Convex Configurations on Nana-kin-san Puzzle

We investigate a silhouette puzzle that is recently developed based on the golden ratio. Traditional silhouette puzzles are based on a simple tile. For example, the tangram is based on isosceles right triangles; that is, each of seven pieces is formed by gluing some identical isosceles right triangles. Using the property, we can analyze it by hand, that is, without computer. On the other hand, if each piece has no special property, it is quite hard even using computer since we have to handle real numbers without numerical errors during computation. The new silhouette puzzle is between them; each of seven pieces is not based on integer length and right angles, but based on golden ratio, which admits us to represent these seven pieces in some nontrivial way. Based on the property, we develop an algorithm to handle the puzzle, and our algorithm succeeded to enumerate all convex shapes that can be made by the puzzle pieces. It is known that the tangram and another classic silhouette puzzle known as Sei-shonagon chie no ita can form 13 and 16 convex shapes, respectively. The new puzzle, Nana-kin-san puzzle, admits to form 62 different convex shapes

Introductory lectures to loop quantum gravity

We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.Comment: Based on lectures given at the 3eme Ecole de Physique Theorique de Jijel, Algeria, 26 Sep -- 3 Oct, 2009. 52 pages, many figures. v2 minor corrections. To be published in the proceeding

Polytopes and Loop Quantum Gravity

The main aim of this thesis is to give a geometrical interpretation of ``spacetime grains'' at Planck scales in the framework of Loop Quantum Gravity. My work consisted in analyzing the details of the interpretation of the quanta of space in terms of polytopes. The main results I obtained are the following: We clarified details on the relation between polytopes and interwiners, and concluded that an intertwiner can be seen unambiguously as the state of a \emph{quantum polytope}. Next we analyzed the properties of these polytopes: studying how to reconstruct the solid figure from LQG variables, the possible shapes and the volume. We adapted existing algorithms to express the geometry of the polytopes in terms of the holonomy-fluxes variables of LQG, thus providing an explicit bridge between the original variables and the interpretation in terms of polytopes of the phase space. Finally we present some direct application of this geometrical picture. We defined a volume operator such as in the large spin limit it reproduce the geometrical volume of a polytope, we computed numerically his spectrum for some elementary cases and we pointed out some asymptotic property of his spectrum. We discuss applications of the picture in terms of polytopes to the study of the semiclassical limit of LQG, in particular commenting a connection between the quantum dynamics and a generalization of Regge calculus on polytopes

Quantum statistical inference and communication

This thesis studies the limits on the performances of inference tasks with quantum data and quantum operations. Our results can be divided in two main parts. In the first part, we study how to infer relative properties of sets of quantum states, given a certain amount of copies of the states. We investigate the performance of optimal inference strategies according to several figures of merit which quantifies the precision of the inference. Since we are not interested in obtaining a complete reconstruction of the states, optimal strategies do not require to perform quantum tomography. In particular, we address the following problems: - We evaluate the asymptotic error probabilities of optimal learning machines for quantum state discrimination. Here, a machine receives a number of copies of a pair of unknown states, which can be seen as training data, together with a test system which is initialized in one of the states of the pair with equal probability. The goal is to implement a measurement to discriminate in which state the test system is, minimizing the error probability. We analyze the optimal strategies for a number of different settings, differing on the prior incomplete information on the states available to the agent. - We evaluate the limits on the precision of the estimation of the overlap between two unknown pure states, given N and M copies of each state. We find an asymptotic expansion of a Fisher information associated with the estimation problem, which gives a lower bound on the mean square error of any estimator. We compute the minimum average mean square error for random pure states, and we evaluate the effect of depolarizing noise on qubit states. We compare the performance of the optimal estimation strategy with the performances of other intuitive strategies, such as the swap test and measurements based on estimating the states. - We evaluate how many samples from a collection of N d-dimensional states are necessary to understand with high probability if the collection is made of identical states or they differ more than a threshold according to a motivated closeness measure. The access to copies of the states in the collection is given as follows: each time the agent ask for a copy of the states, the agent receives one of the states with some fixed probability, together with a different label for each state in the collection. We prove that the problem can be solved with O(pNd=2) copies, and that this scaling is optimal up to a constant independent on d;N; . In the second part, we study optimal classical and quantum communication rates for several physically motivated noise models. - The quantum and private capacities of most realistic channels cannot be evaluated from their regularized expressions. We design several degradable extensions for notable channels, obtaining upper bounds on the quantum and private capacities of the original channels. We obtain sufficient conditions for the degradability of flagged extensions of channels which are convex combination of other channels. These sufficient conditions are easy to verify and simplify the construction of degradable extensions. - We consider the problem of transmitting classical information with continuous variable systems and an energy constraint, when it is impossible to maintain a shared reference frame and in presence of losses. At variance with phase-insensitive noise models, we show that, in some regimes, squeezing improves the communication rates with respect to coherent state sources and with respect to sources producing up to two-photon Fock states. We give upper and lower bounds on the optimal coherent state rate and show that using part of the energy to repeatedly restore a phase reference is strictly suboptimal for high energies

