Estimation of peer pressure in dynamic homogeneous social networks

Jie Liu; Pengyi Wang; Jiayang Zhao; Yu Dong

doi:10.52396/JUSTC-2023-0035

JUSTC > 2023 > Just Accepted > DOI: 10.52396/JUSTC-2023-0035

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Open Access JUSTC Management 17 August 2023

Estimation of peer pressure in dynamic homogeneous social networks

1.
International Institute of Finance, School of Management, University of Science and Technology of China, Hefei 230026, China
2.
School of Economics and Management, Anhui University of Science and Technology, Huainan 232001, China

Cite this: JUSTC, 2023, 53: 1-15

https://doi.org/10.52396/JUSTC-2023-0035

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Author Bio:
Jie Liu is an Associate Professor at the University of Science and Technology of China (USTC). He received his Bachelor’s degree and Ph.D. degree in Statistics from USTC in 2003 and 2008, respectively. His major research interests include random networks, statistical modelling, and network analysis

Jiayang Zhao is currently a Ph.D. student at the University of Science and Technology of China (USTC). His research interests focus on network data modelling and subgroup analysis
Corresponding author:
Jiayang Zhao, E-mail: zhaojy19@mail.ustc.edu.cn
Received Date: March 08, 2023
Accepted Date: May 25, 2023
Available Online: August 17, 2023

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Abstract

Abstract

Social interaction with peer pressure is widely studied in social network analysis. Game theory can be utilized to model dynamic social interaction and one class of game network models assumes that peopleos decision payoff functions hinge on individual covariates and the choices of their friends. However, peer pressure would be misidentified and induce a non-negligible bias when incomplete covariates are involved in the game model. For this reason, we develop a generalized constant peer effects model based on homogeneity structure in dynamic social networks. The new model can effectively avoid bias through homogeneity pursuit and can be applied to a wider range of scenarios. To estimate peer pressure in the model, we first present two algorithms based on the initialize expand merge method and the polynomial-time two-stage method to estimate homogeneity parameters. Then we apply the nested pseudo-likelihood method and obtain consistent estimators of peer pressure. Simulation evaluations show that our proposed methodology can achieve desirable and effective results in terms of the community misclassification rate and parameter estimation error. We also illustrate the advantages of our model in the empirical analysis when compared with a benchmark model.

Abstract

Social interaction with peer pressure is widely studied in social network analysis. Game theory can be utilized to model dynamic social interaction and one class of game network models assumes that peopleos decision payoff functions hinge on individual covariates and the choices of their friends. However, peer pressure would be misidentified and induce a non-negligible bias when incomplete covariates are involved in the game model. For this reason, we develop a generalized constant peer effects model based on homogeneity structure in dynamic social networks. The new model can effectively avoid bias through homogeneity pursuit and can be applied to a wider range of scenarios. To estimate peer pressure in the model, we first present two algorithms based on the initialize expand merge method and the polynomial-time two-stage method to estimate homogeneity parameters. Then we apply the nested pseudo-likelihood method and obtain consistent estimators of peer pressure. Simulation evaluations show that our proposed methodology can achieve desirable and effective results in terms of the community misclassification rate and parameter estimation error. We also illustrate the advantages of our model in the empirical analysis when compared with a benchmark model.
Public Summary
- This paper introduces the Generalized Constant Peer Effect (GCPE) model, a novel network game model that quantifies social interactions within dynamic networks.
- The proposed model can efficiently mitigate estimation inaccuracies related to peer pressure by integrating homogeneity.
- We design innovative algorithms to accurately identify homogeneity. Then we apply the Nested Pseudo-Likelihood Estimation (NPLE) method to obtain consistent estimators of parameters.

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1. Introduction

In recent decades, a variety of macromolecules with complex topologies, including cyclic, star, and hyperbranched polymers, have been synthesized via various synthetic methods. The properties of polymers differ significantly depending on their topology^[1-5]. Cyclic polymers have unique properties compared to their linear analogs with the same molar mass due to the lack of chain ends. These properties include lower intrinsic characteristic viscosity, improved heat stability^[6-8], and smaller hydrodynamic volume^[9,10]. Chemists have extensively investigated the synthetic pathways of cyclic polymers, primarily ring expansion strategies involving the introduction of monomers into cyclic initiators/catalysts or ring-closure techniques via intramolecular coupling of linear precursors terminated with complementary highly reactive groups in dilute solutions^[11-15]. Cyclic polymers exhibit unique self-assembly properties^[16]. For example, micelles formed by self-assembly of amphiphilic cyclic polymers are smaller in size and more stable than those formed by their linear analogs^{[17, 18]}.

