The Planar Motion with Two Bounded Controls - the Acceleration and the Derivative of the Curvature

We study the minimum time problem to go from one given point on the plane to another with given initial and final tangent angles, curvatures and absolute values of speed, the paths joining these given points being $C^1$ and along them the derivative of the curvature and acceleration remaining bounded by two constants $B$ and $A$ respectively (we denote by $u_1$ (by $u_2$) the control of acceleration (of the derivative of the curvature respectively)). After the application of the Maximum Principal of Pontryagin and after the study of all possible forms of concatenation of arcs of curves of any extremal path we obtain the following results: 1) any general optimal path is a $C^1$-jonction of line segments in one and the same direction $\varphi$ ($u_2\equiv 0$; $\varphi \in [0,2\pi]$ and it is defined by the initial and final conditions) and of arcs of curves with linear curvature ($u_2\equiv \pm B$); 2) along any general optimal path the point moves with piecewise-linear absolute value of the speed ($u_1\equiv \pm A$); 3) any optimal path contains at most one line segment; 4) if for some optimal path the point moves along the line segment in the direction $\varphi +\pi$ $(\bmod (2\pi ))$, then this optimal path contains an infinite number of concatenated arcs of curves with linear curvature ($u_2\equiv \pm B$) which accumulate towards each endpoint of the line segment

Survey Of The Necessity To Increase The Quality Of Life Of Patients With Diabetes Mellitus Through A Training Program

The relevance of current problem is determined by the high incidence of diabetes mellitus. The survey revealed the need to improve the quality of life of patients with diabetes mellitus. This is achieved through a training program.Diabetes mellitus is a disease characterized by elevated blood glucose levels in the human body resulting from weakening of insulin cells or insufficient production in the human body.            The purpose of the study is to reveal and outline the need to improve the quality of life of patients with diabetes mellitus through a training program. The training program provides information to learners about: the nature of the disease; improving their quality of life; recognition of the symptoms of hypo- and hyperglycemia; type of insulin, way of application, and place of application.The tasks of the survey are: to examine the need to improve the quality of life of patients with diabetes mellitus through a training program in the city of Sliven; to develop a training program for patients with diabetes mellitus above 18 years of age; to run the training program.The methods used are: survey, program interview, and purposeful observation.The subject of the study is: patients with the diagnosis diabetes mellitus, up to 18 years old in the town of Sliven.The object of the study is: the process and conditions in which the need to improve the quality of life of patients with diabetes mellitus through a training program is proved.The analysis of the results has led to the conclusion that there is a need to improve the quality of life of the patients with diabetes mellitus by conducting a training program. The content of the program is realized through theoretical and practical forms of training. The training ensures the quality of life of these patients

Проценка на здравствениот ризик од водата за пиење во релација со болести поврзани со водата

