Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems

Rate statistics for radio noise from lightning

Radio frequency noise from lightning was measured at several frequencies in the HF - VHF range at the Kennedy Space Center, Florida. The data were examined to determine flashing rate statistics during periods of strong activity from nearby storms. It was found that the time between flashes is modeled reasonably well by a random variable with a lognormal distribution

On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator

The existence of magnetohydrodynamic mean-field alpha^2-dynamos with spherically symmetric, isotropic helical turbulence function alpha is related to a non-self-adjoint spectral problem for a coupled system of two singular second order ordinary differential equations. We establish global estimates for the eigenvalues of this system in terms of the turbulence function alpha and its derivative alpha'. They allow us to formulate an anti-dynamo theorem and a non-oscillation theorem. The conditions of these theorems, which again involve alpha and alpha', must be violated in order to reach supercritical or oscillatory regimes.Comment: 35 pages, 4 figures, to be published in SIAM J. Math. Anal

The a priori Tan Theta Theorem for spectral subspaces

Let A be a self-adjoint operator on a separable Hilbert space H. Assume that the spectrum of A consists of two disjoint components s_0 and s_1 such that the set s_0 lies in a finite gap of the set s_1. Let V be a bounded self-adjoint operator on H off-diagonal with respect to the partition spec(A)=s_0 \cup s_1. It is known that if ||V||<\sqrt{2}d, where d=\dist(s_0,s_1), then the perturbation V does not close the gaps between s_0 and s_1 and the spectrum of the perturbed operator L=A+V consists of two isolated components s'_0 and s'_1 grown from s_0 and s_1, respectively. Furthermore, it is known that if V satisfies the stronger bound ||V||< d then the following sharp norm estimate holds: ||E_L(s'_0)-E_A(s_0)|| \leq sin(arctan(||V||/d)), where E_A(s_0) and E_L(s'_0) are the spectral projections of A and L associated with the spectral sets s_0 and s'_0, respectively. In the present work we prove that this estimate remains valid and sharp also for d \leq ||V||< \sqrt{2}d, which completely settles the issue.Comment: v3: some typos fixed; Examples adde

Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati Equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.Comment: 31 pages, 3 figures; proof of uniqueness of solutions added; to appear in Journal of Evolution Equation

Nuclear Ribosomal Internal Transcribed Spacer (ITS) Region as a Universal DNA Barcode Marker for Fungi

Six DNA regions were evaluated as potential DNA barcodes for Fungi, the second largest kingdom of eukaryotic life, by a multinational, multilaboratory consortium. The region of the mitochondrial cytochrome c oxidase subunit 1 used as the animal barcode was excluded as a potential marker, because it is difficult to amplify in fungi, often includes large introns, and can be insufficiently variable. Three subunits from the nuclear ribosomal RNA cistron were compared together with regions of three representative protein-coding genes (largest subunit of RNA polymerase II, second largest subunit of RNA polymerase II, and minichromosome maintenance protein). Although the protein-coding gene regions often had a higher percent of correct identification compared with ribosomal markers, low PCR amplification and sequencing success eliminated them as candidates for a universal fungal barcode. Among the regions of the ribosomal cistron, the internal transcribed spacer (ITS) region has the highest probability of successful identification for the broadest range of fungi, with the most clearly defined barcode gap between inter- and intraspecific variation. The nuclear ribosomal large subunit, a popular phylogenetic marker in certain groups, had superior species resolution in some taxonomic groups, such as the early diverging lineages and the ascomycete yeasts, but was otherwise slightly inferior to the ITS. The nuclear ribosomal small subunit has poor species-level resolution in fungi. ITS will be formally proposed for adoption as the primary fungal barcode marker to the Consortium for the Barcode of Life, with the possibility that supplementary barcodes may be developed for particular narrowly circumscribed taxonomic groups

Easing Restrictions During Vaccine Scarcity. How Mitigation Measures Help Tackling Associated Moral and Behavioral Challenges

