Scale space consistency of piecewise constant least squares estimators -- another look at the regressogram

We study the asymptotic behavior of piecewise constant least squares regression estimates, when the number of partitions of the estimate is penalized. We show that the estimator is consistent in the relevant metric if the signal is in $L^2([0,1])$, the space of c\`{a}dl\`{a}g functions equipped with the Skorokhod metric or $C([0,1])$ equipped with the supremum metric. Moreover, we consider the family of estimates under a varying smoothing parameter, also called scale space. We prove convergence of the empirical scale space towards its deterministic target.Comment: Published at http://dx.doi.org/10.1214/074921707000000274 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Vertical coherence of short-periodic current variations

A study is described which attempts to obtain information about the vertical correlation of ocean currents at frequencies higher than inertial. Current velocity and temperature data for sensor separations of 4–12 m were taken with a mooring at ‘Site D’. The coherence and phase spectra for velocity component pairs reveals that motions are rotational at low frequencies. A cut-off frequency exists above which coherence drops to low values. The limiting frequency coincides with the minimum Väisälä frequency of the total water column. These cross-spectral properties support the assumption that the motion in this frequency range is governed by internal wave dynamics. The coherence and phase spectra of temperature pairs indicate that a field of temperature structure is superimposed on the mean field which is weakly correlated to the field of motion

The influence of potassium on core and geodynamo evolution

We model the thermal evolution of the core and mantle using a parametrized convection scheme, and calculate the entropy available to drive the geodynamo as a function of time. The cooling of the core is controlled by the rate at which the mantle can remove heat. Rapid core cooling favours the operation of a geodynamo but creates an inner core that is too large; slower cooling reduces the inner core size but makes a geodynamo less likely to operate. Introducing potassium into the core retards inner core growth and provides an additional source of entropy. For our nominal model parameters, a core containing approximate to 400 ppm potassium satisfies the criteria of present-day inner core size, surface heat flux, mantle temperature and cooling rate, and positive core entropy production.We have identified three possibilities that may allow the criteria to be satisfied without potassium in the core. (1) The core thermal conductivity is less than half the generally accepted value of 50 W m(-1) K-1. (2) The core solidus and adiabat are significantly colder and shallower than results from shock experiments and ab initio simulations indicate. (3) The core heat flux has varied by no more than a factor of 2 over Earth history. All models we examined with the correct present-day inner core radius have an inner core age of < 1.5 Gyr; prior to this time the geodynamo was sustained by cooling and radioactive heat production within a completely liquid core

Critical dynamics of ballistic and Brownian particles in a heterogeneous environment

The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed large-scale computer simulations, demonstrating that universality holds at long times in the immediate vicinity of the transition. The scaling function describing the crossover from anomalous transport to diffusive motion is found to vary extremely slowly and spans at least 5 decades in time. To extract the scaling function, one has to allow for the leading universal corrections to scaling. Our findings suggest that apparent power laws with varying exponents generically occur and dominate experimentally accessible time windows as soon as the heterogeneities cover a decade in length scale. We extract the divergent length scales, quantify the spatial heterogeneities in terms of the non-Gaussian parameter, and corroborate our results by a thorough finite-size analysis.Comment: 14 page

Transverse fluctuations of grafted polymers

We study the statistical mechanics of grafted polymers of arbitrary stiffness in a two-dimensional embedding space with Monte Carlo simulations. The probability distribution function of the free end is found to be highly anisotropic and non-Gaussian for typical semiflexible polymers. The reduced distribution in the transverse direction, a Gaussian in the stiff and flexible limits, shows a double peak structure at intermediate stiffnesses. We also explore the response to a transverse force applied at the polymer free end. We identify F-Actin as an ideal benchmark for the effects discussed.Comment: 10 pages, 4 figures, submitted to Physical Review

The key role of nitric oxide in hypoxia: hypoxic vasodilation and energy supply-demand matching

Significance: a mismatch between energy supply and demand induces tissue hypoxia with the potential to cause cell death and organ failure. Whenever arterial oxygen concentration is reduced, increases in blood flow - 'hypoxic vasodilation' - occur in an attempt to restore oxygen supply. Nitric oxide is a major signalling and effector molecule mediating the body's response to hypoxia, given its unique characteristics of vasodilation (improving blood flow and oxygen supply) and modulation of energetic metabolism (reducing oxygen consumption and promoting utilization of alternative pathways). Recent advances: this review covers the role of oxygen in metabolism and responses to hypoxia, the hemodynamic and metabolic effects of nitric oxide, and mechanisms underlying the involvement of nitric oxide in hypoxic vasodilation. Recent insights into nitric oxide metabolism will be discussed, including the role for dietary intake of nitrate, endogenous nitrite reductases, and release of nitric oxide from storage pools. The processes through which nitric oxide levels are elevated during hypoxia are presented, namely (i) increased synthesis from nitric oxide synthases, increased reduction of nitrite to nitric oxide by heme- or pterin-based enzymes and increased release from nitric oxide stores, and (ii) reduced deactivation by mitochondrial cytochrome c oxidase. Critical issues: several reviews covered modulation of energetic metabolism by nitric oxide, while here we highlight the crucial role NO plays in achieving cardiocirculatory homeostasis during acute hypoxia through both vasodilation and metabolic suppression Future directions: we identify a key position for nitric oxide in the body's adaptation to an acute energy supply-demand mismatc

Statistical mechanics of Fofonoff flows in an oceanic basin

We study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin and a linear topography h=by which represents either a real bottom topography or the beta-effect appropriate to oceanic situations. Our minimum enstrophy principle is motivated by different arguments of statistical mechanics reviewed in the article. It leads to steady states of the quasigeostrophic (QG) equations characterized by a linear relationship between potential vorticity q and stream function psi. For low values of the energy, we recover Fofonoff flows [J. Mar. Res. 13, 254 (1954)] that display a strong westward jet. For large values of the energy, we obtain geometry induced phase transitions between monopoles and dipoles similar to those found by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)] in the absence of topography. In the presence of topography, we recover and confirm the results obtained by Venaille and Bouchet [Phys. Rev. Lett. 102, 104501 (2009)] using a different formalism. In addition, we introduce relaxation equations towards minimum potential enstrophy states and perform numerical simulations to illustrate the phase transitions in a rectangular oceanic basin with linear topography (or beta-effect).Comment: 26 pages, 28 figure

Integrated cross-domain object storage in working memory: Evidence from a verbal-spatial memory task

Working-memory theories often include domain-specific verbal and visual stores (e.g., the phonological and visuospatial buffers of Baddeley, 1986), and some also posit more general stores thought to be capable of holding verbal or visuospatial materials (Baddeley, 2000; Cowan, 2005). However, it is currently unclear which type of store is primarily responsible for maintaining objects that include components from multiple domains. In these studies, a spatial array of letters was followed by a single probe identical to an item in the array or differing systematically in spatial location, letter identity, or their combination. Concurrent verbal rehearsal suppression impaired memory in each of these trial types in a task that required participants to remember verbal-spatial binding, but did not impair memory for spatial locations if the task did not require verbal-spatial binding for a correct response. Thus, spatial information might be stored differently when it must be bound to verbal information. This suggests that a cross-domain store such as the episodic buffer of Baddeley (2000) or the focus of attention of Cowan (2001) might be used for integrated object storage, rather than the maintenance of associations between features stored in separate domain-specific buffers