A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

On the origin of the inertia: the modified Newtonian dynamics theory

The sameness between the inertial mass and the gravitational mass is an assumption and not a consequence of the equivalent principle is shown. In the context of the Sciama’s inertia theory, the sameness between the inertial mass and the gravitational mass is discussed and a certain condition which must be experimentally satisfied is given. The inertial force proposed by Sciama, in a simple case, is derived from the Assis’ inertia theory based in the introduction of a Weber type force. The origin of the inertial force is totally justified taking into account that the Weber force is, in fact, an approximation of a simple retarded potential, see [18, 19]. The way how the inertial forces are also derived from some solutions of the general relativistic equations is presented. We wonder if the theory of inertia of Assis is included in the framework of the General Relativity. In the context of the inertia developed in the present paper we establish the relation between the constant acceleration a0 , that appears in the classical Modified Newtonian Dynamics (M0ND) theory, with the Hubble constant H0 , i.e. a0 ≈ cH0 .

Recurrent Macular Edema in Central Retinal Vein Occlusion Treated with Intravitreal Ranibizumab using a Modified Treat and Extend Regimen.

Background: The aim of this study was to evaluate the stability over time of the individually defined interval of intravitreal ranibizumab injection (IVR) for the treatment of recurrent macular edema (ME) in central retinal vein occlusion (CRVO). Patients and Methods: A case series of treatment naïve patients followed in the Jules Gonin Eye Hospital for macular edema due to central retinal vein occlusion is presented. Patients were treated monthly with IVR until complete absence of fluid on qualitative SD-OCT with a minimum of 5 monthly IVR. Thereafter, they were followed according to a modified treat and extend regimen (mTER). Results: Twelve eyes (12 patients) with ME due to CRVO were included. The mean follow-up period was 31.3 months. Analysis showed that best corrected visual acuity (BCVA), central macular thickness and qualitative spectral domain optical coherence tomography (SD-OCT) showed comparable results under monthly interval, after titration of an individualized interval and when performed in a series. 78 % of treating intervals were within ± 2 weeks of the first individually adjusted interval. The mean first defined interval was 4.3 weeks and the mean interval over time was 5.5 weeks (p = 0.003). There was a trend towards longer interval over time. Conclusion: The adjusted interval of retreatment of patients with ME due to CRVO showed a high stability with a trend toward longer duration over time. An mTER regimen seems to be valuable to follow patients with ME with good stabilization of VA.

Sensory characteristics of 'Douradão' peaches submitted to modified atmosphere packaging

The sensory, physical and chemical characteristics of 'Douradão' peaches cold stored in different modified atmosphere packaging (LDPE bags of 30, 50, 60, 75µm thickness) were studied. After 14, 21 and 28 days of cold storage (1 ± 1 ºC and 90 ± 5% RH), samples were withdrawn from MAP and kept during 4 days in ambient air for ripening. Descriptive terminology and sensory profile of the peaches were developed by methodology based on the Quantitative Descriptive Analysis (QDA). The assessors consensually defined the sensory descriptors, their respective reference materials and the descriptive evaluation ballot. Fourteen individuals were selected as judges based on their discrimination capacity and reproducibility. Seven descriptors were generated showing similarities and differences among the samples. The data were analysed by ANOVA, Tukey test and Principal Component Analysis (PCA). The atmospheres that developed inside the different packaging materials during cold storage differed significantly. The PCA showed that MA50 and MA60 treatments were more characterized by the fresh peach flavour, fresh appearance, juiciness and flesh firmness, and were effective for keeping good quality of 'Douradão' peaches during 28 d of cold storage. The Control and MA30 treatments were characterized by the mealiness, the MA75 treatment showed lower intensity for all attributes evaluated and they were ineffective to maintain good quality of the fruits during cold storage. Higher correlation coefficients (positive) were found between fresh appearance and flesh firmness (0.95), fresh appearance and juiciness (0.97), ratio and intensity of fresh peach smell (0.81), as well as higher correlation coefficients (negative) between Hue angle and intensity of yellow colour (-0.91), fresh appearance and mealiness (-0.92), juiciness and mealiness (-0.95), firmness and mealiness (-0.94).

