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 Mathematics , 2009, Abstract: In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the function spaces (cell spaces) defined by graphs and state spaces and Gibbs measure $\mu$. For finite graphs we find some evolution subalgebras and other useful properties of the algebras. We obtain a structure theorem for evolution algebras when graphs are finite and connected. We prove that for a fixed finite graph, the function spaces has a unique algebraic structure since all evolution algebras are isomorphic to each other for whichever Gibbs measures assigned. When graphs are infinite graphs then our construction allows a natural introduction of thermodynamics in studying of several systems of biology, physics and mathematics by theory of evolution algebras.
 BMC Evolutionary Biology , 2007, DOI: 10.1186/1471-2148-7-195 Abstract: AFLP analyses resolved the phylogenetic relationships of the Perissodini, strongly supporting monophyly for each species. The character reconstruction of feeding ecology based on the AFLP tree suggested that scale eating evolved from general carnivorous feeding to highly specialized scale eating. Furthermore, scale eating is suggested to have evolved in deepwater habitats in the lake. Oral jaw tooth shape was also estimated to have diverged in step with specialization for scale eating.The present evolutionary analyses of feeding ecology and morphology based on the obtained phylogenetic tree demonstrate for the first time the evolutionary process leading from generalised to highly specialized scale eating, with diversification in feeding morphology and behaviour among species.Cichlid fishes in the East African Great Lakes exhibit a remarkable diversity of feeding ecology, morphology and behaviour [1]. Lake Tanganyika, the oldest of these lakes with an estimated age of 9–12 Myr [2], contains the the most morphologically and ecologically complex species flock of cichlid fishes [3]. Scale-eating cichlids of the tribe Perissodini is prehaps among the most specialized cichlids [1]. The endemic tribe Perissodini comprises nine species [4,5]. Liem & Stewart [6] classified them into two genera, Perissodus, which includes all scale eaters identified so far in the lake, and Haplotaxodon. We follow their classification here, although Poll [5] further subdivided the former genus into three genera, Perissodus (P. microlepis and P. eccentricus), Plecodus (P. multidentatus, P. paradoxus, P. elaviae, P. straeleni) and Xenochromis (P. hecqui).The scale eaters are characterised by unique oral jaw teeth that vary in shape among species, showing functional specialization to scale eating [6]. Among the species, P. microlepis and P. straeleni, which syntopically inhabit shallow rocky regions of the lake [7], show specialized feeding techniques, employing a variety of specialized morpholog
 Physics , 1999, DOI: 10.1088/0951-7715/13/6/303 Abstract: Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct connection between dynamics and Irreversible Thermodynamics has been claimed to have been found. However, the main quantity used in these studies is a (coarse-grained) Gibbs entropy, which to us does not seem suitable, in its present form, to characterize nonequilibrium states. Various simplified models have also been devised to give explicit examples of how the coarse-grained approach may succeed in giving a full description of the Irreversible Thermodynamics. We analyze some of these models pointing out a number of difficulties which, in our opinion, need to be overcome in order to establish a physically relevant connection between these models and Irreversible Thermodynamics.
 V. Ihnatovych Physics , 2013, Abstract: The analysis of the arguments within the limits of the classical thermodynamics that lead to the Gibbs paradox was made. Features of preconditions used in the derivation of the entropy of mixing of ideal gases that caused the appearance of paradox were established. It was shown that the Gibbs paradox has not connection with the assumption of discrete differences between the parameters of different gases.
 V. Ihnatovych Physics , 2013, Abstract: The formulas for the entropy of ideal gases mixture and the entropy change in mixing of ideal gases on the basis of the third law of thermodynamics were obtained. It is shown that when using these formulas, the Gibbs paradox within the framework of classical thermodynamics does not arise.
 Physics , 2015, Abstract: To solve a long-standing problem of condensed matter physics with determining a proper description of the thermodynamic evolution of the time scale of molecular dynamics near the glass transition, we extend the well-known Adam-Gibbs model to describe the temperature-volume dependence of structural relaxation times, ${\tau}_{\alpha} (T,V)$. We employ the thermodynamic scaling idea reflected in the density scaling power law, ${\tau}_{\alpha}=f(T^{-1} V^{-\gamma } )$, recently acknowledged as a valid unifying concept in the glass transition physics, to discriminate between physically relevant and irrelevant attempts at formulating the temperature-volume representations of the Adam-Gibbs model. As a consequence, we determine a straightforward relation between the structural relaxation time ${\tau}_{\alpha}$ and the configurational entropy $S_c$, giving evidence that also $S_c (T,V)=g(T^{-1} V^{-\gamma} )$ with the exponent {\gamma} that enables to scale ${\tau}_{\alpha} (T,V)$. This important finding has meaningful implications for the linkage between thermodynamics and molecular dynamics near the glass transition, because it implies that ${\tau}_{\alpha}$ can be scaled with $S_c$.
