Drug repositioning via matrix completion with multi‐view side information

In the process of drug discovery and disease treatment, drug repositioning is broadly studied to identify biological targets for existing drugs. Many methods have been proposed for drug–target interaction prediction by taking into account different kinds of data sources. However, most of the existing methods only use one side information for drugs or targets to predict new targets for drugs. Some recent works have improved the prediction accuracy by jointly considering multiple representations of drugs and targets. In this work, the authors propose a drug–target prediction approach by matrix completion with multi‐view side information (MCM) of drugs and proteins from both structural view and chemical view. Different from existing studies for drug–target prediction, they predict drug–target interaction by directly completing the interaction matrix between them. The experimental results show that the MCM method could obtain significantly higher accuracies than the comparison methods. They finally report new drug–target interactions for 26 FDA‐approved drugs, and biologically discuss these targets using existing references.Inspec keywords: proteins, diseases, medical computing, drugs, genetics, molecular biophysicsOther keywords: drug–target interaction prediction, prediction accuracy, matrix completion, multiview side information, structural view, chemical view, drug repositioning, drug discovery, biological targets, FDA‐approved drugs

Nomenclature

P

md×mt known drug–target interaction matrix

As

kd×kt complete low‐rank matrix in the structural view

Ac

kd×kt complete low‐rank matrix in the chemical view

Wds

md×md drug–drug similarity matrix in the structural view

Wts

mt×mt target–target similarity matrix in the structural view

Wdt

md×md drug–drug similarity matrix in the chemical view

Wtt

mt×mt target–target similarity matrix in the chemical view

Ds

md×kd drugs feature matrix in the structural view

Gs

mt×kt protein targets feature matrix in the structural view

Dc

md×kd drugs feature matrix in the chemical view

Gc

mt×kt protein targets feature matrix in the chemical view

Q

md×mt the common complete drug–target interaction matrix

Z

kd×kt any given matrix

⟨⋅,⋅⟩

inner product for matrices

∇

gradient operator

λ1, λ2

trade‐off parameters

     

Preparation of Ti1− zNbzN ceramics by spark plasma sintering Ti1− zNbzOxNy nanopowders

Ti_1−zNb_zN ceramics were fabricated by sintering nanocrystalline titanium-niobium oxynitride (Ti_1−zNb_zO_xN_y) powders using spark plasma sintering (SPS) technique at 1060 °C for 3 min in an N₂ atmosphere. The phase composition and microstructure were characterized by XRD, SEM, TEM and EDS. The results showed that Ti_1−zNb_zN ceramics remained the cubic structures of Ti_1−zNb_zO_xN_y powders. There were XRD peak shifts in the cubic phases between Ti_1−zNb_zN ceramics and corresponding Ti_1−zNb_zO_xN_y powders. During the sintering process, oxygen separated from Ti_1−zNb_zO_xN_y to form titanium-niobium oxides. Ti_1−zNb_zN (0 < z < 1) had a more compact structure than TiO_xN_y and NbO_xN_y. Ti_0.5Nb_0.5N ceramic had the biggest grain size in the series of Ti_1−zNb_zN.     

基于卷积神经网络图像分类的轴承故障模式识别

针对传统的基于数据驱动的机械故障模式识别方法中需要人工构造算法提取特征以及人工构造特征提取算法繁琐的问题,结合卷积神经网络(CNN)在图像特征自动提取与图像分类识别中的广泛应用,提出了一种基于CNN图像分类的轴承故障模式识别方法。首先,利用集合经验模态分解(EEMD)方法对轴承振动信号进行自适应分解并用相关系数对得到的本征模函数分量进行筛选。其次,对筛选得到的本征模函数分量进行伪魏格纳-威利时频分析(PWVD)计算得到信号的时频分布图,并对时频图进行预处理。最后,将轴承15种不同工况预处理后的时频图利用CNN进行特征提取与分类识别。将该方法与同类方法进行了对比,分类正确率提高了4.26%。     