Healthy and safe drinking water in sufficient quantities provided to consumers improves living conditions, raises health culture at a higher level and promotes the environment as a whole. The aim is to see if there is a correlation between irregular water samples with intestinal infectious diseases related to drinking water. Materials and method. The preparation of the Republic Computer Program (1996) for issuing laboratory findings (RCP) from the analyses of samples of drinking water (physico-chemical and bacteriological), in accordance with the methodology for application of ID numbers in the computer system in the Public Health Centers has created the possibility of complete health records of drinking water supply facilities under health surveillance for the territory of the entire Republic. Evaluation has been made of the results of basic physicо-chemical and bacteriological analyses of drinking water in the settlements of the Republic of North Macedonia and the water-related diseases – waterborne intestinal infectious diseases in the period 2014-2018. Results. Drinking water from city water supply in the examined period in terms of physico-chemical analysis ranged 2.9-4.3%, while in relation to bacteriological analysis 0.9-2.6%.. Waterborne intestinal infectious diseases show a decline in their incidence in 2018. Conclusion. The registered data from the physicо-chemical and bacteriological analysis showed that the drinking water from the city water supply systems in the period 2014-2018 was safe. According to the processed data, access to safe drinking water for the population was 97% by 2018, which ranks the country in the group of countries in the world with the highest access to safe drinking water, and there is no significant connection with drinking water related diseases.Безбедна и здравствено исправна вода за пиење во доволни количини обезбедена на потрошувачите ги подобрува условите за живот, ја подигнува на повисоко ниво здравствената култура и ја унапредува животната средина во целост. Цел на трудот е да се утврди дали постои поврзаност помеѓу неисправните примероци вода со цревните заразни болести поврзани со водата за пиење. Материјали и методи: Со изготвувањето на Републичкиот компјутерски програм (1996 година) за издавање на лабораториски наоди (РКП) од извршени анализи на примероци вода за пиење (физичко-хемиски и бактериолошки), согласно методологијата за примена на матични броеви во компјутерскиот систем во Центрите за јавно здравје е создадена основа за целосна здравствена евиденција на објектите за водоснабдување со вода за пиење кои се под здравствен надзор за територијата на целата Република. Извршена е евалуација на резултатите од основната физичко-хемиска и бактериолошка анализа на водата за пиење во населените места од Република Северна Македонија и на болестите поврзани со водата за пиење-цревните заразни заболувања од хидрично потекло во период 2014-2018 година. Резултати:  Водата за пиење од градските водоводи во горенаведениот период во однос на физичко-хемиската анализа се движела во опсег 2,9-4,3%, додека во однос на бактериолошката анализа 0,9-2,6%. Цревните заразни заболувања од хидрично потекло прикажуваат опаѓање на нивната инциденција во 2018 година. Заклучок: Согласно регистрираните податоци од физичко-хемиската и бактериолошката анализа водата за пиење од градските водоснабдителни системи во периодот 2014-2018 година била безбедна. Според обработените податоци пристап до безбедна вода за пиење на населението изнесувал 97% до 2018 година, што ја рангира земјата во групата земји во светот со највисок пристап да безбедна вода за пиење и не се забележува значителна поврзаност со болестите поврзани со водата за пиење

Irregularity of Optimal Trajectories in a Control Problem for a Car-like Robot

We study the problem to find (a) shortest plane curve(s) joining two given points with given tangent angles and curvatures. The tangent angle and the curvature of the path are continuous and the derivative of the curvature is bounded by $2$. At a regular (i.e. of the class $C^3$) point such a curve must be locally a piece of a clothoid or a line segment (up to isometry a clothoid is given by Fresnel's integrals $x(t)=\int _0^t\cos \tau ^2d\tau$, $y(t)=\int _0^t\sin \tau ^2d\tau$). We prove that if the distance between the initial and final points is greater than $320\sqrt{\pi }$, then a generic shortest curve contains infinitely many switching points

Double versus single intrauterine insemination (IUI) in stimulated cycles for subfertile couples

