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In the present work, simulation function is applied to establish fixed point results of $ \mathcal{F} $-contraction in the setting of Bi-polar metric space. Our results are extensions or generalizations of results proved in the literature. The derived results are substantiated with suitable examples and an application to find the solution to the integral equation.

In this paper, we establish the fixed point results for an orthogonal extended interpolative Ciric Reich-Rus type $ \psi\mathcal{F} $-contraction mapping on an orthogonal complete $ \mathfrak{b} $-metric spaces and give an example to strengthen our main results. Furthermore, we present an application to fixed point results to find analytical solutions for functional equation.

PurposeNeuroBlu is a real-world data (RWD) repository that contains deidentified electronic health record (EHR) data from US mental healthcare providers operating the MindLinc EHR system. NeuroBlu enables users to perform statistical analysis through a secure web-based interface. Structured data are available for sociodemographic characteristics, mental health service contacts, hospital admissions, International Classification of Diseases ICD-9/ICD-10 diagnosis, prescribed medications, family history of mental disorders, Clinical Global Impression—Severity and Improvement (CGI-S/CGI-I) and Global Assessment of Functioning (GAF). To further enhance the data set, natural language processing (NLP) tools have been applied to obtain mental state examination (MSE) and social/environmental data. This paper describes the development and implementation of NeuroBlu, the procedures to safeguard data integrity and security and how the data set supports the generation of real-world evidence (RWE) in mental health.ParticipantsAs of 31 July 2021, 562 940 individuals (48.9% men) were present in the data set with a mean age of 33.4 years (SD: 18.4 years). The most frequently recorded diagnoses were substance use disorders (1 52 790 patients), major depressive disorder (1 29 120 patients) and anxiety disorders (1 03 923 patients). The median duration of follow-up was 7 months (IQR: 1.3 to 24.4 months).Findings to dateThe data set has supported epidemiological studies demonstrating increased risk of psychiatric hospitalisation and reduced antidepressant treatment effectiveness among people with comorbid substance use disorders. It has also been used to develop data visualisation tools to support clinical decision-making, evaluate comparative effectiveness of medications, derive models to predict treatment response and develop NLP applications to obtain clinical information from unstructured EHR data.Future plansThe NeuroBlu data set will be further analysed to better understand factors related to poor clinical outcome, treatment responsiveness and the development of predictive analytic tools that may be incorporated into the source EHR system to support real-time clinical decision-making in the delivery of mental healthcare services.

The aim of this work is to modify the invariant subspace method (ISM) in order to obtain closed form solutions of fractional differential-difference equations with Ψ-Riemann–Liouville (Ψ-RL) fractional derivative for first time. We have investigated the cases of two-dimensional and the three-dimensional invariant subspaces (ISs) in the suggested scheme. Using the modified ISM, new exact generalized solutions for the general fractional mKdV Lattice equation and the fractional Volterra lattice system are obtained. Compared with similar solution techniques in literature, the presented solution scheme is highly efficient and is capable to find new general exact solutions which cannot be attained by other methods.

In this article, we establish fixed point results by defining the concept of F-Khan contraction of an orthogonal set by modifying the symmetry of usual contractive conditions. We also provide illustrative examples to support our results. The derived results have been applied to find analytical solutions to integral equations. The analytical solutions are verified with numerical simulation.

In this paper, we introduce the new notion of contravariant (α−ψ) Meir–Keeler contractive mappings by defining α-orbital admissible mappings and covariant Meir–Keeler contraction in bipolar metric spaces. We prove fixed point theorems for these contractions and also provide some corollaries of main results. An example is also be given in support of our main result. In the end, we also solve an integral equation using our result.

Fixed point results and metric fixed point theory play a vital role to find the unique solution to differential and integral equations. Likewise, fractal calculus has vast physical applications. In this article, we introduce the concept of bipolar-controlled metric space and prove fixed point theorems. The derived results expand and extend certain well-known results from the research literature and are supported with a non-trivial example. We have applied the fixed point result to find the analytical solution to the integral equation and fractional differential equation. The analytical solution has been supplemented with numerical simulation.

In this present study, we propose the concept of tricomplex-controlled metric spaces as a generalization of both controlled metric-type spaces and tricomplex metric-type spaces. In this work, we establish fixed point results using Banach, Kannan and Fisher-type contractions supported with nontrivial examples in the setting of the proposed space. We apply the derived result to find the analytical solution of an integral equation using the fixed point technique under the same metric.

