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The statistical concept of causality in continuous time between filtered probability spaces considered in this paper is based on Granger's definition of causality. The given concept of causality ca...

In December 2019, the virus SARS-CoV-2 responsible for the COVID-19 pandemic was detected in the Chinese city of Wuhan. The virus started to spread from China and dispersed over the rest of the world. In March 2020, WHO (World Health Organization) declared COVID-19 a pandemic. The transmission path of the pandemic was accelerated by different types of transportation. With complete analysis of spatial data, population density, types of traffic networks, and their properties, the spatial distribution of COVID-19 was estimated. GIS (Geographical Information System), numerical methods, and software for network analysis were used in this research to model scenarios of virus distribution on a global scale. The analyzed data included air, railway, marine, and road traffic. In the pandemic research, numerous models of possible trajectory of viruses can be created. Many have a stochastic character. This study includes all countries in the world affected by the COVID-19 up to date. In this study, GIS methods such as buffer, interpolations, and numerical analysis were used in order to estimate and visualize ongoing COVID-19 pandemic situation. According to the availability of new data, trajectory of virus paths was estimated. On the other hand, sparsely populated areas with poorly developed and small traffic networks (and isolated island territories) tend to be less or not affected as shown by the model. This low-cost approach can be used in order to define important measures that need to be addressed and implemented in order to successfully mitigate the implications of COVID-19 not only on global, but local and regional scales as well.

The aim of this study was to determine colour characteristics (lightness - L* , redness - a* and yellowness - b* ) of dry fermented sausage Petrovska klobasa smoked in traditional (T - direct smoking) and industrial (I - indirect smoking) conditions, at the end of drying period and the end of storage period. Also, the content of polycyclic aromatic hydrocarbons -PAH (acenaphthylene, fluorene, phenanthrene, anthracene, pyrene, benz[a] anthracene chrysene, benzo[ b ]fluoranthene, benzo[k]flouranthene, benzo[a] pyrene, indeno[1,2,3- cd ]pyrene, dibenz[a,h]anthracene and benzo[ghi] perylene) from Environmental Protection Agency list (US-EPA) were determined in both examined groups of sausages. According to the results obtained in this study, Petrovska klobasa smoked in traditional conditions had significantly lower (P a* ) at end of drying period, but colour characteristics ( L*; a*; b* ) were not significantly different (P > 0.05) at the end of storage period comparing to sausages smoked in industrial conditions. Also, Petrovska klobasa smoked in traditional conditions at both examined periods had significantly higher total content of 13 US-EPA PAH (118.7 μg/kg; 168.0 μg/kg respectively) comparing to sausages smoked in industrial conditions (30.5 μg/kg; 61.3 μg/kg respectively).

In this paper we consider the concept of statistical causality between filtrations associated with stopping times, which is based on Granger?s definition of causality. Especially, we consider a generalization of a causality relationship ?G is a cause of E within H? from fixed to stopping time. Then we apply the given causality concept to local uniqueness for the solution of the martingale problem. Also, we give some applications in finance.

The paper considers a statistical concept of causality in continuous time in the filtered probability spaces which is based on the Granger’s definition of causality. The given causality concept is then applied to the solution of the martingale problem (associated with the stochastic differential equation driven with semimartingales). More precisely, we show that the given causality concept is closely connected to the concept of extremality of measures for the solutions of the martingale problem, for the stopped martingale problem and for the local martingale problem. We also show the equivalence between some models of causality and local uniqueness (for the solutions of the martingale problem).

In this paper we consider the statistical concept for continuous-time stochastic processes, which is based on Granger’s definition of causality. We, also, show that separability is directly related to causality concepts. More precisely, we provide necessary conditions, in terms of statistical causality, for the space L p ( Ω , G ∞ , P ) to be separable. The concept of statistical causality is related to the notion separability of stochastic processes, too.

We consider causality relationships between σ-fields (filtrations) associated by stopping times, which can be applied to the stopped processes. These results are motivated by the causality relationship between filtrations “( $$ \mathcal{G} $$ t) is a cause of (ℋt) within (ℱt)” and which is based on Granger’s definition of causality. Then we give some basic properties of causality up to some stopping time. The given concept of causality associated to stopping times is equivalent with the preservation of the martingale property for the stopped processes when the filtration is getting larger.