Amphiphilic block copolymers (ABCs) often undergo phase separation in selective solvents due to their hydrophilic/ hydrophobic nature, forming nanoparticles with diverse morphologies such as micelles, worm-like micelles, lamellae, and vesicles^[19-21]. These morphologies are utilized extensively in biomedicine, nanoreactors, catalysis, and other fields^[22,23]. The development of controlled radical polymerization (CRP) has provided a versatile strategy for the synthesis of ABCs. This technology significantly facilitates the study of ABCs during self-assembly. Conventional self-assembly of ABCs is usually performed in a dilute solution and involves multiple steps. These tedious and inefficient processes limit the large-scale preparation of nanoparticles, which hinders their potential commercial application^[24,25]. Polymerization-induced self-assembly (PISA) is a combination of polymerization and phase separation that facilitates the efficient and scalable preparation of nanoparticles by dispersion or emulsion polymerization in a highly concentrated solution^[26-33]. Soluble precursors function as macromolecular chain transfer agents (macroCTAs) and stabilizers in dispersion polymerization systems for PISA, while large amounts of soluble monomers are introduced for CRP. As polymerization proceeds, block copolymers become insoluble at certain critical degrees of polymerization (DP), and spherical micelles develop when microphase separation occurs in the initial polymerization stage. Further growth of the hydrophobic chain segments leads to the emergence of nanoparticles with different morphologies^[34-38]. Although PISA has been extensively studied, the majority of currently available nano-objects are composed of linear block copolymers, and cyclic architectures have not been explored to the best of our knowledge. This is a limitation of the PISA approach as topology plays a significant role during phase separation.

Herein, linear poly (ethylene oxide) (PEO) and cyclic PEO (CPEO) with 4-(4-cyanopentanoic acid) dithiobenzoate (CPADB) groups were synthesized and utilized as macro-CTAs to prepare nanoparticles by reversible addition-fragmentation chain transfer (RAFT) dispersion polymerization via PISA. Additionally, the influence of topology on the polymerization kinetics and morphology of the block copolymer assemblies was investigated. The nucleation period of the linear PEO (LPEO) was slightly shorter than that of the cyclic analog. The increased solubility of the cyclic hydrophilic segment delayed the morphological transition of the block copolymer nanoparticles during PISA.

2. Materials and methods

2.1 Materials

Benzyl methacrylate (BzMA) and 2,3,4,5,6-pentafluorostyrene (PFSt) were purchased from Aladdin Reagents, China, and stored at −20 °C after removal of the inhibitor with an alkaline alumina column. Styrene (St, 99%) was distilled under reduced pressure and stored at −20 °C. 2,2'-Azobisobutyronitrile (AIBN) was recrystallized from ethanol and stored at 4 °C. Propargyl alcohol was distilled under reduced pressure and stored in the dark until use. Copper(I) bromide (CuBr, 95%) was stirred overnight in acetic acid, filtered, washed thrice with ethanol, and dried under reduced pressure. Sodium azide (NaN₃), 2-bromoisobutyryl bromide (98%), 2,2-dimethylol propionic acid, N,N′-dicyclohexylcarbodiimide (DCC), 4-dimethylaminopyridine (DMAP), and triethylamine (TEA, 99%) were purchased from Aladdin Reagent, China and used as received. Poly(ethylene oxide) (PEO-OH, M_n = 4000 g/mol), 9-anthracenecarboxylic acid, p-toluene sulfonyl chloride (TsCl), and pentamethyldiethylenetriamine (PMDETA) were purchased from TCI and used as received. Sodium hydroxide (NaOH), anhydrous sodium sulfate (Na₂SO₄), 2,2-dimethoxypropane, concentrated hydrochloric acid (HCl), thionyl chloride (SOCl₂), N,N-dimethylformamide (DMF), Dichloromethane (DCM) and Tetrahydrofuran (THF) were purchased from Sinopharm Chemical Reagent and were used without further purification. CPADB was synthesized according to a previous study^[39].

