Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.

Extending the roughness of the data via transitive closures of similarity indexes

One main assumption in the theory of rough sets applied to information tables is that the elements that exhibit the same information are indiscernible (similar) and form blocks that can be understood as elementary granules of knowledge about the universe. We propose a variant of this concept defining a measure of similarity between the elements of the universe in order to consider that two objects can be indiscernible even though they do not share all the attribute values because the knowledge is partial or uncertain. The set of similarities define a matrix of a fuzzy relation satisfying reflexivity and symmetry but transitivity thus a partition of the universe is not attained. This problem can be solved calculating its transitive closure what ensure a partition for each level belonging to the unit interval [0,1]. This procedure allows generalizing the theory of rough sets depending on the minimum level of similarity accepted. This new point of view increases the rough character of the data because increases the set of indiscernible objects. Finally, we apply our results to a not real application to be capable to remark the differences and the improvements between this methodology and the classical one

Truth, laws and the progress of science

In this paper I analyze the difficult question of the truth of mature scientific theories by tackling the problem of the truth of laws. After introducing the main philosophical positions in the field of scientific realism, I discuss and then counter the two main arguments against realism, namely the pessimistic meta-induction and the abstract and idealized character of scientific laws. I conclude by defending the view that well-confirmed physical theories are true only relatively to certain values of the variables that appear in the laws.

Structural aspects and floristic similarity among tropical dry forest fragments with different management histories in northern Minas Gerais, Brazil

In order to produce useful knowledge to the initiatives of protection and management of forest fragments, more specifically for tropical dry forests which suffer with frequent anthropic activities, and due to the lack of specific studies, this article aimed describe the structure and the floristic similarity among three areas of dry forest with different management histories. The study was developed in Capitão Enéas municipality, Northern Minas Gerais, Brazil, where three fragments were evaluated, being one in regeneration for 30 years, another submitted to occasional fire and the third with selective cut in small scale. The sampling was developed through the point quarter method considering all the alive phanerophyte individuals with circumference at breast height (CBH) > 15 cm. In the three fragments, 512 individuals, distributed in 60 species, 47 genera, and 23 families were sampled. The most representative families were Fabaceae (26), Anacardiaceae (4), Bignoniaceae (3) and Combretaceae (3). However, fourteen families were represented by only one species. Only eight species were common to all fragments - Myracrodruon urundeuva standed out with 26.9% of all sampled individuals - while a great number of species were exclusive of each fragment. The floristic and structural differences between the fragments are possibly related to the history and intensity of management in each area besides the topography variations and the presence or absence of limestone outcrops. These results show the importance of each fragment, indicating that the loss of anyone would cause negative impacts on the regional flora and consequently to the associated biodiversity.

Feature selection using Fuzzy Entropy measures with Yu's Similarity measure

In this study, feature selection in classification based problems is highlighted. The role of feature selection methods is to select important features by discarding redundant and irrelevant features in the data set, we investigated this case by using fuzzy entropy measures. We developed fuzzy entropy based feature selection method using Yu's similarity and test this using similarity classifier. As the similarity classifier we used Yu's similarity, we tested our similarity on the real world data set which is dermatological data set. By performing feature selection based on fuzzy entropy measures before classification on our data set the empirical results were very promising, the highest classification accuracy of 98.83% was achieved when testing our similarity measure to the data set. The achieved results were then compared with some other results previously obtained using different similarity classifiers, the obtained results show better accuracy than the one achieved before. The used methods helped to reduce the dimensionality of the used data set, to speed up the computation time of a learning algorithm and therefore have simplified the classification task

Conservation laws for non-potential operators

The aim of this work is to study the conservation laws of continuous means mechanics and also to extend the Hamiltonian method for these kind of systems in order to valid for non-potential operators through variational approach. Besides illustrating with various examples of mechanical applications we also introduce in this work the new technique in order to treat such problems as the non-potential problem.