In this paper we consider a statistical concept of causality in continuous time in filtered probability spaces which is based on Granger's definitions of causality. The given causality concept is closely connected to the preservation of the property being a local martingale if the filtration is getting larger. Namely, the local martingale remains unpredictable if the amount of information is increased. We proved that the preservation of this property is equivalent with the concept of causality.

The aim of this study was to determine the content of 13 polycyclic aromatic hydrocarbons (acenaphthylene, fluorene, phenanthrene, anthracene, pyrene, benz[ a ]anthracene, chrysene, benzo[ b ]fluoranthene, benzo[ k ]fluoranthene, benzo[ a ]pyrene, indeno[1,2,3- cd ]pyrene, dibenz[ a,h ]anthracene and benzo[ ghi ]perylene) from Environmental Protection Agency list (US-EPA PAHs) in traditional dry fermented sausage Petrovska klobasa. Sausages, stuffed in collagen and natural casings, were smoked in traditional (A1, A2, B1 and B2 - direct smoking) and industrial (B3 and B4 - indirect smoking) conditions. The highest total content of 13 US-EPA PAHs was determined in sausages stuffed in natural casings and smoked in traditional conditions at both examined periods, at the end of drying, as well as at the end of storage period (220 μg/kg and 495 μg/kg, respectively). The lowest content of these compounds was determined in sausages stuffed in collagen casings and smoked in industrial conditions, also at both examined periods (31.3 μg/kg; 54.1 μg/kg respectively). Phenanthrene (A1-120; A2-119; B2-37.6 and B4-13.1 μg/kg) and acenaphthylene (B1-45.0 and B3-18.3 μg/kg) were the most abundant PAHs in all examined sausage samples at the end of drying period, while at the end of storage period the most abundant PAHs were phenanthrene (A1-201; A2-107; B2-49.4 and B3-38.7 μg/kg) and anthracene (B1-34.4 and B4-20.1 μg/kg). Benzo[ a ]pyrene, whose maximum allowed content in smoked meat products is 5 μg/kg (EC No. 1881/2006), was below the limit of detection in all examined samples. Also, PAH4 (sum content of benz[ a ]anthracene, chrysene, benzo[ b ]fluoranthene and benzo[ a ]pyrene) a more suitable indicator for the occurrence of PAHs, with maximum allowed content in smoked meat products of 30 μg/kg (EC No. 835/2011), was below the limit of detection in all examined samples. According to the results obtained in this study, traditional dry fermented sausage Petrovska klobasa , smoked in traditional and industrial conditions was safe for its consumers regarding European regulation on PAHs content.

The paper considers a statistical concept of causality in continuous time between filtered probability spaces, based on Granger’s definition of causality. This causality concept is connected with the preservation of the martingale representation property when the filtration is getting smaller. We also give conditions, in terms of causality, for every martingale to be a continuous semimartingale, and we consider the equivalence between the concept of causality and the preservation of the martingale representation property under change of measure. In addition, we apply these results to weak solutions of stochastic differential equations. The results can be applied to the economics of securities trading.

Production of traditional dry-fermented sausages is associated with natural contamination by environmental flora. This microbiota is usually referred to as 'house flora'. This contamination occurs during slaughtering and increases during manufacturing. The diversity of microbiota in small-scale processing units, during production process of the traditional fermented dry sausages - Petrovská klobása, is reviewed in the present paper. Test samples were collected in two village households in Bački Petrovac, where the preparation of Petrovská klobása samples was performed in a traditional manner. The total number of 43 samples was subjected to laboratory examination. Generally, before stuffing, Listeria monocytogenes and Staphylococcus aureus were detected in 6.97 and 9.30%, respectively. Escherichia coli was found in 18.60%. The tested samples of end product at the end of the storage period (270th day) were safe with presence of bacteria populations from the working environment, such as: aerobic bacteria, Micrococcaceae, Lactic acid bacteria and Enterococcus spp. Examination of the hygienic status of the food processing environment, equipment, raw materials and final product provides an overview of growth trends and the disappearance of bacterial populations.

