Optimum power allocation for parallel Gaussian channels with arbitrary input distributions

The mutual information of independent parallel Gaussian-noise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signalling constellations with limited peak-to-average ratios (m-PSK, m-QAM, etc) are used in lieu of the ideal Gaussian signals. This paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions. Such policy admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition. The relationship between mutual information of Gaussian channels and nonlinear minimum mean-square error proves key to solving the power allocation problem.

Optimum power allocation for multiuser OFDM with arbitrary signal constellations

This paper formulates power allocation policies that maximize the region of mutual informationsachievable in multiuser downlink OFDM channels. Arbitrary partitioning ofthe available tones among users and arbitrary modulation formats, possibly different forevery user, are considered. Two distinct policies are derived, respectively for slow fadingchannels tracked instantaneously by the transmitter and for fast fading channels knownonly statistically thereby. With instantaneous channel tracking, the solution adopts theform of a multiuser mercury/waterfilling procedure that generalizes the single-user mercury/waterfilling introduced in [1, 2]. With only statistical channel information, in contrast,the mercury/waterfilling interpretation is lost. For both policies, a number of limitingregimes are explored and illustrative examples are provided.

Parental investments in children: how bargaining and educational homogamy affect time allocation

This study examines parental time investment in their children, distinguishing between developmental and non-developmental care. Our analyses centre on three influential determinants: educational background, marital homogamy, and spouses' relative bargaining power. We find that the emphasis on quality care time is correlated with parents' education, and that marital homogamy reduces couple specialization, but only among the highly educated. In line with earlier research, we identify gendered parental behaviour. The presence of boys is an important condition for fathers' time dedication, but primarly among lower educated fathers. To the extent that parental stimulation is decisive for child outcomes, our findings suggest the persistence of important inequalities. This emerges through our special attention to behavioural differences across the educational distribution among households.

Male reproductive success and multiple paternity in wild, low-density populations of the adder (Vipera berus).

We studied for the first time the occurrence of multiple paternity, male reproductive success, and neonate survival in wild, low-density adder (Vipera berus) populations using 13 microsatellite loci. Paternity was assigned for 15 clutches, collected during 3 years. Our data demonstrated that multiple paternity can occur at a high level (69%) in natural populations of V. berus, even if the density of adults is low. The high proportion of multiple sired clutches was comparable to the proportion observed in captive populations. Male reproductive success significantly increased with body length, and only the largest males successfully sired entire clutches. Finally, no relationship was detected between the number of fathers per clutch and neonate survival. These results suggest that multiple matings could be beneficial in populations with high level of inbreeding or low male fecundity.

Estimating the basic reproductive number from viral sequence data.

Epidemiological processes leave a fingerprint in the pattern of genetic structure of virus populations. Here, we provide a new method to infer epidemiological parameters directly from viral sequence data. The method is based on phylogenetic analysis using a birth-death model (BDM) rather than the commonly used coalescent as the model for the epidemiological transmission of the pathogen. Using the BDM has the advantage that transmission and death rates are estimated independently and therefore enables for the first time the estimation of the basic reproductive number of the pathogen using only sequence data, without further assumptions like the average duration of infection. We apply the method to genetic data of the HIV-1 epidemic in Switzerland.

On Certain Greedoid Polyhedra, Partially Indexable Scheduling Problems, and Extended Restless Bandit Allocation Indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid (whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then the problem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Money, Fame and the Allocation of Talent: Brain Drain, the Matthew Effect and the Institution of Science

The earning structure in science is known to be flat relative to the one in the private sector, which could cause a brain drain toward the private sector. In this paper, we assume that agents value both money and fame and study the role of the institution of science in the allocation of talent between the science sector and the private sector. Following works on the Sociology of Science, we model the institution of science as a mechanism distributing fame (i.e. peer recognition). We show that since the intrinsic performance is less noisy signal of talent in the science sector than in the private sector, a good institution of science can mitigate the brain drain. We also find that providing extra monetary incentives through the market might undermine the incentives provided by the institution and thereby worsen the brain drain. Finally, we study the optimal balance between monetary and non-monetary incentives in science.

Financial Repression in a Natural Experiment: Loan Allocation and the Change in the Usury Laws in 1714

If financial deepening aids economic growth, then financial repression should be harmful. We use a natural experiment – the change in the English usury laws in 1714 – to analyze the effects of interest rate restrictions. We use a sample of individual loan transactions to demonstrate how the reduction of the legal maximum rate of interest affected the supply and demand for credit. Average loan size and minimum loan size increased strongly, and access to credit worsened for those with little ‘social capital.’ While we have no direct evidence that loans were misallocated, the discontinuity in loan receipts makes this highly likely. We conclude that financial repression can undermine the positive effects of financial deepening.

