Phys. 35 272 Wu X B, Mo J, Yang M H, Zheng Q H, Gu H G and Ren W 2008 Chin. Phys. Lett. 25 2799 Li L, Gu H G, Yang M H, Liu Z Q and Ren W 2004 Int. J. Bifur. Chaos 14 1813 Gu H G, Ren W, Lu Q S, Wu S G, Yang M H and Chen W J 2001 Phys. Lett. A 285 63 Zheng Q H, Liu Z Q, Yang M H, Wu X B, Gu H G and Ren W 2009 Phys. Lett. A 373 540 Chay T R 1985 Physica D 16 233 Pomeau Y and Manneville P 1980 Commun. Math. Phys. 74 189 Bauer M, Habip S, He D R and Martienssen W 1992 Phys. Rev. Lett. 68 1625

Chinese Physics Letters Volume 27

Number 7

2010

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ATOMIC AND MOLECULAR PHYSICS 073101 Effect of S Substitution for P Point Defects in KDP Crystals: First-Principles Study GAO Hui, SUN Xun, Liu Bao-An, XU Ming-Xia, HU Guo-Hang, XU Xin-Guang, ZHAO Xian 073201 Two Kinds of Cavity Geometry for Enhanced Laser Cooling of Solids JIA You-Hua, ZHONG Biao, YIN Jian-Ping 073301 Theoretical Study of the Influence of Femtosecond Laser Wavelength on the Evolution of a Double-Minimum Electronic Excited State Wave Packet for NaRb MA Ning, WANG Mei-Shan, XIONG De-Lin, YANG Chuan-Lu, MA Xiao-Guang, WANG De-Hua 073401 Excitation Transfer for K2 in High-Lying States by N2 CUI Xiu-Hua, MU Bao-Xia, DAI Kang, SHEN Yi-Fan 073402 Two Electron Transfer and Stabilization in Slow O6+ and Rare-Gas Collisions XUE Ying-Li, YU De-Yang, LU Rong-Chun, SHAO Cao-Jie, RUAN Fang-Fang, YANG Zhi-Hu, CAI XiaoHong 073403 Interpretation of the Experimental Electron Momentum Spectra of 5e1/2 and 5e3/2 Orbitals of CF3 I with Relativistic Calculations LIU Kun, NING Chuan-Gang, DENG Jing-Kang

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) 074201 Third-Order Nonlinear Optical Properties of a Series of Polythiophenes ZHANG Xiao-Qiang, WANG Chang-Shun, LU Guo-Yuan, HE Ting-Chao 074202 Adiabatic Passage Based on the Calcium Active Optical Clock XIE Xiao-Peng, ZHUANG Wei, CHEN Jing-Biao 074203 Theoretical Analysis of the Critical Phenomena of a Brillouin Laser SU Yu-Huan, SHI Jin-Wei, OUYANG Min, YANG Guo-Jian, LIU Da-He 074204 High Efficiency One-Way Transmission by One-Dimensional Photonic Crystals with Gratings on One Side KANG Xiu-Bao, TAN Wei, WANG Zhan-Shan, WANG Zhi-Guo, CHEN Hong 074205 Photonic Band Gap Properties of Three-Dimensional SiO2 Photonic Crystals LIU Yan-Ping, YAN Zhi-Jun, LI Zhi-Gang, LI Qin-Tao, WANG Yin-Yue 074206 A Novel Micro-Displacement Measuring Method Based on Optical Path Modulation QU Wei, YE Hong-An 074207 A Microwave Photonic Notch Filter Using a Microfiber Ring Resonator ZHANG Yu, ZHANG Xin-Liang, CHEN Guo-Jie, XU En-Ming, HUANG De-Xiu 074208 Stable Narrow Linewidth 689 nm Diode Laser for the Second Stage Cooling and Trapping of Strontium Atoms LI Ye, LIN Yi-Ge, ZHAO Yang, WANG Qiang, WANG Shao-Kai, YANG Tao, CAO Jian-Ping, LI Tian-Chu, FANG Zhan-Jun, ZANG Er-Jun 074209 Supercontinuum Generation with High Birefringence SF6 Soft Glass Photonic Crystal Fibers FU Bo, LI Shu-Guang, YAO Yan-Yan, ZHANG Lei, ZHANG Mei-Yan anchen Displacements for TE- and TM-Polarized Beams Transmitting 074210 Opposite Goos–H¨ through a Slab of Indefinite Metamaterial LIN Yan-He, ZHU Qi-Biao, ZHANG Yan 074211 Polarization-Independent Guided-Mode Resonance Filters under Oblique Incidence HU Xu-Hui, GONG Ke, SUN Tian-Yu, WU Dong-Min

