Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

An ordinal shapley value for economic environments (Revised version)

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the Ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapely value for TU games, we construct a weighted OSV as well.

An ordinal shapley value for economic environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.

Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By anessential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur inmany compositional situations, such as household budget patterns, time budgets,palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful insuch situations. From consideration of such examples it seems sensible to build up amodel in two stages, the first determining where the zeros will occur and the secondhow the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data

Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance

We address the problem of scheduling a multiclass $M/M/m$ queue with Bernoulli feedback on $m$ parallel servers to minimize time-average linear holding costs. We analyze the performance of a heuristic priority-index rule, which extends Klimov's optimal solution to the single-server case: servers select preemptively customers with larger Klimov indices. We present closed-form suboptimality bounds (approximate optimality) for Klimov's rule, which imply that its suboptimality gap is uniformly bounded above with respect to (i) external arrival rates, as long as they stay within system capacity;and (ii) the number of servers. It follows that its relativesuboptimality gap vanishes in a heavy-traffic limit, as external arrival rates approach system capacity (heavy-traffic optimality). We obtain simpler expressions for the special no-feedback case, where the heuristic reduces to the classical $c \mu$ rule. Our analysis is based on comparing the expected cost of Klimov's ruleto the value of a strong linear programming (LP) relaxation of the system's region of achievable performance of mean queue lengths. In order to obtain this relaxation, we derive and exploit a new set ofwork decomposition laws for the parallel-server system. We further report on the results of a computational study on the quality of the $c \mu$ rule for parallel scheduling.

A two-mean reverting-factor model of the term structure of interest rates

This paper presents a two--factor model of the term structure ofinterest rates. We assume that default free discount bond prices aredetermined by the time to maturity and two factors, the long--term interestrate and the spread (difference between the long--term rate and theshort--term (instantaneous) riskless rate). Assuming that both factorsfollow a joint Ornstein--Uhlenbeck process, a general bond pricing equationis derived. We obtain a closed--form expression for bond prices andexamine its implications for the term structure of interest rates. We alsoderive a closed--form solution for interest rate derivatives prices. Thisexpression is applied to price European options on discount bonds andmore complex types of options. Finally, empirical evidence of the model'sperformance is presented.

Value of clinical factors in selecting postmenopausal women with rheumatoid arthritis for bone densitometry.

Criteria to decide which patients with rheumatoid arthritis (RA) should be examined by dual energy x ray absorptiometry (DXA) are currently not available. The rheumatologists from Amsterdam have proposed preliminary criteria based on clinical risk factors (age, disease activity, and functional status). These criteria are preliminary and not widely accepted but might be helpful in practice. The value of the proposal in a group of Spanish postmenopausal women with RA is analysed. METHODS DXA (lumbar spine and femoral neck) was performed in 128 patients recruited from a clinical setting, and the proposed criteria were applied. T and Z scores were established for a Spanish reference population. RESULTS The mean (SD) age of the patients was 61.3 (10.7) and mean duration of the postmenopausal period 14.5 (10.1) years. Mean duration of RA was 13.7 (7.7) years. Mean C reactive protein was 22 (21) mg/l; mean erythrocyte sedimentation rate 26 (18) mm/1st h; and mean Health Assessment Questionnaire score 1.25 (0.79). Ninety (70%) patients fulfilled the proposed criteria. Their sensitivity for the diagnosis of osteoporosis (T score ¿¿2.5 SD) was 86% and their specificity, 43%. Positive predictive value was 54% and negative predictive value, 79%. CONCLUSIONS The proposed criteria seem a good screening method for the selection of those patients with RA whose bone mineral density should be assessed as the sensitivity and negative predictive value are acceptable.

Lattice-gas model of particles with orientational and positional degrees of freedom: Mean-field treatment

We consider a lattice-gas model of particles with internal orientational degrees of freedom. In addition to antiferromagnetic nearest-neighbor (NN) and next-nearest-neighbor (NNN) positional interactions we also consider NN and NNN interactions arising from the internal state of the particles. The system then shows positional and orientational ordering modes with associated phase transitions at Tp and To temperatures at which long-range positional and orientational ordering are, respectively, lost. We use mean-field techniques to obtain a general approach to the study of these systems. By considering particular forms of the orientational interaction function we study coupling effects between both phase transitions arising from the interplay between orientational and positional degrees of freedom. In mean-field approximation coupling effects appear only for the phase transition taking place at lower temperatures. The strength of the coupling depends on the value of the long-range order parameter that remains finite at that temperature.