Dry fermented sausage (Petrovska klobasa) was coated with chitosan–caraway film. Effect of coating on fatty acid profile, lipid oxidation and sensory property of odor and taste were investigated during five months storage. At the end of storage period, sum of unsaturated and polyunsaturated fatty acids was significantly higher (p Contents of propanal and pentanal were significantly higher in the control sausage, while the rest of aldehydes content (hexanal, heptanal and octanal) did not differ between control and coated sausage. In both coated and control sausage, TBARS values content increased after two months storage and then remained unchanged until the end of storage period. Between examinated groups of sausages no significant difference was observed (p > 0.05). After two months of storage, sensory property of odor and taste did not differ between examinated groups of sausages, but at the end of storage period this value was significantly higher for coated sausage. Chitosan–caraway coated sausage showed lower intensity of lipid oxidative changes and better sensory properties for odor and taste at the end of five months storage in comparison to control.

Proteolytic changes and formation of biogenic amines in Serbian traditional dry-fermented sausage were determined during 120 days long ripening period. The sausage was made during winter (low ambient temperature) without the use of additives and microbial starters, resulting in slow decrease in water activity (aw) and pH. The aw gradually decreased from initial value of 0.95 to 0.86 ( P

The effect of a chitosan coating with added essential oil of oregano ( Origanum vulgare ) on lipid oxidation of dry fermented sausage (Petrovska klobasa) was investigated. Fatty acid profile, aldehyde contents and sensory analysis of odor and flavor were determined after drying and during seven months of storage. Between coated and control sausage, a difference was observed after two months storage in fatty acid profiles (myristic, oleic and linoleic acids), but after seven months storage there was no difference. Decrease in polyunsaturated acid content was observed (from 17.25% to 15.70%), as well as an increase in total aldehydes (from 4.54 μg/g to 31.80 μg/g), due to lipid oxidation during storage. After seven months storage, the content of most aldehydes was significantly lower in coated sausage than in the control. Sensory characteristics of odor and flavor were better for coated sausage, after seven months of storage. Results suggest that chitosan–oregano coating can be successfully applied to protect dry fermented sausages from lipid oxidation.

The objective of this study was to examine the quality characteristics of packaging materials and packaging units, and the viability and acceptability of the colour and sensorial properties of fresh pork meat during storage in low oxygen and high carbon dioxide modified atmosphere packaging up to 16 days at two temperatures (0°C and 4°C), as well as the sensorial properties of cooked meat. Packaging materials had good mechanical and barrier properties and were suitable for packaging in selected atmosphere. The concentration of oxygen during the whole storage period was less than 0.5% at both temperatures. The proportion of red colour (a*) was successfully maintained although the colour was slightly darker (L*) and the sensory value was lower when evaluated at the end of the storage period. Based on the obtained results and discussion, it can be concluded that samples packaged in a modified atmosphere with 40% CO2 and 60% N2 can be stored at 0°C for 15 days and at 4°C for 10 days. Samples had a good sensory quality until the 16th day, with the best results achieved on the 7th day. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper we consider a problem that follows directly from realization problem: how to find Markovian representations , even minimall, for a given family of Hilbert spaces, understood as outputs of a stochastic dynamic system S1, provided it is in a certain causality relationship with another family of Hilbert spaces , i. e. with some informations about states of a stochastic dynamic system S2. This paper is continuation of the papers Gill and Petrovic [7] and Petrovic [16,17].

Effects of rapid chilling of carcasses (at − 31 °C in the first 3 h of chilling, and then at 2–4 °C) and earlier deboning (8 h post-mortem ), compared to rapid (till 24 h post-mortem ) and conventional chilling (at 2–4 °C, till 24 h post-mortem ), on quality characteristics of pork M. semimebranosus and cooked ham were investigated. Quality measurements included pH value, colour (CIE L*a*b* values) and total aerobic count of M. semimebranosus , as well as sensory (colour, juiciness, texture, and flavour), physical (pH value, colour – CIE L*a*b* values and texture – Warner–Bratzler shear and penetration forces) and chemical (protein, total fat, and moisture content) characteristics of cooked ham. The cooked ham was manufactured from pieces of M. semimebranosus with ultimate lightness (CIE L* value) lower than 50. Rapid chilling and earlier deboning significantly increased quantity of M. semimebranosus desirable for cooked ham manufacturing. Earlier start of pork fabrication did not affect important quality characteristics of cooked ham.