074212 Enhancement and Suppression of Four-Wave Mixing in a Four-Level Atomic System CHEN Ru-Lin, YUAN Chen-Zhi, WANG Zhi-Guo, NIE Zhi-Qiang, LI Yuan-Yuan, ZHANG Yan-Peng 074213 Efficient Tm:YAG Ceramic Laser at 2 µm ZOU Yu-Wan, ZHANG Yong-Dong, ZHONG Xin, WEI Zhi-Yi, ZHANG Wen-Xin, JIANG Ben-Xue, PAN Yu-Bai 074214 Narrow Linewidth Tm3+ -Doped Large Core Fiber Laser Based on a Femtosecond Written Fiber Bragg Grating ZHANG Yun-Jun, WANG Wei, ZHOU Ren-Lai, SONG Shi-Fei, TIAN Yi, WANG Yue-Zhu 074215 Laser Resistance of Ta2 O5 /SiO2 and ZrO2 /SiO2 Optical Coatings under 2 µm Femtosecond Pulsed Irradiation LIU Na, WANG Ying-Jian, ZHOU Ming, JING Xu-Feng, WANG Yan-Zhi, CUI Yun, JIN Yun-Xia 074216 A Multilayered Configuration Broadband Polarization Insensitive Reflector Utilizing a MultiSubpart Profile Grating Structure WU Hua-Ming, HOU Jin, GAO Ding-Shan, ZHOU Zhi-Ping 074301 Influence of the Nonlinearity of Loudspeakers on the Performance of Thermoacoustic Refrigerators Driven by Current and Voltage FAN Li, ZHANG Shu-Yi, ZHANG Hui 074302 Performance of Non-Contact Linear Actuators Driven by Surface Acoustic Waves CHENG Li-Ping, ZHANG Shu-Yi, GU Huan-Huan, ZHOU Feng-Mei, SHUI Xiu-Ji 074303 Symmetric and Anti-Symmetric Lamb Waves in a Two-Dimensional Phononic Crystal Plate LI Yong, HOU Zhi-Lin, FU Xiu-Jun, Badreddine M Assouar 074501 On the Intrinsic Concordance between the Wide Scattering Feature of Synchronized Flow and the Empirical Spacing Distributions CHEN Xi-Qun, LI Li, JIANG Rui, YANG Xin-Miao 074701 Hopf Bifurcations for the Recently Proposed Smooth-and-Discontinuous Oscillator TIAN Rui-Lan, CAO Qing-Jie, LI Zhi-Xin 074702 Nonlinear Flow Numerical Simulation of an Ultra-Low Permeability Reservoir YU Rong-Ze, LEI Qun, YANG Zheng-Ming, BIAN Ya-Nan

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES 075201 Non-Uniformity of Ion Implantation in Direct-Current Plasma Immersion Ion Implantation LIU Cheng-Sen, WANG De-Zhen, FAN Yu-Jia, ZHANG Nan, GUAN Li, YAO Yuan

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES 076101 Influence of Fe Contamination on the Minority Carrier Lifetime of Multi-crystalline Silicon MENG Xia-Jie, MA Zhong-Quan, LI Feng, SHEN Cheng, YIN Yan-Ting, ZHAO Lei, LI Yong-Hua, XU Fei 076102 Evolutions of Crystal Structure, Stoichiometry and Electrochemical Behavior with Co Substitution in LiNi1−y Coy O2 Positive Electrodes XIA Rong-Sen, CUI Zhong-Hui, LIU Bi-Qiu, GUO Xiang-Xin, ZHAO Jing-Tai 076103 Influence of Rare-Earth Substitution for Iron in FeCrMoCB Bulk Metallic Glasses Abderrezak Bouchareb, Badis Bendjemil, Rafael Piccin, Marcello Baricco 076201 A Simple Theoretical Method to Predict the Hardness of Pure Metal Crystals JIN Yun-Fei, YE Xiang-Xi, LI Jing-Tian, ZHANG Wen-Xian, ZHUANG Jun, NING Xi-Jing 076401 Transition to Film Boiling in Microgravity: Influence of Subcooling ZHAO Jian-Fu, LI Jing, YAN Na, WANG Shuang-Feng 076402 Investigation of the Potts Model on Triangular Lattices by the Second Renormalization of Tensor Network States WANG Meng-Xiong, CAI Jian-Wei, XIE Zhi-Yuan, CHEN Qiao-Ni, ZHAO Hui-Hai, WEI Zhong-Chao 076801 Non-Axisymmetric Oscillation of Acoustically Levitated Water Drops at Specific Frequencies SHEN Chang-Le, XIE Wen-Jun, WEI Bing-Bo 076802 A Model for the Contact Angle of Liquid Droplets on Rough Surfaces MEI Mao-Fei, YU Bo-Ming, LUO Liang, CAI Jian-Chao