Microwave dielectric properties of Li2TiO3 ceramics sintered at low temperatures

Li₂TiO₃ ceramics were prepared at the sintering temperatures from 1050 to 1250 °C. The optimal microwave dielectric properties were ?_r = 23.29, Q × f = 15,525 GHz (5.9 GHz), and τ_f = 35.05 ppm/ °C for the sample sintered at 1200 °C. The microwave dielectric properties were improved obviously when the Li₂TiO₃ ceramics were sintered at low temperatures with small additions of H₃BO₃ (B₂O₃ in the form of H₃BO₃). Only monoclinic Li₂TiO₃ was found in the pure or H₃BO₃-doped Li₂TiO₃ ceramics. About 1.0 wt.% H₃BO₃ addition aided the sintering of Li₂TiO₃ ceramics effectively while excessive H₃BO₃ (≥2.5 wt.%) was not favorable. Typically the best microwave dielectric properties were ?_r = 23.28, Q × f = 37,110 GHz (6.3 GHz), and τ_f = 30.43 ppm/ °C for the 1.0 wt.% H₃BO₃-doped Li₂TiO₃ ceramic sintered at 920 for 3 h, which is promising for LTCC applications.     

Effect of loading history on stress corrosion cracking in high strength steel

The effect of preloading on crack nucleation time was examined with compact tension specimens having various notch radius in 0.1N-H²SO⁴ aqueous solution for 200°C tempered AISI 4340 steel. Crack nucleation time t_n increases by preloading for a given apparent stress intensity factor K_p2. The curve K_?2 vs. t_n deviates upward from the curve for the non preloading case. A linear relationship between the crack nucleation time and parameter is seen in semi-log diagram, where is taken as the value at t_n=α due to preloading. The apparent threshold stress intensity factor increases with K_?2 which is the apparent stress intensity factor of preloading. A detached crack is nucleated at some distance from the notch root and extends in a form of circle. This distance increases with increasing K_?2. The effect of load reduction during crack growth was examined. When the K-value was reduced from K₁ to K₂, an incubation time was observed before the crack started growing under the K₂-value. The incubation time t_m tends to increase with increasing ΔK = K₁-K₂. The threshold stress intensity factor was also found to increase for high load reduction.In order to explain these experimental results, a new dislocation model is proposed on the basis of stress induced diffusion of hydrogen in high stress region ahead of the notch root or a crack. This model suggests that the change in the crack nucleation time and the increase of the incubation time due to preloading or load reduction are caused by reducing the hydrostatic pressure and by spreading the hydrogen saturated region which requires more time for the hydrogen accumulation due to preloading or load reduction. The theory predicts the experimentally observed relations between and t_n and between log t_in and ΔK.     

Fabrication and photocatalytic property of Pt-intercalated layered perovskite niobates H1−xLaNb2−xMoxO7 (x = 0–0.15)

H_1−xLaNb_2−xMo_xO₇ was prepared by solid-state reaction followed by an ion-exchange reaction. Pt was incorporated in the interlayer of H_1−xLaNb_2−xMo_xO₇ by the stepwise intercalation reaction. The H_1−xLaNb_2−xMo_xO₇ showed hydrogen production activity and the activities were greatly enhanced by Pt co-incorporating. The x value in H_1−xLaNb_2−xMo_xO₇ had an important effect on the photocatalytic activity of the catalyst. When the x = 0.05, the H_1−xLaNb_2−xMo_xO₇/Pt showed a photocatalytic activity of 80 cm³ h⁻¹ g⁻¹ hydrogen evolution rate in 10 vol.% methanol solution under irradiation from a 100 W mercury lamp at 333 K.     

Dielectric properties of bismuth doped Ba1−xCaxTiO3 ceramics

The dielectric properties of (Ba_1−xCa_x)_1−1.5yBi_yTiO₃ (x = 0.10, 0.20 and 0.30, y = 0.05) ceramics were investigated. XRD analysis shows that 5 at.% of Bi doping can be fully incorporated into the perovskite lattice of (Ba_1−xCa_x)TiO₃. The maximal dielectric constant K_m of (Ba_1−xCa_x)_1−1.5yBi_yTiO₃ ceramics decreases significantly with increasing x for all the compositions. Compared with undoped Ba_1−xCa_xTiO₃ ceramics [Mater. Chem. Phys. 77 (2002)], Bi doping remarkably shifts the temperature of the peak dielectric constants T_m to lower temperature and a broad dielectric peak exhibits strong frequency dispersion. With increasing frequency, K_m decreases and T_m shifts to higher temperatures in (Ba_1−xCa_x)_1−1.5yBi_yTiO₃ ceramics. A typical behavior to well-known relaxor ferroelectric is observed. The relaxation behavior observation is suggested due to a random electric field induced domain state.     