peer-reviewed, Proteolysis and texture profile of Petrovská klobása, made with addition of starter culture, were investigated during the ripening in different conditions (traditional versus industrial). Due to intensive degradation of myofibrillar proteins, significant increases of non-protein nitrogen and free amino acids nitrogen contents were registered in all samples. Similar proteolytic changes were found in both starter and non-starter sausages, but were more pronounced in samples ripened in industrial room. In relation to ripening conditions hardness and chewiness differed significantly, while starter culture had significant effect only on hardness of sausages processed in industrial room., The authors wish to express their sincere gratitude to the Ministry of Education, Science and Technological Development of the Republic of Serbia (Project: TR31032), as well as to Provincial Secretariat for Science and Technological Development of the Autonomous Province of Vojvodina (Project: 114-451-1440/2014) for their financial support.

In this paper we consider the statistical concept of causality in continuous time between filtered probability spaces, based on Granger’s definitions of causality. Then we consider some stable subspaces of $H^p$ which contain right continuous modifications of martingales $P(A \mid {\mathcal {G}}_t)$. We give necessary and sufficient conditions, in terms of statistical causality, for these spaces to coincide with $H^p$. These results can be applied to extremal measures and regular weak solutions of stochastic differential equations.

Motivated by Florens et al. (1993) and recent studies of stochastic systems with memory, we suggest the new concept of causality for continuous time stochastic processes which deal with finite horizon of the past. Also, we present results which show connections between the given concept of causality and marginalization of continuous time Markov processes.

In this work we consider the concept of statistical causality between filtrations, and in particular a generalization of the causality relationship “G is a cause of J within H”. Then we apply this concept to strongly orthogonal martingales. We show the equivalence between the concepts of causality and orthogonality of local martingales. The orthogonality of martingales is a property which can be associated with the theory of option trading.

The aim of this study was to determine the content of nine biogenic amines (tryptamine, phenylethylamine, putrescine, cadaverine, histamine, serotonin, tyramin, spermidine and spermine) and total biogenic amines in traditional dry fermented sausage Petrovska klobasa at the end of drying period, as possible indicators of good manufacturing practice (GMP). Chromatographic separation of dansyl chloride derivatizated amines was completed in 8 min. Analyses were performed by HPLC-DAD on Eclipse XDB-C18 column. Tryptamine and spermine were determined in all analyzed samples, while histamine, serotonin and spermidine were not detected in any samples. Average content of individual biogenic amine ranged from 5.54 mg/kg (putrescin) to 75.1 mg/kg (tryptamine) and total content of biogenic amines varied from 77.8 mg/kg to 174 mg/kg. The results obtained in this study provided no evidence for deviations from good manufacturing practice in Petrovska klobasa production.

A significant factor in the protection of consumer health is the systematic and constant implementation of control for the presence of residue of biologically active substances and their metabolites in raw materials and in primary products of animal origin. As regards meat, an essential aspect of security is definitely the control of possible residue of veterinary medicines and environmental contaminants. In that respect, the objective of the national project entitled „Development of technology for drying and fermentation of the sausage petrovacka kobasica (Petrovska klobasa - registered geographic origin) under controlled conditions“, Number TR - 20037, was to protect the product petrovacka kobasica (Petrovska klobasa) with the appropriate appellation. A part of the compulsory investigations also included the establishing of the presence of residue of veterinary medicines and environmental contaminants in raw materials and in the finished product, which was also the aim of this work. [Projekat Ministarstva nauke Republike Srbije, br. TR-20037: Petrovska klobasa - oznaka geografskog porekla u kontrolisanim uslovima]

The drying behaviour of dry-fermented sausage Petrovsk? klob?sa ripened in traditional and industrial conditions has been studied. Obtained results indicated that sausages dried in industrial room (batch I) had higher weight loss and lower water activity (aw) values than counterparts from traditional/artisanal production (batch T). Difference in drying intensity between internal and external fractions of sausages was much more marked for batch I. The experimental data of water content in Petrovsk? klob?sa, dried in respective conditions, were compared with values predicted by seven different mathematical models. Comparing the coefficient of determination (r2), root mean square error (ERMS) and the reduced chi-square (?2) values of all equations, it was concluded that the Page mathematical model satisfactorily represents drying characteristics of Petrovsk? klob?sa both in traditional (0.990; 2.22 x 10-2 and 6.01 x 10-4, respectively) and industrial conditions (0.995; 1.79 x 10-2; 3.91 x 10-4, respectively).

