An extension of the Kreiss stability theorem to families of matrices of unbounded order

AbstractThe Kreiss matrix theorem asserts three necessary and sufficient conditions for a family of matrices of fixed finite order to be L2-stable: a resolvent condition (R), a triangularization condition (S) and a Hermitian norm condition (H). We extend the Kreiss theorem to families of matrices of finite but unbounded order with the restriction that the degrees of the minimal polynomials of all matrices in the family are less than a fixed constant. For such matrix families, we show that (R) and (H) remain necessary and sufficient for L2-stability, while (S) must be replaced by a somewhat stronger “block triangularization” condition (S′). This extended Kreiss theorem permits a corresponding extension of the Buchanan stability theorem

Multi-Way Multi-Group Segregation and Diversity Indices

Background: How can we compute a segregation or diversity index from a three-way or multi-way contingency table, where each variable can take on an arbitrary finite number of values and where the index takes values between zero and one? Previous methods only exist for two-way contingency tables or dichotomous variables. A prototypical three-way case is the segregation index of a set of industries or departments given multiple explanatory variables of both sex and race. This can be further extended to other variables, such as disability, number of years of education, and former military service. Methodology/Principal Findings: We extend existing segregation indices based on Euclidean distance (square of coefficient of variation) and Boltzmann/Shannon/Theil index from two-way to multi-way contingency tables by including multiple summations. We provide several biological applications, such as indices for age polyethism and linkage disequilibrium. We also provide a new heuristic conceptualization of entropy-based indices. Higher order association measures are often independent of lower order ones, hence an overall segregation or diversity index should be the arithmetic mean of the normalized association measures at all orders. These methods are applicable when individuals selfidentify as multiple races or even multiple sexes and when individuals work part-time in multiple industries. Conclusions/Significance: The policy implications of this work are enormous, allowing people to rigorously test whethe

Statistical Model Selection for TID Hardness Assurance

Radiation Hardness Assurance (RHA) methodologies against Total Ionizing Dose (TID) degradation impose rigorous statistical treatments for data from a part's Radiation Lot Acceptance Test (RLAT) and/or its historical performance. However, no similar methods exist for using "similarity" data - that is, data for similar parts fabricated in the same process as the part under qualification. This is despite the greater difficulty and potential risk in interpreting of similarity data. In this work, we develop methods to disentangle part-to-part, lot-to-lot and part-type-to-part-type variation. The methods we develop apply not just for qualification decisions, but also for quality control and detection of process changes and other "out-of-family" behavior. We begin by discussing the data used in the study and the challenges of developing a statistic providing a meaningful measure of degradation across multiple part types, each with its own performance specifications. We then develop analysis techniques and apply them to the different data sets

Unbiased Shape Compactness for Segmentation

We propose to constrain segmentation functionals with a dimensionless, unbiased and position-independent shape compactness prior, which we solve efficiently with an alternating direction method of multipliers (ADMM). Involving a squared sum of pairwise potentials, our prior results in a challenging high-order optimization problem, which involves dense (fully connected) graphs. We split the problem into a sequence of easier sub-problems, each performed efficiently at each iteration: (i) a sparse-matrix inversion based on Woodbury identity, (ii) a closed-form solution of a cubic equation and (iii) a graph-cut update of a sub-modular pairwise sub-problem with a sparse graph. We deploy our prior in an energy minimization, in conjunction with a supervised classifier term based on CNNs and standard regularization constraints. We demonstrate the usefulness of our energy in several medical applications. In particular, we report comprehensive evaluations of our fully automated algorithm over 40 subjects, showing a competitive performance for the challenging task of abdominal aorta segmentation in MRI.Comment: Accepted at MICCAI 201

Relative importance of dispersion and rate-limited mass transfer in highly heterogeneous porous media: Analysis of a new tracer test at the Macrodispersion Experiment (MADE) site