Lecture series — unconfined gas explosions,von Karman Institute for Fluid Dynamics,Rhode-Saint-Genèse,Belgium, February 7–11, 1983

The literature on the spread and vaporisation of cryogenic liquids on water is reviewed and a new model proposed. The model incorporates the features o

T001. List of symbols

     

11.

Electronic Structures of Rare-earth Half-metallic Ferromagnet CoLa<Subscript>2</Subscript>O<Subscript>4</Subscript>     

Jun Liu  Yu Liu  Hui-Ning Dong  Li Li 《Journal of Superconductivity and Novel Magnetism》2010,23(6):957-960

The half-metallic ferromagnet CoLa₂O₄ was predicted based on density function theory. Its magnetic and electric properties were studied systematically. Results show that CoLa₂O₄ has half-metallicity and its molecular magnetic moment is 3.00 μ_B, which is lower than 4.0 μ_B of Fe₃O₄. CoLa₂O₄ is more sensitive than Fe₃O₄ in the same applied field. La-ions have little spin polarization. The electronic structures of a Co-ion and a La-ion are a_1g ¹↑a_1g ¹↓t_1u ³↑t_1u ³↓e_g ²↑e_g ²↓t_2g ³↑ and a_1g ¹↑a_1g ¹↓t_1u ³↑t_1u ³↓ t_2g ³↑t_2g ³↓e_g ²↑e_g ²↓e_g ^2*↑e_g ^2*↓, respectively.     

12.

On the effective reducibility of a class of Quasi-periodic nonlinear systems near the equilibrium     

Jia Li  Chunpeng Zhu 《Dynamical Systems: An International Journal》2019,34(3):385-398

     

13.

Numerical prediction of cyclone efficiency curve using an Eulerian-Eulerian approach     

《Advanced Powder Technology》2022,33(1):103340

     

14.

Calcium zinc manganites, Ca₄Mn₇Zn₃O_21 − δ (0.5 < δ < 2.5) with beta-alumina or magnetoplumbite-type structure and their nonlinear electrical transport and magnetic properties     

K. Vijayanandhini 《Materials Letters》2007,61(17):3652-3657

Phase-pure calcium zinc manganite, Ca₄Mn₇Zn₃O_21 − δ has been synthesized by the solid-state reaction between CaMnO₃, ZnO and Mn₃O₄ at ∼ 1300 °C. Conversion of Ca₄Mn₇Zn₃O_21 − δ to Ca₄Mn₇Zn₃O_19 ± δ occurs at 1330-1350 °C which is influenced by the oxygen nonstoichiometry associated with increasing Mn³⁺/Mn⁴⁺ ratio. The Ca₄Mn₇Zn₃O_21 − δ phase is rhombohedral (space group = R3¯m) and has the β″-alumina (BA)-type structure consisting dominantly of Mn⁴⁺ (3d³) ions. The Ca₄Mn₇Zn₃O_19 ± δ is hexagonal (space group = P6₃/mmc) having the magnetoplumbite (MP)-type structure containing dominantly Mn³⁺ (3d⁴) ions. The electrical transport properties of Ca₄Mn₇Zn₃O_21 − δ and Ca₄Mn₇Zn₃O_19 ± δ are indicative of the activated-type small polaron hopping conductivity below 366 and 392 K respectively. The anisotropic charge transport is influenced only in a limited way by the mixed-valency of Mn prevailing in the manganite spinel blocks. Highly nonlinear current-voltage (I-V) curves with nonlinearity coefficient, α, up to 64 was achieved at the turn-on field strength E_t ∼ 110-160 V/mm. Magnetic properties of Ca₄Mn₇Zn₃O_21 − δ and Ca₄Mn₇Zn₃O_19 ± δ have been investigated which showed the antiferromagnetic-insulating (AFI) behavior with T_N = 103 and 80 K and with an AF-ordered effective magnetic moment, μ_eff = 3.54 and 4.28 μ_B/Mn respectively. The Ca₄Mn₇Zn₃O_19 ± δ phase showed the ferrimagnetic interaction below T_N (at ∼ 20 K).     

15.