Weak and Strong Altruism in Trait Groups: Reproductive Suicide, Personal Fitness, and Expected Value

A simple variant of trait group selection, employing predators as the mechanism underlying group selection, supports contingent reproductive suicide as altruism (i.e., behavior lowering personal fitness while augmenting that of another) without kin assortment. The contingent suicidal type may either saturate the population or be polymorphic with a type avoiding suicide, depending on parameters. In addition to contingent suicide, this randomly assorting morph may also exhibit continuously expressed strong altruism (sensu Wilson 1979) usually thought restricted to kin selection. The model will not, however, support a sterile worker caste as such, where sterility occurs before life history events associated with effective altruism; reproductive suicide must remain fundamentally contingent (facultative sensu West Eberhard 1987; Myles 1988) under random assortment. The continuously expressed strong altruism supported by the model may be reinterpreted as probability of arbitrarily committing reproductive suicide, without benefit for another; such arbitrary suicide (a "load" on "adaptive" suicide) is viable only under a more restricted parameter space relative to the necessarily concomitant adaptive contingent suicide.

Sex allocation and sex-dependent selection for body size in Trypoxylon rogenhoferi Kohl (Hymenoptera, Sphecidae)

Two populations of the wasp Trypoxylon rogenhoferi Kohl, 1884 from São Carlos and Luís Antônio, State of São Paulo, Brazil, were observed and sampled from May 1999 to February 2001 using trap-nests. This mass-provisioning wasp was used to test some aspects of optimal sex allocation theory. Both populations fit all the predictions of the models of Green and Brockmann and Grafen. Maternal provisions determined the size of each offspring, and females allocated well-stocked brood cells to daughters, the sex that benefits most being large. This strategy resulted in a difference in size between the sexes. In São Carlos, female weight at emergence was 1.18 times that of males, in Luís Antônio this value was 1.13. The brood cell volume was correlated with both wing length and weight at emergence in both sexes, and the chance that a given brood cell contained a male offspring decreased with increased brood cell volume. In T. rogenhoferi female body size was related to fitness. Larger females were able to collect more mass of spiders per day, the spiders they captured were heavier, and they provisioned more brood cells per day. They also produced larger daughters. For males, no relationship between body size and fitness was found, but the data were scarce. Since the patterns of provisioning were variable among different females in both study sites, it is possible that the females not follow a unique strategy for sex allocation. The sex ratio and/or investment ratio in the São Carlos population was female-biased and in Luís Antônio, male-biased. In spite of the influence of trap-nests diameters on male production in Luís Antônio, there is some evidence that in São Carlos population the local availability of prey and/or lower rate of parasitism may be major forces in determining the observed sex ratio, but further studies are necessary to verify such hypothesis.

Regional allocation of skills

This paper addresses three questions: (1) why does the share of skilledworkers in regional population tend to be higher in wealthier regions? (2)what determines changes in this share over time? and (3) why is it that internalmigration tends to raise average skill levels of the receiving regions relativeto that of the sending regions? I construct a two--region dynamic model withagglomeration and congestion to answer these questions. It is shown that,under certain relationship between wages and demand for land, unskilledworkers are discouraged more strongly from living in a wealthier region andare less mobile than skilled workers.

Nestling barn owls beg more intensely in the presence of their mother than in the presence of their father

Nestling begging behaviour may be an honest signal of need used by parents to adjust optimally both feeding rate and within-brood food allocation. Although several studies showed that mothers and fathers can be differentially responsive to nestling begging behaviour with one parent showing a stronger tendency to feed the offspring that beg the most, little information is yet available on whether offspring beg for food at different intensities from the mother than father. In the present study, we investigated in nestling barn owls whether the intensity of vocal begging behaviour in the presence of the mother and in the presence of the father is different. A difference is expected because reproductive tasks are divided between the sexes with fathers bringing more food items to the nest than mothers. The results show that although mothers transfer their prey item to one of the offspring more rapidly than fathers once in their nestbox, nestlings begged more intensely in the presence of their mother than in the presence of their father. To our knowledge, this is the first empirical evidence that offspring vocalize to different levels in the presence of their mother than in the presence of their father.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Population based resource allocation: The use of hybrid risk adjustment

The emphasis on integrated care implies new incentives that promote coordinationbetween levels of care. Considering a population as a whole, the resource allocation systemhas to adapt to this environment. This research is aimed to design a model that allows formorbidity related prospective and concurrent capitation payment. The model can be applied inpublicly funded health systems and managed competition settings.Methods: We analyze the application of hybrid risk adjustment versus either prospective orconcurrent risk adjustment formulae in the context of funding total health expenditures for thepopulation of an integrated healthcare delivery organization in Catalonia during years 2004 and2005.Results: The hybrid model reimburses integrated care organizations avoiding excessive risktransfer and maximizing incentives for efficiency in the provision. At the same time, it eliminatesincentives for risk selection for a specific set of high risk individuals through the use ofconcurrent reimbursement in order to assure a proper classification of patients.Conclusion: Prospective Risk Adjustment is used to transfer the financial risk to the healthprovider and therefore provide incentives for efficiency. Within the context of a National HealthSystem, such transfer of financial risk is illusory, and the government has to cover the deficits.Hybrid risk adjustment is useful to provide the right combination of incentive for efficiency andappropriate level of risk transfer for integrated care organizations.