Constitutive laws for strong geometric non-linearity

This paper is divided into two different parts. The first one provides a brief introduction to the fractal geometry with some simple illustrations in fluid mechanics. We thought it would be helpful to introduce the reader into this relatively new approach to mechanics that has not been sufficiently explored by engineers yet. Although in fluid mechanics, mainly in problems of percolation and binary flows, the use of fractals has gained some attention, the same is not true for solid mechanics, from the best of our knowledge. The second part deals with the mechanical behavior of thin wires subjected to very large deformations. It is shown that starting to a plausible conjecture it is possible to find global constitutive equations correlating geometrical end energy variables with the fractal dimension of the solid subjected to large deformations. It is pointed out the need to complement the present proposal with experimental work.

Similarity among periphyton algal communities in a lentic-lotic gradient of the upper Paraná river floodplain, Brazil

Floristic comparison of periphyton communities from three systems with different hydrodynamic regimes (lentic, semilotic, and lotic) was carried out during high and low water periods on the Upper Paraná River floodplain. For each period and system, glass slides were sampled every two days during 18-day periods, and Eichhornia azurea Kunth petioles were sampled three times. A total of 228 species was collected, representing 12 classes, mainly diatoms and desmids. The highest species-richness was found in communities from lentic system and during high water. Species richness in the lotic system was more stable over succession and hydrological periods. Algal taxonomic structure in river community was clearly separated from the other two systems, with 43% of similarity level. The hydrological period was next in importance, followed last by the substratum type, with communities associated at 65-78% similarity levels, depending on system and hydrological period. The type of system, but not the water levels,was the main factor that influenced community richness, followed by disturbances caused by flood pulses and the operation of reservoirs upstream. The periphyton on artificial and natural substrata presented high degree of similarity.

Floristic composition and similarity analysis of an Atlantic rain forest fragment in Cananéia, São Paulo State, Brazil

The aim of this study is to investigate the floristic composition of an Atlantic rain forest fragment located in Cananéia, São Paulo, Brazil, and to contribute to the knowledge on Atlantic forest through the comparative analysis of this and other floristic surveys both on the southern and southeastern Brazil, in different soil and relief types. We surveyed 215 species in 132 genera and 51 families. Classification and ordination analysis were applied to a binary matrix in order to analyze the similarity among 24 surveys, including the present one, of Atlantic forest from the south and southeast coast of Brazil. Higher floristic similarity was observed among this area and the ones where there was marine influence and more rugged relief. The surveys in areas with greater marine influence (sandy soil) were separated from those in other conditions, possibly indicating a species replacement gradient from the steep slopes towards the lowland and were probably related to different edaphic conditions. A latitudinal gradient was found among the surveys apparently confirming a continuous species replacement along the Atlantic forest, related to a restricted distribution of the species. This suggests that it is essential to preserve areas from the whole Atlantic coast. Atlantic forest distribution is quite complex and its composition cannot be adequately represented by small localized areas.

Effects of melatonin on the ovarian response to pinealectomy or continuous light in female rats: similarity with polycystic ovary syndrome

The current study was conducted to investigate the relationship between melatonin and chronic anovulation. Adult (3-4 months old) female Wistar rats were submitted to pinealectomy: group I: pinealectomized ovariectomized melatonin-treated (N = 10); group II: pinealectomized ovariectomized placebo-treated (N = 12); group III: pinealectomized light-treated placebo-treated(N = 10) or maintained under continuous light; group IV: maintained under continuous light, ovariectomized melatonin-treated (N = 22); group V: maintained under continuous light, ovariectomized placebo-treated (N = 10); group VI: maintained under continuous light placebo-treated (N = 10). In order to assess ovarian modifications, unilateral ovariectomy was performed during the fourth month in groups I, II, IV, V and the other ovary was removed after 8 months. Ovariectomy was performed in groups III and VI only after eight months. Melatonin (200 µg/100 g body weight) dissolved in 0.02 ml absolute ethanol was injected intramuscularly daily during the last 4 months into groups I and IV. The other groups were treated with placebo (NaCl). The ovarian cysts were analyzed and their area, perimeter and maximum diameter, as well as the thickness of the ovarian capsule were measured. Daily colpocytological smears were performed throughout the study. Persistent estrous condition and ovarian cysts were observed in all groups. In pinealectomized rats the ovarian and vaginal alterations disappeared at the end of the study and in rats maintained under continuous light the vaginal and ovarian polycystic aspect was reversed only in those treated with melatonin. We conclude that melatonin may act on the ovarian response reverting chronic anovulation induced by pinealectomy or continuous light.

