Improved Bounds on Quantum Learning Algorithms

In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum black-box queries which are required to exactly identify an unknown function from C is $O(\frac{\log |C|}{\sqrt{{\hat{\gamma}}^{C}}})$, where $\hat{\gamma}^{C}$ is a combinatorial parameter of the class C. We essentially resolve this conjecture in the affirmative by giving a quantum algorithm that, for any class C, identifies any unknown function from C using $O(\frac{\log |C| \log \log |C|}{\sqrt{{\hat{\gamma}}^{C}}})$ quantum black-box queries. We consider a range of natural problems intermediate between the exact learning problem (in which the learner must obtain all bits of information about the black-box function) and the usual problem of computing a predicate (in which the learner must obtain only one bit of information about the black-box function). We give positive and negative results on when the quantum and classical query complexities of these intermediate problems are polynomially related to each other. Finally, we improve the known lower bounds on the number of quantum examples (as opposed to quantum black-box queries) required for $(\epsilon,\delta)$-PAC learning any concept class of Vapnik-Chervonenkis dimension d over the domain $\{0,1\}^n$ from $\Omega(\frac{d}{n})$ to $\Omega(\frac{1}{\epsilon}\log \frac{1}{\delta}+d+\frac{\sqrt{d}}{\epsilon})$. This new lower bound comes closer to matching known upper bounds for classical PAC learning.Comment: Minor corrections. 18 pages. To appear in Quantum Information Processing. Requires: algorithm.sty, algorithmic.sty to buil

Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

The relationship between the phosphate and structural carbonate fractionation of fallow deer bioapatite in tooth enamel

The species‐specific relationship between phosphate (δ18OP values) and structural carbonate (δ18OC values) oxygen isotope ratios has been established for several modern and fossil animal species but until now it has not been investigated in European fallow deer (Dama dama dama). This study describes the relationship between phosphate and structural carbonate bioapatite in tooth enamel of extant fallow deer, which will help us further understand the species' unique environmental and cultural history. Methods The oxygen isotope composition of phosphate (δ18OP value) and structural carbonate (δ18OC value) of hydroxylapatite was determined in 51 modern fallow deer tooth enamel samples from across Europe and West Asia. The δ18OC values were measured on a GV IsoPrime dual‐inlet mass spectrometer and the δ18OP values on a temperature‐controlled elemental analyser (TC/EA) coupled to a DeltaPlus XL isotope ratio mass spectrometer via a ConFlo III interface. Results This study establishes a direct and linear relationship between the δ18OC and δ18OP values from fallow deer tooth enamel (δ18OC = +9.244(±0.216) + 0.958 * δ18OP (±0.013)). Despite the successful regression, the variation in δ18O values from samples collected in the same geographical area is greater than expected, although the results cluster in broad climatic groupings when Koppen‐Geiger classifications are taken into account for the individuals' locations. Conclusions This is the first comprehensive study of the relationship between ionic forms of oxygen (phosphate oxygen and structural carbonate) in fallow deer dental enamel. The new equation will allow direct comparison with other herbivore data. Variable δ18O values within populations of fallow deer broadly reflect the ecological zones they are found in which may explain this pattern of results in other euryphagic species

A novel lineage of the Capra genus discovered in the Taurus Mountains of Turkey using ancient genomics

Direkli Cave, located in the Taurus Mountains of southern Turkey, was occupied by Late Epipaleolithic hunters-gatherers for the seasonal hunting and processing of game including large numbers of wild goats. We report genomic data from new and published Capra specimens from Direkli Cave and, supplemented with historic genomes from multiple Capra species, find a novel lineage best represented by a ~14,000 year old 2.59 X genome sequenced from specimen Direkli4. This newly discovered Capra lineage is a sister clade to the Caucasian tur species (Capra cylindricornis and Capra caucasica), both now limited to the Caucasus region. We identify genomic regions introgressed in domestic goats with high affinity to Direkli4, and find that West Eurasian domestic goats in the past, but not those today, appear enriched for Direkli4-specific alleles at a genome-wide level. This forgotten 'Taurasian tur' likely survived Late Pleistocene climatic change in a Taurus Mountain refuge and its genomic fate is unknown

Perfect Hash Families: The Generalization to Higher Indices

Perfect hash families are often represented as combinatorial arrays encoding partitions of kitems into v classes, so that every t or fewer of the items are completely separated by at least a specified number of chosen partitions. This specified number is the index of the hash family. The case when each t-set must be separated at least once has been extensively researched; they arise in diverse applications, both directly and as fundamental ingredients in a column replacement strategy for a variety of combinatorial arrays. In this paper, construction techniques and algorithmic methods for constructing perfect hash families are surveyed, in order to explore extensions to the situation when each t-set must be separated by more than one partition.https://digitalcommons.usmalibrary.org/books/1029/thumbnail.jp

The spatial structure of lithic landscapes : the late holocene record of east-central Argentina as a case study

Fil: Barrientos, Gustavo. División Antropología. Facultad de Ciencias Naturales y Museo. Universidad Nacional de La Plata; ArgentinaFil: Catella, Luciana. División Arqueología. Facultad de Ciencias Naturales y Museo. Universidad Nacional de La Plata; ArgentinaFil: Oliva, Fernando. Centro Estudios Arqueológicos Regionales. Facultad de Humanidades y Artes. Universidad Nacional de Rosario; Argentin

Endpoints in pediatric pain studies

Assessing pain intensity in (preverbal) children is more difficult than in adults. Tools to measure pain are being used as primary endpoints [e.g., pain intensity, time to first (rescue) analgesia, total analgesic consumption, adverse effects, and long-term effects] in studies on the effects of analgesic drugs. Here, we review current and promising new endpoints used in pediatric pain assessment studies