In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. These inequalities generalize the noninteger Hadamard inequalities for a convex IVM, (p,h)-convex IVM, p-convex IVM, h-convex, s-convex in the second sense and many other related well-known classes of functions implicitly. An apt number of numerical examples are provided as supplements to the derived results.

Fixed-point results on covariant maps and contravariant maps in a C★-algebra-valued bipolar metric space are proved. Our results generalize and extend some recently obtained results in the existing literature. Our theoretical results in this paper are supported with suitable examples. We have also provided an application to find an analytical solution to the integral equation and the electrical circuit differential equation.

In this paper, we consider and extend some fixed point results in F-complete F-metric spaces by relaxing the symmetry of complete metric spaces. We generalize α,β-admissible mappings in the setting of F-metric spaces. The derived results are supplemented with suitable examples, and the obtained results are applied to find the existence of the solution to the integral equation. The analytical results are compared through numerical simulation. We pose certain open problems for extending and applying our results in the future.

In mathematical analysis, the Hausdorff derivatives or the fractal derivatives play an important role. Fixed-point theorems and metric fixed-point theory have varied applications in establishing a unique common solution to differential equations and integral equations. In the present work, some fixed-point theorems using the extension of Meir–Keeler contraction in the setting of bipolar metric spaces have been proved. The derived results have been supplemented with non-trivial examples. Our results extend and generalise the results established in the past. We have provided an application to find an analytical solution to an Integral Equation to supplement the derived result.

We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types of such inequalities are obtained, such as (p,h) fractional type inequality and many others, as the (p,h)-convexity is the generalization of the other convex inequalities. As a consequence of the (h,m)-convexity, the fractional inequality of the (s,m)-type is obtained. Many consequences of such fractional inequalities and generalizations are obtained.

In this paper, a discrete fractional Susceptible-Infected-Treatment-Recovered-Susceptible (SITRS) model for simulating the coronavirus (COVID-19) pandemic is presented. The model is a modification to a recent continuous-time SITR model by taking into account the possibility that people who have been infected before can lose their temporary immunity and get reinfected. Moreover, a modification is suggested in the present model to correct the improper assumption that the infection rates of both normal susceptible and old aged/seriously diseased people are equal. This modification complies with experimental data. The equilibrium points for the proposed model are found and results of thorough stability analysis are discussed. A full numerical simulation is carried out and gives a better analysis of the disease spread, influences of model’s parameters, and how to control the virus. Comparisons with clinical data are also provided.

Metric fixed point theory has vast applications in various domain areas, as it helps in finding analytical solutions under various contractive conditions, including non-linear integral-type contractions. In our present work, we have established fixed point results in the setting of complex valued partial metric space. Our results extend the results proven in literature. Using our main result, we have provided an application to find the solution to the Urysohn-type integral equation.

Two-dimensional electron gas (2DEG) formed at the interface between SrTiO3 (STO) and LaAlO3 (LAO) insulating layer is supposed to possess strong Rashba spin-orbit coupling. To date, the inverse Edelstein effect (i.e. spin-to-charge conversion) in the 2DEG layer is reported. However, the direct effect of charge-to-spin conversion, an essential ingredient for spintronic devices in a current induced spin-orbit torque scheme, has not been demonstrated yet. Here we show, for the first time, a highly efficient spin generation with the efficiency of ~6.3 in the STO/LAO/CoFeB structure at room temperature by using spin torque ferromagnetic resonance. In addition, we suggest that the spin transmission through the LAO layer at high temperature range is attributed to the inelastic tunneling via localized states in the LAO band gap. Our findings may lead to potential applications in the oxide insulator based spintronic devices., Comment: 16 pages, 4 figures