Food production in solidarity economy: an issue that goes beyond laws

Abstract Food production within the context of solidarity economy is an alternative way to offer employment and income for a significant part of the Brazilian population. The purpose of this study was to carry out a business diagnosis in order to evaluate the facilities, the production process and hygiene practices of seven solidarity economy enterprises located in the city of Novo Hamburgo, Southern Brazil, that work with food production and sales. Visits took place at the enterprises and a check-list was used to record data. Although food production happens in places with space and setting restrictions, it guarantees distinctive foods with aggregate value, where handlers follow the whole process, from raw materials selection to sales. Basic hygiene principles are followed, as they guarantee the production of food with quality, which contributes towards income generation for participating families. Specific laws that apply to the characteristics and needs of small-scale food production must be written in order to regulate solidarity economy enterprises.

Mr. Giles' speech, delivered in the Senate of the United States, on Thursday, 24th November, 1808, on the resolution of Mr. Hillhouse, to repeal the embargo laws. --

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"Re-huminization": the role of human-animal similarity in predicting prejudice towards immigrants and non-human animals

Research implies that there ~ay be an association between attitudes toward margil1alized human outgroups and non-human animals. Very few studies, however, have specifically tested this relation empirically. The general purpose of the present research was to determine if such a relation exists and if perceptions of human-animal similarity avail as a common predictor of both types of attitudes. Ideological orientations associated with prejudiced attitudes (Social Dominance Orientation, Right-Wing Authoritarianism, and Universal Orientation) were also examined as individual differences in predicting perceptions of human-animal similarity. As predicted, people who endorsed prejudiced attitudes toward human outgroups (Study 1) and immigrants in particular (Studies 2 and 3), were more likely to endorse prejudiced attitudes toward non-human animals. In Study 2, perceptions that humans are superior (versus similar) to other animals directly predicted higher levels of prejudice toward non-human animals, whereas the effect of human superiority beliefs on immigrant prejudice was mediated by dehumanization. In other words, greater perceptions of humans as superior (versus similar) to other animals "allowed for" greater dehumanization of immigrants, which in turn resulted in heightened immigrant prejudice. Furthermore, people higher in Social Dominance Orientation or Right-Wing Authoritarianism were particularly likely to perceive humans as superior (versus similar) to other animals, whereas people characterized by a greater Universal Orientation were more likely to perceive humans and non-human animals as similar. Study 3 examined whether inducing perceptions of human-animal similarity through experimental manipulation would lead to more favourable attitudes toward non-human animals and immigrants. Participants were randomly assigned to read one of four 11 editorials designed to highlight either the similarities or differences between humans and other animals (i.e., animals are similar to humans; humans are similar to animals;~~nimals are inferior to humans; humans are superior to animals) or to a neutral control condition. Encouragingly, when animals were described as similar to humans, prejudice towards non-human animals and immigrants was significantly lower, and to some extent this finding was also true for people naturally high in prejudice (i.e., high in Social Dominance Orientation or Right-Wing Authoritarianism). Inducing perceptions that nonhuman animals are similar to humans was particularly effective at reducing the tendency to dehumanize immigrants ("re-humanization"), lowering feelings of personal threat regarding one's animal-nature, and at increasing inclusive intergroup representations and empathy, all of which uniquely accounted for the significant decreases in prejudiced attitudes. Implications for research, theory and prejudice interventions are considered.