2.2 Synthesis

2.2.1 Synthesis of PEO-Ts

A 250 mL round-bottom flask was charged with PEO-OH (20.0 g, 5.0 mmol), TEA (28.0 mL, 200.0 mmol), and anhydrous dichloromethane (50.0 mL). The reaction flask was subsequently placed in an iced-water bath. TsCl (1.9 g, 10.0 mmol) dissolved in dichloromethane (2.5 mL) was added dropwise to the reaction mixture and stirred at 50 °C for 12 h after moving placing the flask in an oil bath. The reaction mixture was thrice washed with 1 mol/L HCl (3 × 100.0 mL). The organic phase was subsequently dried with anhydrous Na₂SO₄ and Na₂CO₃. The polymer solution was added dropwise to a large excess of cold diethyl ether (3 × 500.0 mL) to precipitate to obtain PEO-Ts as a white solid (18.8 g, yield 90%).

2.2.2 Synthesis of PEO-N₃

A 250 mL round-bottom flask was successively charged with PEO-Ts (14.0 g, 3.0 mmol), sodium nitride (7.1 g, 60.0 mmol), and DMF (60.0 mL). The mixture was stirred at 90 °C overnight. The DMF was removed by rotary evaporation. The residual NaN₃ was removed by passing through a neutral alumina column. After the removal of DMF and residual NaN₃, the residual polymer was dissolved in THF and subsequently precipitated into a large excess of cold diethyl ether. The polymer was dried under vacuum to yield a white solid (13.6 g, yield 95%).

2.2.3 Synthesis of PEO-ant

AHAnt (Scheme 1) was synthesized as previously reported^[40]. A 100 mL reaction flask was successively charged with PEO-N₃ (10.6 g, 2.5 mmol), AHAnt (2.1 g, 5.5 mmol), PMDETA (1.0 mL, 5.0 mmol), cuprous bromide (717.0 mg, 5.0 mmol) and 40.0 mL DMF. The mixture was thoroughly deoxygenated by purging with nitrogen for 30 min. The reaction was allowed to proceed at 60 °C overnight. After the removal of DMF, the residual polymer was dissolved in THF. The copper salt was removed by passing through a neutral alumina column. The THF solution without the copper salt was concentrated and precipitated into cold ethyl ether (3 × 500.0 mL) and dried under vacuum to yield a yellow solid (11.6 g, yield 84%).

1.. Synthesis of LPEO-CPADB and CPEO-CPADB.

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2.2.4 Synthesis of CPEO-OH

PEO-ant (100.0 mg, 0.02 mmol) was dissolved in 500 mL anhydrous THF and irradiated with 365 nm UV light for 4 h. When the irradiation was complete, the polymer solution was concentrated, precipitated into cold ether, and dried under vacuum to yield a pale yellow powder (98 mg, yield 98%).

2.2.5 Synthesis of CPEO-CPADB

A 100 mL flask was charged with CPEO-OH (5.0 g, 1.3 mmol), CPADB (2.7 g, 10.0 mmol), DMAP (0.6 g, 5.0 mmol), and anhydrous dichloromethane (50.0 mL). DCC (1.6 g, 7.5 mmol) in 5 mL CH₂Cl₂ was added dropwise to this mixture and stirred at 2 °C for 72 h. The reaction mixture was subsequently filtered and washed with water (3 × 100.0 mL). The organic phase was dried over anhydrous Na₂SO₄, and the solvent was removed under reduced pressure. The concentrated polymer solution was precipitated into cold ethyl ether. A red solid was obtained (5.1 g, yield 95%).

2.2.6 Synthesis of LPEO-CPADB

A 10 mL flask was charged with PEO-OH (5.0 g, 1.3 mmol), CPADB (2.7 g, 10.0 mmol), DMAP (0.6 g, 5.0 mmol), and anhydrous dichloromethane (50.0 mL). DCC (1.6 g, 7.5 mmol) in 5 mL CH₂Cl₂ was added slowly to the reaction mixture and stirred at 2 °C for 72 h. The reaction mixture was subsequently filtered and washed with water (3 × 100.0 mL). The organic phase was dried over anhydrous Na₂SO₄ and the solvent was removed under reduced pressure. The concentrated polymer solution was precipitated into cold ethyl ether. A red solid was obtained (5.2 g, yield 97%).

2.. Synthesis of diblock copolymer nano-objects via polymerization-induced self-assembly (PISA) using (a) CPEO-CPADB and (b) LPEO-CPADB as macroCTA, respectively.