The European market of dry-cured meat products is characterized by a wide range of traditional fermented sausages, which come from different parts of the continent, primarily from the Mediterranean. Production of these products has lasted for centuries and when the first sausage was produced remains uncertain, because its production dates from the period before written history. Traditional dry-fermented sausages, originating from different countries and regions, are characterized by specific sensory and physicochemical properties affected by the environmental conditions, raw materials, production method, activity and composition of present microflora, biochemical and physicochemical changes occurring during the smoking, fermentation, drying, and ripening process, and specificities of the local population (customs, habits, traditions, religion, etc.). Diversity in appearance, color, taste, smell, and texture of these products can contribute to the preservation of gastronomic heritage and culture, as well as economic development of rural areas by increasing consumption and production volume (Santos et al. 1998; Casaburi et al. 2007; Aquilanti et al. 2007; Talon et al. 2007; Latorre-Moratalla et al. 2008; Roseiro et al. 2008; Settanni and Moschetti 2014).

Concentration of cadmium was investigated in the kidney of 480 pigs from 10 different genetic lines, produced in Vojvodina (northern Serbia). This element was determined by flame atomic absorption spectrometry after mineralisation by dry ashing. The genetic line of pigs had no influence on the cadmium levels of kidney ( P > 0.05). The cadmium levels ranged from 0.168 to 1.160 mg/kg, with an average of 0.368 mg/kg. Only 1.9% of kidney slightly exceeded the maximum level set by EU and Serbian legislation.

In this paper we prove the invariance of some causality relationships between flows of information (represented by filtrations) under some types of convergence. We consider a statistical concept of causality which is based on Granger’s definition of causality, but instead of time series we focus on continuous time processes.

In the paper D. Hoover, J. Keisler: Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is hard to prove directly, so we continue the work of Keisler and Hoover in finding sufficient conditions for two stochastic processes to have the same adapted distribution. For this purpose we use the concept of causality between stochastic processes, which is based on Granger’s definition of causality. Also, we provide applications of our results to solutions of some stochastic differential equations.

The content of phosphorous (P), potassium (K), sodium (Na), magnesium (Mg), calcium (Ca), zinc (Zn), iron (Fe), copper (Cu) and manganese (Mn) was investigated in the M. semimembranosus and liver of 69 pigs from 10 different genetic lines, produced in Vojvodina (northern Serbia). Phosphorous was determined by the standard spectrophotometric method. Metals were determined by the flame atomic absorption spectrometry after mineralisation by dry ashing. The difference in the mineral content among the different genetic lines of pigs, reared under the same conditions, was not significant (P > 0.05) in the analysed muscle and liver tissues. The order of the minerals in the meat samples and their content ranges in mg/100 g was K (214–328, on average 280) > P (200–263, on average 225) > Na (39.0–82.7, on average

Petrovac Sausage ( Petrovska Kolbasa ) is a traditional dry fermented sausage from Backi Petrovac (province Vojvodina, Serbia). In this study, the in vitro antioxidant and angiotensin-I converting enzyme (ACE) inhibitory activities in the water-soluble (pH 7.4) protein extracts were evaluated throughout the sausage ripening. In the protein extract from the sausage mixture (day 0) degree of hydrolysis (DH) of 6.07 ± 0.84% was determined, which reached 17.71 ± 0.76% after 90 days. The protein extract at day 0 showed free radical (2.2-diphenyl-1-picrylhydrazyl, DPPH ) scavenging assay (RSA) and reducing power (RP) of 27.61 ± 0.73% and 0.493 ± 0.016, respectively. In fermented sausage at day 90, RSA and RP increased up to 50.08 ± 1.25% and 0.972 ± 0.065%, respectively. The examined protein extracts exhibited ACE inhibitory activity, which also enhanced; from 27.11 ± 2.163% (day 0) to 73.74 ± 3.299% (day 90). These results suggested that in Petrovska Kolbasa , the final products of meat proteins hydrolysis during sausage ripening might be hydrolysates with antioxidant and ACE inhibitory properties.

