A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the endpoint of an interval of definition. Thus, to overcome this issue, several new definitions of fractional derivatives have been introduced. The Caputo–Fabrizio fractional order is one of these nonsingular definitions. This paper is concerned with the analyses and design of an optimal control strategy for a Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic. The Caputo–Fabrizio fractional-order model of HIV/AIDS is considered to prevent the singularity problem, which is a real concern in the modeling of real-world systems and phenomena. Firstly, in order to find out how the population of each compartment can be controlled, sensitivity analyses were conducted. Based on the sensitivity analyses, the most effective agents in disease transmission and prevalence were selected as control inputs. In this way, a modified Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic is proposed. By changing the contact rate of susceptible and infectious people, the atraumatic restorative treatment rate of the treated compartment individuals, and the sexual habits of susceptible people, optimal control was designed. Lastly, simulation results that demonstrate the appropriate performance of the Caputo–Fabrizio fractional-order model and proposed control scheme are illustrated.     

Knowledge Discovery from Medical Data and Development of an Expert System in Immunology

Artificial intelligence is one of the fastest-developing areas of science that covers a remarkably wide range of problems to be solved. It has found practical application in many areas of human activity, also in medicine. One of the directions of cooperation between computer science and medicine is to assist in diagnosing and proposing treatment methods with the use of IT tools. This study is the result of collaboration with the Children’s Memorial Health Institute in Warsaw, from where a database containing information about patients suffering from Bruton’s disease was made available. This is a rare disorder, difficult to detect in the first months of life. It is estimated that one in 70,000 to 90,000 children will develop Bruton’s disease. But even these few cases need detailed attention from doctors. Based on the data contained in the database, data mining was performed. During this process, knowledge was discovered that was presented in a way that is understandable to the user, in the form of decision trees. The best models obtained were used for the implementation of expert systems. Based on the data introduced by the user, the system conducts expertise and determines the severity of the course of the disease or the severity of the mutation. The CLIPS language was used for developing the expert system. Then, using this language, software was developed producing six expert systems. In the next step, experimental verification was performed, which confirmed the correctness of the developed systems.     

Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes

Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity.     

Stochastic Order and Generalized Weighted Mean Invariance

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.     

Ultra high performance liquid chromatography-quadrupole-time of flight analysis for the identification and the determination of resveratrol and its metabolites in mouse plasma

Resveratrol is a polyphenol that has numerous interesting biological properties, but, per os, it is quickly metabolized. Some of its metabolites are more concentrated than resveratrol, may have greater biological activities, and may act as a kind of store for resveratrol. Thus, to understand the biological impact of resveratrol on a physiological system, it is crucial to simultaneously analyze resveratrol and its metabolites in plasma. This study presents an analytical method based on UHPLC-Q-TOF mass spectrometry for the quantification of resveratrol and of its most common hydrophilic metabolites. The use of ¹³C- and D-labeled standards specific to each molecule led to a linear calibration curve on a larger concentration range than described previously. The use of high resolution mass spectrometry in the full scan mode enabled simultaneous identification and quantification of some hydrophilic metabolites not previously described in mice. In addition, UHPLC separation, allowing run times lower than 10 min, can be used in studies that requiring analysis of many samples.     

Micellar Mediated Halodecarboxylation of α,β‐Unsaturated Aliphatic and Aromatic Carboxylic Acids—A Novel Green Hunsdiecker–Borodin Reaction

A Novel Hunsdiecker‐Borodin reaction (HBR) has been carried out efficiently with α,β‐unsaturated aliphatic and aromatic carboxylic acids by using N‐halo succinimides such as N‐chloro succinimide (NCS), N‐bromo succinimide (NBS), and N‐iodo succinimide (NIS) under micellar media. The reaction with α,β‐unsaturated aromatic carboxylic acids afforded β‐halo styrenes in excellent yield while α,β‐unsaturated aliphatic carboxylic acids underwent decarboxylation and to give corresponding halo derivatives. The reactions are dramatically accelerated in micellar media. This procedure works efficiently in CTAB (cetyl trimethyl ammonium bromide), SDS (sodium dodecyl sulfate), and TX (Triton‐X‐100) media under stirred conditions at room temperature. At reflux temperatures the yield of reaction products were further enhanced from good to excellent.     

Applications of Dithioacetals in Ester Synthesis

The α-oxoketene dithioacetals are simple synthetic intermediates widely utilized and implicated for the synthesis of a variety of heterocyclic compounds other than alicyclic and aromatic compounds. They act as 1,3-electrophilic three-carbon synthons. The α-oxoketene dithioacetal of pyrazolone derivatives can be efficiently converted through a base-catalyzed alcoholysis into the corresponding ester in a single one-step reaction with good yield of pure products. In this article, we summarize recent direct conversion of α-oxoketene dithioacetals to highly desirable esters. The overall process is an example of intramolecular rearrangement of bonds. Characterization and identification of all synthesized compounds were assigned through ¹H NMR and mass spectroscopy.     

The Reaction of 1-Nitro-4-(4-nitrophenylsulfonylmethyl)benzene with α,β-Unsaturated Esters

Under solid-liquid PTC conditions, treatment of 1-nitro-4-(4-nitrophenylsulfonyl-methyl)benzene(1) with α,β -unsaturated esters (2a-h) at 35–75°C gave tandem addition-rearrangement products(3a-h). While at higher temperature(75°C), addition-rearrangement-addition products (4a-b) were obtained when acrylates were used. Finally a possible mechanism is proposed.     

Synthesis of (R)‐Japonilure and (4R,9Z)‐9‐Octadecen‐4‐olide,Pheromones of the Japanese Beetle and Currant Stem Girdler

Asymmetric total synthesis of the sex pheromones of Japanese beetle and currant stem girdler, (R)‐japonilure (1) and (4R,9Z)‐9‐octadecen‐4‐olide (2), has been achieved.     

One‐Pot,High‐Yielding Synthesis of Novel Dihydrothiazolo[3,2‐a]pyrimidinones

Reaction between 6‐(un)substituted‐2‐thiouracils and E‐ethyl 4‐bromocrotonate under basic conditions at room temperature is an easy, mild, high‐yielding, and regioselective method for the preparation of 7‐(un)substituted dihydrothiazolo[3,2‐a]pyrimidinone derivatives.