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2.3 Characterization

2.3.1 Nuclear magnetic resonance (NMR)

All NMR spectra were recorded on a Bruker NMR spectrometer (resonance frequency of 400 MHz for ¹H) operated in Fourier transform mode. The samples were dissolved in chloroform-d, with tetramethylsilane (TMS) as an internal reference.

2.3.2 Gel permeation chromatography (GPC)

Molecular weight and dispersity (Đ) were determined using gel permeation chromatography (GPC, Waters 1515) equipped with an RI 2414 detector at 35 °C and microstyragel columns (500, 10³, and 10⁴ Å) calibrated with monodisperse polystyrene standards. THF was used as eluent at a flow rate of 1.0 mL/min.

2.3.3 Transmission electron microscopy (TEM)

TEM was conducted using a Hitachi H-800 electron microscope at an acceleration voltage of 100 kV. To prepare the TEM samples, 10.0 μL of the diluted copolymer solution was placed onto a carbon-coated copper grid and dried in the dark.

2.3.4 Dynamic light scattering (DLS)

DLS was used to determine the size of the nanoparticles on a commercial laser light scattering (LLS) spectrometer (Zetasizer Nano ZS90, Malven Instruments Ltd., Malvern, UK) equipped with a 90° fixed-angle He-Ne laser (4.0 mW, 633 nm). DLS samples were prepared by diluting the nanoparticle dispersion formed by PISA to 0.01% w/w. The tests were performed in triplicate at 25 °C.

3. Results and discussion

3.1 Synthesis of linear and cyclic macroCTAs

The synthetic routes for the two macro-RAFT reagents with different topological structures are shown in Scheme 1. First, anthracene-terminated PEO (PEO-ant) was prepared via sequential esterification, azidation, and click reaction with AHAnt. AHAnt contains multiple functional groups, including an anthryl group for cyclization, a hydroxyl group for esterification, and an alkynyl group for the click reaction. To further obtain the cyclic analog, cyclization was achieved via intramolecular coupling of the anthryl end-groups as previously reported^[41]. Linear and cyclic PEO were subsequently modified with CPADB via esterification to afford the macroCTAs. The ¹H-NMR spectrum of LPEO-CPADB is shown in Fig. 1a. The peaks at 8.5 ppm (a), 8.0 ppm (b, c), and 7.5 ppm (d, e) are characteristic signals of the aromatic protons of the anthryl groups. The signals at 1.7 ppm (m) and 3.6 ppm (n) are assigned to the methyl protons of CPADB and the ethylene protons of the PEO backbone, respectively. According to the integrated intensity ratio of signals m and n, the grafting efficiency of CPADB onto LPEO-CPADB was calculated as 96%. The GPC trace of LPEO-CPADB, shown in Fig. 2 (black line), is symmetrical and unimodal. The corresponding M_n and M_w/M_n values are 4700 g/mol and 1.05, respectively.

Figure 1. ¹H-NMR spectra of LPEO-CPADB (a) and CPEO-CPADB (b) (in CDCl₃).

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Figure 2. GPC traces of LPEO-CPADB and CPEO-CPADB with THF as eluent.

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Fig. 1b shows the ¹H-NMR spectrum of CPEO-CPADB. Compared with that of LPEO-CPADB, the characteristic signals of the anthryl groups disappeared, and the signals for the anthracene dimer (6.9−6.5 ppm) appeared, indicating that the dimerization reaction proceeded successfully. Similarly, the grafting efficiency of CPADB was calculated as approximately 95%. The GPC trace of CPEO-CPADB, shown in Fig. 2 (red line), is similar to that of LPEO-CPADB with decreased M_n (4700 g/mol for LPEO-CPADB and 4200 g/mol for CPEO-CPADB). This is consistent with decreased hydrodynamic volume owing to its cyclic architecture^[42].

