Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well behaved mixed quantum states for tori for which the corresponding Schrodinger equation has no solutions, as well as an extended spectrum for tori where the Schrodinger equation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density $\rho(p,q,t)$ going to the correct classical limit. An application to the cat map yields, in a direct manner, nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the correspondence limit.Comment: 36 pages, RevTex preprint forma

Relating microfossil distribution patterns to deep-water depositional processes: a new biofacies model based on Oligocene-Miocene deposits

Abstrac

Preschool Mathematics Performance and Executive Function: Rural-Urban Comparisons Across Time

This longitudinal study, with urban and rural preschool children, examines the relationship between executive function (EF) and mathematics. A panel of direct and indirect measures of EF were used to determine which EF measures were most predictive and a measure of mathematics assessed both numeracy and geometry skill. One hundred eighteen children, ages 39 to 68 months, and their preschool teachers were included, with assessments given twice, about six months apart. EF measures were compared by the amount of variance in mathematics skill each claimed, including the influence of a child’s age, gender, and rural-urban context. Results suggest the child’s age determines if a panel of direct EF measures is a better predictor of numeracy and geometry skills than the use of a single EF measure. Different EF measures were more strongly related to numeracy versus geometry at Time 1 and Time 2. Differences unrelated to income were found between rural and urban children on numeracy skill but not geometry skill. These results are particularly important to state and regional early childhood directors who work across urban and rural areas, legislators and policymakers, teachers and parents

Effect of rapidly resorbable bone substitute materials on the temporal expression of the osteoblastic phenotype \u3cem\u3ein vitro\u3c/em\u3e

Ideally, bioactive ceramics for use in alveolar ridge augmentation should possess the ability to activate bone formation and, thus, cause the differentiation of osteoprogenitor cells into osteoblasts at their surfaces. Therefore, in order to evaluate the osteogenic potential of novel bone substitute materials, it is important to examine their effect on osteoblastic differentiation. This study examines the effect of rapidly resorbable calcium–alkali– orthophosphates on osteoblastic phenotype expression and compares this behavior to that of ß-tricalcium phosphate (TCP) and bioactive glass 45S5. Test materials were three materials (denominated GB14, GB9, GB9/25) with a crystalline phase Ca2KNa(PO4)2 and with a small amorphous portion containing either magnesium potassium phosphate (GB14) or silica phosphate (GB9 and GB9/25, which also contains Ca2P2O7); and a material with a novel crystalline phase Ca10[K/Na](PO4)7 (material denominated 352i). SaOS-2 human bone cells were grown on the substrata for 3, 7, 14, and 21 days, counted, and probed for an array of osteogenic markers. GB9 had the greatest stimulatory effect on osteoblastic proliferation and differentiation, suggesting that this material possesses the highest potency to enhance osteogenesis. GB14 and 352i supported osteoblast differentiation to the same or a higher degree than TCP, whereas, similar to bioactive glass 45S5, GB9/25 displayed a greater stimulatory effect on osteoblastic phenotype expression, indicating that GB9/25 is also an excellent material for promoting osteogenesis

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground state configuration of all the members of the family on a periodic chain. The ground state is two-fold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.

Apoptosis and proliferation in the trigeminal placode

The neurogenic trigeminal placode develops from the crescent-shaped panplacodal primordium which delineates the neural plate anteriorly. We show that, in Tupaia belangeri, the trigeminal placode is represented by a field of focal ectodermal thickenings which over time changes positions from as far rostral as the level of the forebrain to as far caudal as opposite rhombomere 3. Delamination proceeds rostrocaudally from the ectoderm adjacent to the rostral midbrain, and contributes neurons to the trigeminal ganglion as well as to the ciliary ganglion/oculomotor complex. Proliferative events are centered on the field prior to the peak of delamination. They are preceded, paralleled and, finally, outnumbered by apoptotic events which proceed rostrocaudally from non-delaminating to delaminating parts of the field. Apoptosis persists upon regression of the placode, thereby exhibiting a massive “wedge” of apoptotic cells which includes the postulated position of the “ventrolateral postoptic placode” (Lee et al. in Dev Biol 263:176–190, 2003), merges with groups of lens-associated apoptotic cells, and disappears upon lens detachment. In conjunction with earlier work (Washausen et al. in Dev Biol 278:86–102, 2005) our findings suggest that apoptosis contributes repeatedly to the disintegration of the panplacodal primordium, to the elimination of subsets of premigratory placodal neuroblasts, and to the regression of placodes

Unemployment and digital public goods contribution

Economic crises often result in massive job loss. However, although reduced employment has been shown to have many negative consequences for the affected individuals, it may also push them into new activities, such as provision of service to their communities. In this paper, we show how individuals engage in socially useful activities after an increase in unemployment. Specifically we document increased online content generation at Wikipedia, the world's largest user generated knowledge repository. Leveraging German district-level and European country-level unemployment data we analyze the relationship between the economic crisis in 2008-2010 and contributions to Wikipedia. For both data sets we find increased socially valuable activity in the form of knowledge acquisition and contributions to Wikipedia. For German districts, we observe an increased rate of content generation on Wikipedia in districts that faced greater increases in unemployment. The effect of unemployment on content generation is even stronger at the European country level. Our findings suggest that public goods provision increases as a positive side effect of economic crises

Exact ground states for a class of one-dimensional frustrated quantum spin models

We have found the exact ground state for two frustrated quantum spin-1/2 models on a linear chain. The first model describes ferromagnet- antiferromagnet transition point. The singlet state at this point has double-spiral ordering. The second model is equivalent to special case of the spin-1/2 ladder. It has non-degenerate singlet ground state with exponentially decaying spin correlations and there is an energy gap. The exact ground state wave function of these models is presented in a special recurrent form and recurrence technics of expectation value calculations is developed.Comment: 16 pages, 3 figures, RevTe

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

Does past unemployment experience explain the transition happiness gap?

The profound economic and political changes of the 1990s had detrimental social effects in many domains of life in post-socialist countries, including diminishing life expectancy and growing unhappiness. Despite economic improvements in the second decade of transition, research has documented that happiness lagged behind. We test whether past unemployment experience can explain this “transition happiness gap in the context of Ukraine”, a country with a painful delayed transition from planned to market economy. We analyze unique longitudinal data for the period 2003–2012. Current unemployment substantially reduces subjective wellbeing, and the effect is roughly 50% larger for men than for women. The effect of past unemployment is significant, but small in magnitude compared to the effect of current unemployment. However, it does correspond to around 8% of the ‘’transition happiness gap” found by Guriev and Melnikov (2017), suggesting that past unemployment experience can be considered as a partial explanation