Improving Transient Performance of Adaptive Control Architectures using Frequency-Limited System Error Dynamics

We develop an adaptive control architecture to achieve stabilization and command following of uncertain dynamical systems with improved transient performance. Our framework consists of a new reference system and an adaptive controller. The proposed reference system captures a desired closed-loop dynamical system behavior modified by a mismatch term representing the high-frequency content between the uncertain dynamical system and this reference system, i.e., the system error. In particular, this mismatch term allows to limit the frequency content of the system error dynamics, which is used to drive the adaptive controller. It is shown that this key feature of our framework yields fast adaptation with- out incurring high-frequency oscillations in the transient performance. We further show the effects of design parameters on the system performance, analyze closeness of the uncertain dynamical system to the unmodified (ideal) reference system, discuss robustness of the proposed approach with respect to time-varying uncertainties and disturbances, and make connections to gradient minimization and classical control theory.Comment: 27 pages, 7 figure

Entanglement for all quantum states

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.Comment: 9 page

Classification of Generalized Symmetries for the Vacuum Einstein Equations

A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. To begin, we analyze symmetries that can be built from the metric, curvature, and covariant derivatives of the curvature to any order; these are called natural symmetries and are globally defined on any spacetime manifold. We next classify first-order generalized symmetries, that is, symmetries that depend on the metric and its first derivatives. Finally, using results from the classification of natural symmetries, we reduce the classification of all higher-order generalized symmetries to the first-order case. In each case we find that the generalized symmetries are infinitesimal generalized diffeomorphisms and constant metric scalings. There are no non-trivial conservation laws associated with these symmetries. A novel feature of our analysis is the use of a fundamental set of spinorial coordinates on the infinite jet space of Ricci-flat metrics, which are derived from Penrose's ``exact set of fields'' for the vacuum equations.Comment: 57 pages, plain Te

Understanding the shape of the galaxy two-point correlation function at z ≃ 1 in the COSMOS field

We investigate how the shape of the galaxy two-point correlation function as measured in the zCOSMOS survey depends on local environment, quantified in terms of the density contrast on scales of 5 h^(−1) Mpc. We show that the flat shape previously observed at redshifts between z= 0.6 and 1 can be explained by this volume being simply 10 per cent overabundant in high-density environments, with respect to a universal density probability distribution function. When galaxies corresponding to the top 10 per cent tail of the distribution are excluded, the measured w_(p)(r_(p)) steepens and becomes indistinguishable from Lambda cold dark matter (ΛCDM) predictions on all scales. This is the same effect recognized by Abbas & Sheth in the Sloan Digital Sky Survey (SDSS) data at z ≃ 0 and explained as a natural consequence of halo–environment correlations in a hierarchical scenario. Galaxies living in high-density regions trace dark matter haloes with typically higher masses, which are more correlated. If the density probability distribution function of the sample is particularly rich in high-density regions because of the variance introduced by its finite size, this produces a distorted two-point correlation function. We argue that this is the dominant effect responsible for the observed ‘peculiar’ clustering in the COSMOS field

In silico karyotyping of chromosomally polymorphic malaria mosquitoes in the Anopheles gambiae complex

Chromosomal inversion polymorphisms play an important role in adaptation to environmental heterogeneities. For mosquito species in the Anopheles gambiae complex that are significant vectors of human malaria, paracentric inversion polymorphisms are abundant and are associated with ecologically and epidemiologically important phenotypes. Improved understanding of these traits relies on determining mosquito karyotype, which currently depends upon laborious cytogenetic methods whose application is limited both by the requirement for specialized expertise and for properly preserved adult females at specific gonotrophic stages. To overcome this limitation, we developed sets of tag single nucleotide polymorphisms (SNPs) inside inversions whose biallelic genotype is strongly correlated with inversion genotype. We leveraged 1,347 fully sequenced An. gambiae and Anopheles coluzzii genomes in the Ag1000G database of natural variation. Beginning with principal components analysis (PCA) of population samples, applied to windows of the genome containing individual chromosomal rearrangements, we classified samples into three inversion genotypes, distinguishing homozygous inverted and homozygous uninverted groups by inclusion of the small subset of specimens in Ag1000G that are associated with cytogenetic metadata. We then assessed the correlation between candidate tag SNP genotypes and PCA-based inversion genotypes in our training sets, selecting those candidates with >80% agreement. Our initial tests both in held-back validation samples from Ag1000G and in data independent of Ag1000G suggest that when used for in silico inversion genotyping of sequenced mosquitoes, these tags perform better than traditional cytogenetics, even for specimens where only a small subset of the tag SNPs can be successfully ascertained

Lamellar Structures of MUC2-Rich Mucin: A Potential Role in Governing the Barrier and Lubricating Functions of Intestinal Mucus

Mucus is a ubiquitous feature of mammalian wet epithelial surfaces, where it lubricates and forms a selective barrier that excludes a range of particulates, including pathogens, while hosting a diverse commensal microflora. The major polymeric component of mucus is mucin, a large glycoprotein formed by several MUC gene products, with MUC2 expression dominating intestinal mucus. A satisfactory answer to the question of how these molecules build a dynamic structure capable of playing such a complex role has yet to be found, as recent reports of distinct layers of chemically identical mucin in the colon and anomalously rapid transport of nanoparticles through mucus have emphasized. Here we use atomic force microscopy (AFM) to image a MUC2-rich mucus fraction isolated from pig jejunum. In the freshly isolated mucin fraction, we find direct evidence for trigonally linked structures, and their assembly into lamellar networks with a distribution of pore sizes from 20 to 200 nm. The networks are two-dimensional, with little interaction between lamellae. The existence of persistent cross-links between individual mucin polypeptides is consistent with a non-self-interacting lamellar model for intestinal mucus structure, rather than a physically entangled polymer network. We only observe collapsed entangled structures in purified mucin that has been stored in nonphysiological conditions

Evaluating First-Generation Students’ Career Readiness

Research shows that first-generation students have historically had less guidance and resources to support their educational attainment and career development (Tate et al., 2015). This has resulted in considerable growth in the amount of support systems, programs, and services implemented by educational institutions across the United States to help first-generation college students thrive in higher education and their future careers. This study sought to improve my understanding of the career readiness of first-generation students at USD. By engaging with and gathering data from first-generation students, I have greater insight about ways of supporting first-generation students’ career readiness and vocational confidence through heightened support from the Career Development Center in navigating career resources and processes. Themes that arose include social and familial pressures, uncertainty, and unfamiliarity. Recommendations include demystifying the meaning of career readiness, tailoring programming and outreach efforts, and implementing resource-specific workshops

On Unitary Evolution of a Massless Scalar Field In A Schwarzschild Background: Hawking Radiation and the Information Paradox

We develop a Hamiltonian formalism which can be used to discuss the physics of a massless scalar field in a gravitational background of a Schwarzschild black hole. Using this formalism we show that the time evolution of the system is unitary and yet all known results such as the existence of Hawking radiation can be readily understood. We then point out that the Hamiltonian formalism leads to interesting observations about black hole entropy and the information paradox.Comment: 45 pages, revte