This is the published version. Copyright American Geophysical Union[1] A single-well injection-withdrawal (SWIW) bromide tracer test was conducted to further investigate transport processes at the Macrodispersion Experiment (MADE) site on Columbus Air Force Base in Mississippi. The bromide breakthrough curve is highly asymmetric and exhibits an early time high-concentration peak followed by an extended period of low-concentration tailing. Comparisons of results simulated by advection-dispersion (AD) and dual-domain mass transfer (DDMT) models with the field data show that the DDMT model more accurately represents the magnitudes of both the early high-concentration peak and the later low-concentration tail. For both the AD and DDMT models, the match with field data is enhanced by incorporating hydraulic conductivity information from new direct-push profiling methods. The Akaike information criterion for the DDMT models is much smaller than that for the AD models in both the homogeneous and heterogeneous cases investigated in this work. The improved match of the DDMT model with the SWIW test data supports the hypothesis of mass transfer processes occurring at this highly heterogeneous site

A cluster-separable Born approximation for the 3D reduction of the three-fermion Bethe-Salpeter equation

We perform a 3D reduction of the two-fermion Bethe-Salpeter equation based on Sazdjian's explicitly covariant propagator, combined with a covariant substitute of the projector on the positive-energy free states. We use this combination in the two fermions in an external potential and in the three-fermion problems. The covariance of the two-fermion propagators insures the covariance of the two-body equations obtained by switching off the external potential, or by switching off all interactions between any pair of two fermions and the third one, even if the series giving the 3D potential is limited to the Born term or more generally truncated. The covariant substitute of the positive energy projector preserves the equations against continuum dissolution without breaking the covariance.Comment: 21 pages, 1 figure This article has been deeply modified after refereeing. The presentation has been improved and examples have been added. Three subsections have been added (transition matrix elements, two-body limits, covariant Salpeter's equation). submitted to Journal of Physics

Vif is a RNA chaperone that could temporally regulate RNA dimerization and the early steps of HIV-1 reverse transcription

HIV-1 Vif (viral infectivity factor) is associated with the assembly complexes and packaged at low level into the viral particles, and is essential for viral replication in non-permissive cells. Viral particles produced in the absence of Vif exhibit structural defects and are defective in the early steps of reverse transcription. Here, we show that Vif is able to anneal primer tRNALys3 to the viral RNA, to decrease pausing of reverse transcriptase during (–) strand strong-stop DNA synthesis, and to promote the first strand transfer. Vif also stimulates formation of loose HIV-1 genomic RNA dimers. These results indicate that Vif is a bona fide RNA chaperone. We next studied the effects of Vif in the presence of HIV-1 NCp, which is a well-established RNA chaperone. Vif inhibits NCp-mediated formation of tight RNA dimers and hybridization of tRNALys3, while it has little effects on NCp-mediated strand transfer and it collaborates with nucleocapsid (NC) to increase RT processivity. Thus, Vif might negatively regulate NC-assisted maturation of the RNA dimer and early steps of reverse transcription in the assembly complexes, but these inhibitory effects would be relieved after viral budding, thanks to the limited packaging of Vif in the virions

Spatial connectivity in a highly heterogeneous aquifer: From cores to preferential flow paths

This is the published version. Copyright American Geophysical Union[1] This study investigates connectivity in a small portion of the extremely heterogeneous aquifer at the Macrodispersion Experiment (MADE) site in Columbus, Mississippi. A total of 19 fully penetrating soil cores were collected from a rectangular grid of 4 m by 4 m. Detailed grain size analysis was performed on 5 cm segments of each core, yielding 1740 hydraulic conductivity (K) estimates. Three different geostatistical simulation methods were used to generate 3-D conditional realizations of the K field for the sampled block. Particle tracking calculations showed that the fastest particles, as represented by the first 5% to arrive, converge along preferential flow paths and exit the model domain within preferred areas. These 5% fastest flow paths accounted for about 40% of the flow. The distribution of preferential flow paths and particle exit locations is clearly influenced by the occurrence of clusters formed by interconnected cells with K equal to or greater than the 0.9 decile of the data distribution (10% of the volume). The fraction of particle paths within the high-K clusters ranges from 43% to 69%. In variogram-based K fields, some of the fastest paths are through media with lower K values, suggesting that transport connectivity may not require fully connected zones of relatively homogenous K. The high degree of flow and transport connectivity was confirmed by the values of two groups of connectivity indicators. In particular, the ratio between effective and geometric mean K (on average, about 2) and the ratio between the average arrival time and the arrival time of the fastest particles (on average, about 9) are consistent with flow and advective transport behavior characterized by channeling along preferential flow paths