Chaos, but in voting and apportionments?

Mathematical chaos and related concepts are used to explain and resolve issues ranging from voting paradoxes to the apportioning of congressional seats.

Dynamic Localization of the Swe1 Regulator Hsl7 During the Saccharomyces cerevisiae Cell Cycle

In Saccharomyces cerevisiae, entry into mitosis requires activation of the cyclin-dependent kinase Cdc28 in its cyclin B (Clb)-associated form. Clb-bound Cdc28 is susceptible to inhibitory tyrosine phosphorylation by Swe1 protein kinase. Swe1 is itself negatively regulated by Hsl1, a Nim1-related protein kinase, and by Hsl7, a presumptive protein-arginine methyltransferase. In vivo all three proteins localize to the bud neck in a septin-dependent manner, consistent with our previous proposal that formation of Hsl1-Hsl7-Swe1 complexes constitutes a checkpoint that monitors septin assembly. We show here that Hsl7 is phosphorylated by Hsl1 in immune-complex kinase assays and can physically associate in vitro with either Hsl1 or Swe1 in the absence of any other yeast proteins. With the use of both the two-hybrid method and in vitro binding assays, we found that Hsl7 contains distinct binding sites for Hsl1 and Swe1. A differential interaction trap approach was used to isolate four single-site substitution mutations in Hsl7, which cluster within a discrete region of its N-terminal domain, that are specifically defective in binding Hsl1. When expressed in hsl7Δ cells, each of these Hsl7 point mutants is unable to localize at the bud neck and cannot mediate down-regulation of Swe1, but retains other functions of Hsl7, including oligomerization and association with Swe1. GFP-fusions of these Hsl1-binding defective Hsl7 proteins localize as a bright perinuclear dot, but never localize to the bud neck; likewise, in hsl1Δ cells, a GFP-fusion to wild-type Hsl7 or native Hsl7 localizes to this dot. Cell synchronization studies showed that, normally, Hsl7 localizes to the dot, but only in cells in the G1 phase of the cell cycle. Immunofluorescence analysis and immunoelectron microscopy established that the dot corresponds to the outer plaque of the spindle pole body (SPB). These data demonstrate that association between Hsl1 and Hsl7 at the bud neck is required to alleviate Swe1-imposed G2-M delay. Hsl7 localization at the SPB during G1 may play some additional role in fine-tuning the coordination between nuclear and cortical events before mitosis.

Nonlinear control of heart rate variability in human infants.

Nonlinear analyses of infant heart rhythms reveal a marked rise in the complexity of the electrocardiogram with maturation. We find that normal mature infants (gestation greater than or equal to 35 weeks) have complex and distinctly nonlinear heart rhythms (consistent with recent reports for healthy adults) but that such nonlinearity is lacking in preterm infants (gestation > or = to 27 weeks) where parasympathetic-sympathetic interaction and function are presumed to be less well developed. Our study further shows that infants with clinical brain death and those treated with atropine exhibit a similar lack of nonlinear feedback control. These three lines of evidence support the hypothesis championed by Goldberger et al. [Goldberger, A.L., Rigney, D.R. & West, B.J. (1990) Sci. Am. 262, 43-49] that autonomic nervous system control underlies the nonlinearity and possible chaos of normal heart rhythms. This report demonstrates the acquisition of nonlinear heart rate dynamics and possible chaos in developing human infants and its loss in brain death and with the administration of atropine. It parallels earlier work documenting changes in the variability of heart rhythms in each of these cases and suggests that nonlinearity may provide additional power in characterizing physiological states.

Unusual dynamics of extinction in a simple ecological model.

Studies on natural populations and harvesting biological resources have led to the view, commonly held, that (i) populations exhibiting chaotic oscillations run a high risk of extinction; and (ii) a decrease in emigration/exploitation may reduce the risk of extinction. Here we describe a simple ecological model with emigration/depletion that shows behavior in contrast to this. This model displays unusual dynamics of extinction and survival, where populations growing beyond a critical rate can persist within a band of high depletion rates, whereas extinction occurs for lower depletion rates. Though prior to extinction at lower depletion rates the population exhibits chaotic dynamics with large amplitudes of variation and very low minima, at higher depletion rates the population persists at chaos but with reduced variation and increased minima. For still higher values, within the band of persistence, the dynamics show period reversal leading to stability. These results illustrate that chaos does not necessarily lead to population extinction. In addition, the persistence of populations at high depletion rates has important implications in the considerations of strategies for the management of biological resources.

