Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems

We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying the posterior using its precision operator. Working with the unbounded precision operator enables us to use partial differential equations (PDE) methodology to obtain rates of contraction of the posterior distribution to a Dirac measure centered on the true solution. Our methods assume a relatively weak relation between the prior covariance, noise covariance and forward operator, allowing for a wide range of applications.     

Toward a situation model in a cognitive architecture

The ability to coherently represent information that is situationally relevant is vitally important to perform any complex task, especially when that task involves coordinating with team members. This paper introduces an approach to dynamically represent situation information within the ACT-R cognitive architecture in the context of a synthetic teammate project. The situation model represents the synthetic teammate’s mental model of the objects, events, actions, and relationships encountered in a complex task simulation. The situation model grounds textual information from the language analysis component into knowledge usable by the agent-environment interaction component. The situation model is a key component of the synthetic teammate as it provides the primary interface between arguably distinct cognitive processes modeled within the synthetic teammate (e.g., language processing and interactions with the task environment). This work has provided some evidence that reasoning about complex situations requires more than simple mental representations and requires mental processes involving multiple steps. Additionally, the work has revealed an initial method for reasoning across the various dimensions of situations. One purpose of the research is to demonstrate that this approach to implementing a situation model provides a robust capability to handle tasks in which an agent must construct a mental model from textual information, reason about complex relationships between objects, events, and actions in its environment, and appropriately communicate with task participants using natural language. In this paper we describe an approach for modeling situationally relevant information, provide a detailed example, discuss challenges faced, and present research plans for the situation model.     

High-strength, healable, supramolecular polymer nanocomposites

A supramolecular polymer blend, formed via π-π interactions between a π-electron rich pyrenyl end-capped oligomer and a chain-folding oligomer containing pairs of π-electron poor naphthalene-diimide (NDI) units, has been reinforced with cellulose nanocrystals (CNCs) to afford a healable nanocomposite material. Nanocomposites with varying weight percentage of CNCs (from 1.25 to 20.0 wt %) within the healable supramolecular polymeric matrix have been prepared via solvent casting followed by compression molding, and their mechanical properties and healing behavior have been evaluated. It is found that homogeneously dispersed films can be formed with CNCs at less than 10 wt %. Above 10 wt % CNC heterogeneous nanocomposites were obtained. All the nanocomposites formed could be rehealed upon exposure to elevated temperatures although, for the homogeneous films, it was found that the healing rate was reduced with increasing CNC content. The best combination of healing efficiency and mechanical properties was obtained with the 7.5 wt % CNC nanocomposite which exhibited a tensile modulus enhanced by as much as a factor of 20 over the matrix material alone and could be fully rehealed at 85 °C within 30 min. Thus it is demonstrated that supramolecular nanocomposites can afford greatly enhanced mechanical properties relative to the unreinforced polymer, while still allowing efficient thermal healing.     

Chemoenzymatic synthesis of O-mannosylpeptides in solution and on solid phase

O-mannosyl glycans are known to play an important role in regulating the function of α-dystroglycan (α-DG), as defective glycosylation is associated with various phenotypes of congenital muscular dystrophy. Despite the well-established biological significance of these glycans, questions regarding their precise molecular function remain unanswered. Further biological investigation will require synthetic methods for the generation of pure samples of homogeneous glycopeptides with diverse sequences. Here we describe the first total syntheses of glycopeptides containing the tetrasaccharide NeuNAcα2-3Galβ1-4GlcNAcβ1-2Manα, which is reported to be the most abundant O-mannosyl glycan on α-DG. Our approach is based on biomimetic stepwise assembly from the reducing end and also gives access to the naturally occurring mono-, di-, and trisaccharide substructures. In addition to the total synthesis, we have developed a "one-pot" enzymatic cascade leading to the rapid synthesis of the target tetrasaccharide. Finally, solid-phase synthesis of the desired glycopeptides directly on a gold microarray platform is described.     

Surface‐enhanced Raman spectra of melamine and other chemicals using a 1550 nm (retina‐safe) laser

Many trace chemical analyses are being transitioned from the lab to the field, among which is surface‐enhanced Raman spectroscopy. Although initial portable Raman analyzers primarily employ 785 nm laser excitation, recent studies suggest longer wavelengths, with an appropriate surface‐enhanced Raman‐active substrate, may provide equal sensitivity. Furthermore, 1550 nm excitation may provide added safety for the user, in that permanent retina damage does not occur. Here, we show that a reasonable enhancement factor can be obtained for melamine using 1550 nm laser excitation that is nearly equivalent to those obtained using 785 and 1064 nm laser excitation. We also demonstrate that a number of other chemicals of interest can be measured by 1550 nm surface‐enhanced Raman scattering, albeit only modest sensitivity is achieved because of instrument limitations, not enhancement factors. Copyright © 2011 John Wiley & Sons, Ltd.     

