Variable selection by searching for good subsets

Machine learning and statistical models are increasingly used in a prediction context and in the process of building these models the question of which variables to include often arises. Over the last 50 years a number of procedures have been proposed, especially in the statistical literature. In this paper a newvariable selection procedure is introduced for linear models. A subset of variables is defined here to be “good at margin λ” if it has two properties, namely (i) its associated criterion of fit will be improved in relative terms by less than λ if any variable is added to it, and (ii) its criterion of fit will deteriorate in relative terms by at least λ if any variable inside it, is dropped from it. Thus, such a subset contains all variables that are individually important and none that are unimportant at a given margin λ ≥ 0. This paper discusses calculation of such λ-good subsets. The “good” approach extends readily to generalised linear and many other models by using an appropriate criterion of performance. The approach is illustrated on an artificial data set and a number of real data sets

A framework for normal mean variance mixture innovations with application to GARCH modelling

GARCH models are useful to estimate the volatility of financial return series. Historically the innovation distribution of a GARCH model was assumed to be standard normal but recent research emphasizes the need for more general distributions allowing both asymmetry (skewness) and kurtosis in the innovation distribution to obtain better fitting models. A number of authors have proposed models which are special cases of the class of normal mean variance mixtures. We introduce a general framework within which this class of innovation distributions may be discussed. This entails writing the innovation term as a standardised combination of two variables, namely a normally distributed term and a mixing variable, each with its own interpretation. We list the existing models that fit into this framework and compare the corresponding innovation distributions, finding that they tend to be quite similar. This is confirmed by an empirical illustration which fits the models to the monthly excess returns series of the US stocks. The illustration finds further support for the ICAPM model of Merton, thus supporting recent results of Lanne and Saikonnen (2006)

Spin Stiffness in the Hubbard model

The spin stiffness $\rho_{\rm s}$ of the repulsive Hubbard model that occurs in the hydrodynamic theory of antiferromagnetic spin waves is shown to be the same as the thermodynamically defined stiffness involved in twisting the order parameter. New expressions for $\rho_{\rm s}$ are derived, which enable easier interpretation, and connections with superconducting weight and gauge invariance are discussed.Comment: 21 Pages LaTeX2e, to be published in Journal of Physics

Heat Capacity and Magnetic Phase Diagram of the Low-Dimensional Antiferromagnet Y2_2BaCuO5_5

A study by specific heat of a polycrystalline sample of the low-dimensional magnetic system Y$_2$BaCuO$_5$ is presented. Magnetic fields up to 14 T are applied and permit to extract the ($T$,$H$) phase diagram. Below $\mu_0H^*\simeq2$ T, the N\'eel temperature, associated with a three-dimensional antiferromagnetic long-range ordering, is constant and equals $T_N=15.6$ K. Above $H^*$, $T_N$ increases linearly with $H$ and a field-induced increase of the entropy at $T_N$ is related to the presence of an isosbestic point at $T_X\simeq20$ K, where all the specific heat curves cross. A comparison is made between Y$_2$BaCuO$_5$ and the quasi-two-dimensional magnetic systems BaNi$_{2}$V$_{2}$O$_{8}$, Sr$_2$CuO$_2$Cl$_2$, and Pr$_2$CuO$_4$, for which very similar phase diagrams have been reported. An effective field-induced magnetic anisotropy is proposed to explain these phase diagrams.Comment: 14 pages, 7 figure

Phase Diagram of the BCC S=1/2 Heisenberg Antiferromagnet with First and Second Neighbor Exchange

We use linked-cluster series expansions, both at T=0 and high temperature, to analyse the phase structure of the spin-\half Heisenberg antiferromagnet with competing first and second-neighbor interactions on the 3-dimensional body-centred-cubic lattice. At zero temperature we find a first-order quantum phase transition at $J_2/J_1 \simeq 0.705 \pm 0.005$ between AF$_1$ (Ne\'el) and AF$_2$ ordered phases. The high temperature series yield quite accurate estimates of the bounding critical line for the AF$_1$ phase, and an apparent critical line for the AF$_2$ phase, with a bicritical point at $J_1/J_2\simeq 0.71$, $kT/J_1\simeq 0.34$. The possibility that this latter transition is first-order cannot be excluded.Comment: 10 pages, 4 figure

A cross-sectional study of psychological complaints and quality of life in severely injured patients

Purpose: The purpose of this study was to examine the incidence of psychological complaints and the relationship of these complaints with the quality of life (QOL) and accident- and patient-related factors among severely injured patients after the rehabilitation phase. Methods: Patients of 18 years or older with an injury severity score above 15 were included 15-53 months after their accident. Accident and patient characteristics were obtained from questionnaires and the trauma registry. Several questionnaires (Hospital Anxiety and Depression Scale, Impact of Events Scale, and Cognitive Failure Questionnaire) were used to determine the symptoms of psychological problems (anxiety or depression, post-traumatic stress disorder, or subjective cognitive complaints, respectively). The World Health Organization Quality of Life-Bref was used to determine QOL. A reference group of the Dutch general population was used for comparison of QOL scores. Results: The participation rate was 62 % (n = 173). At the time of the study, 30.1 % (n = 52) of the investigated patients had psychological complaints. No relation between psychological complaints and somatic severity or type of injury was found. Patients who were employed before the accident or resumed working reported less psychological complaints. Use of any medication before the accident and treatment for pre-accidental psychological problems were positively related to psychological complaints afterwards. QOL of severely injured patients was impaired in comparison with the general Dutch population, but only for those with psychological complaints. Conclusions: Psychological complaints seem to be an important and underestimated factor for a decreased QOL among severely injured patients

Electronic density of states derived from thermodynamic critical field curves for underdoped La-Sr-Cu-O

Thermodynamic critical field curves have been measured for $La_{2-x}Sr_{x}CuO_{4+\delta}$ over the full range of carrier concentrations where superconductivity occurs in order to determine changes in the normal state density of states with carrier concentration. There is a substantial window in the $H-T$ plane where the measurements are possible because the samples are both thermodynamically reversible and the temperature is low enough that vortex fluctuations are not important. In this window, the data fit Hao-Clem rather well, so this model is used to determine $H_c$ and $\kappa_c$ for each temperature and carrier concentration. Using N(0) and the ratio of the energy gap to transition temperature, $\Delta (0)/k_BT_c$, as fitting parameters, the $H_c vs T$ curves give $\Delta (0)/k_BT_c \sim 2.0$ over the whole range of $x$. Values of N(0) remain rather constant in the optimum-doped and overdoped regime, but drops quickly toward zero in the underdoped regime.

Quality of life in severely injured patients depends on psychosocial factors rather than on severity or type of injury

Background: Former studies have demonstrated that health-related quality of life is decreased in severely injured patients. However, in those studies patients were asked about their functioning and not about their (dis)contentment concerning their functioning. Little is known about how severely injured patients experience their quality of life (QOL). The objective of this cross-sectional study was to measure this subjective QOL of severely injured patients after their rehabilitation phase and to examine which accident- and patient-related factors affect the QOL of these patients. Methods: Patients of 18 years or older with an injury severity score (ISS) above 15 were included 15-53 months after their accident. Comorbidity before the accident, accident and sociodemographic characteristics, and QOL were obtained from the trauma registry and questionnaires. The WHOQOL-BREF was used to measure QOL. A reference group of the Dutch general population was used for comparison. Results: The participation rate was 61% (n = 173). Compared with the reference data, severely injured patients experienced a significantly worse QOL in all domains except social relations. The QOL scores were significantly decreased in all domains for patients with intracranial injury in combination with other injuries. Patients with a severe intracranial injury (AIS > 3) only reported significantly impaired QOL in the general and physical domains. Patients who resumed working or lived with others had significantly higher scores in all domains of QOL than patients who did not work anymore or were living alone. Significantly lower QOL scores were obtained from patients with comorbidity before the accident and from patients with longer durations of intensive care unit (ICU) treatment or hospitalisation. Gender, accident characteristics and time since the accident did not appear to be important for experienced QOL. Conclusions: The experience of impaired QOL appears to depend on living alone, inability to return to work and pre-accidental comorbidity rather than on the injured body area or the severity of the injury. Duration of hospital or ICU stay is important to subsequent QOL, even if ISS or body region is not

Dynamics and thermalization of the nuclear spin bath in the single-molecule magnet Mn12-ac: test for the theory of spin tunneling

The description of the tunneling of a macroscopic variable in the presence of a bath of localized spins is a subject of great fundamental and practical interest, and is relevant for many solid-state qubit designs. Instead of focusing on the the "central spin" (as is most often done), here we present a detailed study of the dynamics of the nuclear spin bath in the Mn12-ac single-molecule magnet, probed by NMR experiments down to very low temperatures (T = 20 mK). We find that the longitudinal relaxation rate of the 55Mn nuclei in Mn12-ac becomes roughly T-independent below T = 0.8 K, and can be strongly suppressed with a longitudinal magnetic field. This is consistent with the nuclear relaxation being caused by quantum tunneling of the molecular spin, and we attribute the tunneling fluctuations to the minority of fast-relaxing molecules present in the sample. The transverse nuclear relaxation is also T-independent for T < 0.8 K, and can be explained qualitatively and quantitatively by the dipolar coupling between like nuclei in neighboring molecules. We also show that the isotopic substitution of 1H by 2H leads to a slower nuclear longitudinal relaxation, consistent with the decreased tunneling probability of the molecular spin. Finally, we demonstrate that, even at the lowest temperatures, the nuclear spins remain in thermal equilibrium with the lattice phonons, and we investigate the timescale for their thermal equilibration. After a review of the theory of macroscopic spin tunneling in the presence of a spin bath, we argue that most of our experimental results are consistent with that theory, but the thermalization of the nuclear spins is not.Comment: 24 pages, 18 figures. Experimental study of the spin bath dynamics in quantum nanomagnets, plus an extensive review and application of the theor