Increased risk of cardiovascular disease (CVD) with age in HIV-positive men : a comparison of the D:A:D CVD risk equation and general population CVD risk equations

OBJECTIVES: The aim of the study was to statistically model the relative increased risk of cardiovascular disease (CVD) per year older in Data collection on Adverse events of anti-HIV Drugs (D:A:D) and to compare this with the relative increased risk of CVD per year older in general population risk equations. METHODS: We analysed three endpoints: myocardial infarction (MI), coronary heart disease (CHD: MI or invasive coronary procedure) and CVD (CHD or stroke). We fitted a number of parametric age effects, adjusting for known risk factors and antiretroviral therapy (ART) use. The best-fitting age effect was determined using the Akaike information criterion. We compared the ageing effect from D:A:D with that from the general population risk equations: the Framingham Heart Study, CUORE and ASSIGN risk scores. RESULTS: A total of 24 323 men were included in analyses. Crude MI, CHD and CVD event rates per 1000 person-years increased from 2.29, 3.11 and 3.65 in those aged 40-45 years to 6.53, 11.91 and 15.89 in those aged 60-65 years, respectively. The best-fitting models included inverse age for MI and age + age(2) for CHD and CVD. In D:A:D there was a slowly accelerating increased risk of CHD and CVD per year older, which appeared to be only modest yet was consistently raised compared with the risk in the general population. The relative risk of MI with age was not different between D:A:D and the general population. CONCLUSIONS: We found only limited evidence of accelerating increased risk of CVD with age in D:A:D compared with the general population. The absolute risk of CVD associated with HIV infection remains uncertain.

Modified atmosphere packaging extending the storage life of 'douradão' peach

'Douradão' peach is a perishable product and when cold stored is subject to chilling injury. The objective of the experiment was to evaluate the effect of modified atmosphere packaging (MAP) and cold storage on quality and storage life of these peaches. Fruits were packed in polypropylene (PP) trays and placed inside low density polyethylene (LDPE) bags (30, 50, 60, 75 μm thickness) with active modified atmosphere (10 kPa CO2 + 1.5kPa O2, balance N2). The control was made with peaches held in nonwrapped PP trays. Fruits were kept at 1 ± 1 °C and 90 ± 5% relative humidity (RH) for 28 days and CO2 and O2 within packages was monitored every two days. After 14, 21 and 28 days, samples were withdrawn from MAP and kept in air at 25 ± 1 °C and 90 ± 5% RH for ripening. On the day of removal from the cold storage and after 4 days, peaches were evaluated for weight loss, decay incidence, flesh firmness, woolliness incidence, soluble solids content (SSC), titratable acidity (TA) and juice content. The results showed that MAP had influence on reducing weight loss and prevented postharvest decay. MAP of 1-2 kPa O2 and 3-6 kPa CO2 at 1 °C (from 50 and 60 μm LDPE films) were effective for keeping good quality of 'Douradão' peaches during 28 days of storage, the ripe fruits showed reduced incidence of woolliness, adequate juiciness and flesh firmness. Packages of 30 and 75 μm LDPE films were ineffective for reducing woolliness during cold storage. MAP fruits showed lower SSC and no relevant effect on TA. Control fruits did not present marketable conditions after 14 days of cold storage.

Effects of modified atmosphere packaging on ripening of 'Douradão' peach related to pectolytic enzymes activities and chilling injury symptoms

The present study evaluated the effects of modified atmosphere packaging on inhibition of the development of chilling injury symptoms in 'Douradão' peach after cold storage and the possible involvement of cell wall enzymes. Fruits were harvested at the middle stadium of ripening, packed in polypropylene trays and placed inside low density polyethylene (LDPE) bags (30, 50, 60 and 75 µm of thickness) with active modified atmosphere (10 kPa CO2 + 1.5 kPa O2, balance N2). The following treatments were tested: Control: peaches held in nonwrapped trays; MA30: LDPE film - 30 µm; MA50: LDPE film - 50 µm; MA60: LDPE film - 60 µm and MA75: LDPE film - 75 µm. Fruits were kept at 1±1ºC and 90±5% relative humidity (RH) for 28 days. After 14, 21 and 28 days, samples were withdrawn from MAP and kept in air at 25±1ºC and 90±5% RH for ripening. On the day of removal and after 4 days, peaches were evaluated for woolliness incidence, pectolytic enzymes activities. The respiratory rate and ethylene synthesis were monitored during 6 days of ripening. The results showed that MA50 and MA60 treatments had positive effect on the inhibition of the development of woolly texture and reduced pectin methylesterase activity on the ripe fruits, keeping good quality of 'Douradão' peach during 28 days of cold storage. The treatments Control, MA30 and MA75 showed higher woolliness incidence and did not present marketable conditions after 14 days of cold storage.

