The Limitations of Optimization from Samples

In this paper we consider the following question: can we optimize objective functions from the training data we use to learn them? We formalize this question through a novel framework we call optimization from samples (OPS). In OPS, we are given sampled values of a function drawn from some distribution and the objective is to optimize the function under some constraint. While there are interesting classes of functions that can be optimized from samples, our main result is an impossibility. We show that there are classes of functions which are statistically learnable and optimizable, but for which no reasonable approximation for optimization from samples is achievable. In particular, our main result shows that there is no constant factor approximation for maximizing coverage functions under a cardinality constraint using polynomially-many samples drawn from any distribution. We also show tight approximation guarantees for maximization under a cardinality constraint of several interesting classes of functions including unit-demand, additive, and general monotone submodular functions, as well as a constant factor approximation for monotone submodular functions with bounded curvature

Susceptibility or resilience? Prenatal stress predisposes male rats to social subordination, but facilitates adaptation to subordinate status

Mood disorders such as major depressive disorder (MDD) affect a significant proportion of the population. Although progress has been made in the development of therapeutics, a large number of individuals do not attain full remission of symptoms and adverse side effects affect treatment compliance for some. In order to develop new therapies, there is a push for new models that better reflect the multiple risk factors that likely contribute to the development of depressive illness. We hypothesized that early life stress would exacerbate the depressive-like phenotype that we have previously observed in socially subordinate (SUB) adult male rats in the visible burrow system (VBS), a semi-natural, ethologically relevant environment in which males in a colony form a dominance hierarchy. Dams were exposed to chronic variable stress (CVS) during the last week of gestation, resulting in a robust and non-habituating glucocorticoid response that did not alter maternal food intake, body weight or litter size and weight. As adults, one prenatal CVS (PCVS) and one non-stressed (NS) male were housed in the VBS with adult females. Although there were no overt differences between PCVS and NS male offspring prior to VBS housing, a greater percentage of PCVS males became SUB. However, the depressive-like phenotype of SUB males was not exacerbated in PCVS males; rather, they appeared to better cope with SUB status than NS SUB males. They had lower basal plasma corticosterone than NS SUB males at the end of VBS housing. In situ hybridization for CRH in the PVN and CeA did not reveal any prenatal treatment or status effects, while NPY expression was higher within the MeA of dominant and subordinate males exposed to the VBS in comparison with controls, but with no effect of prenatal treatment. These data suggest that prenatal chronic variable stress may confer resilience to offspring when exposed to social stress in adulthood

Accretion Disks and Dynamos: Toward a Unified Mean Field Theory

Conversion of gravitational energy into radiation in accretion discs and the origin of large scale magnetic fields in astrophysical rotators have often been distinct topics of research. In semi-analytic work on both problems it has been useful to presume large scale symmetries, necessarily resulting in mean field theories. MHD turbulence makes the underlying systems locally asymmetric and nonlinear. Synergy between theory and simulations should aim for the development of practical mean field models that capture essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion theory exemplify such ongoing pursuits. 21st century MFD theory has more nonlinear predictive power compared to 20th century MFD theory, whereas accretion theory is still in a 20th century state. In fact, insights from MFD theory are applicable to accretion theory and the two are artificially separated pieces of what should be a single theory. I discuss pieces of progress that provide clues toward a unified theory. A key concept is that large scale magnetic fields can be sustained via local or global magnetic helicity fluxes or via relaxation of small scale magnetic fluctuations, without the kinetic helicity driver of 20th century textbooks. These concepts may help explain the formation of large scale fields that supply non-local angular momentum transport via coronae and jets in a unified theory of accretion and dynamos. In diagnosing the role of helicities and helicity fluxes in disk simulations, each disk hemisphere should be studied separately to avoid being misled by cancelation that occurs as a result of reflection asymmetry. The fraction of helical field energy in disks is expected to be small compared to the total field in each hemisphere as a result of shear, but can still be essential for large scale dynamo action.Comment: For the Proceedings of the Third International Conference and Advanced School "Turbulent Mixing and Beyond," TMB-2011 held on 21 - 28 August 2011 at the Abdus Salam International Centre for Theoretical Physics, Trieste, http://users.ictp.it/~tmb/index2011.html Italy, To Appear in Physica Scripta (corrected small items to match version in print

Laboratory Plasma Dynamos, Astrophysical Dynamos, and Magnetic Helicity Evolution