Cell cycling and patterned cell proliferation in the wing primordium of Drosophila.

The pattern of cell proliferation in the Drosophila imaginal wing primordium is spatially and temporally heterogeneous. Direct visualization of cells in S, G2, and mitosis phases of the cell cycle reveals several features invariant throughout development. The fraction of cells in the disc in the different cell cycle stages is constant, the majority remaining in G1. Cells in the different phases of the cell cycle mainly appear in small synchronic clusters that are nonclonally derived but result from changing local cell-cell interactions. Cluster synchronization occurs before S and in the G2/M phases. Rates of cell division are neither constant nor clonal features. Cell cycle progression is linear rather than concentric. Clusters appear throughout the disc but with symmetries related to presumptive wing patterns, compartment boundaries, and vein clonal restrictions.

Cell cycle-related shifts in subcellular localization of BCR: association with mitotic chromosomes and with heterochromatin.

The disruption of the BCR gene and its juxtaposition to and consequent activation of the ABL gene has been implicated as the critical molecular defect in Philadelphia chromosome-positive leukemias. The normal BCR protein is a multifunctional molecule with domains that suggest its participation in phosphokinase and GTP-binding pathways. Taken together with its localization to the cytoplasm of uncycled cells, it is therefore presumed to be involved in cytoplasmic signaling. By performing a double aphidicolin block for cell cycle synchronization, we currently demonstrate that the subcellular localization of BCR shifts from being largely cytoplasmic in interphase cells to being predominantly perichromosomal in mitosis. Furthermore, with the use of immunogold labeling and electron microscopy, association of BCR with DNA, in particular heterochromatin, can be demonstrated even in quiescent cells. Results were similar in cell lines of lymphoid or myeloid origin. These observations suggest a role for BCR in the phosphokinase interactions linked to condensed chromatin, a network previously implicated in cell cycle regulation.

Temperature chaos in 3D Ising spin glasses is driven by rare events

Temperature chaos has often been reported in the literature as a rare-event–driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a largedeviations functional that allows to discuss the size dependences. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances.

Linear chaos for the Quick-Thinking-Driver model.

In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.

Glacial geomorphology of the flank of the Hecates Tholus Volcano, Marrs

El volcán Hecates Tholus (32.18°N, 150.28ºE; cuadrante MC-7), de unos 180 km de diámetro y 5.300 metros de altura, es el único edificio de la provincia volcánica de Elysium, en las Tierras Bajas de Marte, en el que se han descrito rasgos geomorfológicos que podrían estar causados por procesos glaciares. Además, distintos autores relacionan la red radial de canales que surcan las laderas del volcán como causadas por la fusión de un antiguo casquete glaciar en la cima del edificio, siendo éste un ejemplo más de las intensas interacciones magma-agua en esta región del planeta, cercana al antiguo océano marciano y que dieron lugar a fenómenos muy interesantes, como los terrenos caóticos de Galaxias Chaos, a pocos kilómetros del volcán. Una característica muy particular de este edificio volcánico es la presencia de dos depresiones anidadas en la base de la ladera Noroeste, de 20 y 60 km de diámetro. La menor de ellas (Depresión A), situada a mayor altitud, ha sido interpretada por algunos autores como causada por una erupción lateral del volcán hace unos 350 Ma. Sin embargo, la de mayor diámetro y situada a menor altitud (Depresión B), no tiene un origen claro, aunque se han discutido distintas hipótesis. En cualquier caso, es especialmente en el interior de estas depresiones donde se han encontrado los rasgos geomorfológicos que podrían estar causados por actividad glacial, como posibles cordones morrénicos y depósitos de till...

Chemical Reactors. Problem 1: A simple ODE (chaos in the atmosphere) (2011-2012 Course)

Wording of problem 1: A simple ODE (chaos in the atmosphere).