Resistive and magnetic properties of Y1−x Zr x Ba2Cu3O7−δ and Y1−2x Zr x Eu x Ba2Cu3O7−δ superconductive compounds     

E. Burzo  V. Pop 《Journal of Materials Science》1992,27(19):5253-5258

The results of X-rays, electrical resistivities and magnetic studies performed on Y_−x Zr _x Ba₂Cu₃O_t7−δ and Y_1−2x Zr _x Eu _x Ba₂Cu₃O_7−δ superconducting compounds, in the temperature range 4.2–500 K and external fields up to 50 kOe are reported. The presence of zirconium decreases the superconducting transition temperatures,T _c. BelowT _c, the hysteresis loops narrow when the zirconium content increases. From the magnetization curves, the critical current densities were determined. A time dependence of the magnetizations of logarithmic form was found. The flux-pinning energy was estimated to beU ≃0.03 eV. Above the transition temperatures, Y_−x Zr _x Ba₂Cu₃O_t7−δ samples show a Pauli-type paramagnetism, while Y_1−2x Zr _x Eu _x Ba₂Cu₃O_7−δ compounds have, in addition, temperature-dependent contributions to the magnetic susceptibilities. The effective europium moments are ∼3.40 μ_B suggesting that the ion is in (+3) valence state.     

16.

Do innovation in environmental-related technologies asymmetrically affect carbon dioxide emissions in the United States?     

《Technology in Society》2021

     

17.

Preparation,phase structure and microwave dielectric properties of a new low cost MgLi_2/3Ti_4/3O₄ compound     

Huanfu Zhou  Xiaobin Liu  Xiuli Chen  Liang Fang 《Materials Chemistry and Physics》2012

A novel Li-based spinel compound with the composition of MgLi_2/3Ti_4/3O₄ was synthesized by the conventional solid-state reaction method. The phase structure was studied by X-ray diffraction (XRD) technique. When the calcination temperature was over 1050 °C, a single phase compound which has a cubic structure [Fd-3m (227)] with cell parameters of a = 8.4057 Å, V = 593.91 Å³, ρ = 3.51 g cm⁻³ and Z = 8 was obtained. MgLi_2/3Ti_4/3O₄ ceramic could be well densified after sintering above 1125 °C. The microwave dielectric properties were measured using a microwave vector network analyzer in the frequency range of 7–9 GHz MgLi_2/3Ti_4/3O₄ ceramic sintered at 1125 °C for 2 h showed microwave dielectric properties of ?_r = 20.2, Q × f = 62,300 GHz, and τ_f = −27.1 ppm °C⁻¹. Furthermore, 0.95MgLi_2/3Ti_4/3O₄–0.05CaTiO₃ ceramic sintered at 1200 °C for 2 h exhibited good properties of ?_r = 22.6, Q × f = 48,000 GHz, and τ_f = −2.3 ppm °C⁻¹.     

18.

Influence of Al2O3 nano powder on performance of solar collector considering turbulent flow     

《Advanced Powder Technology》2020,31(9):3695-3705

     

19.

First passage times for Gaussian processes by Slepian models     

《Probabilistic Engineering Mechanics》2020

     

20.

Synthesis and electrical characteristics of (1 − x)BaTiO₃–xK_0.5Bi_0.5TiO₃ PTCR ceramics     

T.A. Plutenko  O.I. V'yunovA.G. Belous 《Materials Chemistry and Physics》2012

Solid solutions of (1 − x)BaTiO₃–xK_0.5Bi_0.5TiO₃ were prepared by the solid state reaction technique. Samples were sintered in reducing atmosphere of N₂/H₂ in the temperature range 1100–1240 °C with subsequent oxidation at 700 °C. Phase composition and crystal structure were investigated by X-ray powder diffractometry (XRPD). It was shown that all samples of (1 − x)BaTiO₃–xK_0.5Bi_0.5TiO₃ (0 ≤ x < 0.4) exhibit a tetragonal structure at room temperature, the parameters a and c decrease with increasing x. With increasing x the Curie temperature of solid solutions (1 − x)BaTiO₃–xK_0.5Bi_0.5TiO₃ (0.1 ≤ x < 0.4) increases from 150 to 220 °C. The values of potential barriers at grain boundaries were calculated on the basis of Heywang model. With increasing x, the potential barrier at grain boundaries increases. It was shown that the grain size decreases with increasing the bismuth–potassium titanate content. The complex impedance results indicate that the grain boundary and the outer layer region, located between the boundary and the core of the grain, make a contribution to the positive temperature coefficient of resistance (PTCR) effect in (1 − x)BaTiO₃–xK_0.5Bi_0.5TiO₃ solid solutions. With increasing x ρ_max increases due to an increase in potential barrier at grain boundaries.     