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES 077101 Strain Effects on Electronic Properties of Boron Nitride Nanoribbons LI Jin, SUN Li-Zhong, ZHONG Jian-Xin 077102 Electrical Characterization of Deep Trap Properties in High-k Thin-Film HfO2 Dielectric YANG Lu 077103 Preparation and Photocurrent Performance of Highly Ordered Titania Nanotube Implanted with Ag/Cu Metal Ions LIAO Bin, WU Xian-Ying, LIANG Hong, ZHANG Xu, LIU An-Dong 077201 Band Structures of Metal-Oxide Capped Graphene: A First Principles Study LIU Han, SUN Qing-Qing, CHEN Lin, XU Yan, DING Shi-Jin, ZHANG Wei, GONG Xin-Gao, ZHANG Shi-Li 077301 The Topological Structure of the SU (2) Chern–Simons Topological Current in the FourDimensional Quantum Hall Effect ZHANG Xiu-Ming, DUAN Yi-Shi 077302 Effect of Magnetic Field on a p-Type δ-Doped GaAs Layer E. OZTURK 077303 Electric Field Analysis of Space Charge Injection from a Conductive Nano-Filler Electrode XIAO Chun, ZHANG Ye-Wen, ZHENG Fei-Hu, WEI Wen-Jie, AN Zhen-Lian 077304 Influence of High Atomic Hydrogenation on the Electronic Structure of Zigzag Carbon Nanotubes: A First-Principles Study PAN Li-Jun, CHEN Wei-Guang, ZHANG Rui-Qin, HU Xing, JIA Yu 077305 Growth and Characterization of GaSb-Based Type-II InAs/GaSb Superlattice Photodiodes for Mid-Infrared Detection WANG Guo-Wei, XU Ying-Qiang, GUO Jie, TANG Bao, REN Zheng-Wei, HE Zhen-Hong, NIU Zhi-Chuan 077401 Film Thickness Dependence of Rectifying Properties of La1.85 Sr0.15 CuO4 /Nb-SrTiO3 Junctions CHEN Lei-Ming, LI Guang-Cheng, ZHANG Yan, GUO Yan-Feng 077501 Out-of-Plane Torque Influence on Magnetization Switching and Susceptibility in Magnetic Multilayers SUN Chun-Yang, WANG Zheng-Chuan 077502 Structural and Magnetic Properties of [Fe/Ni]N Multilayers TANG Jia, MA Bin, ZHANG Zong-Zhi, JIN Qing-Yuan 077801 Focal Shift of Paraxial Gaussian Beams in a Left-Handed Material Slab Lens ZHANG Kang-Kang, LUO Hai-Lu, WEN Shuang-Chun 077802 Effect of Rapid Thermal Annealing on the Formation of In-N Clusters in Strained InGaNAs ZHAO Chuan-Zhen, ZHANG Rong, LIU Bin, LI Ming, XIE Zi-Li, XIU Xiang-Qian, ZHENG You-Dou

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY 078101 Development and Characterization of Metal-Insulator-Metal Capacitors with SiNx Thin Films by Plasma-Enhanced Chemical Vapor Deposition WANG Cong, ZHANG Fang, KIM Nam-Young 078102 Influence of Substrate on the Transportation Properties of Co/Alq3 Granular Films on a Si Wafer ZHANG Yan, SHENG Peng, LIU Wen-Ming, SHU Qi, GU Zhi-Hua, NI Gang 078103 Molecular Dynamic Simulation on Graphitization and Dehydrogenization of Hydrogenated Carbon Films in Vacuum QUAN Wei-Long, LI Hong-Xuan, ZHAO Fei, JI Li, DU Wen, ZHOU Hui-Di, CHEN Jian-Min 078401 An Interconnect Bus Power Optimization Method EN Yun-Fei, ZHU Zhang-Ming, HAO Yue

078501 Magnetic Properties and Magnetoresistance of CdMnS:Au Based Structures Prepared by Coevaporation HE Jun, LI Ming, D. H. Kim, J. C. Lee, D. J. Lee, FU De-Jun, T. W. Kang 078502 Low-Voltage Depletion-Mode Indium-Tin-Oxide Thin-Film Transistors Gated by Ba0.4 Sr0.6 TiO3 Dielectric WANG Li-Ping, LU Ai-Xia, DOU Wei, WAN Qing 078701 Effect of Laser Field and Mechanical Force on Deoxyribonucleic Acid Melting PAN Bing-Yi, ZHANG Ling-Yun, DOU Shuo-Xing, WANG Peng-Ye 078901 Evidence of Scaling in Chinese Income Distribution XU Yan, GUO Liang-Peng, DING Ning, WANG You-Gui 078902 Natural Connectivity of Complex Networks WU Jun, Mauricio Barahona, TAN Yue-Jin, DENG Hong-Zhong

GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS 079801 Bianchi Type-IX String Cosmological Models for Perfect Fluid Distribution in General Relativity Atul Tyagi, Keerti Sharma, Payal Jain

ERRATA AND OTHER CORRECTIONS 079901 Comment on “Q-Switched Tm:YAG Laser Intracavity-Pumped by a 1064 nm Laser” PAVEL Nicolaie 079902 Reply to “Comment on ‘Q-switched Tm:YAG Laser Intracavity-Pumped by a 1064 nm Laser’ ” MA Qing-Lei, ZONG Nan, XIE Shi-Yong, YANG Feng, GUO Ya-Ding, XU Jia-Lin, BO Yong, PENG Qin-Jun, CUI Da-Fu, XU Zu-Yan