Dynamic Visual Servoing With Chaos Control for Redundant Robots

This paper presents a new dynamic visual control system for redundant robots with chaos compensation. In order to implement the visual servoing system, a new architecture is proposed that improves the system maintainability and traceability. Furthermore, high performance is obtained as a result of parallel execution of the different tasks that compose the architecture. The control component of the architecture implements a new visual servoing technique for resolving the redundancy at the acceleration level in order to guarantee the correct motion of both end-effector and joints. The controller generates the required torques for the tracking of image trajectories. However, in order to guarantee the applicability of this technique, a repetitive path tracked by the robot-end must produce a periodic joint motion. A chaos controller is integrated in the visual servoing system and the correct performance is observed in low and high velocities. Furthermore, a method to adjust the chaos controller is proposed and validated using a real three-link robot.

Descent from banking union to political chaos. CEPS Commentary, 24 January 2014

To counteract the powerful anti-Europe sentiments swirling throughout the EU today and to motivate EU citizens to vote in a constructive spirit in the upcoming European elections, Karel Lannoo argues in this commentary that the functioning of the EU institutions needs to be openly discussed and proposals need to be aired for improving the decision-making process to render it more transparent and democratic. This process would encompass, in his view, the proper role and functioning of the European Commission, the European Parliament and the member states in the EU Council and the interrelationships between these institutions.

Regional Business Cycle Synchronization in Europe? Bruges European Economic Research (BEER) Papers 11/June 2007

We analyse regional business cycle synchronization in the Euro Area, using Gross Value Added in 53 NUTS 1 regions for a period of thirty years (1975-2005), detrended by Hodrick-Prescott and the Christiano-Fitzgerald filters. We conclude that, on average, synchronization has increased for the period considered with exceptions during the eighties and the beginning of the nineties. Still, the correlation of the business cycle in some regions with the benchmark remained low or even decreased. Our findings also support the hypothesis of the existence of a ‘national border’ effect.

Supporting the Revolution: America, Democracy, and the End of the Cold War in Poland, 1981-1989. ACES Working Paper (Report) No. 8, 2007

Early on the morning of December 13, 1981, General Wojciech Jaruzelski, the leader of the communist Polish United Workers' Party (PZPR), declared martial law, ending the so-called "Polish Crisis," which began with the creation of the Independent Free Trade Union "Solidamosc" in August 1980. Over the next eight years, the Communist government and the opposition struggled over power, culminating in 1989 with the creation of a Solidamosc-led government which ended fifty years of Communist rule in Poland and led the way to further democratic revolutions throughout Eastern Europe. The purpose of this dissertation is to utilize newly available and underutilized archival sources as well as oral history interviews, from both international and American perspectives, to fully chronicle American policy toward Poland from the declaration of martial law until the creation of the Solidarnosc government. Rather than explaining Polish-American relations in bilateral terms, the dissertation illuminates the complex web of influences that determined American policy in Washington and affected its implementation within Poland. This includes descriptions of internal tensions within the Reagan administration, differences between American decisions in Washington and implementation in Warsaw, lobbying from Polish-American groups, clashes between Capitol Hill and the White House, coordination with American labor organizations to support Solidarnosc, disagreements with West European allies in NATO and international financial organizations, cooperation with the Vatican and the Polish Catholic Church, synchronization with American humanitarian organizations working in Poland, limitations caused by the realities of Soviet power in Eastern Europe, and complications caused by domestic Polish concerns. By taking a broad view of American policy and highlighting internal Polish decisions, with both the Communist government and the democratic opposition, the dissertation provides concrete examples of America's role in Poland's transformation, arguing, however, that this role was very limited. These conclusions are relevant to arguments about the end of the Cold War, the nature of American power, as well as current discussions about possibilities to promote democracy within hostile regimes.

Europe in limbo while the UK descends into chaos. EPC Post-Summit Commentary, 30 June 2016

The EU Summit and the separate meeting of the EU27 without the UK on 28/29 June 2016 demonstrated that the EU is in limbo. Following the initial shock, frustration and anger after the unexpected result of the UK ‘in/out’ referendum, the future relationship between the European Union (EU) and the United Kingdom (UK) monopolised the meetings of EU leaders. The EU has entered uncharted waters and leaders are struggling to figure out how exactly to deal with the manifold (potential) consequences of the ‘Brexit crisis’. Despite the many uncertainties, the EU27 managed to reach some common lines, trying to convey four key messages, although the final outcome of the crisis and its effects on the Union’s overall future are still very unclear: