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"The Moon Goddess in the Classic period The traditional Mayas generally assume the Moon to be female, and the Moon's perceived phases are accordingly conceived as the stages of a woman's life. The Maya moon goddess wields great influence in many areas. Being in the image of a woman, she is associated with sexuality and procreation, fertility and growth, not only of human beings, but also of the vegetation and the crops. Since growth can also cause all sorts of ailments, the moon goddess is also a goddess of disease. Everywhere in Mesoamerica, including the Mayan area, she is specifically associated with water, be it wells, rainfall, or the rainy season. In the codices, she has a terrestrial counterpart in goddess I. Lunar mythology The sources for Maya lunar mythology are almost entirely contemporaneous, with the exception of the Popol Vuh. A division can be made according to the moon's kinship roles. *Moon as a male sibling: celestial power. In the Popol Vuh (16th century), the Maya Hero Twins are finally transformed into sun and moon, implying the recognition of a male moon, in a departure from the main Maya tradition. However, the Popol Vuh hardly belongs to lunar mythology, and becoming Sun and Moon may well be a metonym for acquiring dominance over the sky and thus, metaphorically, political predominance. *Moon as a wife: origin of menstruation. True lunar mythology is first and foremost represented by the Qʼeqchiʼ myth of Sun and Moon first studied by Eric Thompson.Thompson 1930: 126-132, 125-138, and Thompson 1939 It makes the Moon Goddess (Po) the daughter of the Earth God, or 'Mountain-Valley'. She is wooed and finally captured by Sun. They sleep together. When this is discovered and the couple flees, the angry father reacts by having his daughter destroyed. In all likelihood, this patriarchal punishment of a basic infraction of the rules of alliance represents the origin of menstruation, the 'evil blood' of a disobedient daughter colouring the water of sea and lake red, or sinking into the earth.Braakhuis 2005:175-176; 2010:184-214 The menstrual blood is stored in thirteen jars. In the jars, it is first transformed into creatures such as snakes and insects, a transformation leading up to the origin of poison and the diseases caused by it. However, some jars also hold medicinal plants. The thirteenth jar is the lunar jar: On being opened, the Moon is reborn from it. The creation of her vagina on instigation of, or directly by, her husband represents the origin of human procreation. Subsequent episodes make the Moon Goddess cohabit with Sun's elder brother, Cloud, and with the devil in the shape of a king vulture, thus connecting her to rainfall and black sorcery. *Moon as a (grand)mother: the rabbit in the moon. Among the Mayas of Chiapas and the Northwestern Highlands of Guatemala, Moon is not Sun's wife, but his mother or grandmother, while Sun is a young boy harassed by his elder brethren. Only in this mythology do we find the origin of the lunar rabbit, either as one of the elder brethren transformed into wild animals and caught by his mother,Thompson 1970: 362 or as a creature responsible for the resurgence of the wild vegetation on Sun's maize field. In the latter case, the rabbit is caught by Sun, passed on to his mother, and again taken into the sky.Milbrath 1999: 24 In Northwestern Guatemala, the rabbit in the moon is sometimes replaced by a deer in the moon. The moon goddess in the Post- Classic and Classic periods In the three Post-Classic codices, the Moon Goddess is underrepresented. Instead, one finds almanacs devoted to what appears to be her terrestrial counterpart, the Goddess I ('White Woman'). In Classic Maya art, however, the Moon Goddess occurs frequently.Taube 1992: 64-68 She is shown as a young woman holding her rabbit, and framed by the crescent of the waxing moon, which is her most important, identifying attribute. The Moon Goddess may also be sitting on a throne, alone (as in the Dresden codex), or behind god D (Itzamna). Although, in oral tradition, the goddess is often treated as the consort of the Sun Deity, Classic iconography does not insist on this (see Kinich Ahau). The lunar rabbit (perhaps a Trickster character) has an important role to play in a poorly understood episode involving the Moon Goddess, the Twins, the Maya maize god, and the