In this paper we consider different concepts of causality in filtered probability spaces. Especially, we consider a generalization of a causality relationship “G is a cause of J within H ” which was first given by Mykland (1986) and which is based on Granger’s definition of causality (Granger, Econometrica 37:424–438, 1969). Then we apply this concept on weak solutions of stochastic differential equations with driving semimartingales. We also show that the given causality concept is closely connected to the concept of extremality of measures and links Granger’s causality with the concept of adapted distribution. Finally, the concept of causality is applied on solution of martingale problem.

Immune Complexes and Complement in Serum and Synovial Fluid of Rheumatoid Arthritis PatientsRheumatoid arthritis (RA) is predominantly an intraarticular inflammatory and autoimmune disease that involves different autoantibodies and effector mechanisms. The aim of the study was to determine the utility of Circulating Immune Complexes (CIC) and complement components (C3c, C4) as possible markers for the disease activity in laboratory diagnostics. In a cross-section study 59 patients, according to the clinical criteria, were categorized into two groups: group with moderate (MA, n=24), and group with severe activity (SA, n=35) of RA. The concentration of CIC, C3c and C4 in sera (S) and synovial fluids (SF) was examined by an immunonephelometric method in both groups and compared with values in the control group (n=15) of patients with lesions of the menisci. Obtained results showed that there was no statistical significance in the values of C3c and C4, in both biological fluids, among all tested groups. Significant differences were found in the levels of CIC in both fluids, while testing the parameters (× ± SD, IU/mL) in the sera of groups with SA and MA of RA: 7.43 ± 13.40; 3.01 ± 2.92 (p

Arthrosonography and the Biomarker Cartilage Oligomeric Matrix Protein in the Detection of Knee Osteoarthrosis Effusion Osteoarthrosis of the knee is a degenerative disease with inflammatory episodes objectively shown by arthrosonography. Cartilage Oligomeric Matrix Protein - COMP is a useful biomarker for early cartilage destruction. The aim of this paper is a comparative analysis of the clinical, arthrosonographic findings and the COMP concentration in the sera of patients for the detection of joint inflammation. The analysis included 88 patients with knee OA. Clinical examination determined the outflow, arthrosonography the size of synovitis and effusion, and serum analysis the COMP concentration (ng/ml). Minimum outflow had 34.1% of patients, moderate 22.7%, and significant 4.5%. Sensitivity of the clinical diagnosis of outflow is 73%, and specificity 73% (p=0.000). Seventy five percent of patients had effusion; 28.4% of patients in the suprapatellar recessus (SR), 27.3% in the medial (MR), and 62.5% in the lateral (LR). In SR, effusion was 10.13±4.35 mm, MR 8.53±2.27 mm, LR 11.38±4.44 mm. Synovitis was found in 67% of patients, in SR the size of 4.84±3.57 mm, in MR 3.15±1.86 mm, in LR 6.09±2.80 mm. The average value of the size of effusion in patients with significant outflow in SR was 13.85 (10.36-17.43) mm (p=0.000), MR 4.9 (0-10.22) mm (p=0.008), LR 12.0 (11.34-14.50) mm (p=0.000), in LR with moderate outflow 6.94 (1.16-8.13) mm and minimum outflow 4.9 (0-7.25) mm. There is a significant correlation between the size of synovitis and effusion in the SR, MR and LR (p=0.000). The average value of the concentration of COMP in patients without effusion was 54 (44.5-58) ng/ml, with effusion 57 (48.75-64.25) ng/ml (p=0.030). Arthrosonography and the determination of the COMP concentration are sensitive methods for diagnosing joint effusion.

