Differential calculus with imprecise input and its logical framework

We develop a domain-theoretic Differential Calculus for locally Lipschitz functions on finite dimensional real spaces with imprecise input/output. The inputs to these functions are hyper-rectangles and the outputs are compact real intervals. This extends the domain of application of Interval Analysis and exact arithmetic to the derivative. A new notion of a tie for these functions is introduced, which in one dimension represents a modification of the notion previously used in the one-dimensional framework. A Scott continuous sub-differential for these functions is then constructed, which satisfies a weaker form of calculus compared to that of the Clarke sub-gradient. We then adopt a Program Logic viewpoint using the equivalence of the category of stably locally compact spaces with that of semi-strong proximity lattices. We show that given a localic approximable mapping representing a locally Lipschitz map with imprecise input/output, a localic approximable mapping for its sub-differential can be constructed, which provides a logical formulation of the sub-differential operator

A comparative study of preliminary dosimetry for human based on distribution data in rats with 111In, 90Y, 153Sm, and 177Lu labeled rituximab

Radio immunotherapy is one of the most important and effective therapies for B-cell non Hoddgkin’s lymphoma treatment. Today, anti CD-20 antibodies labeled with beta emitter radionuclides are used in radio immunotherapy. Various radionuclides for labeling anti CD-20 antibodies have been studied and developed for the treatment and diagnosis of malignancies. This paper describes the preparation, bio-distribution and absorbed dose rate of 111In, 90Y, 177Lu, and 153Sm labeled anti CD-20 antibodies (rituximab) in human organs, after injection to rats. The macro cyclic bifunctional chelating agent, N-succinimidyl-1, 4, 7, 10-tetraazacyclododecane-1, 4, 7, 10-tetraacetic acid (DOTA-NHS) for conjugation to antibody, was used to prepare DOTA-rituximab. The conjugates were purified by molecular filtration, the average number of DOTA conjugated per mAb was calculated and total concentration was determined by spectrophotometric method. Radio-labeling was performed at 40 °C for 24 hours. After the quality control studies, the final radioactive solution was injected intravenously into rats through their tail vein. The tissue uptakes of each injection were measured. Then we calculated S values for 177Lu and 153Sm by using specific absorbed fractions and data used in the manner of radio-labeled analysis and dosimetry for humans. The absorbed dose rate of each organ was calculated in the specific time by medical internal radiation dose method with linear approximation in the activity measurements

Probabilistic Bisimulation: Naturally on Distributions

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a long-standing open problem concerning the representation of memoryless continuous time by memory-full continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems

Role of synovial fibroblast subsets across synovial pathotypes in rheumatoid arthritis: a deconvolution analysis

OBJECTIVES: To integrate published single-cell RNA sequencing (scRNA-seq) data and assess the contribution of synovial fibroblast (SF) subsets to synovial pathotypes and respective clinical characteristics in treatment-naïve early arthritis. METHODS: In this in silico study, we integrated scRNA-seq data from published studies with additional unpublished in-house data. Standard Seurat, Harmony and Liger workflow was performed for integration and differential gene expression analysis. We estimated single cell type proportions in bulk RNA-seq data (deconvolution) from synovial tissue from 87 treatment-naïve early arthritis patients in the Pathobiology of Early Arthritis Cohort using MuSiC. SF proportions across synovial pathotypes (fibroid, lymphoid and myeloid) and relationship of disease activity measurements across different synovial pathotypes were assessed. RESULTS: We identified four SF clusters with respective marker genes: PRG4(+) SF (CD55, MMP3, PRG4, THY1(neg)); CXCL12(+) SF (CXCL12, CCL2, ADAMTS1, THY1(low)); POSTN(+) SF (POSTN, collagen genes, THY1); CXCL14(+) SF (CXCL14, C3, CD34, ASPN, THY1) that correspond to lining (PRG4(+) SF) and sublining (CXCL12(+) SF, POSTN(+) + and CXCL14(+) SF) SF subsets. CXCL12(+) SF and POSTN(+) + were most prominent in the fibroid while PRG4(+) SF appeared highest in the myeloid pathotype. Corresponding, lining assessed by histology (assessed by Krenn-Score) was thicker in the myeloid, but also in the lymphoid pathotype + the fibroid pathotype. PRG4(+) SF correlated positively with disease severity parameters in the fibroid, POSTN(+) SF in the lymphoid pathotype whereas CXCL14(+) SF showed negative association with disease severity in all pathotypes. CONCLUSION: This study shows a so far unexplored association between distinct synovial pathologies and SF subtypes defined by scRNA-seq. The knowledge of the diverse interplay of SF with immune cells will advance opportunities for tailored targeted treatments