aged god L. In some cases, the Moon Goddess is fused with the main Maya maize god, making it uncertain whether what we see is a Moon Goddess with a maize aspect (that is, a maize-bringing moon), or a Maize God with a lunar aspect or function. Calendrical functions The Moon Goddess is the patroness of the month of Chʼen 'Well'. ("Moon has gone to her well" is an expression referring to New Moon.Thompson 1960: 238) She is also the patroness of one of the Venus 'years'. Her importance is reflected by the eclipse tables of the Dresden Codex and by the Lunar Series of the Long Count. Glyph C of the Lunar Series (indicating sequences of six lunations for purposes of eclipse prediction)Milbrath 1999: 107-109 connects her to other deities, such as the death god (God A), the Jaguar God of the Underworld, and, perhaps, the Maize God.Thompson 1960: 240-241 and figs. 36, 37 See also *Awilix *List of lunar deities Notes Bibliography *H.E.M. Braakhuis, Xbalanque's Canoe. The Origin of Poison in Qʼeqchiʼ-Mayan Hummingbird Myth. Anthropos 100-1 (2005): 173-191. *H.E.M. Braakhuis, Xbalanque's Marriage: A Commentary on the Qʼeqchiʼ Myth of Sun and Moon. Thesis, Leiden University (2010; online). *Susan Milbrath, Star Gods of the Maya: Astronomy in Art, Folklore, and Calendars. Austin: University of Texas Press 1999. *Karl Taube, The Major Gods of Ancient Yucatan. Dumbarton Oaks, Washington 1992. *Karl Taube, An Illustrated Dictionary of the Gods and Symbols of Ancient Mexico and the Maya. Thames and Hudson 1997. *J.E.S. Thompson, Maya History and Religion. Norman: University of Oklahoma Press 1970. *J.E.S. Thompson, An Introduction to Maya Hieroglyphic Writing. Norman: University of Oklahoma Press 1960. *J.E.S. Thompson, The Moon Goddess in Middle America with Notes on Related Deities. Washington: Carnegie Institute of Washington 1939. Maya goddesses Lunar goddesses Menstrual cycle "
"Jurgis Karnavičius (born 1957, in Vilnius) is a Lithuanian pianist. Karnavičius comes from a renowned family of musicians: his grandfather, Jurgis Karnavičius (1884–1941), was a composer, and his father, also named Jurgis (1912–2001), was a pianist and the long-time rector of the Lithuanian Academy of Music. Karnavičius graduated from the Lithuanian Academy of Music in 1980, specializing in the piano. He then continued his studies at the Moscow Conservatory for several more years. Jurgis Karnavičius is a piano soloist who has played with different orchestras, and he often accompanies his wife, the opera singer Sigutė Stonytė. In recent years he has been actively collaborating with several chamber ensembles, preparing concert programmes with the M. K. Čiurlionis String Quartet, Lithuanian Art Museum Quartet, Sostinės String Trio, and others. He has played well over one hundred solo concerts. In 2004, Jurgis Karnavičius earned a professorship with the Lithuanian Academy of Music. References * 1957 births Living people Music educators Lithuanian classical pianists Musicians from Vilnius 21st-century classical pianists "
"Kinetic logic, developed by René Thomas, is a Qualitative Modeling approach feasible to model impact, feedback, and the temporal evolution of the variables. It uses symbolic descriptions and avoids continuous descriptions e.g. differential equations.The derivation of the dynamics from the interaction graphs of systems is not easy. A lot of parameters have to be inferred, for differential description, even if the type of each interaction is known in the graph. Even small modifications in parameters can lead to a strong change in the dynamics. Kinetic Logic is used to build discrete models, in which such details of the systems are not required. The information required can be derived directly from the graph of interactions or from a sufficiently explicit verbal description. It only considers the thresholds of the elements and uses logical equations to construct state tables. Through this procedure, it is a straightforward matter to determine the behavior of the system.Thomas R., (1973) Boolean formulization of genetic control circuits. Journal of Theoretical Biology. 