Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0domain. Comparing our exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Reflective perspectives: Negotiations at and within the borders of cultural difference: A post-qualitative inquiry of cultural hybridity within third space enunciations

This research explores the in-between space of intercultural collaboration between Aboriginal and Torres Strait Islander peoples and non-Indigenous peoples in Australia. Using critical and third space theories and a post-qualitative inquiry, I examine negotiations of cultural difference through articulated moments of intercultural collaboration in order to inform intercultural pedagogical practices. This research also explores how ideology, imbued through discourse, has the power to enforce or challenge cultural and social domination. This in turn creates cultural hegemony, a process whereby a particular social and cultural group has the power to influence the thoughts, expectations and behaviours of a particular society.

Albert Einstein (front row, third from right) in school group portrait Portraits Groups

Digital Image

Portrait of the dancing school class of Therese Molling (second row third from right); Germany.

Mille Ottling ran the dancing school. Therese Molling's daughter Liesel (Elizabeth) Gottschalk and brother Hal attended the same school during the mid 1920s

Group US Army military portrait including Dr. William Levison (top row, third from left); Schofield Barracks, Hawaii Portraits Groups Men

Digital Image

Genetic alterations in microsatellite-unstable colorectal cancer

Colorectal cancer (CRC) is the third most common cancer in Finland. Of all CRC tumors, 15% display microsatellite-instability (MSI) caused by defective cellular mismatch repair. Cells displaying MSI accumulate a high number of mutations genome-wide, especially in short repeat areas, microsatellites. When targeting genes essential for cell growth or death, MSI can promote tumorigenesis. In non-coding areas, microsatellite mutations are generally considered as passenger events. Since the discovery of MSI and its linkage to cancer, more that 200 genes have been investigated for a role in MSI tumorigenesis. Although various criteria have been suggested for MSI target gene identification, the challenge has been to distinguish driver mutations from passenger mutations. This study aimed to clarify these key issues in the research field of MSI cancer. Prior to this, background mutation rate in MSI cancer has not been studied in a large-scale. We investigated the background mutation rate in MSI CRC by analyzing the spectrum of microsatellite mutations in non-coding areas. First, semenogelin I was studied for a possible role in MSI carcinogenesis. The intronic T9 repeat of semenogelin I was frequently mutated but no evidence for selection during tumorigenesis was obtained. Second, a sequencing approach was utilized to evaluate the general background mutation rate in MSI CRC. Both intronic and intergenic repeats harbored extremely high mutation rates of ≤ 87% and intergenic repeats were more unstable than the intronic repeats. As mutation rates of presumably neutral microsatellites can be high in MSI CRC in the absence of apparent selection pressure, high mutation frequency alone is not sufficient evidence for identification of driver MSI target genes. Next, an unbiased approach was designed to identify the mutatome of MSI CRC. By combining expression array data and a database search we identified novel genes possibly related to MSI CRC carcinogenesis. One of the genes was studied further. In the functional analysis this gene was observed to cause an abnormal cancer-prone cellular phenotype, possibly through altered responses to DNA damage. In our recent study, smooth muscle myosin heavy chain 11 (MYH11) was identified as a novel MSI CRC gene. Additionally, MYH11 has a well established role in acute myeloid leukemia (AML) through an oncogenic fusion protein CBFB-MYH11. We investigated further the role of MYH11 in AML by sequencing. Three novel missense variants of MYH11 were identified. None of the variants were present in the population-based control material. One of the identified variants, V71A, lies in the N-terminal SH3-like domain of MYH11 of unknown function. The other two variants, K1059E and R1792Q are located in the coil-coiled myosin rod essential for the regulation and filament formation of MYH11. The variant K1059E lies in the close proximity of the K1044N that has been functionally assessed in our earlier work of CRC and has been reported to cause total loss of MYH11 protein regulation. As the functional significance of the three novel variants examined in this work remains unknown, future studies should clarify the further role of MYH11 in AML leukaemogenesis and in other malignancies.

Portrait of the dancing school class of Therese Molling (second row third from right); Germany.

