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Product co-creation based on company-sponsored online community has come to be a paradigm of developing new products collaboratively with customers. In such a product co-creation campaign, the sponsoring company needs to interact intensively with active community members about the design scheme of the product. We call the collection of the rates of the company's response to active community members at all time in the co-creation campaign as a company response policy (CRP). This paper addresses the problem of finding a cost-effective CRP (the CRP problem). First, we introduce a novel community state evolutionary model and, thereby, establish an optimal control model for the CRP problem (the CRP model). Second, based on the optimality system for the CRP model, we present an iterative algorithm for solving the CRP model (the CRP algorithm). Thirdly, through extensive numerical experiments, we conclude that the CRP algorithm converges and the resulting CRP exhibits excellent cost benefit. Consequently, we recommend the resulting CRP to companies that embrace product co-creation. Next, we discuss how to implement the resulting CRP. Finally, we investigate the effect of some factors on the cost benefit of the resulting CRP. To our knowledge, this work is the first attempt to study value co-creation through optimal control theoretic approach.

The rapid proliferation of Internet of Things (IoT) devices in recent years has resulted in a significant surge in the number of cyber-attacks targeting these devices. Recent data indicates that the number of such attacks has increased by over 100 percent, highlighting the urgent need for robust cybersecurity measures to mitigate these threats. In addition, a cyber-attack will begin to spread malware across the network once it has successfully compromised an IoT network. However, to mitigate this attack, a new patch must be applied immediately. In reality, the time required to prepare and apply the new patch can vary significantly depending on the nature of the cyber-attack. In this paper, we address the issue of how to mitigate cyber-attacks before the new patch is applied by formulating an optimal control strategy that reduces the impact of malware propagation and minimise the number of infected devices across IoT networks in the smart home. A novel node-based epidemiological model susceptible, infected high, infected low, recover first, and recover complete(SI_HI_LR_FR_C) is established with immediate response state for the restricted environment. After that, the impact of malware on IoT devices using both high and low infected rates will be analyzed. Finally, to illustrate the main results, several numerical analyses are carried out in addition to simulate the real-world scenario of IoT networks in the smart home, we built a dataset to be used in the experiments., Comment: 17 pages, 12 figures

We report an unusual evolution of superconductivity (SC) in the three-dimensional Dirac semimetal PdTe with increasing pressure up to $\sim$50 GPa. The compressed PdTe exhibits a sudden reversal in the superconducting transition temperature $T\mathrm{_c}$, from an initial decrease with pressure to an increase above a critical pressure $P\mathrm{_c} \approx$ 15 GPa, showing a V-shaped feature composed of SC-I and SC-II phases due to a structural phase transition through $P\mathrm{_c}$. Subsequently, the $T\mathrm{_c}$ goes into a plateau around 2.5 K when the pressure is higher than $\sim$32 GPa. In addition, we find the variations of carrier concentrations and mobilities also manifest a similar trend on the pressure response as the $T\mathrm{_c}$, and the normal-state electronic properties change from the electron-dominated single-band model to two-carrier model after the structural phase transition, implying the close correlation between electronic properties and two SC phases. Our findings establish the SC of PdTe is highly tunable under varying pressures., Comment: 7 pages, 5 figures

The Hohenberg-Mermin-Wagner theorem states that a two-dimensional system cannot spontaneously break a continuous symmetry at finite temperature. This is supported by the observation of layer-dependent superconductivity in the quasi-two-dimensional superconductor NbSe2, in which the superconducting transition temperature (Tc) is reduced by about 60% in the monolayer limit. However, for the extremely anisotropic copper-based high-Tc superconductor Bi2Sr2CaCu2O8+{\delta} (Bi-2212), the Tc of the monolayer is almost identical to that of its bulk counterpart. To clarify the effect of dimensionality on superconductivity, here we successfully fabricate ultrathin flakes of CsCa2Fe4As4F2, a highly anisotropic iron-based high-Tc superconductor, down to monolayer. The monolayer flake exhibits the highest Tc of 24 K (after tuning to the optimal doping by ionic liquid gating), which is about 20% lower than that of the bulk crystal. We also fabricate ultrathin flakes of CaKFe4As4, another iron-based superconductor with much smaller anisotropy. The Tc of the 3-layer flake decreases by 46%, showing a more pronounced dimensional effect than that of CsCa2Fe4As4F2. By carefully examining their anisotropy and the c-axis coherence length, we reveal the general trend and empirical law of the layer-dependent superconductivity in these quasi-two-dimensional superconductors. From this, the Tc of a new monolayer superconductor can be extrapolated., Comment: 34 pages, 5 figures, 1 table

We report the structure and physical properties of two newly-discovered compounds AV8Sb12 and AV6Sb6 (A = Cs, Rb), which have C2 (space group: Cmmm) and C3 (space group: R-3m) symmetry, respectively. The basic V-kagome unit is present in both compounds, but stacking differently. A V2Sb2 layer is sandwiched between two V3Sb5 layers in AV8Sb12, altering the V-kagome lattice and lowering the symmetry of kagome layer from hexagonal to orthorhombic. In AV6Sb6, the building block is a more complex slab made up of two half-V3Sb5 layers that are intercalated by Cs cations along the c-axis. Transport property measurements demonstrate that both compounds are nonmagnetic metals, with carrier concentrations at around 1021cm-3. No superconductivity has been observed in CsV8Sb12 above 0.3 K under in-situ pressure up to 46 GPa. In contrast to CsV3Sb5, theoretical calculations and angle-resolved photoemission spectroscopy (ARPES) reveal a quasi-two-dimensional electronic structure in CsV8Sb12 with C2 symmetry and no van Hove singularities near the Fermi level. Our findings will stimulate more research into V-based kagome quantum materials., Comment: 11 pages 6 figures

Superatomic crystal is a class of hierarchical materials composed of atomically precise clusters assembled via van der Waals or covalent-like interactions. AuTe$_2$Se$_{4/3}$, an all-inorganic superatomic superconductor exhibiting superatomic-charge-density-wave (S-CDW), provides a first platform to study the response of their collectively quantum phenomenon to the external pressure in superatomic crystals. We reveal a competition between S-CDW and superconductivity using cutting-edge measurements on thin flakes at low pressures. Prominently, the pressure modulation of S-CDW ordering is 1$\sim$2 order of magnitudes (0.1 GPa) lower than that of conventional atomic superconductors. As pressure increases to 2.5 GPa, the $T_{\mathrm{CDW}}$ is suppressed and the superconducting transition temperature ($T_{\mathrm{c}}$) is firstly enhanced, and reaches the maximum then quenches with increasing pressure. Above 7.3 GPa, a second superconducting phase emerges, and then a three-fold enhancement in the transition temperature ($T_{\mathrm{c}}$) happens. Analyses of the crystal structure and theoretical calculations suggest a pressure-mediated switch of the conduction channel from the $a$- to the $b$-axis occur, followed by a dimensional crossover of conductivity and the Fermi surface from 2D to 3D., Comment: 6 pages, 4 figures