42 (3): 565–583. Formalism A. Steps of Application of Kinetic Logic B. Sigmoid Curve C. Step function D. Naive Kinetic Logic E. Generalized Kinetic Logic F. Example of Generalized Kinetic Logic in Software G. State Table for D H. Time Delays J. Statetable 2 Following is René Thomas’s formalism for Kinetic Logic : In a directed graph G = (V, A), we note G− (v) and G+ (v) the set of predecessors and successors of a node v ∈ V respectively. Definition 1: A biological regulatory network (BRN) is a tuple G = (V, A, l, s, t, K) where (V, A) is a directed graph denoted by G, l is a function from V to N, s is a function from A to {+, −}, t is a function from A to N such that, for all u ∈ V, if G+(u) is not empty then {t(u, v) v ∈ G+(u)} = { 1, . . . , l(u)}. K = {Kv v ∈ V} is a set of maps: for each v ∈ V, Kv is a function from 2G− (v) to {0, . . . , l(v)} such that Kv(ω) ≤ Kv(ω_) for all ω ⊆ ω_ ⊆ G−(v). The map l describes the domain of each variable v: if l (v) = k, the abstract concentration on v holds its value in {0, 1, . . . , k}. Similarly, the map s represents the sign of the regulation (+ for an activation, − for an inhibition). t (u, v) is the threshold of the regulation from u to v: this regulation takes place iff the abstract concentration of u is above t(u, v), in such a case the regulation is said active. The condition on these thresholds states that each variation of the level of u induces a modification of the set of active regulations starting from u. For all x ∈ [0, . . ., l(u) − 1], the set of active regulations of u, when the discrete expression level of u is x, differs from the set when the discrete expression level is x + 1. Finally, the map Kv allows us to define what is the effect of a set of regulators on the specific target v. If this set is ω ⊆ G− (v), then, the target v is subject to a set of regulations which makes it to evolve towards a particular level Kv(ω). Definition 2 (States): A state μ of a BRN G = (V, A, l, s, t, K) is a function from V to N such that μ (v) ∈ {0 .., l (v)} for all variables v ∈ V. We denote EG the set of states of G. When μ (u) ≥ t (u, v) and s (u, v) = +, we say that u is a resource of v since the activation takes place. Similarly when μ (u) < t (u, v) and s (u, v) = −, u is also a resource of v since the inhibition does not take place (the absence of the inhibition is treated as an activation). Definition 3 (Resource function): Let G = (V, A, l, s, t, K) be a BRN. For each v ∈ V we define the resource function ωv: EG → 2G− (v) by: ωv (μ) = {u ∈ G−(v) (μ(u) ≥ t(u, v) and s(u, v) = +) or (μ (u) < t (u, v) and s (u, v) = −)}. As said before, at state μ, Kv (ωv(μ)) gives the level towards which the variable v tends to evolve. We consider three cases, * if μ(v) < Kv(ωv(μ)) then v can increase by one unit * if μ(v) > Kv(ωv(μ)) then v can decrease by one unit * if μ(v) = Kv (ωv (μ)) then v cannot evolve. Definition 4 (Signs of derivatives): Let G = (V, A, l, s, t, K) be a BRN and v ∈ V. We define αv: EG → {+1, 0, −1} by αv(μ) = +1 if Kv (ωv(μ)) > μ(u) 0 if Kv (ωv(μ)) = μ(u) −1 if Kv (ωv(μ)) < μ(u) The signs of derivatives show the tendency of the solution trajectories. The state graph of BRN represents the set of the states that a BRN can adopt with transitions among them deduced from the previous rules: Definition 5 (State graph): Let G = (V, A, b, s, t,K) be a BRN. The state graph of G is a directed graph G = (EG, T) with (μ, μ_) ∈ T if there exists v ∈ V such that: αv (μ) ≠ 0 and μ’ (v) = μ (v) + αv (μ) and μ (u) = μ’ (u), ∀u ∈ V \ {v}.Thomas R., (1978) Logical analysis of systems comprising feedback loops. J Theor Biol.73(4): 631–656. = Critical Assumptions = The critical assumptions of Kinetic Logic are: # The elements of system have slight effect on each other until they reach a threshold. # At high levels the effect on each other tends to reach a plateau. So an element is present when greater than the threshold level and absent when it is below the threshold level.Kupper Z and Hoffmann H., (1995) Modeling the Dynamics of Psychosis by Kinetic Logic (4-95). Bern, Switzerland: University of Bern, Department of Social and Community Psychiatry. Steps of Application Following are the steps of Application of Kinetic Logic (Also shown in figure A).Thomas R., and D’Ari R., (1990) Biological feedback. FL: CRC Press, Boca Raton. =Biological Regulatory Network (BRN)= Keeping the research problem in mind, the behavior of elements in the system and their interactions are studied. Elements of a system can interact positively or negatively, that is, the level of an element may activate or reduce the rate of production of other elements or of itself. These interactions are represented as