Observing scale-invariance in non-critical dynamical systems

Recent observation for scale invariant neural avalanches in the brain have been discussed in details in the scientific literature. We point out, that these results do not necessarily imply that the properties of the underlying neural dynamics are also scale invariant. The reason for this discrepancy lies in the fact that the sampling statistics of observations and experiments is generically biased by the size of the basins of attraction of the processes to be studied. One has hence to precisely define what one means with statements like `the brain is critical'. We recapitulate the notion of criticality, as originally introduced in statistical physics for second order phase transitions, turning then to the discussion of critical dynamical systems. We elucidate in detail the difference between a 'critical system', viz a system on the verge of a phase transition, and a 'critical state', viz state with scale-invariant correlations, stressing the fact that the notion of universality is linked to critical states. We then discuss rigorous results for two classes of critical dynamical systems, the Kauffman net and a vertex routing model, which both have non-critical states. However, an external observer that samples randomly the phase space of these two critical models, would find scale invariance. We denote this phenomenon as 'observational criticality' and discuss its relevance for the response properties of critical dynamical systems

Criticality in conserved dynamical systems: Experimental observation vs. exact properties

Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for these routing models and governed by cyclic attractors. We consider two classes of information flow, Markovian routing without memory and vertex routing involving a one-step routing memory. Investigating the respective cycle length distributions for complete graphs we find log corrections to power-law scaling for the mean cycle length, as a function of the number of vertices, and a sub-polynomial growth for the overall number of cycles. When observing experimentally a real-world dynamical system one normally samples stochastically its phase space. The number and the length of the attractors are then weighted by the size of their respective basins of attraction. This situation is equivalent to `on the fly' generation of routing tables for which we find power law scaling for the weighted average length of attractors, for both conserved routing models. These results show that critical dynamical systems are generically not scale-invariant, but may show power-law scaling when sampled stochastically. It is hence important to distinguish between intrinsic properties of a critical dynamical system and its behavior that one would observe when randomly probing its phase space

Decoding neighbour volatiles in preparation for future competition and implications for tritrophic interactions

Plant volatile signals can provide important information about the physiological status and genetic identity of the emitter, and nearby plants can use this information to detect competitive neighbours. The novelty of these signals is that plants eavesdropping to volatiles of undamaged neighbours respond with typical competition responses, even before competition takes place, initiating specific growth responses that can increase their competitive capacity. This preparing for future competition mechanism affects the behaviour and abundance of herbivore pests and their natural enemies. Previously, such responses were only known to occur in response to volatiles released by damaged plants. However, volatile interactions occur only in specific combination of species/genotypes, indicating that plants use volatile signals in the detection and adaption only to substantial competitive neighbours. (C) 2016 The Author(s). Published by Elsevier GmbH

Uticaj termina prikraćivanja mladara na karakteristike letorasta kod kruške (Pyrus communis L)

U voćarskoj proizvodnji Republike Srpske (BiH) posle jabuke i šljive kruška ima najveći ekonomski značaj. Dominantna upotreba sejanca divlje kruške (Pyrus communis L) kao podloge, uslovljava intenzivan porast i odloženo stupanje u plodonošenje. Intenzivan vegetativan porast u prvim godinama uzgoja utiče na formiranje dugih letorasta sa formiranjem mešovitih pupoljaka na vrhu porasta, koje najčešće prati odumiranje tačaka rasta u njihovom baznom delu. Cilj rada je ispitivanje uticaja termina prikraćivanja mladara tokom vegetacije na karakteristike rasta i razvoja letorasta kod kruške. Istraživanje je izvršeno u proizvodnom zasadu kruške, starosti 2 godine koji se nalazi u selu Jasenje (45o 09' 32'',16o 44' 43'') opština Kozarska Dubica. Voćnjak je površine 1,2 ha sa ukupno 1350 sadnica. U sortimentu dominira sorta Vilijamovka, sa sortama Abate fetel i Pakhams trijumf kao pratećim. Sve sorte su kalemljene na sejancu divlje kruške (Pyrus communis L). Uzgojni oblik je vitko vreteno i u zasadu se primenjuju standardne pomotehničke i agrotehničke mere. Tretmani novoformiranih mladara na stožini izvršeni su tokom 2015. godine, a analiza formiranih letorasta obavljena je početkom 2016. godine. Mladari su prikraćeni na dužinu od 10 pupoljaka u tri različita termina u periodu intenzivnog porasta, počevši od 25.05.2015. godine; II termin – 15.06.2015. i III termin – 05.07.2015. Razmak između prikraćivanja je u proseku 20 dana. Kontrolni mladari nisu prikraćivani. Svaki tretman je izvršen na po 20 mladara (10 stabala sa po 2 mladara). Kod formiranih letorasta izvršena je analiza rasta (broj novih prirasta i njihova prosečna i ukupna dužina) i razvoja (karakteristike formiraih prirasta, kao i broj formiranih mešovitih pupoljaka). Sve ispitivane sorte najbolju reakciju u pogledu inciranja novih tačaka rasta i intenziteta obrastanja, pokazale su pri prikraćivanju u prvom terminu. Intenzitet obrastanja predstavlja sortnu karakteristiku i najizraženiji je kod sorte Abate fetel, bez obzira na termin prikraćivanja

Talking Different Languages: The Role of Plant-Plant Communication When an Invader Beats up a Strange Neighborhood

Communication through airborne volatile organic compounds (VOCs) and root exudates plays a vital role in the multifarious interactions of plants. Common ragweed (Ambrosia artemesiifolia L.) is one of the most troublesome invasive alien species in agriculture. Below- and aboveground chemical interactions of ragweed with crops might be an important factor in the invasive species' success in agriculture. In laboratory experiments, we investigated the contribution of intra- and interspecific airborne VOCs and root exudates of ragweed to its competitiveness. Wheat, soybean, and maize were exposed to VOCs emitted from ragweed and vice versa, and the adaptation response was measured through plant morphological and physiological traits. We observed significant changes in plant traits of crops in response to ragweed VOCs, characterized by lower biomass production, lower specific leaf area, or higher chlorophyll contents. After exposure to ragweed VOCs, soybean and wheat produced significantly less aboveground dry mass, whereas maize did not. Ragweed remained unaffected when exposed to VOCs from the crops or a conspecific. All crops and ragweed significantly avoided root growth toward the root exudates of ragweed. The study shows that the plant response to either above- or belowground chemical cues is highly dependent on the identity of the neighbor, pointing out the complexity of plant-plant communication in plant communities

Context-Dependent Risk Aversion: A Model-Based Approach

Most research on risk aversion in behavioral science with human subjects has focused on a component of risk aversion that does not adapt itself to context. More recently, studies have explored risk aversion adaptation to changing circumstances in sequential decision-making tasks. It is an open question whether one can identify evidence, at the single subject level, for such risk aversion adaptation. We conducted a behavioral experiment on human subjects, using a sequential decision making task. We developed a model-based approach for estimating the adaptation of risk-taking behavior with single-trial resolution by modeling a subject's goals and internal representation of task contingencies. Using this model-based approach, we estimated the subject-specific adaptation of risk aversion depending on the current task context. We found striking inter-subject variations in the adaptation of risk-taking behavior. We show that these differences can be explained by differences in subjects' internal representations of task contingencies and goals. We discuss that the proposed approach can be adapted to a wide range of experimental paradigms and be used to analyze behavioral measures other than risk aversion