Budget Feasible Mechanisms for Experimental Design

In the classical experimental design setting, an experimenter E has access to a population of $n$ potential experiment subjects $i\in \{1,...,n\}$, each associated with a vector of features $x_i\in R^d$. Conducting an experiment with subject $i$ reveals an unknown value $y_i\in R$ to E. E typically assumes some hypothetical relationship between $x_i$'s and $y_i$'s, e.g., $y_i \approx \beta x_i$, and estimates $\beta$ from experiments, e.g., through linear regression. As a proxy for various practical constraints, E may select only a subset of subjects on which to conduct the experiment. We initiate the study of budgeted mechanisms for experimental design. In this setting, E has a budget $B$. Each subject $i$ declares an associated cost $c_i >0$ to be part of the experiment, and must be paid at least her cost. In particular, the Experimental Design Problem (EDP) is to find a set $S$ of subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i}) under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to the information gain in parameter $\beta$ that is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. Further, the subjects are strategic and may lie about their costs. We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant factor approximation to EDP. In particular, for any small $\delta > 0$ and $\epsilon > 0$, we can construct a (12.98, $\epsilon$)-approximate mechanism that is $\delta$-truthful and runs in polynomial time in both $n$ and $\log\log\frac{B}{\epsilon\delta}$. We also establish that no truthful, budget-feasible algorithms is possible within a factor 2 approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression

The sequence of the 5.8 S ribosomal RNA of the crustacean <i>Artemia salina</i>. With a proposal for a general secondary structure model for 5.8 S ribosomal RNA

We report the primary structure of 5.8 S rRNA from the crustacean Artemia salina. The preparation shows length heterogeneity at the 5′-terminus, but consists of uninterrupted RNA chains, in contrast to some insect 5.8 S rRNAs, which consist of two chains of unequal length separated in the gene by a short spacer. The sequence was aligned with those of 11 other 5.8 S rRNAs and a general secondary structure model derived. It has four helical regions in common with the model of Nazar et al. (J. Biol. Chem. 250, 8591–8597 (1975)), but for a fifth helix a different base pairing scheme was found preferable, and the terminal sequences are presumed to bind to 28 S rRNA instead of binding to each other. In the case of yeast, where both the 5.8 S and 26 S rRNA sequences are known, the existence of five helices in 5.8 S rRNA is shown to be compatible with a 5.8 S - 26 S rRNA interaction model

Improved quantum algorithms for the ordered search problem via semidefinite programming

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find new quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm.Comment: 8 pages, 4 figure

Quantum Detection with Unknown States

We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the probability of a detection error have been derived. In this work, we assume that each of the states in our collection is a mixture of a known state and an unknown state. We investigate two criteria for optimality. The first is minimization of the worst-case probability of a detection error. For the second we assume a probability distribution on the unknown states, and minimize of the expected probability of a detection error. We find that under both criteria, the optimal detectors are equivalent to the optimal detectors of an ``effective ensemble''. In the worst-case, the effective ensemble is comprised of the known states with altered prior probabilities, and in the average case it is made up of altered states with the original prior probabilities.Comment: Refereed version. Improved numerical examples and figures. A few typos fixe

Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards

We consider the effect of spin-orbit coupling on the low energy excitation spectrum of an Andreev billiard (a quantum dot weakly coupled to a superconductor), using a dynamical numerical model (the spin Andreev map). Three effects of spin-orbit coupling are obtained in our simulations: In zero magnetic field: (1) the narrowing of the distribution of the excitation gap; (2) the appearance of oscillations in the average density of states. In strong magnetic field: (3) the appearance of a peak in the average density of states at zero energy. All three effects have been predicted by random-matrix theory.Comment: 5 pages, 4 figure

Energy Harvesting from the Beating Heart by a Mass Imbalance Oscillation Generator

Energy-harvesting devices attract wide interest as power supplies of today's medical implants. Their long lifetime will spare patients from repeated surgical interventions. They also offer the opportunity to further miniaturize existing implants such as pacemakers, defibrillators or recorders of bio signals. A mass imbalance oscillation generator, which consists of a clockwork from a commercially available automatic wrist watch, was used as energy harvesting device to convert the kinetic energy from the cardiac wall motion to electrical energy. An MRI-based motion analysis of the left ventricle revealed basal regions to be energetically most favorable for the rotating unbalance of our harvester. A mathematical model was developed as a tool for optimizing the device's configuration. The model was validated by an in vitro experiment where an arm robot accelerated the harvesting device by reproducing the cardiac motion. Furthermore, in an in vivo experiment, the device was affixed onto a sheep heart for 1h. The generated power in both experiments—in vitro (30μW) and in vivo (16.7μW)—is sufficient to power modern pacemaker

Use of hatch date for broiler breeder production planning

Data on 109 batches of broiler breeders belonging to six strains and bred in conventional sheds were analyzed to determine the possible influence of natural day length cycle phase on age at start of laying, at sexual maturity, and at peak egg production. The dependence of these variables on date of hatching was characterized by polynomial regression analysis. The resulting equations constitute simple, novel empirical models that are in keeping with current theory on the effects of photoperiod on sexual maturation, and should facilitate production planning in broiler breeder farmsS

Grain-size characterization of reworked fine-grained aeolian deposits

After a previous review of the grain-size characteristics of in situ (primary) fine-grained aeolian deposits, reworked (secondary) aeolian deposits, as modified in lacustrine environments and by alluvial and pedogenic processes, are discussed in this paper. As a reference, the grain-size characteristics of primary loess deposits are shortly described. Commonly, pedogenesis and weathering of primary loess may lead to clay neoformation and thus to an enrichment in grain diameters of 4-8 mu m, a size which is comparable to the fine background loess. Remarkably, the modal grain-size values of primary loess are preserved after re -deposition in lakes and flood plains. But, secondary lacustrine settings show a very characteristic admixture with a clayey population of 1-2,5 mu m diameter due to the process of settling in standing water. Similarly, alluvial settings show often an addition with coarse-grained sediment supplied by previously eroded sediment. However, floodplain settings show also often the presence of pools and other depressions which behave similarly to lacustrine environments. As a result, alluvial secondary loess sediments are characterized by the poorest grain-size sorting when compared with the other secondary loess and primary loess. Despite the characteristic texture of each of these deposits, grain-size characteristics of the described individual sediment categories are not always fully diagnostic and thus grain-size analysis should be complemented by other information, as sedimentary structures and fauna or flora, to reliably reconstruct the sedimentary processes and environments