Cauchyness and convergence in fuzzy metric spaces

[EN] In this paper we survey some concepts of convergence and Cauchyness appeared separately in the context of fuzzy metric spaces in the sense of George and Veeramani. For each convergence (Cauchyness) concept we find a compatible Cauchyness (convergence) concept. We also study the relationship among them and the relationship with compactness and completeness (defined in a natural sense for each one of the Cauchy concepts). In particular, we prove that compactness implies p-completeness.Almanzor Sapena acknowledges the support of Ministry of Economy and Competitiveness of Spain under grant TEC2013-45492-R. Valentín Gregori acknowledges the support of Ministry of Economy and Competitiveness of Spain under grant MTM 2012-37894-C02-01.Gregori Gregori, V.; Miñana, J.; Morillas, S.; Sapena Piera, A. (2017). Cauchyness and convergence in fuzzy metric spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 111(1):25-37. https://doi.org/10.1007/s13398-015-0272-0S25371111Alaca, C., Turkoglu, D., Yildiz, C.: Fixed points in intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 29, 1073–1078 (2006)Edalat, A., Heckmann, R.: A computational model for metric spaces. Theor. Comput. Sci. 193, 53–73 (1998)Engelking, R.: General topology. PWN-Polish Sci. Publ, Warsawa (1977)Fang, J.X.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 46(1), 107–113 (1992)George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395–399 (1994)George, A., Veeramani, P.: Some theorems in fuzzy metric spaces. J. Fuzzy Math. 3, 933–940 (1995)George, A., Veeramani, P.: On some results of analysis for fuzzy metric spaces. Fuzzy Sets Syst. 90, 365–368 (1997)Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1989)Gregori, V., Romaguera, S.: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115, 485–489 (2000)Gregori, V., Romaguera, S.: On completion of fuzzy metric spaces. Fuzzy Sets Syst. 130, 399–404 (2002)Gregori, V., Romaguera, S.: Characterizing completable fuzzy metric spaces. Fuzzy Sets Syst. 144, 411–420 (2004)Gregori, V., López-Crevillén, A., Morillas, S., Sapena, A.: On convergence in fuzzy metric spaces. Topol. Appl. 156, 3002–3006 (2009)Gregori, V., Miñana, J.J.: Some concepts realted to continuity in fuzzy metric spaces. In: Proceedings of the conference in applied topology WiAT’13, pp. 85–91 (2013)Gregori, V., Miñana, J.-J., Sapena, A.: On Banach contraction principles in fuzzy metric spaces (2015, submitted)Gregori, V., Miñana, J.-J.: std-Convergence in fuzzy metric spaces. Fuzzy Sets Syst. 267, 140–143 (2015)Gregori, V., Miñana, J.-J.: Strong convergence in fuzzy metric spaces Filomat (2015, accepted)Gregori, V., Miñana, J.-J., Morillas, S.: Some questions in fuzzy metric spaces. Fuzzy Sets Syst. 204, 71–85 (2012)Gregori, V., Miñana, J.-J., Morillas, S.: A note on convergence in fuzzy metric spaces. Iran. J. Fuzzy Syst. 11(4), 75–85 (2014)Gregori, V., Morillas, S., Sapena, A.: On a class of completable fuzzy metric spaces. Fuzzy Sets Syst. 161, 2193–2205 (2010)Gregori, V., Morillas, S., Sapena, A.: Examples of fuzzy metric spaces and applications. Fuzzy Sets Syst. 170, 95–111 (2011)Kramosil, I., Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetika 11, 326–334 (1975)Mihet, D.: On fuzzy contractive mappings in fuzzy metric spaces. Fuzzy Sets Syst. 158, 915–921 (2007)Mihet, D.: Fuzzy $$\varphi$$ φ -contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets Syst. 159, 739–744 (2008)Mihet, D.: A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets Syst. 144, 431–439 (2004)Mishra, S.N., Sharma, N., Singh, S.L.: Common fixed points of maps on fuzzy metric spaces Internat. J. Math. Math. Sci. 17(2), 253–258 (1994)Morillas, S., Sapena, A.: On Cauchy sequences in fuzzy metric spaces. In: Proceedings of the conference in applied topology (WiAT’13), pp. 101–108 (2013)Ricarte, L.A., Romaguera, S.: A domain-theoretic approach to fuzzy metric spaces. Topol. Appl. 163, 149–159 (2014)Sherwood, H.: On the completion of probabilistic metric spaces. Z.Wahrschein-lichkeitstheorie verw. Geb. 6, 62–64 (1966)Sherwood, H.: Complete Probabilistic Metric Spaces. Z. Wahrschein-lichkeitstheorie verw. Geb. 20, 117–128 (1971)Tirado, P.: On compactness and G-completeness in fuzzy metric spaces. Iran. J. Fuzzy Syst. 9(4), 151–158 (2012)Tirado, P.: Contraction mappings in fuzzy quasi-metric spaces and [0,1]-fuzzy posets. Fixed Point Theory 13(1), 273–283 (2012)Vasuki, R., Veeramani, P.: Fixed point theorems and Cauchy sequences in fuzzy metric spaces. Fuzzy Sets Syst. 135(3), 415–417 (2003)Veeramani, P.: Best approximation in fuzzy metric spaces. J. Fuzzy Math. 9, 75–80 (2001