Background In subfertile couples, couples who have tried to conceive for at least one year, intrauterine insemination (IUI) with ovarian hyperstimulation (OH) is one of the treatment modalities that can be offered. When IUI is performed a second IUI in the same cycle might add to the chances of conceiving. In a previous update of this review in 2010 it was shown that double IUI increases pregnancy rates when compared to single IUI. Since 2010, different clinical trials have been published with differing conclusions about whether double WI increases pregnancy rates compared to single IUI. Objectives To determine the effectiveness and safety of double intrauterine insemination (IUI) compared to single IUI in stimulated cycles for subfertile couples. Search methods We searched the Cochrane Gynaecology and Fertility (CGF) Group trials register, CENTRAL, MEDLI NE, Embase and CINAHL in July 2020 and LILACS, Google scholar and Epistemoni kos in February 2021, together with reference checking and contact with study authors and experts in the field to identify additional studies. Selection criteria We included randomised controlled, parallel trials of double versus single lUls in stimulated cycles in subfertile couples. Data collection and analysis Two authors independently assessed trial quality and extracted data. We contacted study authors for additional information. Main results We identified in nine studies involving subfertile women. The evidence was of low quality; the main limitations were unclear risk of bias, inconsistent results for some outcomes and imprecision, due to small trials with imprecise results. We are uncertain whether double IUI improves live birth rate compared to single IUI (odds ratio (OR) 1.15, 95% confidence interval (CI) 0.71 to 1.88; I-2 = 29%; studies= 3, participants =468; low quality evidence). The evidence suggests that if the chance of live birth following single IUI is 16%, the chance of live birth following double IUI would be between 12% and 27%. Performing a sensitivity analysis restricted to only randomised controlled trials (RCTs) with low risk of selection bias showed similar results. We are uncertain whether double IUI reduces miscarriage rate compared to single IUI (OR 1.78, 95% CI 0.98 to 3.24; I-2 = 0%; studies = 6, participants = 2363; low quality evidence). The evidence suggests that chance of miscarriage following single IUI is 1.5% and the chance following double IUI would be between 1.5% and 5%. The reported clinical pregnancy rate per woman randomised may increase with double 11.11 group (OR 1.51, 95% CI 1.23 to 1.86; I-2 = 34%; studies = 9, participants = 2716; low quality evidence). This result should be interpreted with caution due to the low quality of the evidence and the moderate inconsistency. The evidence suggests that the chance of a pregnancy following single IUI is 14% and the chance following double IUI would be between 16% and 23%. We are uncertain whether double IUI affects multiple pregnancy rate compared to single IUI (OR 2.04, 95% CI 0.91 to 4.56; I-2 = 8%; studies = 5; participants = 2203; low quality evidence). The evidence suggests that chance of multiple pregnancy following single IUI is 0.7% and the chance following double ILA would be between 0.85% and 3.7%. We are uncertain whether double IUI has an effect on ectopic pregnancy rate compared to single IUI (OR 1.22, 95% CI 0.35 to 4.28; I-2 = 0%; studies =4, participants= 1048; low quality evidence). The evidence suggests that the chance of an ectopic pregnancy following single IUI is 0.8% and the chance following double IUI would be between 0.3% and 3.2%. Authors' conclusions Our main analysis, of which the evidence is low quality, shows that we are uncertain if double IUI improves live birth and reduces miscarriage compared to single IUI. Our sensitivity analysis restricted to studies of low risk of selection bias for both outcomes is consistent with the main analysis. Clinical pregnancy rate may increase in the double IUI group, but this should be interpreted with caution due to the low quality evidence. We are uncertain whether double IUI has an effect on multiple pregnancy rate and ectopic pregnancy rate compared to single IUI

Suboptimal paths in the problem of a planar motion with bounded derivative of the curvature

We consider the planar motion of a car-like robot with a bounded derivative of the curvature, with given initial and final configuration (i.e. positions, tangent angles and curvatures). The tangent angle and the curvature of the path are assumed to be continuous. When the distance between the initial and the final point is much greater than the initial and final curvatures and the curvature's derivative, we show how to construct a suboptimal path (the cost is the path length). We admit a finite number of cusps in the path

Of macrophages and red blood cells; a complex love story

Macrophages tightly control the production and clearance of red blood cells (RBC). During steady state hematopoiesis, approximately 10(10) RBC are produced per hour within erythroblastic islands in humans. In these erythroblastic islands, resident bone marrow macrophages provide erythroblasts with interactions that are essential for erythroid development. New evidence suggests that not only under homeostasis but also under stress conditions, macrophages play an important role in promoting erythropoiesis. Once RBC have matured, these cells remain in circulation for about 120 days. At the end of their life span, RBC are cleared by macrophages residing in the spleen and the liver. Current theories about the removal of senescent RBC and the essential role of macrophages will be discussed as well as the role of macrophages in facilitating the removal of damaged cellular content from the RBC. In this review we will provide an overview on the role of macrophages in the regulation of RBC production, maintenance and clearance. In addition, we will discuss the interactions between these two cell types during transfer of immune complexes and pathogens from RBC to macrophages

Clinically relevant aberrant Filip1l DNA methylation detected in a murine model of cutaneous squamous cell carcinoma