Human glycoprotein of cartilage (YKL-40) synthesizes chondrocytes and synovial cells in inflammatory conditions or remodels the outer cell matrix in osteoarthritis. The aim of this study was to conduct a parallel analysis between thickness of cartilage and length of osteophytes, ultrasound indicators of joint destruction, with levels of YKL-40 in serum in patients with primary osteoarthritis. Ultrasound findings and concentration of YKL-40(ng/ml) were examined in 88 patients. The average value cartilage thickness measured on medial condyles of the femur was 1.30 +/- 0.23 mm and on lateral was 1.39 +/- 0.27 mm. Median YKL-40 in patients with shorter osteophytes was 62.0 (44.5-90) ng/ml, and with longer osteophytes was 119 (range 80-171) ng/ml (p = 0.000). YKL-40 can be a marker for the appearance of longer osteophytes (sensitivity = 79.1%; specificity = 61.9%; cut off = 75.0 ng/ml). The duration of illness is very much connected to values of YKL-40 (r = 0.651, p = 0.000). After an illness duration of five years, the concentration of YKL-40 was 83.68 +/- 33.65 ng/ml, after ten years it was 138.22 +/- 48.88 ng/ml, and after 15 and 20 years it was 209.30 +/- 79.36 ng/ml and 218.50 +/- 106.51 ng/ml, respectively. Higher concentrations of YKL-40 indicate the level of cartilage destruction and can be used for assessment of destruction.

The problem on existence of a minimal Markovian (in the wide sense) process which contains a given stochastic process as a component is considered and partially solved in Rozanov [1977. On Markovian extensions of random process. Theory Probab. Appl. 22 (1), 194–199]. In this paper the problem (to be formulated precisely below) of finding all Markovian (in the wide sense) extensions for a given stochastic process is solved. In the first part of this paper we give some definitions and known results related to splitting subspaces with respect to arbitrary Hilbert spaces. In the second part we apply these results to the problem of finding all Markovian (in the wide sense) extensions of an arbitrary stochastic process. The approach adopted in this paper is that of Lindquist and Picci [1985. On the stochastic realization problem. SIAM J. Control Optim. 17 (3), 365–389] and Rozanov [1977. On Markovian extensions of random process. Theory Probab. Appl. 22 (1), 194–199].

The paper considers a statistical concept of causality in continuous time between filtered probability spaces which is based on Granger’s definition of causality. Then, the given causality concept is connected with a local weak solutions of the stochastic differential equations driven with semimartingales. Also, we establish connection between the local solution and the local weak solution.

We give a survey of known results regarding Schur-convexity of probability distribution functions. Then we prove that the functionF(p 1,...,pn;t)=P(X1+...+Xn≤t) is Schur-concave with respect to (p 1,...,pn) for every realt, whereX i are independent geometric random variables with parametersp i. A generalization to negative binomial random variables is also presented.

In this paper we consider a problem (that follows directly from realization problem): find all minimal Markovian representations for a given family of Hilbert spaces such that each of these two families provides exactly the same amount of information about some other family of Hilbert spaces (see Definition 2.5).