3.2 RAFT dispersion polymerization of BzMA mediated by linear and cyclic macroCTAs

In this study, macro-RAFT reagents with linear and cyclic topologies were synthesized. BzMA was selected as the hydrophobic monomer for dispersion polymerization. The effect of topology on polymerization kinetics was investigated by ¹H-NMR spectroscopy (Fig. 3). The conversion of BzMA throughout the polymerization reaction was calculated based on the integral ratio of BzMA vinyl protons (6.2−4.8 ppm) and PEO ethylene protons (3.6 ppm). The conversion-time plots, polymerization kinetics, and GPC traces of the block copolymers are shown in Fig. 4. Initially, the rate of BzMA polymerization was low but increased significantly after 3 h (Fig. 4). Additionally, the ln([M]₀/[M]) vs. time plot demonstrates two stages during the polymerization process. Homogeneous polymerization was conducted during the first stage (within 2 h) of polymerization. Initially, the monomer was consumed slowly, and the newly formed copolymer might be dissolved in the solvent. After the formation of spherical micelles (at 2.1 h), heterogeneous polymerization occurred. The apparent enhancement of the polymerization rate after phase separation might be induced by the relatively high local monomer concentration in the nanoparticles and segregated confined reaction environments^[43]. The GPC curves of LPEO-b-PbzMA shifted to shorter retention times throughout the polymerization. The molecular weight distribution (M_w/M_n) of the synthesized block copolymers is reported in Table 1.

Table 1. Summary of monomer conversions, actual DP of PBzMA, M_n, and Đ of LPEO-b-PBzMA copolymers, and D_DLS of LPEO-b-PBzMA nano-objects.

Samples	Feed ratio	Time (h)	Conversion (%)	Actual DP	M_n,NMR (g/mol)	M_n,GPC (g/mol)	M_w/M_n	D_DLS (nm)
1	1/0.4/400	0.5	1.9	8	6690	5380	1.12	−
2	1/0.4/400	1.0	5.1	20	8970	6340	1.23	−
3	1/0.4/400	1.5	12.1	48	13890	9900	1.26	125
4	1/0.4/400	2.0	20.0	80	19470	11840	1.23	114
5	1/0.4/400	2.5	32.5	130	28230	21600	1.21	130
6	1/0.4/400	3.0	54.4	218	43680	37570	1.24	237
7	1/0.4/400	3.5	68.6	274	53730	48820	1.23	252
8	1/0.4/400	4.0	73.4	294	57050	51440	1.24	259
9	1/0.4/400	4.5	83.6	334	64200	54850	1.42	267
10	1/0.4/400	5.0	88.5	354	67640	59140	1.24	214
11	1/0.4/400	6.0	94.0	376	71530	63510	1.28	176
12	1/0.4/400	10.0	97.6	390	74080	67070	1.31	218
13	1/0.4/400	12.0	98.6	394	74790	69500	1.35	347

| Show Table

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Figure 3. Polymerizations were conducted using [BzMA]₀ : [macro-RAFT agent]₀ : [AIBN]₀ = 400:1:0.4. ¹H-NMR spectra of PEO-b-PBzMA recorded during the RAFT dispersion polymerization of BzMA using (a) LPEO-CPADB and (b) CPEO-CPADB as the macroCTA in an ethanol/water mixture (70/30, w/w). Solid concentration, 10% w/w (in CDCl₃).

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Figure 4. Conversion vs. time (black line) and ln([M]₀/[M]_t) vs. time (red line) plots of BzMA during the RAFT dispersion polymerization using (a) LPEO-CPADB and (c) CPEO-CPADB as the macroCTA. GPC traces of (b) LPEO-b-PBzMA and (d) CPEO-b-PBzMA copolymers were obtained at different polymerization times.

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The RAFT dispersion polymerization of BzMA mediated by CPEO-CPADB demonstrated a similar conversion profile to that of LPEO-CPADB (Fig. 4c). The difference lies in the increased homogeneous polymerization phase for CPEO-CPADB (2.5 h), which could be facilitated by the increased solubility of the cyclic macroCTA. GPC traces of CPEO-b-PBzMA obtained throughout the polymerization are summarized in Fig. 4d. The detailed M_n and M_w/M_n values are reported in Table 2.

Table 2. Summary of monomer conversions, actual DP of PBzMA, M_n, and Đ of CPEO-b-PBzMA copolymers, and D_DLS of CPEO-b-PBzMA nano-objects.

Samples	Feed ratio	Time (h)	Conversion (%)	Actual DP	M_n,NMR (g/mol)	M_n,GPC (g/mol)	Đ	D_DLS (nm)
1	1/0.4/400	0.5	1.5	6	6390	5220	1.10	−
2	1/0.4/400	1.0	4.1	16	8250	6330	1.23	−
3	1/0.4/400	1.5	12.0	48	13780	9720	1.24	114
4	1/0.4/400	2.0	20.9	84	20080	14590	1.27	140
5	1/0.4/400	2.5	27.0	108	24390	17200	1.22	149
6	1/0.4/400	3.0	48.1	192	39230	33080	1.37	154
7	1/0.4/400	3.5	69.1	276	54000	49970	1.25	179
8	1/0.4/400	4.0	76.6	306	59290	51850	1.30	264
9	1/0.4/400	4.5	86.0	344	65930	58000	1.26	220
10	1/0.4/400	5.0	90.5	362	69080	61300	1.23	144
11	1/0.4/400	6.0	91.5	366	69780	62940	1.29	246
12	1/0.4/400	10.0	97.4	390	73930	66500	1.31	278
13	1/0.4/400	12.0	98.0	392	74360	68100	1.34	310

| Show Table

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3.3 The preparation of nanoparticles with different morphologies