Computational modelling of wound healing insights to develop new treatments

About 1% of the population will suffer a severe wound during their life. Thus, it is really important to develop new techniques in order to properly treat these injuries due to the high socioeconomically impact they suppose. Skin substitutes and pressure based therapies are currently the most promising techniques to heal these injuries. Nevertheless, we are still far from finding a definitive skin substitute for the treatment of all chronic wounds. As a first step in developing new tissue engineering tools and treatment techniques for wound healing, in silico models could help in understanding the mechanisms and factors implicated in wound healing. Here, we review mathematical models of wound healing. These models include different tissue and cell types involved in healing, as well as biochemical and mechanical factors which determine this process. Special attention is paid to the contraction mechanism of cells as an answer to the tissue mechanical state. Other cell processes such as differentiation and proliferation are also included in the models together with extracellular matrix production. The results obtained show the dependency of the success of wound healing on tissue composition and the importance of the different biomechanical and biochemical factors. This could help to individuate the adequate concentration of growth factors to accelerate healing and also the best mechanical properties of the new skin substitute depending on the wound location in the body and its size and shape. Thus, the feedback loop of computational models, experimental works and tissue engineering could help to identify the key features in the design of new treatments to heal severe wounds

Numerical Model‐Software for Predicting Rock Formation Failure‐Time Using Fracture Mechanics

Real‐time integrated drilling is an important practice for the upstream petroleum industry. Traditional pre‐drill models, tend to offset the data gathered from the field since information obtained prior to spudding and drilling of new wells often become obsolete due to the changes in geology and geomechanics of reservoir‐rocks or formations. Estimating the complicated non‐linear failure‐time of a rock formation is a difficult but important task that helps to mitigate the effects of rock failure when drilling and producing wells from the subsurface. In this study, parameters that have the strongest impact on rock failure were used to develop a numerical and computational model for evaluating wellbore instability in terms of collapse, fracture, rock strength and failure‐time. This approach presents drilling and well engineers with a better understanding of the fracture mechanics and rock strength failureprediction procedure required to reduce stability problems by forecasting the rock/formation failuretime. The computational technique built into the software, uses the stress distribution around a rock formation as well as the rock’s responses to induced stress as a means of analyzing the failure time of the rock. The results from simulation show that the applied stress has the most significant influence on the failure‐time of the rock. The software also shows that the failure‐time varied over several orders of magnitude for varying stress‐loads. Thus, this will help drilling engineers avoid wellbore failure by adjusting the stress concentration properly through altering the mud pressure and well orientation with respect to in‐situ stresses. As observed from the simulation results for the failure time analysis, the trend shows that the time dependent strength failure is not just a function of the applied stress. Because, at applied stress of 6000–6050 psi there was time dependent failure whereas, at higher applied stress of 6350–6400 psi there was no time dependent strength failure

