Hard Phase

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Lenka Zdeborova - One of the best experts on this subject based on the ideXlab platform.

  • asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
    Physical Review E, 2011
    Co-Authors: Aurelien Decelle, Florent Krzakala, Cristopher Moore, Lenka Zdeborova
    Abstract:

    In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the Phase diagram. We describe in detail properties of the detectability/undetectability Phase transition and the easy/Hard Phase transition for the community detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance.

Andreas Taden - One of the best experts on this subject based on the ideXlab platform.

  • thermoset thermoplastic hybrid nanoparticles and composite coatings
    Polymer, 2014
    Co-Authors: Yang Zhang, Rebecca Foos, Katharina Landfester, Andreas Taden
    Abstract:

    The present invention relates to a method for the generation of thermoset-thermoplastic hybrid nanoparticles with a Hard Phase and a soft Phase, wherein the Hard Phase comprises or consists of a thermosetting polymer and the soft Phase comprises or consists of a thermoplastic polymer, the method including a) providing a mixture of a thermosetting resin, monomers of a thermoplastic polymer, and a curing agent for the thermosetting resin; b) dispersing the mixture into an aqueous medium to form a miniemulsion, c) polymerizing the thermosetting resin in the miniemulsion by stepwise polymerization to form a seed emulsion of thermoplastic monomer swollen thermosetting polymer nanoparticles; d) adding monomers of the thermoplastic polymer to the seed emulsion; and e) adding a polymerization initiator and polymerizing the monomers of the thermoplastic polymer by free radical polymerization to form the core-shell nanoparticle. Also encompassed are the thus produced thermoset-thermoplastic hybrid nanoparticles and their use in thin films for the application in coatings and adhesives.

Aurelien Decelle - One of the best experts on this subject based on the ideXlab platform.

  • asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
    Physical Review E, 2011
    Co-Authors: Aurelien Decelle, Florent Krzakala, Cristopher Moore, Lenka Zdeborova
    Abstract:

    In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the Phase diagram. We describe in detail properties of the detectability/undetectability Phase transition and the easy/Hard Phase transition for the community detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance.

Zohar Nussinov - One of the best experts on this subject based on the ideXlab platform.

  • algorithm independent bounds on community detection problems and associated transitions in stochastic block model graphs
    Journal of Complex Networks, 2015
    Co-Authors: Richard K Darst, David R Reichman, Peter Ronhovde, Zohar Nussinov
    Abstract:

    We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community “noise” (inter-community edges) on any “community detection” algorithm’s ability to correctly group nodes assigned to a planted partition, a problem which has been proven to be NP complete in a standard rendition. Our result does not rely on the use of any one particular algorithm nor on the analysis of the limitations of inference. Rather, we turn the problem on its head and work backwards to examine when, in the first place, well defined structure may exist in SBMs. The method that we introduce here could potentially be applied to other computational problems. The objective of community detection algorithms is to partition a given network into optimally disjoint subgraphs (or communities). Similar to k−SAT and other combinatorial optimization problems, “community detection” exhibits different Phases. Networks that lie in the “unsolvable Phase” lack well-defined structure and thus have no partition that is meaningful. Solvable systems splinter into two disparate Phases: those in the “HardPhase and those in the “easy” Phase. As befits its name, within the easy Phase, a partition is easy to achieve by known algorithms. When a network lies in the Hard Phase, it still has an underlying structure yet finding a meaningful partition which can be checked in polynomial time requires an exhaustive computational effort that rapidly increases with the size of the graph. When taken together, (i) the rigorous results that we report here on when graphs have an underlying structure and (ii) recent results concerning the limits of rather general algorithms, suggest bounds on the Hard Phase.

Ailing Sun - One of the best experts on this subject based on the ideXlab platform.

  • tuning Hard Phase towards synergistic improvement of toughness and self healing ability of poly urethane urea by dual chain extenders and coordinative bonds
    Chemical Engineering Journal, 2020
    Co-Authors: Wenjuan Guo, Xin Liu, Hao Zhu, Jinping Zhang, Xingjiang Liu, Liuhe Wei, Ailing Sun
    Abstract:

    Abstract It is challenging to simultaneously improve the toughness and self-healing ability of thermoplastic polyurethane (TPU) due to mutually exclusive dependence on chain motion and Hard Phase. In this work, a novel poly(urethane urea) (PUU) was synthesized by using 2, 6-diamimopyridine (Py) and cystamine (Cy) as chain extenders and subsequently complexed with Zn2+ ions. It is revealed that the pyridine moieties together with formation of coordinative bonds significantly influences microPhase separation by interfering with hydrogen bonding. A Py/Cy molar ratio of 1:2 is optimal to remarkably improve the toughness and self-healing ability. Specifically, its tensile strength, toughness and self-healing efficiency simultaneously improve to 9.40 ± 0.10 MPa, 64.49 ± 1.75 MJ/m3, and 96.64 ± 1.52% with 92%, 139% and 29% increment compared to PUU-Cy, respectively. The synergistic enhancing effect is the consequence of compromised Hard Phase and coordinative bonds. Firstly, decrease of Hard domain content leads to loosely packed Hard segments dispersing in soft Phase, facilitating disulfide exchange. Secondly, the coordinative bonds serving as dynamic crosslinking joints not only restrict chain dislocation but also contribute to better self-healing ability than hydrogen bonds. An electrode film derived from embedding silver nanowires (AgNWs) into this material exhibits self-repairable and robust sensing properties due to reconstructing conducting network by self-healable matrix. This unique feature endows it with a great potential in the field of flexible electronics and wearable devices.