To assess the effect of macroCTA architecture on the morphological evolution during PISA, a library of PEO-b-PBzMA block copolymer nano-objects with increased DP of PBzMA (50, 100, 150, 200, 300, and 400) was synthesized at 20% solid content using linear and cyclic macroCTA (Scheme 2). A polymerization time of 12 h was required to achieve near-quantitative BzMA conversion. The morphologies of the PEO-b-PBzMA assemblies were tracked by transmission electron microscopy (TEM) (Fig. 5).

Figure 5. TEM images of the PEO-b-PBzMA copolymer nano-objects with different DPs of PBzMA in the ethanol/water mixture (70/30, w/w), and the solid content = 20% (w/w).

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Both LPEO-b-PBzMA and CPEO-b-PBzMA copolymer nano-objects evolve from spherical micelles to long entangled nanowires, to coexisting of nanowires and lamella, and finally to vesicles, as the PBzMA block increases. However, there are some distinctions between the linear and cyclic morphologies. A morphological transition from spherical to worm-like occurred for linear PEO when BzMA was increased to 150 (LPEG-b-PBzMA₁₅₀). However, CPEG-b-PBzMA₁₅₀ still demonstrated a spherical morphology. Increasing the DP to afford LPEG-b-PBzMA₃₀₀ resulted in a morphological change to vesicles, whereas CPEG-b-PBzMA₃₀₀ resulted in worms with a minor population of lamella. The delayed morphological transformation of CPEG-b-PBzMA may be attributed to the increased solubility of the cyclic hydrophilic segment^[44]. CPEO-b-PBzMA copolymers with longer PBzMA segments were more stable than their linear analogs.

To further illustrate the topological effect on the morphology of nanoparticles during PISA, more hydrophobic 2,3,4,5,6-pentafluorostyrene (FSt) was selected as the monomer. RAFT-mediated dispersion polymerization of FSt was performed in an ethanol/DMF mixture (95/5, w/w) at 70 °C using LPEO-CPADB and CPEO-CPADB as macroCTAs. The target DPs of PFSt were 40, 80, 120, 160, and 200. As shown in Fig. 6, a morphological evolution from spherical micelles (DP = 40) to vesicles (DP > 40) was observed for the LPEO-b-PPFSt nano-objects. However, nanowires were observed for CPEO-b-PPFSt when the DP of PPFSt was 80 and 120. This result demonstrates the effect of macroCTA architecture on the morphological transitions during PISA.

Figure 6. TEM images of the PEO-b-PPFSt copolymer nano-objects with different DPs of PPFSt in the ethanol/DMF mixture (95/5, w/w), and the solid content = 25% (w/w).

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4. Conclusions

In summary, RAFT-mediated dispersion polymerization was performed to study the influence of two distinct hydrophilic topologies on the polymerization kinetics and morphological evolution of block copolymer nanoparticles. The polymerization process demonstrated two distinct stages. The nucleation period of the linear analog was slightly shorter than that of the cyclic analog. Different hydrophobic monomers were selected to assess the influence of topology on the morphological evolution of ABC nanoparticles. The increased solubility of the cyclic hydrophilic macroCTA further stabilized the nanoparticles and subsequently delayed morphological transitions during PISA.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22131010, 52021002) and the Fundamental Research Funds for the Central Universities (WK2060000012).

Conflict of interest

The authors declare that they have no conflict of interest.

Acknowledgements

This work was supported by the National Nature Science Foundation of China (71771201, 71973001).

Conflict of interest

The authors declare that they have no conflict of interest.

1 https://www.stats.ox.ac.uk/snijders/siena/Glasgow_data.htm

This paper introduces the Generalized Constant Peer Effect (GCPE) model, a novel network game model that quantifies social interactions within dynamic networks. The proposed model can efficiently mitigate estimation inaccuracies related to peer pressure by integrating homogeneity. We design innovative algorithms to accurately identify homogeneity. Then we apply the Nested Pseudo-Likelihood Estimation (NPLE) method to obtain consistent estimators of parameters.