Background: When vaccines became first available during the Covid-19 pandemic, their demand significantly exceeded their supply. In consequence, the access to vaccines, initially, was distributed unequally. At the same time, governments started easing pandemic restrictions for vaccinated and recovered persons and restoring their freedoms since their risk of transmitting the virus is significantly reduced. Evidence: We show that restoring freedoms for vaccinated and recovered persons – while upholding restrictions for the rest of the population – is morally unfair during vaccine scarcity. Further, it may yield unintended side-effects, including perverse incentives, growing rifts in society, and the expansion of marginalization. olicy Options & Recommendations: We recommend accompanying easing for vaccinated and recovered individuals by mitigation measures for those who are neither vaccinated nor recovered. We propose, first, to temporarily lift the same restrictions for negative-tested individuals, as for vaccinated or recovered people. Second, the state must ensure broad and easy access to testing for everyone – free of charge. Conclusion: If done right, these mitigation measures create (at least temporarily) equal access to freedom for everybody – solving the moral problem of unfair access to freedoms and counteracting possible negative consequences

A comparison of learning with haptic and visual modalities.

The impact of haptic feedback on the perception of unknown objects (10 without texture, 10 with texture, and 2 complex shapes) was examined. Using a point probe (a PHANTOM), three treatment groups of students (visual, haptic, and visual plus haptic feedback) explored a set of virtual objects. The visual treatment group observed the objects through a small circular aperture. Accuracy of perception, exploration time, and description of objects were compared for the three treatment groups. Participants included 45 visually normal undergraduate students distributed across the three treatment groups and 4 blind students composing a second hapticonly group. Results showed that, within the normally sighted students, the haptic and haptic plus visual groups were slightly slower in their explorations than the visual group. The haptic plus visual group was more accurate in identifying objects than the visual or haptic-only groups. The terms used by the haptic treatment group to describe the objects differed from the visual and visual plus haptic groups, suggesting that these modalities are processed differently. There were no differences across the three groups for long-term memory of the objects. The haptic group was significantly more accurate in identifying the complex objects than the visual or visual plus haptic groups. The blind students using haptic feedback were not significantly different from the other haptic-only treatment group of normally-sighted participants for accuracy, exploration pathways, and exploration times. The haptic-only group of participants spent more time exploring the back half of the virtual objects than the visual or visual plus haptic participants. This finding supports previous research showing that the use of the PHANTOM with haptic feedback tends to support the development of 3-dimensional understandings of objects

Examining New Phylogenetic Markers to Uncover the Evolutionary History of Early-Diverging Fungi: Comparing MCM7, TSR1 and rRnA Genes for Single- and Multi-Gene Analyses of the Kickxellomycotina

The recently recognised protein-coding genes MCM7 and TSR1 have shown significant promise for phylogenetic resolution within the Ascomycota and Basidiomycota, but have remained unexamined within other fungal groups (except for Mucorales). We designed and tested primers to amplify these genes across early-diverging fungal clades, with emphasis on the Kickxellomycotina, zygomycetous fungi with characteristic flared septal walls forming pores with lenticular plugs. Phylogenetic tree resolution and congruence with MCM7 and TSR1 were compared against those inferred with nuclear small (SSU) and large subunit (LSU) rRNA genes. We also combined MCM7 and TSR1 data with the rDNA data to create 3- and 4-gene trees of the Kickxellomycotina that help to resolve evolutionary relationships among and within the core clades of this subphylum. Phylogenetic inference suggests that Barbatospora, Orphella, Ramicandelaber and Spiromyces may represent unique lineages. It is suggested that these markers may be more broadly useful for phylogenetic studies among other groups of early-diverging fungi

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential $V$ lie in the disjoint union of two disks in the right and left half plane, respectively, provided that the $L^1-norm$ of $V$ is bounded from above by the speed of light times the reduced Planck constant. An analogous result for the Schr\"odinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on $V$ implies the absence of nonreal eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials