Hypothesis test for normal mixture models: The EM approach

Normal mixture distributions are arguably the most important mixture models, and also the most technically challenging. The likelihood function of the normal mixture model is unbounded based on a set of random samples, unless an artificial bound is placed on its component variance parameter. Moreover, the model is not strongly identifiable so it is hard to differentiate between over dispersion caused by the presence of a mixture and that caused by a large variance, and it has infinite Fisher information with respect to mixing proportions. There has been extensive research on finite normal mixture models, but much of it addresses merely consistency of the point estimation or useful practical procedures, and many results require undesirable restrictions on the parameter space. We show that an EM-test for homogeneity is effective at overcoming many challenges in the context of finite normal mixtures. We find that the limiting distribution of the EM-test is a simple function of the $0.5\chi^2_0+0.5\chi^2_1$ and $\chi^2_1$ distributions when the mixing variances are equal but unknown and the $\chi^2_2$ when variances are unequal and unknown. Simulations show that the limiting distributions approximate the finite sample distribution satisfactorily. Two genetic examples are used to illustrate the application of the EM-test.Comment: Published in at http://dx.doi.org/10.1214/08-AOS651 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Efficient Integrated Circuit Simulator And Time Domain Adjoint Sensitivity Analysis

In this paper, we revisit time-domain adjoint sensitivity with a circuit theoretic approach and an efficient solution is clearly stated in terms of device level. Key is the linearization of the energy storage elements (e.g., capacitance and inductance) and nonlinear memoryless elements (e.g., MOS, BJT DC characteristics) at each time step. Due to the finite precision of computation, numerical errors that accumulate across timesteps can arise in nonlinear elements

Long-Term Changes of Hypolimnetic Dissolved Oxygen and Phytoplankton Community Composition in a Large Lake, Lake Simcoe, Ontario and Revisit Dissolved Oxygen Profile Models for Lakes in Central Ontario

Long-term changes in volume-weighted hypolimnetic dissolved oxygen (VWHDO) and phytoplankton community composition were examined as important water quality indicator in Lake Simcoe, a large freshwater lake with impacts by various drivers such as dreissenid mussel (DM) invasion, reduction in phosphorus (P) loading and climatic change and oscillations. VWHDO dynamics were examined by several multiple linear regressions which revealed that VWHDOmin was positively correlated with the invasion of DM and negatively correlated with hypolimnetic water temperature; VWHDO depletion rate (DR) was positively correlated with ammonia and total phosphorus (TP) annual loading. Hence, longer period of thermal stratification (L) may have offset improvements in VWHDOmin generated by P controls and invasive species. Redundancy analysis and variation partitioning revealed that DM acted on phytoplankton composition indirectly by changing the environmental conditions because environmental variables and DM individually explained little variance in phytoplankton composition but water chemistry variables and DM collectively explained a large portion of the variation. A series of models predicting the uppermost plane of the DO-depleted zone (Zox), spring dissolved oxygen (DOi) profile and end-of-summer dissolved oxygen (DOf) profile built by Molot et al. (1992) were re-analyzed, re-calibrated with more recent data (A lakes during 1990-2013), and validated (B lakes during 1990-2013). With the current brownification trend (increased DOC), we expected to see increased DOf at all depths; however, increased reduced N species (ammonia) in the hypolimnion would offset the brownification effect

Analysis of Design Philosophy and Utility Function of Library Building

The design of most modern library buildings is based on the characteristics and service objects of library, for which the latest achievements of modern technology are made full use of. Usually, modern libraries are designed to be with various different functional zones and boundaries, and uncrossed reader, book and librarian transportation streamline. The design ideas of “openness, factualism, containment, innovation, and people and service first” are reflected in library services via construction planning and design. Besides, library buildings are given certain functions in combination with the actual situation of library and readers’ needs. This paper is intended to, in combination with the author’s several years of work experience, discuss the design philosophy and utility functions of the library building from the aspects of design of major structure of building, foundation facilities design, furniture design, and color design, which is of certain reference value.

Quantum Interference of Stored Coherent Spin-wave Excitations in a Two-channel Memory

Quantum memories are essential elements in long-distance quantum networks and quantum computation. Significant advances have been achieved in demonstrating relative long-lived single-channel memory at single-photon level in cold atomic media. However, the qubit memory corresponding to store two-channel spin-wave excitations (SWEs) still faces challenges, including the limitations resulting from Larmor procession, fluctuating ambient magnetic field, and manipulation/measurement of the relative phase between the two channels. Here, we demonstrate a two-channel memory scheme in an ideal tripod atomic system, in which the total readout signal exhibits either constructive or destructive interference when the two-channel SWEs are retrieved by two reading beams with a controllable relative phase. Experimental result indicates quantum coherence between the stored SWEs. Based on such phase-sensitive storage/retrieval scheme, measurements of the relative phase between the two SWEs and Rabi oscillation, as well as elimination of the collapse and revival of the readout signal, are experimentally demonstrated