positive (activation) or negative (inhibition). When elements are connected in a topologically circular way, they exert an influence on their own rate of synthesis and they form a feedback loop. A feedback loop is positive or negative according to whether it contains an even or odd number of negative interactions. In a positive loop, each element of the system exerts a positive effect on its own rate of synthesis, whereas in a simple negative loop, each element has a negative effect on its own rate of synthesis. A simple positive feedback loop results in epigenetic regulation and have multiple steady states and a simple negative feedback loop results in homeostatic regulation. Abstraction: A chain of positive interactions is equivalent to a direct positive interaction between the two extreme elements, and any two negative interactions cancel out each other’s effect. In this way, any simple feedback loop can be abridged to a one-element loop, positive or negative according to the number of negative interactions (even or odd) in the original loop. Accordingly, through extensive literature survey and the application of the above-mentioned rules, a BRN is abstracted. =Logical Variable and Functions= Logical variables are associated with the elements of the system to describe the state of the system. They consist of the logical values. For example, a system whose state is appropriately described by the levels of substances a, b, and c, each of which can be absent, present at low level, or present at high level are represented by logical values 0, 1, and 2 respectively. If a product an acts to stimulate the production of b, it is a positive regulator. In this case, the rate of synthesis of b increases with increasing concentration of a, and makes a curve similar to that shown in figure B. There is little effect of a, until it reaches a threshold concentration theta, and at higher concentrations a plateau is reached which shows the maximal rate of synthesis of b. Such a nonlinear, bounded curve is called a sigmoid. It can be suggested that a is "absent" for a < theta and "present" for a > theta. The sigmoid curve can be approximated by the step function, as in figure C. Not only logical variables (x, y, z ...) are associated to the elements, that represent their level (e.g., concentration), but also logical functions (X, Y, Z ...) whose value reflects the rate of synthesis of the element. Thus, x = 0 means "gene product absent" x = 1 means "gene product present" & X = 0 means "gene off" X = 1 means "gene on" =Graph of Interactions and Logical Equations= Kinetic Logic has two forms depending on the following two types of descriptions: Naïve Logical Description Consider a simple two-element system in which product x activates gene Y and product y represses gene X as shown in figure D. Each variable takes only two values; 0 and 1. In other words, X = 1 if y = 0 (X "on” if y absent) Y = 1 if x = 1 (Y "on" if x present) The logical relation of the system can be written: X =y Y=x Generalized Kinetic Logic The naive logical description can be generalized and made to accommodate situations in which some variables take more than two values, without complicating the analysis. Any variable has a number of biologically relevant levels, determined by the number of elements regulated by the product x. There is a specific threshold for each regulatory interaction, so if x regulates n elements, it will have up to n different thresholds. For the logical sum, there is a procedure that assigns a specific weight to each term in the logical relation. According to the scale of thresholds of the corresponding variable, the weighted algebraic sum is then discretized, so an n-valued variable is associated with an n-valued function. After discretization the integers of certain weights or sums of weights are called logical parameters. Generalized Kinetic Logic, although maintaining the analytic simplicity of the naive description, has certain features in common with the differential description. The generalized logical relations are completely independent of the differential description and can be directly derived from the graph of interactions or from an explicit verbal description. Consider an example of two elements in figure E. Using a software, this graph of interactions is drawn as shown in figure F. There are two thresholds assigned to element y: Ѳ12, concerning