 Leonid S. Metlov Physics , 2010, DOI: 10.1103/PhysRevLett.106.165506 Abstract: A new approach - nonequilibrium evolution thermodynamics, is compared with classical variant of Landau approach
 PLOS Computational Biology , 2010, DOI: 10.1371/journal.pcbi.1000719 Abstract: Organismal development and many cell biological processes are organized in a modular fashion, where regulatory molecules form groups with many interactions within a group and few interactions between groups. Thus, the activity of elements within a module depends little on elements outside of it. Modularity facilitates the production of heritable variation and of evolutionary innovations. There is no consensus on how modularity might evolve, especially for modules in development. We show that modularity can increase in gene regulatory networks as a byproduct of specialization in gene activity. Such specialization occurs after gene regulatory networks are selected to produce new gene activity patterns that appear in a specific body structure or under a specific environmental condition. Modules that arise after specialization in gene activity comprise genes that show concerted changes in gene activities. This and other observations suggest that modularity evolves because it decreases interference between different groups of genes. Our work can explain the appearance and maintenance of modularity through a mechanism that is not contingent on environmental change. We also show how modularity can facilitate co-option, the utilization of existing gene activity to build new gene activity patterns, a frequent feature of evolutionary innovations.
 Physics , 2005, DOI: 10.1103/PhysRevE.73.066119 Abstract: The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small difference, but vanishes for identical gases. The resolution offered in the literature, with help of quantum mixing entropy, was later shown to be unsatisfactory precisely where it sought to resolve the paradox. Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining the paradox, since it does not deal explicitly with the difference between the gases. The proper approach employs quantum thermodynamics, which deals with finite quantum systems coupled to a large bath and a macroscopic work source. Within quantum thermodynamics, entropy generally looses its dominant place and the target of the paradox is naturally shifted to the decrease of the maximally available work before and after mixing (mixing ergotropy). In contrast to entropy this is an unambiguous quantity. For almost identical gases the mixing ergotropy continuously goes to zero, thus resolving the paradox. In this approach the concept of difference between the gases'' gets a clear operational meaning related to the possibilities of controlling the involved quantum states. Difficulties which prevent resolutions of the paradox in its entropic formulation do not arise here. The mixing ergotropy has several counter-intuitive features. It can increase when less precise operations are allowed. In the quantum situation (in contrast to the classical one) the mixing ergotropy can also increase when decreasing the degree of mixing between the gases, or when decreasing their distinguishability. These points go against a direct association of physical irreversibility with lack of information.
 BMC Evolutionary Biology , 2010, DOI: 10.1186/1471-2148-10-159 Abstract: The specialized parasites were most infective on their own isofemale line and least infective on other isofemale lines, while the generalist parasites had intermediate infection success on all lines. The success of a specialist on its matched mosquito line was negatively correlated with its success on other lines, suggesting an evolutionary cost to specialization. This trade-off was corroborated by the observation that the generalists had higher average mean infectivity than the specialists over all isofemale lines.Overall, our experiment reveals the potential for specialization of a parasite to individual genotypes of its host and provides experimental evidence of the cost associated with the evolution of specialization, an important feature for understanding the coevolutionary dynamics between hosts and parasites.Parasitic species' strategies of host exploitation fall into a very wide range, from specialists, which can infect and develop in a restricted variety of hosts, to generalists, which can use a wide range of hosts. Specialization on a given host is a selective process that increases the fitness of the parasite on this host. If the host population is homogeneous and remains constant through time, evolution is expected to favor parasites that are best adapted to this host, and therefore select for specialist strategies. On the other hand, the selective pressures operating in variable or heterogeneous host populations can mitigate this specialization process [1,2]. If evolution of the parasite is rapid with respect to the time scale of variation, temporal variation in a host population might lead to repeated evolution of parasites specialized on the different hosts, as has been observed for example in bacteriophages adapting to alternate hosts [3].In a more rapidly changing or spatially heterogeneous host population, a parasite might find itself exposed to a variety of possible hosts. In this context, theory predicts that evolution favors parasitic strategies
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