Symbols
Cp	Heat capacity.
g	Acceleration due to gravity.
Gm	Molar vaporisation rate.
h	Latent heat with two suffices denoting phase change.
h	Pool thickness (no suffices).
i	Enthalpy.
k,K	Constants.
KA,KB	Functions of pool temperature and composition.
kw	Thermal diffusivity of water.
l	Depth in water where temperature is constant.
L	Length scale of an oil spill.
Lm	Molar liquid spill rate.
Lwi	Latent heat of fusion of ice.
M	Pool mass, M0 initially.
Ms,Mv	Mass spilled, mass vaporised.
q	Heat flux to cryogenic liquid.
r	Radial co-ordinate
R,R*	Radius of pool.
t	Time.
T	Temperature.
U	Velocity.
Wm	Number of moles of material in the pool.
xA	Molar methane portion of liquid pool (xB, ethane).
xAS	Molar methane portion of spilling liquid.
yA	Molar methane portion of vapour (yB, ethane).
z	Vertical coordinate.
δ	Vapour layer thickness.
ΔT	Temperature difference.
?	Ice layer thickness.
θ	Temperature relative to freezing point of water.
λ	Effective thermal conductivity.
μ	Viscosity.
?	Density.
σ	Surface tension.
ø	Heat flux to liquid pool = q.
Suffices
A	Average (or methane fraction with x,y).
B	Boiling point of cryogen (or ethane fraction with x,y).
fc	Film collapse.
fg	Liquid to vapour phase change.
F	Freezing of water.
i	Ice.
l, L	Liquid.
lv	Liquid to vapour phase change.
LE	Leading edge.
m	Molar.
O	Initial
o	Oil.
p	Pool.
s	Spilling liquid.
v	Vapour.
w	Water.

Electronic Structures of Rare-earth Half-metallic Ferromagnet CoLa<Subscript>2</Subscript>O<Subscript>4</Subscript>

The half-metallic ferromagnet CoLa₂O₄ was predicted based on density function theory. Its magnetic and electric properties were studied systematically. Results show that CoLa₂O₄ has half-metallicity and its molecular magnetic moment is 3.00 μ_B, which is lower than 4.0 μ_B of Fe₃O₄. CoLa₂O₄ is more sensitive than Fe₃O₄ in the same applied field. La-ions have little spin polarization. The electronic structures of a Co-ion and a La-ion are a_1g ¹↑a_1g ¹↓t_1u ³↑t_1u ³↓e_g ²↑e_g ²↓t_2g ³↑ and a_1g ¹↑a_1g ¹↓t_1u ³↑t_1u ³↓ t_2g ³↑t_2g ³↓e_g ²↑e_g ²↓e_g ^2*↑e_g ^2*↓, respectively.     

Calcium zinc manganites, Ca4Mn7Zn3O21 − δ (0.5 < δ < 2.5) with beta-alumina or magnetoplumbite-type structure and their nonlinear electrical transport and magnetic properties

Phase-pure calcium zinc manganite, Ca₄Mn₇Zn₃O_21 − δ has been synthesized by the solid-state reaction between CaMnO₃, ZnO and Mn₃O₄ at ∼ 1300 °C. Conversion of Ca₄Mn₇Zn₃O_21 − δ to Ca₄Mn₇Zn₃O_19 ± δ occurs at 1330-1350 °C which is influenced by the oxygen nonstoichiometry associated with increasing Mn³⁺/Mn⁴⁺ ratio. The Ca₄Mn₇Zn₃O_21 − δ phase is rhombohedral (space group = R3¯m) and has the β″-alumina (BA)-type structure consisting dominantly of Mn⁴⁺ (3d³) ions. The Ca₄Mn₇Zn₃O_19 ± δ is hexagonal (space group = P6₃/mmc) having the magnetoplumbite (MP)-type structure containing dominantly Mn³⁺ (3d⁴) ions. The electrical transport properties of Ca₄Mn₇Zn₃O_21 − δ and Ca₄Mn₇Zn₃O_19 ± δ are indicative of the activated-type small polaron hopping conductivity below 366 and 392 K respectively. The anisotropic charge transport is influenced only in a limited way by the mixed-valency of Mn prevailing in the manganite spinel blocks. Highly nonlinear current-voltage (I-V) curves with nonlinearity coefficient, α, up to 64 was achieved at the turn-on field strength E_t ∼ 110-160 V/mm. Magnetic properties of Ca₄Mn₇Zn₃O_21 − δ and Ca₄Mn₇Zn₃O_19 ± δ have been investigated which showed the antiferromagnetic-insulating (AFI) behavior with T_N = 103 and 80 K and with an AF-ordered effective magnetic moment, μ_eff = 3.54 and 4.28 μ_B/Mn respectively. The Ca₄Mn₇Zn₃O_19 ± δ phase showed the ferrimagnetic interaction below T_N (at ∼ 20 K).     

