Scaling in a general class of critical random Boolean networks

We derive analytically the scaling behavior in the thermodynamic limit of the number of nonfrozen and relevant nodes in the most general class of critical Kauffman networks for any number of inputs per node, and for any choice of the probability distribution for the Boolean functions. By defining and analyzing a stochastic process that determines the frozen core we can prove that the mean number of nonfrozen nodes in any critical network with more than one input per node scales with the network size $N$ as $N^{2/3}$, with only $N^{1/3}$ nonfrozen nodes having two nonfrozen inputs and the number of nonfrozen nodes with more than two inputs being finite in the thermodynamic limit. Using these results we can conclude that the mean number of relevant nodes increases for large $N$ as $N^{1/3}$, with only a finite number of relevant nodes having two relevant inputs, and a vanishing fraction of nodes having more than three of them. It follows that all relevant components apart from a finite number are simple loops, and that the mean number and length of attractors increases faster than any power law with network size.Comment: 11 page

Inverse targeting -- an effective immunization strategy

We propose a new method to immunize populations or computer networks against epidemics which is more efficient than any method considered before. The novelty of our method resides in the way of determining the immunization targets. First we identify those individuals or computers that contribute the least to the disease spreading measured through their contribution to the size of the largest connected cluster in the social or a computer network. The immunization process follows the list of identified individuals or computers in inverse order, immunizing first those which are most relevant for the epidemic spreading. We have applied our immunization strategy to several model networks and two real networks, the Internet and the collaboration network of high energy physicists. We find that our new immunization strategy is in the case of model networks up to 14%, and for real networks up to 33% more efficient than immunizing dynamically the most connected nodes in a network. Our strategy is also numerically efficient and can therefore be applied to large systems

Number and length of attractors in a critical Kauffman model with connectivity one

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a frozen and a disordered phase, and is therefore used for studies of real network problems. We prove here that the mean number and mean length of attractors in critical random Boolean networks with connectivity one both increase faster than any power law with network size. We derive these results by generating the networks through a growth process and by calculating lower bounds.Comment: 4 pages, no figure, no table; published in PR

The phase diagram of random threshold networks

Threshold networks are used as models for neural or gene regulatory networks. They show a rich dynamical behaviour with a transition between a frozen and a chaotic phase. We investigate the phase diagram of randomly connected threshold networks with real-valued thresholds h and a fixed number of inputs per node. The nodes are updated according to the same rules as in a model of the cell-cycle network of Saccharomyces cereviseae [PNAS 101, 4781 (2004)]. Using the annealed approximation, we derive expressions for the time evolution of the proportion of nodes in the "on" and "off" state, and for the sensitivity $\lambda$. The results are compared with simulations of quenched networks. We find that for integer values of h the simulations show marked deviations from the annealed approximation even for large networks. This can be attributed to the particular choice of the updating rule.Comment: 8 pages, 6 figure

Assessment of heavy metal load in chub liver (Cyprinidae – Leuciscus cephalus) from the Nišava River (Serbia)

The Nišava River plays an important role as the source for both drinking water and agricultural irrigation dueto its hydrological and geomorphological characteristics as the largest river in the region of southeast Serbia.In this study we used the liver of the chub (Leiciscus cephalus) as a tool for biomonitoring heavy metalaccumulation along the river. Chub specimens were sampled from two localities (one at the border withBulgaria and a second in the city of Niš). Concentrations were estimated for six heavy metals (iron,cadmium, copper, zinc, lead and manganese) in chub liver. Low bioconcentration level was observed formost of the metals and the concentrations corresponded to the nominal concentration in livers of fishinhabiting metal unpolluted streams and rivers. However, cadmium concentration in the chub liver exceeded0.5 mg kg-1, a several hundred folds increase from nominal concentration indicating a potential toxicexposure of the fish and of the stream ecosystem to this heavy metal. Hepatosomatic indices were calculatedand tested for the impact of metal concentrations on liver size. A decrease of the hepatic index was observedin fish with higher cadmium concentration, suggesting a possible impact on the health of the chub populationin the Nišava River

Mycotoxins in pathophysiology of cattle diet

Depending on the age and production category, cattle show different sensitivity towards certain mycotoxins. Microflora of the rumen degrades to a different degree and inactivates mycotoxins. In the work are presented the most important mycotoxicoses of cattle caused by fungal metabolites from the genera Fusarium, Aspergillus and Penicillium. Poisoning of cattle in our area is most often caused by Zearalenone, Dioxinivalenol, T-2 toxin, Ochratoxin A and Aflatoxin, but in the work are also presented Fumonisin B1 and B2. The work also describes preventive possibilities and protection of animal health from the effects of mycotoxins

Use of Probiotics as Growth Promoters and Immunostimulators in Fingerlings of Cyprinid Fish Species

Intensive aquaculture production has required the development of an individual’s resistance to disease rather than depending upon antibiotics or chemotherapeutics. The role of gastrointestinal microflora in disease resistance has been established in many fish species, which has led to the concept of manipulating gastrointestinal microflora for better health management. A number of studies has been conducted in different fish species with various useful microorganisms called ‘probiotics’ to amplify gastrointestinal microflora to fight against various infectious diseases. Probiotics are beneficial microorganisms which protect the host from diseases. Probiotic protection can be achieved by various mechanisms. Most probiotics used in aquaculture belong to the lactic acid bacteria, the genus Bacillus, the photosynthetic bacteria, the yeast, notwithstanding other genera and species have also been used. The immunostimulatory effect of probiotics has been established in many fish species, but their direct involvement in the immune response is not well established. It has also been proven that the application of probiotics in aquaculture has beneficial effects on growth of fish as well as on the environment. At present, data about the efficacy of probiotics in commercial aquaculture of Serbia is still lacking. This review discusses mainly the studies and applications about effects, problems and perspectives of probiotics used in fingerlings of cyprinid fish species, and highlights immunostimulatory effects and growth promotion effects of commercial probiotic products. In the present paper the results that show positive influence of probiotics in cyprinides nutrition on production performance and immune system are summarized. Special accent is given to criteria for proper selection of probiotics in cyprinides production