CD8+ T Cells as a Source of IFN-γ Production in Human Cutaneous Leishmaniasis

Cutaneous leishmaniasis (CL) is usually a self-healing skin lesion caused by different species of Leishmania parasite. Resistance and susceptibility of mice to Leishmania major infection is associated with two types of CD4+ T lymphocytes development: Th1 type response with production of cytokine IFN-γ is associated with resistance, whereas Th2 type response with production of cytokines IL-4 and IL-5 is associated with susceptibility. A clear Th1/Th2 dichotomy similar to murine model is not defined in human leishmaniasis and we need as much information as possible to define marker(s) of protection. We purified CD4+/CD8+ T cells, stimulated them with Leishmania antigens and analysed gene and protein expression of Th1/Th2 cytokines in volunteers with a history of self-healing CL who are presumed to be protected against further Leishmania infection. We have seen significant upregulation of IFN-γ gene expression and high IFN-γ production in the Leishmania stimulated CD4+ T cells and CD8+ T cells. We concluded that both antigen-specific IFN-γ producing CD4+ Th1 cells and IFN-γ producing CD8+ T cells contribute to the long term protection in individuals with a history of CL. This proves the importance of CD8+ T cells as a source of IFN-γ in Th1-like immune responses

Resting and feeding preferences of Anopheles stephensi in an urban setting, perennial for malaria

Background: The Indian city of Chennai is endemic for malaria and the known local malaria vector is Anopheles stephensi. Plasmodium vivax is the predominant malaria parasite species, though Plasmodium falciparum is present at low levels. The urban ecotype of malaria prevails in Chennai with perennial transmission despite vector surveillance by the Urban Malaria Scheme (UMS) of the National Vector Borne Disease Control Programme (NVBDCP). Understanding the feeding and resting preferences, together with the transmission potential of adult vectors in the area is essential in effective planning and execution of improved vector control measures. Methods: A yearlong survey was carried out in cattle sheds and human dwellings to check the resting, feeding preferences and transmission potential of An. stephensi. The gonotrophic status, age structure, resting and host seeking preferences were studied. The infection rate in An. stephensi and Anopheles subpictus were analysed by circumsporozoite ELISA (CS-ELISA). Results: Adult vectors were found more frequently and at higher densities in cattle sheds than human dwellings. The overall Human Blood Index (HBI) was 0.009 indicating the vectors to be strongly zoophilic. Among the vectors collected from human dwellings, 94.2% were from thatched structures and the remaining 5.8% from tiled and asbestos structures. 57.75% of the dissected vectors were nulliparous whereas, 35.83% were monoparous and the rest 6.42% biparous. Sporozoite positivity rate was 0.55% (4/720) and 1.92% (1/52) for An. stephensi collected from cattle sheds and human dwellings, respectively. One adult An. subpictus (1/155) was also found to be infected with P. falciparum. Conclusions: Control of the adult vector populations can be successful only by understanding the resting and feeding preferences. The present study indicates that adult vectors predominantly feed on cattle and cattle sheds are the preferred resting place, possibly due to easy availability of blood meal source and lack of any insecticide or repellent pressure. Hence targeting these resting sites with cost effective, socially acceptable intervention tools, together with effective larval source management to reduce vector breeding, could provide an improved integrated vector management strategy to help drive down malaria transmission and assist in India's plan to eliminate malaria by 2030