Background: Cutaneous squamous cell carcinomas (cSCC) are among the most common and highly mutated human malignancies. Understanding the impact of DNA methylation in cSCC may provide avenues for new therapeutic strategies. Methods: We used reduced-representation bisulfite sequencing for DNA methylation analysis of murine cSCC. Differential methylation was assessed at the CpG level using limma. Next, we compared with human cSCC Infinium HumanMethylation BeadArray data. Genes were considered to be of major relevance when they featured at least one significantly differentially methylated CpGs (RRBS) / probes (Infinium) with at least a 30% difference between tumour vs. control in both a murine gene and its human orthologue. The human EPIC Infinium data were used to distinguish two cSCC subtypes, stem-cell-like and keratinocyte-like tumours. Findings: We found increased average methylation in mouse cSCC (by 12.8%, p = 0.0011) as well as in stem-cell like (by 3.1%, p=0.002), but not keratinocyte-like (0.2%, p = 0.98), human cSCC. Comparison of differentially methylated genes revealed striking similarities between human and mouse cSCC. Locus specific methylation changes in mouse cSCC often occurred in regions of potential regulatory function, including enhancers and promoters. A key differentially methylated region was located in a potential enhancer of the tumour suppressor gene Filip1l and its expression was reduced in mouse tumours. Moreover, the FILIP1L, locus showed hypermethylation in human cSCC and lower expression in human cSCC cell lines. Interpretation: Deregulation of DNA methylation is an important feature of murine and human cSCC that likely contributes to silencing of tumour suppressor genes, as shown for Filip1l. 2021 The Author(s). Published by Elsevier B.V

Pirin, an Nrf2-regulated protein, is overexpressed in human colorectal tumors

The evolutionary conserved non-heme Fe-containing protein pirin has been implicated as an important factor in cell proliferation, migration, invasion, and tumour progression of melanoma, breast, lung, cervical, prostate, and oral cancers. Here we found that pirin is overexpressed in human colorectal cancer in comparison with matched normal tissue. The overexpression of pirin correlates with activation of transcription factor nuclear factor erythroid 2 p45-related factor 2 (Nrf2) and increased expression of the classical Nrf2 target NAD(P)H:quinone oxidoreductase 1 (NQO1), but interestingly and unexpectedly, not with expression of the aldo-keto reductase (AKR) family members AKR1B10 and AKR1C1, which are considered to be the most overexpressed genes in response to Nrf2 activation in humans. Using pharmacologic and genetic approaches to either downregulate or upregulate Nrf2, we show that pirin is regulated by Nrf2 in human and mouse cells and in the mouse colon in vivo. The small molecule pirin inhibitor TPhA decreased the viability of human colorectal cancer (DLD1) cells, but this decrease was independent of the levels of pirin. Our study demonstrates the Nrf2-dependent regulation of pirin and encourages the pursuit for specific pirin inhibitors

Nrf2 activation does not affect adenoma development in a mouse model of colorectal cancer.

Funder: Stony Brook Foundation Reata PharmaceuticalsTranscription factor nuclear factor erythroid 2 p45-related factor 2 (Nrf2) and its main negative regulator, Kelch-like ECH associated protein 1 (Keap1), are at the interface between redox and intermediary metabolism. Nrf2 activation is protective in models of human disease and has benefits in clinical trials. Consequently, the Keap1/Nrf2 protein complex is a drug target. However, in cancer Nrf2 plays a dual role, raising concerns that Nrf2 activators may promote growth of early neoplasms. To address this concern, we examined the role of Nrf2 in development of colorectal adenomas by employing genetic, pharmacological, and metabolomic approaches. We found that colorectal adenomas that form in Gstp-/-: ApcMin/+ mice are characterized by altered one-carbon metabolism and that genetic activation, but not disruption of Nrf2, enhances these metabolic alterations. However, this enhancement is modest compared to the magnitude of metabolic differences between tumor and peri-tumoral tissues, suggesting that the metabolic changes conferred by Nrf2 activation may have little contribution to the early stages of carcinogenesis. Indeed, neither genetic (by Keap1 knockdown) nor pharmacological Nrf2 activation, nor its disruption, affected colorectal adenoma formation in this model. We conclude that pharmacological Nrf2 activation is unlikely to impact the early stages of development of colorectal cancer