Generic formal fibers and analytically ramified stable rings

Let $A$ be a local Noetherian domain of Krull dimension $d$. Heinzer, Rotthaus and Sally have shown that if the generic formal fiber of $A$ has dimension $d-1$, then $A$ is birationally dominated by a one-dimensional analytically ramified local Noetherian ring having residue field finite over the residue field of $A$. We explore further this correspondence between prime ideals in the generic formal fiber and one-dimensional analytically ramified local rings. Our main focus is on the case where the analytically ramified local rings are stable, and we show that in this case the embedding dimension of the stable ring reflects the embedding dimension of a prime ideal maximal in the generic formal fiber, thus providing a measure of how far the generic formal fiber deviates from regularity. A number of characterizations of analytically ramified local stable domains are also given.Comment: To appear in Nagoya J. Mat

Functional network and spectral analysis of clinical EEG data to identify quantitative biomarkers and classify brain disorders

Many cognitive and neurological disorders today, such as Autism Spectrum Disorders (ASD) and various forms of epilepsy such as infantile spasms (IS), manifest as changes in voltage activity recorded in scalp electroencephalograms (EEG). Diagnosis of brain disease often relies on the interpretation of complex EEG features through visual inspection by clinicians. Although clinically useful, such interpretation is subjective and suffers from poor inter-rater reliability, which affects clinical care through increased variability and uncertainty in diagnosis. In addition, such qualitative assessments are often binary, and do not parametrically measure characteristics of disease manifestations. Many cognitive disorders are grouped by similar behaviors, but may arise from distinct biological causes, possibly represented by subtle electrophysiological differences. To address this, quantitative analytical tools - such as functional network connectivity, frequency-domain, and time-domain features - are being developed and applied to clinically obtained EEG data to identify electrophysiological biomarkers. These biomarkers enhance a clinician’s ability to accurately diagnose, categorize, and select treatment for various neurological conditions. In the first study, we use spectral and functional network analysis of clinical EEG data recorded from a population of children to propose a cortical biomarker for autism. We first analyze a training set of age-matched (4–8 years) ASD and neurotypical children to develop hypotheses based on power spectral features and measures of functional network connectivity. From the training set of subjects, we derive the following hypotheses: 1) The ratio of the power of the posterior alpha rhythm (8–14 Hz) peak to the anterior alpha rhythm peak is significantly lower in ASD than control subjects. 2) The functional network density is lower in ASD subjects than control subjects. 3) A select group of edges provide a more sensitive and specific biomarker of ASD. We then test these hypotheses in a validation set of subjects and show that both the first and third hypotheses, but not the second, are validated. The validated features successfully classified the data with significant accuracy. These results provide a validated study for EEG biomarkers of ASD based on changes in brain rhythms and functional network characteristics. We next perform a follow-up study that utilizes the same group of ASD and neurotypical subjects, but focuses on differences between these two groups in the sleep state. Motivated by the results from the previous study, we utilize the previously validated biomarkers, including the alpha ratio and the subset of edges found to be a sensitive biomarker of ASD, and test their effectiveness in the sleep state. To complement these frequency domain features, we also investigate the efficacy of several time domain measures. This investigation did not lead to significant findings, which may have important implications for the differences between sleep and wake states in ASD, or perhaps generally for clinical assessment, as well as for the effect of noise on signal in clinically obtained data. Finally, we design a similar analysis framework to investigate a set of clinical EEG data recorded from a population of children with active infantile spasms (IS) (2-16 months), and age-matched neurotypical children, in both wake and sleep states. The goal of this analysis is to develop a quantitative biomarker from the EEG signal, which ultimately we will apply to predict the clinical outcome of children with IS. In addition to spectral and functional network analysis, we calculate time domain features previously found to correlate with seizures. We compare the two populations by each feature individually, test the effects of age on these features, use all features in a linear discriminant model to categorize IS versus neurotypical EEG, and test the findings using a leave-one-out validation test. We find almost every feature tested shows significant population differences between IS and control groups, and that taken together they serve as an effective classifier, with potential to be informative as to disease severity and long-term outcome. Furthermore, analysis of these features reveals two groups, indicating a possibility that these features reflect two distinct qualitative characteristics of IS and seizures

Injective hulls of simple modules over finite dimensional nilpotent complex Lie superalgebras

We show that the finite dimensional nilpotent complex Lie superalgebras g whose injective hulls of simple U(g)-modules are locally Artinian are precisely those whose even part g_0 is isomorphic to a nilpotent Lie algebra with an abelian ideal of codimension 1 or to a direct product of an abelian Lie algebra and a certain 5-dimensional or a certain 6-dimensional nilpotent Lie algebra