its interaction with x and Ѳ22, concerning its interaction with itself. The variable y and function Y have three possible values: 0, 1, and 2. Element x have a single threshold, Ѳ21, because of the interaction x to +y, so the variable x and function X will be two-valued. =State Table and State Graph= The state table of graph of interactions in figure D is shown in figure G. This table states for each state of the variables (x, y) i.e. present or absent, which products are synthesized and which are not synthesized at a significant rate. Consider the state 00/10, in which both of the gene products are absent but gene X is on. As product x is absent but being synthesized so it can be expected that in near future it will be present and the logical value of x will change from 0 to 1. This can be described by the notation Ō, in which the dash above the digit is due to the fact that variable x is committed to change its value from 0 to 1. Generally, a dash over the figure representing the logical value of a variable each time this value is different from that of the corresponding function. The state just considered can thus be represented as ŌO. Time Delays The movement of a system from one state to another depends on the time delays. The time delays in systems are short time shifts of arbitrary duration. In view of the relation between a function (gene on or off) and its associated variable (gene product present or absent), the time delays become real entities whose values, far from being arbitrary, reflect specific physical processes (synthesis, degradation, dilution, etc.). The values of the different time delays play an important role in determining the pathway along which the system evolves. The temporal relation between a logical variable x which is associated with the level of an element and a logical function X which is associated with its evolution can be explained as follows. Consider a gene that is off (X = 0) for a considerable time, then is switched on (X = 1) by a signal, and then, after some time, it is switched off again (X= 0) by another signal and the product reappears but not immediately until a proper delay tx has elapsed. If a signal switches the gene off temporarily, the product is still present because it also requires a time delay tx’. This can be represented graphically as shown in figure H. Using the state table the temporal sequence of states of the system can be represented as shown in figure I. =Identifying Cycles and Stable Steady States= Cycles The state table in D can be used to identify the cyclic behavior of the system. We can see that state 01 changes to 00, and 00 changes to 10, 10 changes to 11 and 11 changes back to 01. This represents a cycle as the system starts from the state 01 and returns to the same state. The system keeps oscillating between these states. Deadlocks Consider another example in which: X=y Y=x The state table for the system is shown in figure J. The states that are encircled are stable states, as they do not evolve towards any other state. The logical stable states are defined as those for which the vectors xy . .. and XY ... are equal. When we considered the time delays i.e. from ŌŌ the system will proceed to state 1 0 or to state 01, according to whether tx < ty or ty < tx, and from ĪĪ the system will proceed to state 10 or to state 0 1 according to whether ty < tx or tx < ty. The state graph representing delays is shown in figure K. The sequence of states a system depends on the relative values of the time delays. It is assumed that two delays (or sums of delays) are never exactly equal, therefore that two variables will not change their values at the same instant. But do not exclude the possibility because if this rule is applied rigidly, it could occasionally lead to the loss of interesting pathways. =Analyzing the Results= The cycles and the deadlock states identified by this process are then analyzed by comparing them with the invitro and invivo findings. These results can be used to make important predictions about the system. Cyclic behaviors correspond to homeostatic regulations that retain the level of a variable at or near a fixed or optimal value. Deadlocks represent epigenetic regulation in which the concentrations exist between extreme levels.Thomas R., and D’Ari R., (1990) Biological feedback. FL: CRC Press, Boca Raton. History The first approach for qualitative