Vanadijum u ishrani živine

Vanadium (V) is essential element for poultry nutrition. Relatively low level of V ( lt 10 μg/kg of feed) is known to reduce both growth in chicks and Haugh unit value of eggs. The National Research Council (NRC) recommends the presence of very low levels of V in poultry diets, with the maximum tolerance level (MTL) being 10 mg/kg. Excessive vanadium in poultry diets has been shown to be detrimental to egg production, interior quality of eggs (albumen height), body weight and feed consumption. There is little information on the content of V in feedstuffs. Phosphates are known to be the cause of excessive V in various types of poultry diets. The objective of this study was to obtain information about the content of vanadium in phosphates and poultry feed. The samples were prepared by microwave wet digestion. Content of V was determined by the method of coupled plasma with mass spectrometry on the Agilent ICP-MS 7700. The concentrations of vanadium determined in the examined samples were above the minimum recommended levels for poultry feed, still not exceeding the maximum tolerable values.Vanadijum (V) je esencijalni element u ishrani živine. Relativno niski nivoi V ( lt 10 mg) smanjuju porast pilića i vrednosti Haugh-ovih jedinica jaja. The National Research Council (NRC) preporučuje veoma niske nivoe V u hrani za živinu, pri čemu je za maksimalni nivo tolerancije utvrđena vrednost od 10 mg/kg. Višak vanadijuma u ishrani živine ispoljava štetne efekte u proizvodnji jaja, negativno utiče na unutrašnji kvalitet jaja, telesnu masu živine i efikasnost iskorišćavanja hrane. Podaci o sadržaju V u hrani i hranivima za životinje su oskudni, ali zna se da fosfatna mineralna hraniva često sadrže visoke koncentracije ovog elementa. Cilj ovog istraživanja je bio da se dobiju informacije o sadržaju vanadijuma u hranivima i hrani za živinu. Uzorci hrane za životinje su pripremljeni mikrotalasnom digestijom, a sadržaj V je određen metodom indukovano kuplovane plazme sa masenom spektrometrijom (ICP-MS). Koncentracije vanadijuma u ispitivanim uzorcima bile su iznad minimalnih preporučenih nivoa u ishrani živine, ali nisu prelazile maksimalne tolerantne vrednosti za živinu za ovaj element

Inter-arrival times of message propagation on directed networks

One of the challenges in fighting cybercrime is to understand the dynamics of message propagation on botnets, networks of infected computers used to send viruses, unsolicited commercial emails (SPAM) or denial of service attacks. We map this problem to the propagation of multiple random walkers on directed networks and we evaluate the inter-arrival time distribution between successive walkers arriving at a target. We show that the temporal organization of this process, which models information propagation on unstructured peer to peer networks, has the same features as SPAM arriving to a single user. We study the behavior of the message inter-arrival time distribution on three different network topologies using two different rules for sending messages. In all networks the propagation is not a pure Poisson process. It shows universal features on Poissonian networks and a more complex behavior on scale free networks. Results open the possibility to indirectly learn about the process of sending messages on networks with unknown topologies, by studying inter-arrival times at any node of the network.Comment: 9 pages, 12 figure

Efekat upotrebe fitaze na proizvodne rezultate i čvrstinu tibije brojlera

The effect of microbial phytase in corn/soybean meal diets for broilers on performances and tibia characteristics were investigated. The trial was carried out on 200 Arbor Acres broilers of both sexes divided into four groups. The broilers were fed with complete mixtures with different levels of P (0.80 and 0.57% total P and 0.46 and 0.25% available P), with or without phytase. Reduction of the dietary total and available P levels for experimental broilers induced lower body mass and gain as well as higher fed conversion. However, by introduction phytase into diets negative effects of phosphorus reduction were, to some extent alleviated. Addition of phytase into diets decreased serum Ca and increased serum P. Reduction of the dietary P level had no significant effect on serum Ca, but had negative effects on serum P (p (lt) 0.01). The obtained results of bone analysis show that phytase was effective in increasing investigated parameters, but no significant differences were found among groups.Ispitivan je uticaj mikrobijalne fitaze dodate smešama na bazi kukuruza i sojine sačme na proizvodne rezultate i čvrstinu tibije brojlera. Brojleri podeljeni u 4 grupe, su hranjeni obrocima sa različitim količinama P (0,80 i 0,57% ukupnog P i 0,46 i 0,25% iskoristivog P), bez ili sa dodatkom fitaze. Smanjivanje sadržaja P u smešama izazvalo je proporcionalno smanjivanje telesne mase, dnevnog prirasta i pogoršanje konverzije hrane, dok je dodatak fitaze doprineo poboljšanju vrednosti ispitivanih parametara. Dodatkom fitaze uočeno je smanjivanje koncentracije Ca, odnosno povećanje koncentracije P u krvi. Smanjivanje sadržaja P u smešama, nije imalo značajan uticaj na koncentraciju Ca, ali je značajno negativno uticalo na koncentraciju P u krvi (p (lt) 0,01). Dodatak fitaze u smeše sa smanjenom količinom P nije značajno uticao na koncentraciju Ca i P u krvi. Dodatak fitaze u smeše sa adekvatnim i smanjenim sadržajem P doprineo je povećanju čvrstine tibije, sadržaj pepela i Ca u tibiji. Dodatak fitaze nije imao posebno izražene efekte na sadržaj fosfora u tibiji