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In this present paper, we introduce graphical Branciari $ \aleph $-metric space and prove the fixed point theorem for $ \varOmega $-$ \mathcal{Q} $-contraction on complete graphical Branciari $ \aleph $ -metric spaces. Our result has been supplemented with suitable, non trivial examples. We have applied the derived fixed point result to solve non-linear Fredholm integral equations and fractional differential 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.

In the present work, simulation function is applied to establish fixed point results of 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 article, we use Lie point symmetry analysis to extract some new optical soliton solutions for the generalized Kudryashov’s equation (GKE) with an arbitrary power nonlinearity. Using a traveling wave transformation, the GKE is transformed into a nonlinear second order ordinary differential equation (ODE). Using Lie point symmetry analysis, the nonlinear second-order ODE is reduced to a first-order ODE. This first-order ODE is solved in two cases to retrieve some new bright, dark, and kink soliton solutions of the GKE. These soliton solutions for the GKE are obtained here for the first time.

Abstract Chronic kidney disease (CKD) is a progressive disease that evades early detection and is associated with various comorbidities. Although clinical comprehension and control of these comorbidities is crucial for CKD management, complex pathophysiological interactions and feedback loops make this a formidable task. We have developed a hybrid semimechanistic modeling methodology to investigate CKD progression. The model is represented as a system of ordinary differential equations with embedded neural networks and takes into account complex disease progression pathways, feedback loops, and effects of 53 medications to generate time trajectories of eight clinical biomarkers that capture CKD progression due to various risk factors. The model was applied to real world data of US patients with CKD to map the available longitudinal information onto a set of time‐invariant patient‐specific parameters with a clear biological interpretation. These parameters describing individual patients were used to segment the cohort using a clustering approach. Model‐based simulations were conducted to investigate cluster‐specific treatment strategies. The model was able to reliably reproduce the variability in biomarkers across the cohort. The clustering procedure segmented the cohort into five subpopulations – four with enhanced sensitivity to a specific risk factor (hypertension, hyperlipidemia, hyperglycemia, or impaired kidney) and one that is largely insensitive to any of the risk factors. Simulation studies were used to identify patient‐specific strategies to restrain or prevent CKD progression through management of specific risk factors. The semimechanistic model enables identification of disease progression phenotypes using longitudinal data that aid in prioritizing treatment strategies at individual patient level.

Here, we shall introduce the new notion of C*-algebra valued bipolar b-metric spaces as a generalization of usual metric spaces, C*-algebra valued metric space, b-metric spaces. In the above-mentioned spaces, we shall define (αA−ψA) contractions and prove some fixed point theorems for these contractions. Some existing results from the literature are also proved by using our main results. As an application Ulam–Hyers stability and well-posedness of fixed point problems are also discussed. Some examples are also given to illustrate our results.

Hermite–Hadamard inequalities and their refinements have been investigated for a long period of time. In this paper, we obtained refinements of the Hermite–Hadamard inequality of tensorial type for the convex functions of self-adjoint operators in Hilbert spaces. The obtained inequalities generalize the previously obtained inequalities by Dragomir. We also provide useful Lemmas which enabled us to obtain the results. The examples of the obtained inequalities for specific convex functions have been given in the example and consequences section. Symmetry in the upper and lower bounds can be seen in the last Theorem of the paper given, as the upper and lower bounds differ by a constant.

The aim of this work is to explore and find new closed-form nematicon solutions for different nonlinearities which occur in nematic liquid crystals (NLC) along with proposing optical system application that utilizes NLC nonlinearities. In particular, Lie point symmetry method is employed to scrupulously inspect and acquire solutions for some interesting cases of nonlinearities which have not been fully examined in literature such as quadratic, generalized dual-power law, and eighth-order nonlinearities. A variety of different nematicon dynamics are observed, including bright solitons, dark solitons and periodic behaviors. The explicit solution form for each dynamical behavior is obtained and the solution dependence on model parameters is investigated. The proposed optical system enables the flexible realization of different types of NLC nonlinearities. To the best of our knowledge, this is the first time to attain explicit exact nontrivial solutions for the particular cases of generalized dual-power law and eighth-order nonlinearities.

This work is devoted to explore the possible existence of ghost attractors in a proposed nonautonomous blinking circuit with nonlinear memristors along with their potential application. The nonlinear dynamics of new memristor-based blinking circuit are significantly influenced by the speed of random switchings between its autonomous subcircuits. So, the effects of varying stochastic switching rate on the dynamical behaviors of blinking circuit are examined. It is demonstrated that it is possible to stimulate a non-stationary chaotic attractor for the blinking circuit which is surprisingly different from the attractors of composing subcircuits which exhibit simple periodic dynamics. A sufficiently small time period for random switchings in addition to precise tuning of circuit parameters are the major requirements for establishing these ghost attractors. The fascinating features of the induced ghost attractors render them appropriate noise-like source for secure communications applications. So, we proposed a new pseudo-chaos encryption algorithm that exploits the memristor-based blinking circuit in a more suitable digital platform. The proposed scheme overcomes the usual degradation in performance of digital chaos due to finite precision representation of floating numbers.

Purpose NeuroBlu 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.Participants As 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 date The 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 plans The 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.

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 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.

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 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.

In the present work, we have introduced a new type of (ξ,ω)-weakly cyclic generalized contraction in the setting of metric spaces and established some fixed-point results. Fixed-point results are useful in establishing the existence of unique solution to differential equations. We have supplemented the derived results with suitable non-trivial examples with an application to the Boundary Value Problem, generalizing some known results. The analytical result has been verified with numerical simulation.

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 article, we modify the symmetry of orthogonal metric spaces and we prove common fixed point theorems via simulation functions in orthogonal Rectangular metric spaces. We also provide an illustrative example to support our results. The derived results have been applied to find analytical solutions to integral equations. The analytical solutions are verified with a numerical simulation.

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.

In this paper, we introduce the notion of neutrosophic rectangular triple-controlled metric space, relaxing the symmetry requirement of neutrosophic metric spaces, by replacing triangular inequalities with rectangular inequalities, and prove fixed point theorems. We have derived several interesting results for contraction mappings supplemented with non-trivial examples. The derived results have been applied to prove the existence of a unique analytical solution as well as a closed form of the unique solution to the integral equation.

In the present work, we establish fixed-point results for a pair of mappings satisfying some contractive conditions on rational expressions with coefficients as point-dependent control functions in the setting of tricomplex-valued metric spaces. The proven results are extension and generalisation of some of the literature’s well-known results. We also explore some of the applications to our key results.

In this work, various fractional convex inequalities of the Hermite–Hadamard type in the interval analysis setting have been established, and new inequalities have been derived thereon. Recently defined p interval-valued convexity is utilized to obtain many new fractional Hermite–Hadamard type convex inequalities. The derived results have been supplemented with suitable numerical examples. Our results generalize some recently reported results in the literature.

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.

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.

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.

The application of spin-orbit torque in topological insulator heterostructures is limited only under low temperature. Here, the authors report room temperature magnetization switching in topological insulator-ferromagnet heterostructures by spin-orbit torques.

We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as α -admissible mappings of type S, α * -admissible mappings of type S and α * - orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b-metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R-weakly α -admissible pair of multivalued mappings in a b-metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.