Classifying Serre subcategories via atom spectrum

In this paper, we introduce the atom spectrum of an abelian category as a topological space consisting of all the equivalence classes of monoform objects. In terms of the atom spectrum, we give a classification of Serre subcategories of an arbitrary noetherian abelian category. Moreover we show that the atom spectrum of a locally noetherian Grothendieck category is homeomorphic to its Ziegler spectrum.Comment: 15 page

Femtosecond Pump-Probe Diagnostics Of Preformed Plasma Channels

We report on recent ultrafast pump-probe experiments 28 in He plasma waveguides using 800 nm, 80 fs pump pulses of 0.2 x 1018 W/cm2 peak guided intensity, and single orthogonally-polarized 800 nm probe pulses with similar to0.1% of pump intensity. The main results are: (1) We observe frequency-domain interference between the probe and a weak, depolarized component of the pump that differs substantially in mode shape from the injected pump pulse; (2) we observe spectral blue-shifts in the transmitted probe that are not evident in the transmitted pump. The evidence indicates that pump depolarization and probe blue-shifts both originate near the channel entrance.Physic

Electron density measurements for plasma adaptive optics

This study investigates the feasibility of using plasma as an adaptive optical medium for applications such as beam steering, wavefront control, and adaptive filtering. The optical path length of light propagating through plasma depends on the plasma electron density, which may be controlled via the prescribed voltage, frequency, pressure, gas, and electrode geometry. Accurate control of the optical path length requires characterization of the electron density over all operating conditions. Experimental measurements of plasma electron density were obtained using a dielectric barrier discharge at various voltage and pressure conditions. The plasma was contained in a low--pressure, hollow glass cylinder with flat optical glass at each end. The electron density of the plasma was -measured using a dual-wavelength Michelson interferometer setup. Probing the plasma with two distinct wavelengths (0.633 µm and 3.39 µm) allowed for simultaneous determination of the plasma electron density and background gas heating. Results from the experiment provided critical data for assessing plasma as a medium for adaptive optics

Criteria for flatness and injectivity

Let $R$ be a commutative Noetherian ring. We give criteria for flatness of $R$-modules in terms of associated primes and torsion-freeness of certain tensor products. This allows us to develop a criterion for regularity if $R$ has characteristic $p$, or more generally if it has a locally contracting endomorphism. Dualizing, we give criteria for injectivity of $R$-modules in terms of coassociated primes and (h-)divisibility of certain \Hom-modules. Along the way, we develop tools to achieve such a dual result. These include a careful analysis of the notions of divisibility and h-divisibility (including a localization result), a theorem on coassociated primes across a \Hom-module base change, and a local criterion for injectivity.Comment: 19 page

Inflation and Higgs Phenomenology in a Model Unifying the DFSZ Axion with the Majoron

The Two-Higgs-Doublet-Standard Model-Axion-Seesaw-Higgs-Portal inflation (2hdSMASH) model consisting of two Higgs doublets, a Standard Model (SM) singlet complex scalar and three SM singlet right-handed neutrinos can embed axion dark matter, neutrino masses and address inflation. We report on an investigation of the inflationary aspects of 2hdSMASH and its subsequent impact on low energy phenomenology. In particular, we identify inflationary directions for which the parameter values required for successful inflation do not violate perturbative unitarity and boundedness-from-below conditions. By analyzing the renormalization-group flow of the parameters we identify the necessary and sufficient constraints for running all parameters perturbatively and maintaining stability from the electroweak to the PLANCK scale. We determine typical benchmark points satisfying theoretical and experimental constraints which can be potentially probed by future colliders.Comment: 71 pages, 18 figures, 7 table

Full 3D+1 modelling of the tilted-pulse-front setups for single-cycle terahertz generation

The tilted-pulse-front setup utilizing a diffraction grating is one of the most successful methods to generate single- to few-cycle terahertz pulses. However, the generated terahertz pulses have a large spatial inhomogeneity, due to the noncollinear phase matching condition and the asymmetry of the prism-shaped nonlinear crystal geometry, especially when pushing for high optical-to-terahertz conversion efficiency. A 3D+1 (x,y,z,t) numerical model is necessary in order to fully investigate the terahertz generation problem in the tilted-pulse-front scheme. We compare in detail the differences between 1D+1, 2D+1 and 3D+1 models. The simulations show that the size of the optical beam in the pulse-front-tilt plane sensitively affects the spatio-temporal properties of the terahertz electric field. The terahertz electric field is found to have a strong spatial dependence such that a few-cycle pulse is only generated near the apex of the prism. The part of the beam farther from the apex contains a large fraction of the energy but has a waveform that deviates from a few-cycle. This strong spatial dependence must be accounted for when using the terahertz pulses for strong-field physics and carrier-envelope-phase sensitive experiments such as terahertz acceleration, coherent control of antiferromagnetic spin waves and terahertz high-harmonic generation.Comment: a typo of the minus sign and the ratio of f1/f2 is correcte