Stable gauged maps

We give an introduction to moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet and Schmitt, and the associated integrals giving rise to gauged Gromov-Witten invariants. We survey various applications to cohomological and K-theoretic Gromov-Witten invariants.Comment: Survey for the 2015 AMS Summer Institute on Algebraic Geometry. Split off from the more technical paper "Properness for scaled gauged maps" [arXiv:1606.01383]. There is still substantial overlap between the two papers. This version has minor correction

Work lives amid social change and continuity: occupational trajectories in Monterrey, Mexico

In this paper we use sequence analysis to study the occupational trajectories between the ages 14 and 30 for men in Monterrey, the third largest city of Mexico. We build typologies of trajectories based on life-history data and then explore changes in the frequency of these ´typical´ trajectories over time as well as differences across socioeconomic groups. Cohort trends reveal more continuities than changes in occupational trajectories, despite the structural changes experienced by the city in the last two decades. Career patterns are closely related to family origins and educational attainment, thus suggesting the continuing importance of both ascribed and attained characteristics on occupational outcomes.

Structural change and occupational attainment in Monterrey, Mexico

Latin American societies have experienced profound economic transformations in recent years. Yet, little is known about the effects of these transformations on occupational attainment and mobility. We study these effects in Monterrey, the third largest city of Mexico. We analyze two stages of men’s process of occupational attainment: the entry into the labor force and subsequent job shifts. Despite short-term negative effects in the 1980s, Monterrey’s labor market upgrading has continued, facilitating upward mobility. However, class of origin remains an important determinant of attainment, labor-market segmentation imposes barriers to mobility, and wages in non-manual occupations have decreased, thus imposing particular characteristics to occupational attainment.

Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index

The Kolmogorov-Mandelbrot-van Ness Process is a zero mean Gaussian process indexed by the Hurst Parameter (H). When it models financial data, a controversy arises as to whether or not financial data exhibit short or long-range dependence. This paper argues that the Mixed Fractional Brownian is a more suitable tool for the purpose as it leaves no room for controversy. It is used here to model the S&P-500 Index, sampled daily over the period 1950-2011. The main results are as follows: The S&P-500 Index is characterized by both short and long-term dependence. More explicitly, it is characterized by at least 12 distinct scaling pa-rameters that are, ex hypothesis, determined by investors’ approach to the market. When the market is dominated by “blue-chippers” or ‘long-termists’, or when bubbles are ongoing, the index is persistent; and when the market is dominated by “con-trarians”, the index jumps to anti-persistence that is a far-from-equilibrium state in which market crashes are likely to occur.Gaussian Processes; Mixed Fractional Brownian Motion; Hurst Exponent; Local Self-similarity, Persistence; Anti-persistence; Definiteness of covariance Functions; Dissipative dynamic systems

Synchronization of the Frenet-Serret linear system with a chaotic nonlinear system by feedback of states

A synchronization procedure of the generalized type in the sense of Rulkov et al [Phys. Rev. E 51, 980 (1995)] is used to impose a nonlinear Malasoma chaotic motion on the Frenet-Serret system of vectors in the differential geometry of space curves. This could have applications to the mesoscopic motion of biological filamentsComment: 12 pages, 7 figures, accepted at Int. J. Theor. Phy

Determining The Value-at-risk In The Shadow Of The Power Law: The Case Of The SP-500 Index

In extant financial market models, including the Black-Scholes’ contruct, the dramatic events of October 1987 and August 2007 are totally unexpected, because these models are based on the assumptions of ‘independent price fluctuations’ and the existence of some ‘fixed-point equilibrium’. This paper argues that the convolution of a generalized fractional Brownian motion (into an array in frequency or time domain) and their corresponding amplitude spectra describes the surface of the attractor driving the evolution of prices. This more realistic approach shows that the SP-500 Index is characterized by a high long term Hurst exponent and hence by a ‘black noise’ with a power spectrum proportional to f-b (b > 2). In that set up, the above dramatic events are expected and their frequencies are determined. The paper also constructs an exhaustive frequency-variation relationship which can be used as practical guide to assess the ‘value at risk’.Market Collapse; Fractional Brownian Motion; Fractal Attractors; Maximum Hausdorff Dimension of Markets and Affine Profiles; Hurst Exponent; Power Spectrum Exponent; Value at Risk

Seething Horizontal Magnetic Fields in the Quiet Solar Photosphere

The photospheric magnetic field outside of active regions and the network has a ubiquitous and dynamic line-of-sight component that strengthens from disk center to limb as expected for a nearly horizontal orientation. This component shows a striking time variation with an average temporal rms near the limb of 1.7 G at ~3" resolution. In our moderate resolution observations the nearly horizontal component has a frequency variation power law exponent of -1.4 below 1.5 mHz and is spatially patchy on scales up to ~15 arcsec. The field may be a manifestation of changing magnetic connections between eruptions and evolution of small magnetic flux elements in response to convective motions. It shows no detectable latitude or longitude variations.Comment: 7 pages, 6 figures, submitted to ApJ letters, quality of figures significantly degraded here by compression requirement