Consumption, investment and life insurance strategies with heterogeneous discounting

[cat] En aquest treball s'analitza l'efecte que comporta l'introducció de preferències inconsistents temporalment sobre les decisions òptimes de consum, inversió i compra d'assegurança de vida. En concret, es pretén recollir la creixent importància que un individu dóna a la herència que deixa i a la riquesa disponible per a la seva jubilació al llarg de la seva vida laboral. Amb aquesta finalitat, es parteix d'un model estocàstic en temps continu amb temps final aleatori, i s'introdueix el descompte heterogeni, considerant un agent amb una distribució de vida residual coneguda. Per tal d'obtenir solucions consistents temporalment es resol una equació de programació dinàmica no estàndard. Per al cas de funcions d'utilitat del tipus CRRA i CARA es troben solucions explícites. Finalment, els resultats obtinguts s'il·lustren numèricament.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Consumption, investment and life insurance strategies with heterogeneous discounting

[cat] En aquest treball s'analitza l'efecte que comporta l'introducció de preferències inconsistents temporalment sobre les decisions òptimes de consum, inversió i compra d'assegurança de vida. En concret, es pretén recollir la creixent importància que un individu dóna a la herència que deixa i a la riquesa disponible per a la seva jubilació al llarg de la seva vida laboral. Amb aquesta finalitat, es parteix d'un model estocàstic en temps continu amb temps final aleatori, i s'introdueix el descompte heterogeni, considerant un agent amb una distribució de vida residual coneguda. Per tal d'obtenir solucions consistents temporalment es resol una equació de programació dinàmica no estàndard. Per al cas de funcions d'utilitat del tipus CRRA i CARA es troben solucions explícites. Finalment, els resultats obtinguts s'il·lustren numèricament.

Effective Electrodiffusion equation for non uniform nanochannels

We derive a one dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of of a symmetric binary electrolyte in channels whose section is of nanometric section and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs di fusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non trivial fashion. We consider two kinds of non uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one and three-dimensional solutions of the electrokinetic equations.

The structure of human tRNALys3 anticodon bound to HIV genome is stabilized by modified nucleosides and adjacent mismatch base pairs

Replication of human immunodeficiency virus (HIV) requires base pairing of the reverse transcriptase primer, human tRNA(Lys3), to the viral RNA. Although the major complementary base pairing occurs between the HIV primer binding sequence (PBS) and the tRNA's 3'-terminus, an important discriminatory, secondary contact occurs between the viral A-rich Loop I, 5'-adjacent to the PBS, and the modified, U-rich anticodon domain of tRNA(Lys3). The importance of individual and combined anticodon modifications to the tRNA/HIV-1 Loop I RNA's interaction was determined. The thermal stabilities of variously modified tRNA anticodon region sequences bound to the Loop I of viral sub(sero)types G and B were analyzed and the structure of one duplex containing two modified nucleosides was determined using NMR spectroscopy and restrained molecular dynamics. The modifications 2-thiouridine, s(2)U(34), and pseudouridine, Psi(39), appreciably stabilized the interaction of the anticodon region with the viral subtype G and B RNAs. The structure of the duplex results in two coaxially stacked A-form RNA stems separated by two mismatched base pairs, U(162)*Psi(39) and G(163)*A(38), that maintained a reasonable A-form helix diameter. The tRNA's s(2)U(34) stabilized the interaction between the A-rich HIV Loop I sequence and the U-rich anticodon, whereas the tRNA's Psi(39) stabilized the adjacent mismatched pairs.

Critical reflection on the evaluation plan of the VARPUNEN project

Abstract: Critical reflection on the evaluation plan of the VARPUNEN project