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[21]	Han Q, Xu K, Airoldi E. Consistent estimation of dynamic and multi-layer block models. In: Proceedings of the 32nd International Conference on Machine Learning. Lille, France: JMLR, 2015, 37: 1511–1520.
[22]	Pensky M, Zhang T. Spectral clustering in the dynamic stochastic block model. Electronic Journal of Statistics, 2019, 13: 678–709. DOI: 10.1214/19-EJS1533
[23]	Chunaev P. Community detection in node-attributed social networks: A survey. Computer Science Review, 2020, 37: 100286. DOI: 10.1016/j.cosrev.2020.100286
[24]	Liu M, Guo J, Chen J. Community discovery in weighted networks based on the similarity of common neighbors. Journal of Information Processing Systems, 2019, 15 (5): 1055–1067. DOI: 10.3745/JIPS.04.0133
[25]	Gao C, Ma Z, Zhang A Y, et al. Achieving optimal misclassification proportion in stochastic block models. The Journal of Machine Learning Research, 2017, 18 (1): 1980–2024. DOI: 10.5555/3122009.3153016
[26]	Bickel P J, Chen A. A nonparametric view of network models and Newman–Girvan and other modularities. 2009. Proceedings of the National Academy of Sciences, 2009, 106 (50): 21068–21073. DOI: 10.1073/pnas.0907096106
[27]	Zhao Y, Levina E, Zhu J. Consistency of community detection in networks under degree-corrected stochastic block models. Annals of Statistics, 2012, 40: 2266–2292. DOI: 10.1214/12-AOS1036
[28]	Kasahara H, Shimotsu K. Sequential estimation of structural models with a fixed point constraint. Econometrica, 2012, 80 (5): 2303–2319. DOI: 10.3982/ECTA8291

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Figure 1. Average community misclassification rate for Algorithm 1, which is based on the average of 50 replications.

Figure 2. Average community misclassification rate for Algorithms 1 and 2, which is based on the average of 50 replications.

Figure 3. The standard deviation and mean square error of the estimated peer pressure parameter.

References

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[23]	Chunaev P. Community detection in node-attributed social networks: A survey. Computer Science Review, 2020, 37: 100286. DOI: 10.1016/j.cosrev.2020.100286
[24]	Liu M, Guo J, Chen J. Community discovery in weighted networks based on the similarity of common neighbors. Journal of Information Processing Systems, 2019, 15 (5): 1055–1067. DOI: 10.3745/JIPS.04.0133
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[26]	Bickel P J, Chen A. A nonparametric view of network models and Newman–Girvan and other modularities. 2009. Proceedings of the National Academy of Sciences, 2009, 106 (50): 21068–21073. DOI: 10.1073/pnas.0907096106
[27]	Zhao Y, Levina E, Zhu J. Consistency of community detection in networks under degree-corrected stochastic block models. Annals of Statistics, 2012, 40: 2266–2292. DOI: 10.1214/12-AOS1036
[28]	Kasahara H, Shimotsu K. Sequential estimation of structural models with a fixed point constraint. Econometrica, 2012, 80 (5): 2303–2319. DOI: 10.3982/ECTA8291

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Estimation of peer pressure in dynamic homogeneous social networks

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Abstract

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1. Introduction

2. Materials and methods

2.1 Materials

2.2 Synthesis

2.2.1 Synthesis of PEO-Ts

2.2.2 Synthesis of PEO-N3

2.2.3 Synthesis of PEO-ant

2.2.4 Synthesis of CPEO-OH

2.2.5 Synthesis of CPEO-CPADB

2.2.6 Synthesis of LPEO-CPADB

2.3 Characterization

2.3.1 Nuclear magnetic resonance (NMR)

2.3.2 Gel permeation chromatography (GPC)

2.3.3 Transmission electron microscopy (TEM)

2.3.4 Dynamic light scattering (DLS)

3. Results and discussion

3.1 Synthesis of linear and cyclic macroCTAs

3.2 RAFT dispersion polymerization of BzMA mediated by linear and cyclic macroCTAs

3.3 The preparation of nanoparticles with different morphologies

4. Conclusions

Acknowledgements

Conflict of interest

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2.2.2 Synthesis of PEO-N₃