A Rotating black ring solution in five dimensions

The vacuum Einstein equations in five dimensions are shown to admit a solution describing a stationary asymptotically flat spacetime regular on and outside an event horizon of topology S1S2. It describes a rotating black ring. This is the first example of a stationary asymptotically flat vacuum solution with an event horizon of nonspherical topology. The existence of this solution implies that the uniqueness theorems valid in four dimensions do not have simple five-dimensional generalizations. It is suggested that increasing the spin of a spherical black hole beyond a critical value results in a transition to a black ring, which can have an arbitrarily large angular momentum for a given mass.

Mean first-passage times for systems driven by equilibrium persistent-periodic dichotomous noise

In a recent paper, [J. M. Porrà, J. Masoliver, and K. Lindenberg, Phys. Rev. E 48, 951 (1993)], we derived the equations for the mean first-passage time for systems driven by the coin-toss square wave, a particular type of dichotomous noisy signal, to reach either one of two boundaries. The coin-toss square wave, which we here call periodic-persistent dichotomous noise, is a random signal that can only change its value at specified time points, where it changes its value with probability q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals t. Here we consider the stationary version of this signal, that is, equilibrium periodic-persistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuities or the oscillations found in the case of nonstationary noise. We also discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Nitrogen replacement value of alfalfa to corn and wheat under irrigated Mediterranean conditions

In crop rotations that include alfalfa (Medicago sativa L.), agronomic and environmental concerns mean that it is important to determine the N fertilizer contribution of this legume for subsequent crops in order to help to increase the sustainability of cropping systems. To determine the N fertilizer replacement value (FRV) of a 2-yr alfalfa crop on subsequent crops of corn (Zea mays L.) followed by wheat (Triticum aestivum L.) under irrigated Mediterranean conditions, two 4-yr rotations (alfalfa-corn-wheat and corn-corn-corn-wheat) were conducted from 2001 to 2004 in a Typic Xerofluvent soil. Corn yields were compared after two years of alfalfa and a third year of corn under monoculture and wheat yields were also compared after both rotations. Corn production after alfalfa outyielded monoculture corn at all four rates of N fertilizer application analyzed (0, 100, 200 and 300 kg N/ha). The FRV of 2-yr alfalfa for corn was about 160 kg N/ha. Wheat grown after the alfalfa-corn rotation outyielded that grown after corn under monoculture at both the rates of N studied (0 and 100 kg N/ha). The FRV of alfalfa for wheat following alfalfa-corn was about 76 kg N/ha. Soil NO3 -N content after alfalfa was greater than with the corn monoculture at all rates of N fertilizer application and this higher value persisted during the second crop after alfalfa. This was probably one of the reasons for the better yields associated with the alfalfa rotation. These results make a valuable contribution to irrigated agriculture under mediterranean conditions, show reasons for interest in rotating alfalfa with corn, and explain how it is possible to make savings when applying N fertilizer.

Estimating extreme value cumulative distribution functions using bias-corrected kernel approaches

We propose a new kernel estimation of the cumulative distribution function based on transformation and on bias reducing techniques. We derive the optimal bandwidth that minimises the asymptotic integrated mean squared error. The simulation results show that our proposed kernel estimation improves alternative approaches when the variable has an extreme value distribution with heavy tail and the sample size is small.

Parallel characterizations of a generalized shapley value and a generalized banzhaf value for cooperative games with level structure of cooperation

We present parallel characterizations of two different values in the framework of restricted cooperation games. The restrictions are introduced as a finite sequence of partitions defined on the player set, each of them being coarser than the previous one, hence forming a structure of different levels of a priori unions. On the one hand, we consider a value first introduced in Ref. [18], which extends the Shapley value to games with different levels of a priori unions. On the other hand, we introduce another solution for the same type of games, which extends the Banzhaf value in the same manner. We characterize these two values using logically comparable properties.