Background Conventional statistical methods used in clinical trials lack the ability to predict patient specific risk and very often do not consider the effects of time varying interventions. The aim of this study is to test a novel artificial neural network based model for clinical trial analysis to represent the continuous time evolution of risk. Methods The novel methodology tested utilizes system dynamics and artificial neural networks. This methodology was applied to analyze data from 2,221 patients with acute myocardial infarction enrolled in a well characterized randomized study, the HORIZONS-AMI trial. Outcomes analyzed included: (1) target lesion revascularization (TLR) and (2) stent thrombosis. The proposed neural system dynamics (NSD) model was compared against traditional Cox Proportional Hazards (Cox PH) and Cox neural network (NN) models. Model performance was evaluated using C-statistic at 1, 2 -and 3- years follow-up and model-based simulation studies were performed to examine the effect of different variables on the predicted risk of TLR and stent thrombosis. Results The NSD model achieved comparable performance to Cox models for TLR. For stent thrombosis, the NSD model outperformed Cox models (1-year C-statistic: Stent thrombosis – Cox PH: 0.60, Cox NN: 0.66, neural SD model: 0.69). The neural SD model identified clinically relevant variables such as stent count, stent type and multiple lesions treated as significant predictors for TLR; and stent count and peak platelet count for stent thrombosis. Simulations illustrated change in predicted TLR risk maximal for the neural SD model, compared to other models. For stent thrombosis, simulation scenario illustrated predicted event rate doubling when clopidogrel is discontinued at 6 months compared to extended use. Conclusions We have demonstrated an alternative analytical methodology that combines system dynamics and artificial neural networks to analyze results from a randomized trial. This novel approach can incorporate patient-specific longitudinal data and provide personalized risk prediction.

The Co-Fe-B/MgO system with perpendicular magnetic anisotropy finds extensive application in modern magnetic memories. Critical issues for the practical usage of magnetic tunnel junctions (MTJs) include the limited thermal stability of bit storage, and low switching efficiency. This study elucidates the deterministic influence of Co-Fe-B composition and the MgO interface on an MTJ's fundamental magnetic properties, which affect both thermal stability and switching current. Furthermore, the authors observe an anomalous trend in saturation magnetization, which is attributed to a change in magnetic anisotropy.

Ferromagnetic spintronics has been a main focus as it offers non-volatile memory and logic applications through current-induced spin-transfer torques. Enabling wider applications of such magnetic devices requires a lower switching current for a smaller cell while keeping the thermal stability of magnetic cells for non-volatility. As the cell size reduces, however, it becomes extremely difficult to meet this requirement with ferromagnets because spin-transfer torque for ferromagnets is a surface torque due to rapid spin dephasing, leading to the 1/ferromagnet-thickness dependence of the spin-torque efficiency. Requirement of a larger switching current for a thicker and thus more thermally stable ferromagnetic cell is the fundamental obstacle for high-density non-volatile applications with ferromagnets. Theories predicted that antiferromagnets have a long spin coherence length due to the staggered spin order on an atomic scale, thereby resolving the above fundamental limitation. Despite several spin-torque experiments on antiferromagnets and ferrimagnetic alloys, this prediction has remained unexplored. Here we report a long spin coherence length and associated bulk-like-torque characteristic in an antiferromagnetically coupled ferrimagnetic multilayer. We find that a transverse spin current can pass through > 10 nm-thick ferrimagnetic Co/Tb multilayers whereas it is entirely absorbed by 1 nm-thick ferromagnetic Co/Ni multilayer. We also find that the switching efficiency of Co/Tb multilayers partially reflects a bulk-like-torque characteristic as it increases with the ferrimagnet-thickness up to 8 nm and then decreases, in clear contrast to 1/thickness-dependence of Co/Ni multilayers. Our results on antiferromagnetically coupled systems will invigorate researches towards energy-efficient spintronic technologies.

We explore the second order bilinear magnetoelectric resistance (BMER) effect in the $d$-electron-based two-dimensional electron gas $(2\mathrm{DEG})$ at the ${\mathrm{SrTiO}}_{3}(111)$ surface. We find evidence of a spin-split band structure with the archetypal spin-momentum locking of the Rashba effect for the in-plane component. Under an out-of-plane magnetic field, we find a BMER signal that breaks the sixfold symmetry of the electronic dispersion, which is a fingerprint for the presence of a momentum-dependent out-of-plane spin component. Relativistic electronic structure calculations reproduce this spin texture and indicate that the out-of-plane component is a ubiquitous property of oxide 2DEGs arising from strong crystal field effects. We further show that the BMER response of the ${\mathrm{SrTiO}}_{3}(111)$ 2DEG is tunable and unexpectedly large.