The term ``dynamo'' means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large scale magnetic field against resistive decay and drive the magnetic geometry toward the lowest energy state, 2. flow-driven helical dynamos which amplify or sustain large scale magnetic fields in an otherwise turbulent flow, and 3. flow-driven nonhelical dynamos which amplify fields on scales at or below the driving turbulence. We discuss how all three types occur in astrophysics whereas plasma confinement device dynamos are of the first type. Type 3 dynamos requires no magnetic or kinetic helicity of any kind. Focusing on type 1 and 2 dynamos, we show how different limits of a unified set of equations for magnetic helicity evolution reveal both types. We explicitly describe a steady-state example of a type 1 dynamo, and three examples of type 2 dynamos: (i) closed volume and time dependent; (ii) steady-state with open boundaries; (iii) time dependent with open boundaries.Comment: accepted by MNRA

Bodyweight Perceptions among Texas Women: The Effects of Religion, Race/Ethnicity, and Citizenship Status

Despite previous work exploring linkages between religious participation and health, little research has looked at the role of religion in affecting bodyweight perceptions. Using the theoretical model developed by Levin et al. (Sociol Q 36(1):157–173, 1995) on the multidimensionality of religious participation, we develop several hypotheses and test them by using data from the 2004 Survey of Texas Adults. We estimate multinomial logistic regression models to determine the relative risk of women perceiving themselves as overweight. Results indicate that religious attendance lowers risk of women perceiving themselves as very overweight. Citizenship status was an important factor for Latinas, with noncitizens being less likely to see themselves as overweight. We also test interaction effects between religion and race. Religious attendance and prayer have a moderating effect among Latina non-citizens so that among these women, attendance and prayer intensify perceptions of feeling less overweight when compared to their white counterparts. Among African American women, the effect of increased church attendance leads to perceptions of being overweight. Prayer is also a correlate of overweight perceptions but only among African American women. We close with a discussion that highlights key implications from our findings, note study limitations, and several promising avenues for future research

Bihelical Magnetic Relaxation and Large Scale Magnetic Field Growth

A unified, three-scale system of equations accommodating nonlinear velocity driven helical dynamos, as well as time-dependent relaxation of magnetically dominated unihelical or bihelical systems is derived and solved herein. When opposite magnetic helicities of equal magnitude are injected on the intermediate and small scales, the large scale magnetic helicity grows kinematically (independent of the magnetic Reynolds number) to equal that on the intermediate scale. For both free and driven relaxation large scale fields are rapidly produced. Subsequently, a dissipation-limited dynamo, driven by growth of small scale kinetic helicity, further amplifies the large scale field. The results are important for astrophysical coronae fed with bihelical structures by dynamos in their host rotators. The large scale for the rotator corresponds to the intermediate scale for the corona. That bihelical magnetic relaxation can produce global scale fields may help to explain the formation of astrophysical coronal holes and magnetohydrodynamic outflows.Comment: LaTeX, 29 pages including figures, version in press, Physics of Plasma

Spin dynamics of molecular nanomagnets fully unraveled by four-dimensional inelastic neutron scattering

Molecular nanomagnets are among the first examples of spin systems of finite size and have been test-beds for addressing a range of elusive but important phenomena in quantum dynamics. In fact, for short-enough timescales the spin wavefunctions evolve coherently according to the an appropriate cluster spin-Hamiltonian, whose structure can be tailored at the synthetic level to meet specific requirements. Unfortunately, to this point it has been impossible to determine the spin dynamics directly. If the molecule is sufficiently simple, the spin motion can be indirectly assessed by an approximate model Hamiltonian fitted to experimental measurements of various types. Here we show that recently-developed instrumentation yields the four-dimensional inelastic-neutron scattering function S(Q,E) in vast portions of reciprocal space and enables the spin dynamics to be determined with no need of any model Hamiltonian. We exploit the Cr8 antiferromagnetic ring as a benchmark to demonstrate the potential of this new approach. For the first time we extract a model-free picture of the quantum dynamics of a molecular nanomagnet. This allows us, for example, to examine how a quantum fluctuation propagates along the ring and to directly test the degree of validity of the N\'{e}el-vector-tunneling description of the spin dynamics

Overcoming the Back Reaction on Turbulent Motions in the Presence of Magnetic Fields

Standard magnetohydrodynamic theories, such as the mean field dynamo theory, have been criticized when the back reaction of the magnetic field on turbulent motions is neglected. For the dynamo, this back reaction has been argued to suppress the turbulent motions required for optimal mean field production. Here it is suggested that if the magnetic field is spatially intermittent, for example residing in flux tubes, the back reaction on turbulent flows may be significantly reduced.Comment: Accepted to Physical Review Letters, 15 pages, plain Te