modeling was based on extreme discretization since all genes could be either on (present) or off (absent).Thomas R., (1978) Logical analysis of systems comprising feedback loops. J Theor Biol.73(4): 631–656. This Boolean approach was generalized into a multi-valued approach i.e. Kinetic Logic,Thomas R., (1991) Regulatory networks seen as asynchronous automata: a logical description. J Theor Biol. 153: 1–23.Snoussi E., (1989) Qualitative dynamics of a piecewise-linear differential equations: a discrete mapping approach. DSS. 4:189–207. in which logical identification of all steady states became possible.Snoussi E., and Thomas R., (1993) Logical identification of all steady states : the concept of feedback loop characteristic states. Bull Math Biol. 55(5):973–991. Application Kinetic logic has been employed to study the factors that influence the selection of specific pathway from many different pathways that the system can follow and the factors that lead the system towards stable states and cyclic behaviors. It has been used to reveal the logic that lie behind the functional organization and kinetic behavior of molecules. Model checking techniques have also been applied to models built through kinetic logic, in order to infer their continuous behaviors.J. Ahmad, and O. Roux, “Analysing formal models of genetic regulatory networks with delays,” Int. J. Bioinformatics Research and Applications. vol. 4. pp. 240-262, 2008. Kinetic logic has been applied on many different types of systems in biology, Psychology and Psychiatry.Kupper Z and Hoffman H., (1995) Modeling the Dynamics of Psychosis by Kinetic Logic (4-95). Bern, Switzerland: University of Bern, Department of Social and Community Psychiatry. Mostly Kinetic Logic has been used in modeling the biological networks especially the Gene Regulatory Networks (GRNs). Following are the examples in which Kinetic Logic was employed as the modeling formalism: * To model the dynamics of chronic psychosis and schizophrenia.Kupper Z and Hoffman H., (1995) Modeling the Dynamics of Psychosis by Kinetic Logic (4-95). Bern, Switzerland: University of Bern, Department of Social and Community Psychiatry.Breedlove S.M., Rosenzweig M.R., and Watson N.V., (2010) Biological Psychology (6th Edition): * To show that how residence time of the hormone on the receptor can decide the specificity of signaling between the alternative metabolic or mitogenic pathways,de Jong H., (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol. 9(1):67–103. * To explain the positive (cell proliferation and cytokine production) and negative (anergy induction) signaling of T lymphocytes; to determine how the timing of the binding and intracellular signal-transduction events can influence the properties of receptor signaling and decide the type of cellular responsede Jong H., (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol. 9(1):67–103. * To demonstrate how prion infection proceedsde Jong H., (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol. 9(1):67–103. * To model other biological regulatory networks (BRNs) like toy gene, lambda phage (Ahmad and Roux, 2008), Pseudomonas aeruginosa and circadian rhythm.J. Ahmad, and O. Roux, “Analysing formal models of genetic regulatory networks with delays,” Int. J. Bioinformatics Research and Applications. vol. 4. pp. 240-262, 2008. * To reveal the logic that lie behind the functional organization and kinetic behavior of the thioredoxin system de Jong H., (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol. 9(1):67–103. Tool As theoretical analysis through Kinetic Logic is a time consuming process, a tool known as Genotech, for modeling and analysis of BRNs was developed on the basis of Kinetic Logic and has been used for a number of Kinetic Logic-based studies.J. Ahmad, “Modélisation hybride et analyse des dynamiques des réseaux de régulations biologiques en tenant compte des délais, “ PhD thesis, Ecole Centrale de Nantes, France, 2009. It analyzes behaviors like stable cycles, stable steady states and paths in the state graph (discrete model) of biological systems, accelerating the process of modeling.Thomas R., and D’Ari R., (1990) Biological feedback. FL: CRC Press, Boca Raton. GenoTech is extremely useful as it allows repeated experimentation by automating the whole process. This tool is available on request. Books References Mathematical and theoretical biology "