Probabilistic Fréchet means for time varying persistence diagrams

© 2015, Institute of Mathematical Statistics. All rights reserved.In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (D<inf>p</inf>, W<inf>p</inf>), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards. We fix this problem by altering the original definition of Fréchet mean so that it now becomes a probability measure on the set of persistence diagrams; in a nutshell, the mean of a set of diagrams will be a weighted sum of atomic measures, where each atom is itself a persistence diagram determined using a perturbation of the input diagrams. This definition gives for each N a map (D<inf>p</inf>)^N→ℙ(D<inf>p</inf>). We show that this map is Hölder continuous on finite diagrams and thus can be used to build a useful statistic on vineyards

Performance Cycle Analysis of a Two-Spool, Separate-Exhaust Turbofan With Interstage Turbine Burner

This paper presents the performance cycle analysis of a dual-spool, separate-exhaust turbofan engine, with an Interstage Turbine Burner serving as a secondary combustor. The ITB, which is located at the transition duct between the high- and the low-pressure turbines, is a relatively new concept for increasing specific thrust and lowering pollutant emissions in modern jet engine propulsion. A detailed performance analysis of this engine has been conducted for steady-state engine performance prediction. A code is written and is capable of predicting engine performances (i.e., thrust and thrust specific fuel consumption) at varying flight conditions and throttle settings. Two design-point engines were studied to reveal trends in performance at both full and partial throttle operations. A mission analysis is also presented to assure the advantage of saving fuel by adding ITB

The Role of Socioemotional Wealth in Entrepreneurial Persistence Decisions for Family Businesses

Many factors may influence entrepreneurial persistence in various contexts. For example, scholars find that family business entrepreneurs are more persistent than other entrepreneurs. However, the reasons why they are more persistent are not as well known. Utilizing a conjoint experiment with 64 entrepreneurs and 376 decisions, this paper examines the influence of socioemotional wealth (SEW) on persistence decisions in a family business context. The results of the Hierarchical Linear Modelling show that the expected financial returns, expected non-financial benefits, expected switching costs, and probability of expected outcomes influence entrepreneurial persistence decisions. Further, family business entrepreneurs with higher levels of SEW focus more on non-financial benefits when facing alternative opportunities. This study also provided empirical evidence for different dimensions of SEW. The results show that the emotional attachment of family members and the renewal of family bonds to the firm are effective indicators, which provide a direct measurement of SEW. The findings of this study increase scholarly understanding of both entrepreneurial persistence literature founded in threshold theory and SEW literature

Modified Dispersion Relations from the Renormalization Group of Gravity

We show that the running of gravitational couplings, together with a suitable identification of the renormalization group scale can give rise to modified dispersion relations for massive particles. This result seems to be compatible with both the frameworks of effective field theory with Lorentz invariance violation and deformed special relativity. The phenomenological consequences depend on which of the frameworks is assumed. We discuss the nature and strength of the available constraints for both cases and show that in the case of Lorentz invariance violation, the theory would be strongly constrained.Comment: revtex4, 9 pages, updated to match published versio

Performance (Off-Design) Cycle Analysis for a Turbofan Engine With Interstage Turbine Burner

This report presents the performance of a steady-state, dual-spool, separate-exhaust turbofan engine, with an interstage turbine burner (ITB) serving as a secondary combustor. The ITB, which is located in the transition duct between the high- and the low-pressure turbines, is a relatively new concept for increasing specific thrust and lowering pollutant emissions in modern jet-engine propulsion. A detailed off-design performance analysis of ITB engines is written in Microsoft(Registered Trademark) Excel (Redmond, Washington) macrocode with Visual Basic Application to calculate engine performances over the entire operating envelope. Several design-point engine cases are pre-selected using a parametric cycle-analysis code developed previously in Microsoft(Registered Trademark) Excel, for off-design analysis. The off-design code calculates engine performances (i.e. thrust and thrust-specific-fuel-consumption) at various flight conditions and throttle settings

Nontrivial, Asymptotically Non-free Gauge Theories and Dynamical Unification of Couplings

An evidence for nontriviality of asymptotically non-free (ANF) Yang-Mills theories is found on the basis of optimized perturbation theory. It is argued that these theories with matter couplings can be made nontrivial by means of the reduction of couplings, leading to the idea of dynamical unification of couplings (DUC) The second-order reduction of couplings in the ANF $SU(3)$-gauged Higgs-Yukawa theory, which is assumed to be nontrivial here, is carried out to motivate independent investigations on its nontriviality and DUC

Lorentz Violation of Quantum Gravity

A quantum gravity theory which becomes renormalizable at short distances due to a spontaneous symmetry breaking of Lorentz invariance and diffeomorphism invariance is studied. A breaking of Lorentz invariance with the breaking patterns $SO(3,1)\to O(3)$ and $SO(3,1)\to O(2)$, describing 3+1 and 2+1 quantum gravity, respectively, is proposed. A complex time dependent Schr\"odinger equation (generalized Wheeler-DeWitt equation) for the wave function of the universe exists in the spontaneously broken symmetry phase at Planck energy and in the early universe, uniting quantum mechanics and general relativity. An explanation of the second law of thermodynamics and the spontaneous creation of matter in the early universe can be obtained in the symmetry broken phase of gravity.Comment: 10 pages, minor change and reference added. Typos corrected. To be published in Class. Quant. Grav

Active neutron interrogation for verification of storage of weapons components at the Oak Ridge Y-12 Plant

A nuclear weapons identification system (NWIS), under development since 1984 at the Oak Ridge Y-12 Plant and presently in use there, uses active neutron interrogation with low-intensity {sup 252}Cf sources in ionization chambers to provide a timed source of fission neutrons from the spontaneous fission of {sup 252}Cf. To date, measurements have been performed on {approximately}15 different weapons systems in a variety of configurations both in and out of containers. Those systems included pits and fully assembled systems ready for deployment at the Pantex Plant in Amarillo, Texas, and weapons components at the Oak Ridge Y-12 Plant. These measurements have shown that NWIS can identify nuclear weapons and/or components; nuclear weapons/components can be distinguished from mockups where fissile material has been replaced by nonfissile material; omissions of small amounts (4%) of fissile material can be detected; changes in internal configurations can be determined; trainer parts can be identified as was demonstrated by verification of 512 containers with B33 components at the Y-12 Plant (as many as 32 in one 8-hour shift); and nonfissile components can be identified. The current NWIS activities at the Oak Ridge Y-12 Plant include: (1) further development of the system for more portability and lower power consumption, (2) collection of reference signatures for all weapons components in containers, and (3) confirmation of a particular weapons component in storage and confirmation of receipts. This paper describes the recent measurements with NWIS for a particular weapons component in storage that have resolved an Inspector General (IG`s) audit finding with regard to performance of confirmation of inventory

Charged Dilatonic AdS Black Branes in Arbitrary Dimensions

We study electromagnetically charged dilatonic black brane solutions in arbitrary dimensions with flat transverse spaces, that are asymptotically AdS. This class of solutions includes spacetimes which possess a bulk region where the metric is approximately invariant under Lifshitz scalings. Given fixed asymptotic boundary conditions, we analyze how the behavior of the bulk up to the horizon varies with the charges and derive the extremality conditions for these spacetimes.Comment: References update