The objective of this study is to determine physical, mechanical and barrier properties of chitosan-laminated collagen film. Commercial collagen film, which is used for making collagen casings for dry fermented sausage production, was laminated with chitosan film layer in order to improve the collagen film barrier properties. Different volumes of oregano essential oil per 100 mL of filmogenic solution were added to chitosan film layer: 0, 0.2, 0.4, 0.6 and 0.8 mL to optimize water vapour barrier properties. Chitosan layer with 0.6 or 0.8 % of oregano essential oil lowered the water vapour transmission rate to (1.85±0.10)·10–6 and (1.78±0.03)·10–6 g/(m2·s·Pa) respectively, compared to collagen film ((2.51±0.05)·10–6 g/(m2·s·Pa)). However, chitosan-laminated collagen film did not show improved mechanical properties compared to the collagen one. Tensile strength decreased from (54.0±3.8) MPa of the uncoated collagen film to (36.3±4.0) MPa when the film was laminated with 0.8 % oregano essential oil chitosan layer. Elongation at break values of laminated films did not differ from those of collagen film ((18.4±2.7) %). Oxygen barrier properties were considerably improved by lamination. Oxygen permeability of collagen film was (1806.8±628.0)·10–14 cm3/(m·s·Pa) and values of laminated films were below 35·10–14 cm3/(m·s·Pa). Regarding film appearance and colour, lamination with chitosan reduced lightness (L) and yellowness (+b) of collagen film, while film redness (+a) increased. These changes were not visible to the naked eye., Svrha je ovoga rada bila odrediti fizikalna i kemijska svojstva, te propusnost kolagenskog filma prevučenog kitozanom. Komercijalni kolagenski film, koji se upotrebljava za izradu crijeva za kobasice, prevučen je kitozanom radi poboljšanja propusnosti. Filmu su dodane različite količine esencijalnog ulja origana (0; 0,2; 0,4; 0,6 i 0,8 mL u 100 mL otopine filma), čime se optimirala njegova propusnost za vodenu paru. Sloj kitozana s dodatkom 0,6 % esencijalnog ulja origana smanjio je transmisiju vodene pare na (1,85±0,10)·10-6, a s dodatkom 0,8 % ulja origana na (1,78±0,03)·10-6 g/(m2·s·Pa), u usporedbi s kolagenskim filmom ((2,51±0,05)·10-6 g/(m2·s·Pa)). Film prevučen kitozanom nije imao bolja mehanička svojstva od kolagenskog filma. Granična se čvrstoća filma prevučenog kitozanom s dodatkom 0,8 % esencijalnog ulja origana smanjila s (54,03±3,77) na (36,29±4,02) MPa. Vrijednosti se istezljivosti kolagenskih filmova nisu razlikovale od onih filmova prevučenih kitozanom. Propusnost je kisika znatno poboljšana dodatkom kitozana, pa je u kolagenskom filmu iznosila (1806,79±628,01)·10-14 cm3/(m·s·Pa), a u filmu prevučenom kitozanom 35·10-14 cm3/(m·s·Pa). Dodatkom su se kitozana promijenili izgled i boja filma, tj. smanjio se intenzitet osvjetljenja (L) i žute (+b) boje, a pojačao intenzitet crvene (+a), što nije bilo vidljivo golim okom.

Petrovska Klobasa is an artisan Serbian sausage made only from meat and spices without any additives or starter cultures. In order to characterise lactic acid bacteria (LAB) microflora, a total number of 404 LAB strains were isolated from 15 samples collected during 90 days of the fermentation and 120 days of storage of one batch of Petrovska Klobasa. The isolates were preliminarily identified by phenotypic tests and subjected to (GTG) 5 -PCR fingerprinting. Representatives of each group were identified by 16S rDNA sequencing. The results showed that among the isolates, Lactobacillus sakei and Leuconostoc mesenteroides predominate with 36.4% and 37.1% of total LAB strains, respectively. Pediococcus pentosaceus was also isolated in high proportion (18.4%) whereas Enterococcus durans and Enterococcus caseliflavus made only 1% and 6% of the total isolates, correspondingly. The analysis of vacuum packed and modified atmosphere packed (MAP) samples showed higher presence of L. mesenteroides and L. sakei in the total microflora.

The effect of rapid air chilling of carcasses in the first 3 h of chilling at -31°C (then at 2-4°C, till 24 h post-mortem) and the possibility of earlier deboning (8 h post-mortem) after rapid air chilling, compared to conventional air chilling (at 2-4°C, till 24 h post-mortem) on weight loss and technological quality (pH value, tenderness, drip loss, cooking loss and colour - L(∗)a(∗)b(∗) values) of pork M. semimembranosus was investigated. Under the rapid chilling conditions, weight loss was 0.8% at 8 h post-mortem and increased to 1.4% at 24 h post-mortem when weight loss was 2.0% under conventional chilling. Carcasses that were rapid chilled had significantly lower (P0.001) internal temperature in the deep leg at 4 (25.7°C), 6 (13.0°C), 8 (6.2°C) and 24 h (3.8°C) post-mortem compared to conventional chill treatment (32.7, 24.2, 19.1 and 5.1°C, respectively). Rapid chilling reduced significantly (P0.05) the rate of pH value decline at 8 h (6.02) post-mortem in M. semimembranosus compared to conventional chill treatment (5.88). Compared to conventional chilling, in M. semimembranosus deboned in different time post-mortem, rapid chilling had a positive significant effect on drip loss (P0.05, muscles deboned 8 h post-mortem), cooking loss (P0.001) and incidence of pale colour (L(∗) value). Rapid chilling i.e. rapid chilling and earlier deboning had neither positive nor negative significant effects (P0.05) on other investigated technological quality parameters of M. semimembranosus (tenderness, a(∗) value and b(∗) value) compared to conventional chilling.