Strongly Nonlinear Waves in 3D Phononic Crystals

Three dimensional phononic crystal ("sonic vacuum" without prestress) was assembled from 137 vertical cavities arranged in hexagonal pattern in Silicone matrix filled with stainless steel spheres. This system has unique strongly nonlinear properties with respect to wave propagation inherited from nonlinear Hertz type elastic contact interaction. Trains of strongly nonlinear solitary waves excited by short duration impact were investigated. Solitary wave with speed below sound speed in the air and reflection from the boundary of two "sonic vacuums" were detected

Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture

We consider one-dimensional quantum spin chain, which is called XX model, XX0 model or isotropic XY model in a transverse magnetic field. We study the model on the infinite lattice at zero temperature. We are interested in the entropy of a subsystem [a block of L neighboring spins]. It describes entanglement of the block with the rest of the ground state. G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev showed that for large blocks the entropy scales logarithmically. We prove the logarithmic formula for the leading term and calculate the next term. We discovered that the dependence on the magnetic field interacting with spins is very simple: the magnetic field effectively reduce the size of the subsystem. We also calculate entropy of a subsystem of a small size. We also evaluated Renyi and Tsallis entropies of the subsystem. We represented the entropy in terms of a Toeplitz determinant and calculated the asymptotic analytically.Comment: LATEX, 17 pages, 1 fi

Assessing and Remedying Coverage for a Given Dataset

Data analysis impacts virtually every aspect of our society today. Often, this analysis is performed on an existing dataset, possibly collected through a process that the data scientists had limited control over. The existing data analyzed may not include the complete universe, but it is expected to cover the diversity of items in the universe. Lack of adequate coverage in the dataset can result in undesirable outcomes such as biased decisions and algorithmic racism, as well as creating vulnerabilities such as opening up room for adversarial attacks. In this paper, we assess the coverage of a given dataset over multiple categorical attributes. We first provide efficient techniques for traversing the combinatorial explosion of value combinations to identify any regions of attribute space not adequately covered by the data. Then, we determine the least amount of additional data that must be obtained to resolve this lack of adequate coverage. We confirm the value of our proposal through both theoretical analyses and comprehensive experiments on real data.Comment: in ICDE 201

Forecasting Dynamic Investment Timing under the Cyclic Behavior in Real Estate

This paper applies the Hodrck-Prescott (HP) filter to forecast short-term residential real estate prices under cyclical movements. We separate the trend component from the cyclical component. We show that each regional residential market reacts not only to previous price movements, but also that these regional markets react to previous shocks under Auto Regressive Integrated Moving Average (ARIMA) modeling. Using the S&P Case-Shiller Home Price Index, we compare our forecast to index values from the Chicago Mercantile Exchange (CME) Housing Futures and Options. Our study identifies possible systematic errors from the different price adjustments reflecting current market situations.Real estate investment; Real estate cycle; residential housing futures contract; Real estate risk hedging

Strongly nonlinear waves in a chain of Teflon beads

One dimensional "sonic vacuum" type phononic crystals were assembled from a chain of Teflon spheres with different diameters in a Teflon holder. It was demonstrated for the first time that this polymer-based "sonic vacuum", with exceptionally low elastic modulus of particles, supports propagation of strongly nonlinear solitary waves with a very low speed.Comment: 33 pages, 6 figure