Winona Daily News

https://openriver.winona.edu/winonadailynews/1551/thumbnail.jp

Quantum Cosmology

Within the second half of the last century, quantum cosmology concretely became one of the main research lines within gravitational theory and cosmology. Substantial progress has been made. Furthermore, quantum cosmology can become a domain that will gradually develop further over the next handful of decades, perhaps assisted by technological developments. Indications for new physics (i.e., beyond the standard model of particle physics or general relativity) could emerge and then the observable universe would surely be seen from quite a new perspective. This motivates bringing quantum cosmology to more research groups and individuals.This Special Issue (SI) aims to provide a wide set of reviews, ranging from foundational issues to (very) recent advancing discussions. Concretely, we want to inspire new work proposing observational tests, providing an aggregated set of contributions, covering several lines, some of which are thoroughly explored, some allowing progress, and others much unexplored. The aim of this SI is motivate new researchers to employ and further develop quantum cosmology over the forthcoming decades. Textbooks and reviews exist on the present subject, and this SI will complementarily assist in offering open access to a set of wide-ranging reviews. Hopefully, this will assist new interested researchers, in having a single open access online volume, with reviews that can help. In particular, this will help in selecting what to explore, what to read in more detail, where to proceed, and what to investigate further within quantum cosmology

2017 GREAT Day Program

SUNY Geneseo’s Eleventh Annual GREAT Day.https://knightscholar.geneseo.edu/program-2007/1011/thumbnail.jp

The Bright Continent: African Art History (Second Edition)

Significant original research is included in this textbook. Through nearly 1000 images, it explores both traditional and contemporary African art through general discussion and specifics. The first chapter discusses materials, gender, training, and patronage. Chapter Two covers the elements and principles of design, as well as stylistic and contextual analysis. Chapter Three takes a thematic approach to African art, including numerous case studies. Chapter Four explores how religions—traditional, Christian, and Muslim—impact art and how different types of societies—nomadic, small-scale, and kingdom-based—favor varied arts. Appendices on note-taking and research are included. Maps; index. 668 pages.https://engagedscholarship.csuohio.edu/msl_ae_ebooks/1023/thumbnail.jp

The Knowledge of Good

This book presents Robert S. Hartman’s formal theory of value and critically examines many other twentieth century value theorists in its light, including A.J. Ayer, Kurt Baier, Brand Blanshard, Paul Edwards, Albert Einstein, William K. Frankena, R.M. Hare, Nicolai Hartmann, Martin Heidegger, G.E. Moore, P.H. Nowell-Smith, Jose Ortega y Gasset, Charles Stevenson, Paul W. Taylor, Stephen E. Toulmin, and J.O. Urmson