Mille Ottling ran the dancing school. Therese Molling's daughter Liesel (Elizabeth) Gottschalk and brother Hal attended the same school during the mid 1920s

Group US Army military portrait including Dr. William Levison (top row, third from left); Schofield Barracks, Hawaii Portraits Groups Men

Digital Image

Analysis-By-Synthesis Based Switched Transform Domain Split Vq Using Gaussian Mixture Model

Using analysis-by-synthesis (AbS) approach, we develop a soft decision based switched vector quantization (VQ) method for high quality and low complexity coding of wideband speech line spectral frequency (LSF) parameters. For each switching region, a low complexity transform domain split VQ (TrSVQ) is designed. The overall rate-distortion (R/D) performance optimality of new switched quantizer is addressed in the Gaussian mixture model (GMM) based parametric framework. In the AbS approach, the reduction of quantization complexity is achieved through the use of nearest neighbor (NN) TrSVQs and splitting the transform domain vector into higher number of subvectors. Compared to the current LSF quantization methods, the new method is shown to provide competitive or better trade-off between R/D performance and complexity.

A Fredholm-type theory for third-kind linear integral equations

The third-kind linear integral equation Image where g(t) vanishes at a finite number of points in (a, b), is considered. In general, the Fredholm Alternative theory [[5.]] does not hold good for this type of integral equation. However, imposing certain conditions on g(t) and K(t, t′), the above integral equation was shown [[1.], 49–57] to obey a Fredholm-type theory, except for a certain class of kernels for which the question was left open. In this note a theory is presented for the equation under consideration with some additional assumptions on such kernels.

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

When time ran out : Coming of age in the Third Reich 1925-1982

Memoir based on diaries kept by sculptor Zeller as a boy; Nazi periods in Berlin; primary and secondary school; pogrom (November 1938); emigration to England via Holland; visit to Berlin in 1982

The third logic: Adolf Hitler and abductive logic. A thesis in history of consciousness.

Ph.D. Thesis

Ultrafast Switching Time and Third Order Nonlinear Coefficients of Microwave Treated Single Walled Carbon Nanotube Suspensions

Microwave treated water soluble and amide functionalized single walled carbon nanotubes have been investigated using femtosecond degenerate pump-probe and nonlinear transmission experiments. The time resolved differential transmission using 75 femtosecond pulse with the central wavelength of 790 nm shows a bi-exponential ultrafast photo-bleaching with time constants of 160 fs (130 fs) and 920 fs (300 fs) for water soluble (amide functionalized) nanotubes. Open and closed aperture z-scans show saturation absorption and positive (negative) nonlinear refraction for water soluble (amide functionalized) nanotubes. Two photon absorption coefficient, beta(0) similar to 250 cm/GW (650 cm/GW) and nonlinear index, gamma similar to 15 cm(2)/pW (-30 cm(2)/pW) are obtained from the theoretical fit in the saturation limit to the data for two types of nanotubes.

NMR Spectroscopy of Multi-domain Proteins : Immunoglobulin-like Domains of Human Filamin A

Proteins are complex biomacromolecules playing fundamental roles in the physiological processes of all living organisms. They function as structural units, enzymes, transporters, process regulators, and signal transducers. Defects in protein functions often derive from genetic mutations altering the protein structure, and impairment of essential protein functions manifests itself as pathological conditions. Proteins operate through interactions, and all protein functions depend on protein structure. In order to understand biological mechanisms at the molecular level, one has to know the structures of the proteins involved. This thesis covers structural and functional characterization of human filamins. Filamins are actin-binding and -bundling proteins that have numerous interaction partners. In addition to their actin-organizing functions, filamins are also known to have roles in cell adhesion and locomotion, and to participate in the logistics of cell membrane receptors, and in the coordination of intracellular signaling pathways. Filamin mutations in humans induce severe pathological conditions affecting the brain, bones, limbs, and the cardiovascular system. Filamins are large modular proteins composed of an N-terminal actin-binding domain and 24 consecutive immunoglobulin-like domains (IgFLNs). Nuclear magnetic resonance (NMR) spectroscopy is a versatile method of gaining insight into protein structure, dynamics and interactions. NMR spectroscopy was employed in this thesis to study the atomic structure and interaction mechanisms of C-terminal IgFLNs, which are known to house the majority of the filamin interaction sites. The structures of IgFLN single-domains 17 and 23 and IgFLN domain pairs 16-17 and 18-19 were determined using NMR spectroscopy. The structures of domain pairs 16 17 and 18 19 both revealed novel domain domain interaction modes of IgFLNs. NMR titrations were employed to characterize the interactions of filamins with glycoprotein Ibα, FilGAP, integrin β7 and dopamine receptors. Domain packing of IgFLN domain sextet 16 21 was further characterized using residual dipolar couplings and NMR relaxation analysis. This thesis demonstrates the versatility and potential of NMR spectroscopy in structural and functional studies of multi-domain proteins.