Spatial orientation of different frequencies within the echolocation beam of a Tursiops truncatus and Pseudorca crassidens

A two-dimensional array of 16 hydrophones was created to map the spatial distribution of different frequencies within the echolocation beam of a Tursiops truncatus and a Pseudorca crassidens. It was previously shown that both the Tursiops and Pseudorca only paid attention to frequencies between 29 and 42 kHz while echolocating. Both individuals tightly focused the 30?kHz frequency and the spatial location of the focus was consistently pointed toward the target. At 50?kHz the beam was less focused and less precisely pointed at the target. At 100?kHz the focus was often completely lost and was not pointed at the target. This indicates that these individuals actively focused the beam toward the target only in the frequency range they paid attention to. Frequencies outside this range were left unfocused and undirected. This focusing was probably achieved through sensorimotor control of the melon morphology and nasal air sacs. This indicates that both morphologically different species can control the spatial distribution of different frequency ranges within the echolocation beam to create consistent ensonation of desired targets.     

Actively Q-switched and mode-locked Tm3+-doped silicate 2 μm fiber laser for supercontinuum generation in fluoride fiber

A diode-pumped actively Q-switched and actively mode-locked Tm3+-doped double-clad silicate fiber laser is reported providing up to 5 W of average output power at ~60 kHz Q-switch envelope repetition rate and ~8 μJ subpulses with up to 2.4 kW peak power. Using this source as a pump laser for supercontinuum generation in a ZBLAN fiber, over 1080 mW of supercontinuum from 1.9 μm to beyond 3.6 μm was obtained at an overall efficiency of 3.3% with respect to the diode pump power.     

Shift invariant preduals of ℓ 1(ℤ)

The Banach space ? ₁(?) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ? ₁(?) weak*-continuous. This is equivalent to making the natural convolution multiplication on ? ₁(?) separately weak*-continuous and so turning ? ₁(?) into a dual Banach algebra. We call such preduals shift-invariant. It is known that the only shift-invariant predual arising from the standard duality between C ₀(K) (for countable locally compact K) and ? ₁(?) is c ₀(?). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak*-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c ₀. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ?. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c ₀.     

Metal@COFs: Covalent Organic Frameworks as Templates for Pd Nanoparticles and Hydrogen Storage Properties of Pd@COF-102 Hybrid Material

Three-dimensional covalent organic frameworks (COFs) have been demonstrated as a new class of templates for nanoparticles. Photodecomposition of the [Pd(η(3) -C(3) H(5) )(η(5) -C(5) H(5) )]@COF-102 inclusion compound (synthesized by a gas-phase infiltration method) led to the formation of the Pd@COF-102 hybrid material. Advanced electron microscopy techniques (including high-angle annular dark-field scanning transmission electron microscopy and electron tomography) along with other conventional characterization techniques unambiguously showed that highly monodisperse Pd nanoparticles ((2.4±0.5)?nm) were evenly distributed inside the COF-102 framework. The Pd@COF-102 hybrid material is a rare example of a metal-nanoparticle-loaded porous crystalline material with a very narrow size distribution without any larger agglomerates even at high loadings (30?wt?%). Two samples with moderate Pd content (3.5 and 9.5?wt?%) were used to study the hydrogen storage properties of the metal-decorated COF surface. The uptakes at room temperature from these samples were higher than those of similar systems such as Pd@metal-organic frameworks (MOFs). The studies show that the H(2) capacities were enhanced by a factor of 2-3 through Pd impregnation on COF-102 at room temperature and 20?bar. This remarkable enhancement is not just due to Pd hydride formation and can be mainly ascribed to hydrogenation of residual organic compounds, such as bicyclopentadiene. The significantly higher reversible hydrogen storage capacity that comes from decomposed products of the employed organometallic Pd precursor suggests that this discovery may be relevant to the discussion of the spillover phenomenon in metal/MOFs and related systems.     

Carbon-based leaving group in substitution reactions: functionalization of sp3-hybridized quaternary and tertiary benzylic carbon centers

Lewis acid promoted substitution reactions employing Meldrum's acid and 5-methyl Meldrum's acid as carbon-based leaving groups are described which transform unstrained quaternary and tertiary benzylic C(sp(3))-C(sp(3)) bonds into C(sp(3))-X bonds (X = C, H, N). Importantly, this reaction has a broad scope in terms of both suitable substrates and nucleophiles with good to excellent yields obtained (typically >90%).