Resistive and magnetic properties of Y1−x Zr x Ba2Cu3O7−δ and Y1−2x Zr x Eu x Ba2Cu3O7−δ superconductive compounds

The results of X-rays, electrical resistivities and magnetic studies performed on Y_−x Zr _x Ba₂Cu₃O_t7−δ and Y_1−2x Zr _x Eu _x Ba₂Cu₃O_7−δ superconducting compounds, in the temperature range 4.2–500 K and external fields up to 50 kOe are reported. The presence of zirconium decreases the superconducting transition temperatures,T _c. BelowT _c, the hysteresis loops narrow when the zirconium content increases. From the magnetization curves, the critical current densities were determined. A time dependence of the magnetizations of logarithmic form was found. The flux-pinning energy was estimated to beU ≃0.03 eV. Above the transition temperatures, Y_−x Zr _x Ba₂Cu₃O_t7−δ samples show a Pauli-type paramagnetism, while Y_1−2x Zr _x Eu _x Ba₂Cu₃O_7−δ compounds have, in addition, temperature-dependent contributions to the magnetic susceptibilities. The effective europium moments are ∼3.40 μ_B suggesting that the ion is in (+3) valence state.     

Preparation,phase structure and microwave dielectric properties of a new low cost MgLi2/3Ti4/3O4 compound

A novel Li-based spinel compound with the composition of MgLi_2/3Ti_4/3O₄ was synthesized by the conventional solid-state reaction method. The phase structure was studied by X-ray diffraction (XRD) technique. When the calcination temperature was over 1050 °C, a single phase compound which has a cubic structure [Fd-3m (227)] with cell parameters of a = 8.4057 Å, V = 593.91 Å³, ρ = 3.51 g cm⁻³ and Z = 8 was obtained. MgLi_2/3Ti_4/3O₄ ceramic could be well densified after sintering above 1125 °C. The microwave dielectric properties were measured using a microwave vector network analyzer in the frequency range of 7–9 GHz MgLi_2/3Ti_4/3O₄ ceramic sintered at 1125 °C for 2 h showed microwave dielectric properties of ?_r = 20.2, Q × f = 62,300 GHz, and τ_f = −27.1 ppm °C⁻¹. Furthermore, 0.95MgLi_2/3Ti_4/3O₄–0.05CaTiO₃ ceramic sintered at 1200 °C for 2 h exhibited good properties of ?_r = 22.6, Q × f = 48,000 GHz, and τ_f = −2.3 ppm °C⁻¹.     

Synthesis and electrical characteristics of (1 − x)BaTiO3–xK0.5Bi0.5TiO3 PTCR ceramics

Solid solutions of (1 − x)BaTiO₃–xK_0.5Bi_0.5TiO₃ were prepared by the solid state reaction technique. Samples were sintered in reducing atmosphere of N₂/H₂ in the temperature range 1100–1240 °C with subsequent oxidation at 700 °C. Phase composition and crystal structure were investigated by X-ray powder diffractometry (XRPD). It was shown that all samples of (1 − x)BaTiO₃–xK_0.5Bi_0.5TiO₃ (0 ≤ x < 0.4) exhibit a tetragonal structure at room temperature, the parameters a and c decrease with increasing x. With increasing x the Curie temperature of solid solutions (1 − x)BaTiO₃–xK_0.5Bi_0.5TiO₃ (0.1 ≤ x < 0.4) increases from 150 to 220 °C. The values of potential barriers at grain boundaries were calculated on the basis of Heywang model. With increasing x, the potential barrier at grain boundaries increases. It was shown that the grain size decreases with increasing the bismuth–potassium titanate content. The complex impedance results indicate that the grain boundary and the outer layer region, located between the boundary and the core of the grain, make a contribution to the positive temperature coefficient of resistance (PTCR) effect in (1 − x)BaTiO₃–xK_0.5Bi_0.5TiO₃ solid solutions. With increasing x ρ_max increases due to an increase in potential barrier at grain boundaries.