A Review of Current Applications of Artificial Intelligence and Machine Learning in Medical Science

Artificial Intelligence and Machine Learning are two fields that are causing substantial development in every field specifically in the field of medical sciences; for the stupendous potential that it can provide to assist the clinicians, researchers, in clinical decision making, automate time consuming procedures, medical imaging, and more. Most implementations of AI/ML rely on static data set, and this where the big data steps in. That is, these models are developed and trained on a data set that is already recorded and have been diligently reviewed for accuracy; leading to a precise decision-making process. Experts foresee that AI/ML based overarching care system will develop high-quality patient care and innovative research, aiding advanced decision support tools. In this paper we shall realize what are the current devices that are build and are being used for real time problem solving, also discuss the impact of Software as a Medical Device (SAMD) in future of medical sciences. [2,3,11]

Agent Scheduling in Unrelated Parallel Machines with Sequence- and Agent–Machine–Dependent Setup Time Problem

Assignation-sequencing models have played a critical role in the competitiveness of manufacturing companies since the mid-1950s. The historic and constant evolution of these models, from simple assignations to complex constrained formulations, shows the need for, and increased interest in, more robust models. Thus, this paper presents a model to schedule agents in unrelated parallel machines that includes sequence and agent–machine-dependent setup times (ASUPM), considers an agent-to-machine relationship, and seeks to minimize the maximum makespan criteria. By depicting a more realistic scenario and to address this NP-hard problem, six mixed-integer linear formulations are proposed, and due to its ease of diversification and construct solutions, two multi-start heuristics, composed of seven algorithms, are divided into two categories: Construction of initial solution (designed algorithm) and improvement by intra (tabu search) and inter perturbation (insertions and interchanges). Three different solvers are used and compared, and heuristics algorithms are tested using randomly generated instances. It was found that models that linearizing the objective function by both job completion time and machine time is faster and related to the heuristics, and presents an outstanding level of performance in a small number of instances, since it can find the optimal value for almost every instance, has very good behavior in a medium level of instances, and decent performance in a large number of instances, where the relative deviations tend to increase concerning the small and medium instances. Additionally, two real-world applications of the problem are presented: scheduling in the automotive industry and healthcare.

Mathematical Model of the Process of Ultrasonic wave Propagation in a Relax Environment with its Given Profiles at three Time Moments

Objective: The process of ultrasound oscillations in a relaxed environment, provided that the profiles of the acoustic wave at three time moments are known, is modeled by a three-point problem for the partial differential equation of the third order in time. This equation as a partial case contains a hyperbolic equation of the third order, which is widely used in ultrasound diagnostics. Methods: The differential-symbol method is applied to study a three-point in-time problem. The advantage of this method is the possibility to obtain a solution of the problem only through operations of differentiation. Results: We propose the formula to construct the analytic solution of the problem, which describes the process of ultrasound oscillations propagation in a relax environment. Due to this, the profile of the ultrasonic wave is known at any time and at an arbitrary point of space. The class of quasi-polynomials is distinguished as a class of uniqueness solvability of a three-point problem. Conclusion: Using the proposed method, it is possible to analyze the influence of the main parameters of ultrasound diagnostics problems on the propagation of acoustic oscillations in a relaxed environment. The research example of a specific three-point problem is given.

Testing of biocidal properties of thermal insulation system during material life cycle

With the growing number of realized thermal insulation systems, fast growing number of buildings with facades attacked by microorganisms occurs. Such surface attack can occur even in the first years after thermal insulation completion, and it can be a serious problem in a very short time. Problem is both in realization and maintaining of thermal insulation, and directly in the used material. The paper presents results of laboratory experiments on resistance to biological attack, carried out for five commercial materials available on the Czech market. Before the experiments, materials were subjected to accelerated ageing for 4 and 10 years. Resistance testing comprises regulated application of algae and mould strains on samples and incubation in a defined environment. Materials resistant after ageing simulation of the longer time period were found as well as materials susceptible to attack already after completion of a facade set.

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

On the First-Passage Time Problem for a Feller-Type Diffusion Process

We consider the first-passage time problem for the Feller-type diffusion process, having infinitesimal drift B1(x,t)=α(t)x+β(t) and infinitesimal variance B2(x,t)=2r(t)x, defined in the space state [0,+∞), with α(t)∈R, β(t)>0, r(t)>0 continuous functions. For the time-homogeneous case, some relations between the first-passage time densities of the Feller process and of the Wiener and the Ornstein–Uhlenbeck processes are discussed. The asymptotic behavior of the first-passage time density through a time-dependent boundary is analyzed for an asymptotically constant boundary and for an asymptotically periodic boundary. Furthermore, when β(t)=ξr(t), with ξ>0, we discuss the asymptotic behavior of the first-passage density and we obtain some closed-form results for special time-varying boundaries.

On the nonexistence conditions of solution of two-point in time problem for nonhomogeneous PDE

We investigate the problem with local homogeneous two-point conditions with respect to time for nonhomogeneous PDE of second order in time variable and generally infinite order in spatial variables in the case when the characteristic determinant of the problem identically equals zero. We establish the nonexistence conditions of solution of this problem in the class of entire functions.