Spin-orbit torques, which utilize spin currents arising from the spin-orbit coupling, offer a novel method to electrically switch the magnetization with perpendicular anisotropy. However, the necessity of an external magnetic field to achieve a deterministic switching is an obstacle for realizing practical spin-orbit torque devices with all-electric operation. Here, we report a field-free spin-orbit torque switching by exploiting the domain wall motion in an anti-notched microwire with perpendicular anisotropy, which exhibits multi-domain states stabilized by the domain wall surface tension. The combination of spin-orbit torque, Dzyaloshinskii-Moriya interaction, and domain wall surface tension induced geometrical pinning allows a deterministic control of the domain wall and offers a novel method to achieve a field-free spin-orbit torque switching. Our work demonstrates the proof of concept of a perpendicular memory cell which can be readily adopted in a three-terminal magnetic memory., 19 pages, 5 figures

We explore the second order bilinear magnetoelectric resistance (BMER) effect in the d-electron-based two-dimensional electron gas (2DEG) at the SrTiO_{3}(111) surface. We find evidence of a spin-split band structure with the archetypal spin-momentum locking of the Rashba effect for the in-plane component. Under an out-of-plane magnetic field, we find a BMER signal that breaks the sixfold symmetry of the electronic dispersion, which is a fingerprint for the presence of a momentum-dependent out-of-plane spin component. Relativistic electronic structure calculations reproduce this spin texture and indicate that the out-of-plane component is a ubiquitous property of oxide 2DEGs arising from strong crystal field effects. We further show that the BMER response of the SrTiO_{3}(111) 2DEG is tunable and unexpectedly large.

Deterministic magnetization switching using spin-orbit torque (SOT) has recently emerged as an efficient means to electrically control the magnetic state of ultrathin magnets. The SOT switching still lacks in oscillatory switching characteristics over time, therefore, it is limited to bipolar operation where a change in polarity of the applied current or field is required for bistable switching. The coherent rotation based oscillatory switching schemes cannot be applied to SOT, because the SOT switching occurs through expansion of magnetic domains. Here we experimentally achieve oscillatory switching in incoherent SOT process by controlling domain wall dynamics. We find that a large field-like component can dynamically influence the domain wall chirality which determines the direction of SOT switching. Consequently, under nanosecond current pulses, the magnetization switches alternatively between the two stable states. By utilizing this oscillatory switching behavior, we demonstrate a unipolar deterministic SOT switching scheme by controlling the current pulse duration. Magnetism plays a key role in data storage devices. This paper reports on the experimental observation of spin-orbit torque-driven oscillatory switching due to field-like torque and finds that the magnetization can be switched back through using appropriate pulse duration.

The two-dimensional electron gas (2DEG) formed at the interface between SrTiO

The spin Hall effect (SHE) is a means to electrically control the magnetization of a ferromagnet---one of the prime goals in spintronics. The most-studied material for exploiting the SHE is platinum, but in CMOS electronics the preferred metal is copper, which has a weak SHE. The authors show that Pt-Cu alloy with just 28% Pt can be as efficient as pure Pt at generating spin current. This alloy can also withstand high annealing temperatures, and thus can be readily incorporated into CMOS technology, nudging spintronics that much closer to widespread use.

We report the angular dependence of magnetoresistance in the two-dimensional electron gas at the ${\mathrm{LaAlO}}_{3}$/${\mathrm{SrTiO}}_{3}$ interface. We find that this interfacial magnetoresistance exhibits a similar angular dependence to the spin Hall magnetoresistance observed in ferromagnet/heavy metal bilayers, which has been so far discussed in the framework of the bulk spin Hall effect of the heavy metal layer. The observed magnetoresistance is in qualitative agreement with a theoretical model calculation including both Rashba spin-orbit coupling and an exchange interaction. Our result suggests that magnetic interfaces subject to spin-orbit coupling can generate a non-negligible contribution to the spin Hall magnetoresistance, and the interfacial spin-orbit coupling effect is therefore key to the understanding of various spin-orbit-coupling-related phenomena in magnetic/nonmagnetic bilayers.

Current induced spin orbit torques (SOTs) offer an efficient pathway to manipulate the magnetization of a ferromagnet for future magnetic memories and logic devices. Among the various non-magnets utilized, the topological insulators, such as Bi2Se3, have proven to be one of most efficient spin current generators for SOTs. So far, the preferred growth technique for such materials is the molecular beam epitaxy technique which is not compatible with the magnetic memory industry. In this study, we utilize a sputter deposited Bi2Se3 to demonstrate highly efficient SOT generation and subsequently magnetization switching.

The magnitude of spin-orbit torque (SOT), exerted to a ferromagnet (FM) from an adjacent heavy metal (HM), strongly depends on the amount of spin currents absorbed in the FM. We exploit the large spin absorption at the Ru interface to manipulate the SOTs in HM/FM/Ru multilayers. While the FM thickness is smaller than its spin dephasing length of 1.2 nm, the top Ru layer largely boosts the absorption of spin currents into the FM layer and substantially enhances the strength of SOT acting on the FM. Spin-pumping experiments induced by ferromagnetic resonance support our conclusions that the observed increase in the SOT efficiency can be attributed to an enhancement of the spin-current absorption. A theoretical model that considers both reflected and transmitted mixing conductances at the two interfaces of FM is developed to explain the results., Comment: Accepted for publication in Physical Review Letters

We investigate the influence of ferromagnet crystalline structures on spin Hall angle (SHA) in ferromagnet (FM)/heavy metal (HM) bilayers with reversed stacking order. X-ray diffraction and transmission electron microscopy show that a pronounced permalloy (Py) (111) texture emerges in substrate/Ta/Py compared to that in substrate/Py/Ta. Spin torque ferromagnetic resonance measurements show that the out-of-plane SHA (θ⊥, associated with Rashba-like effective field) is ∼2 times larger in substrate/Ta/Py than that in substrate/Py/Ta, while in-plane SHA (θǁ, associated with spin Hall-like effective field) shows no distinct difference. We ascribe the FM structure dependent SHA to the interfacial symmetry breaking between the FM and HM, which is tuned by the work functions due to different crystalline structures of the FM. The emergence of the Py (111) structure enlarges the interfacial symmetry breaking and consequently enhances the Rashba effect at the FM/HM interface.

The ability of spintronic devices to utilize an electric current for manipulating the magnetization has resulted in large-scale developments, such as, magnetic random access memories and boosted the spintronic research area. In this regard, over the last decade, magnetization manipulation using spin-orbit torque has been devoted a lot of research attention as it shows a great promise for future ultrafast and power efficient magnetic memories. In this review, we summarize the latest advancements in spin-orbit torque research and highlight some of the technical challenges for practical spin-orbit torque devices. We will first introduce the basic concepts and highlight the latest material choices for spin-orbit torque devices. Then, we will summarize the important advancements in the study of magnetization switching dynamics using spin-orbit torque, which are important from scientific as well as technological aspect. The final major section focuses on the concept of external assist field free spin-orbit torque switching which is a requirement for practical spin-orbit torque devices., 50 pages, 15 figures, Accepted in Applied Physics Reviews

The recently discovered spin-orbit torque could be used to flip bits in spintronic devices. The authors investigate its less-studied component, the fieldlike torque, and find that with the help of this piece, there is no need for an external magnetic field to achieve the deterministic reversal of magnetization. In principle this solves one of the critical issues in spintronics, and is promising for applications in terms of speed and energy efficiency.

Current-induced spin-orbit torque (SOT) is a very recently discovered phenomenon which provides efficient ways to control and manipulate the magnetization. It allows to use the spin-orbit interaction in the bulk or at the interface of a heavy metal (HM) to inject angular momentum in an adjacent ferromagnet (FM) [1-3]. Even though its origin either from Rashba or spin Hall effects is still under debate, switching the magnetization of nanostructures by spin-orbit torques is very promising for applications both in terms of speed and energetic efficiency. In this work, we study the influence of one of the components of the torques, the field-like torque, for example in Ta/CoFeB/MgO trilayers [4]. This study focuses on the macrospin-based magnetization switching of small devices with a uniform magnetization (50×50 nm2) which are of significant interest for applications.

We have studied the spin-orbit torques in perpendicularly magnetized Hf/CoFeB/MgO system, by systematically varying the thickness of Hf underlayer. We have observed a sign change of effective fields between Hf thicknesses of 1.75 and 2 nm, indicating that competing mechanisms, such as the Rashba and spin Hall effects, contribute to spin-orbit torques in our system. For larger Hf thicknesses (>2 nm), both the components of spin-orbit torques arise predominantly from the bulk spin Hall effect. We have also confirmed these results using spin-orbit torque induced magnetization switching measurements. Our results could be helpful in designing Hf based SOT devices.