Advancing Shannon entropy for measuring diversity in systems

From economic inequality and species diversity to power laws and the analysis of multiple trends and trajectories, diversity within systems is a major issue for science. Part of the challenge is measuring it. Shannon entropy H has been used to re-think diversity within probability distributions, based on the notion of information. However, there are two major limitations to Shannon's approach. First, it cannot be used to compare diversity distributions that have different levels of scale. Second, it cannot be used to compare parts of diversity distributions to the whole. To address these limitations, we introduce a re-normalization of probability distributions based on the notion of case-based entropy Cc as a function of the cumulative probability c. Given a probability density p(x), Cc measures the diversity of the distribution up to a cumulative probability of c, by computing the length or support of an equivalent uniform distribution that has the same Shannon information as the conditional distribution of ^pc(x) up to cumulative probability c. We illustrate the utility of our approach by re-normalizing and comparing three well-known energy distributions in physics, namely, the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distributions for energy of sub-atomic particles. The comparison shows that Cc is a vast improvement over H as it provides a scale-free comparison of these diversity distributions and also allows for a comparison between parts of these diversity distributions

EAC: A program for the error analysis of STAGS results for plates

A computer code is now available for estimating the error in results from the STAGS finite element code for a shell unit consisting of a rectangular orthotropic plate. This memorandum contains basic information about the computer code EAC (Error Analysis and Correction) and describes the connection between the input data for the STAGS shell units and the input data necessary to run the error analysis code. The STAGS code returns a set of nodal displacements and a discrete set of stress resultants; the EAC code returns a continuous solution for displacements and stress resultants. The continuous solution is defined by a set of generalized coordinates computed in EAC. The theory and the assumptions that determine the continuous solution are also outlined in this memorandum. An example of application of the code is presented and instructions on its usage on the Cyber and the VAX machines have been provided

Geosynthetic Reinforced Segmental Retaining Wall Failure: Forensic Investigation and Remediation

At UNC Charlotte, the authors have used a retaining wall failure case history to cover the different modes of failure of retaining wall and to highlight the importance of global stability failure. Specifically, this case study has been used by the authors in undergraduate and graduate courses of geotechnical engineering to highlight the importance to include in the design process the assessment of global stability. The project is valuable to students due to wealth of data including field and laboratory site investigation, monitoring data from slope inclinometers, amongst other data. The students are presented with the initial design information including wall height, backfill information, geosynthetic reinforcement type and layout, etc. The first assignment requires students to check conventional internal and external stability. Then the students are presented with post failure photos of the wall. The failure incident is discussed in detail and the students are then asked to take a second closer look of the project information to try to explain the failure. This time around they also have access to the post failure inclinometer data and field reports that included evidence of surface cracks on the pavement built on the top of the wall. With this available information students successfully explain the failure mode via global slope stability analyses

Involvement of Serine Threonine Protein Kinase, PknL, from Mycobacterium Tuberculosis H37Rv in Starvation Response of Mycobacteria

The adaptation to nutrient depletion in bacteria involves a highly organized series of intracellular events that enable them to adapt to starvation conditions. The regulatory effect of serine threonine protein kinase, PknL, from Mycobacterium tuberculosis strain H37Rv was investigated under nutrient deprived conditions that simulate circumstances leading to latency. Recombinant PknL was expressed in Mycobacterium smegmatis strain mc2155 in its wild type and mutant forms. In vitro growth kinetics experiments revealed that clone expressing active PknL had a significant growth advantage under nutrient limiting conditions. Experiments were conducted to ascertain the in silico predictions of the involvement of PknL in regulating glutamine metabolism in mycobacteria. Furthermore, a role for PknL in cell wall biogenesis/cell division was shown by scanning electron microscopy

Effect of protein deficiency on absorption, transport and distribution of α-tocopherol in the rat

The absorption, transport and distribution of α-[3H]tocopherol were greatly decreased in protein deficiency. This was reflected in the subcellular distribution of α-[3H]tocopherol in livers of protein-deficient rats. The ratio, bound: free for α-[3H]tocopherol, also decreased in both serum and liver cytosol. After protein refeeding, absorption, transport and distribution patterns of α-[3H]tocopherol for the protein-deficient rats were restored to patterns similar to those of control animals

Involvement of binding lipoproteins in the absorption and transport of α-tocopherol in the rat

1. Specific lipoproteins binding α-tocopherol but not its known metabolites have been isolated and identified from cytosol of rat intestinal mucosa and from serum. 2. A timestudy of the appearance of the orally administered α-[3H]tocopherol with these lipoproteins indicates that very-low-density lipoprotein of serum acts as a carrier of the vitamin. 3. The involvement of the mucosal lipoprotein in the absorption of the vitamin from the intestine has been inferred from observations on the amounts of α-tocopherol in serum of orotic acid-fed rats where release of lipoproteins from the liver to serum is completely inhibited. A considerable decrease in the association of α-tocopherol with serum very-low-density lipoprotein under this condition is interpreted to mean that serum lipoproteins are limiting factors for the transport of the vitamin across the intestine and that this is possibly effected by exchange of α-tocopherol between serum very-low-density lipoprotein and mucosal lipoprotein

A multi-modal data resource for investigating topographic heterogeneity in patient-derived xenograft tumors.

Patient-derived xenografts (PDXs) are an essential pre-clinical resource for investigating tumor biology. However, cellular heterogeneity within and across PDX tumors can strongly impact the interpretation of PDX studies. Here, we generated a multi-modal, large-scale dataset to investigate PDX heterogeneity in metastatic colorectal cancer (CRC) across tumor models, spatial scales and genomic, transcriptomic, proteomic and imaging assay modalities. To showcase this dataset, we present analysis to assess sources of PDX variation, including anatomical orientation within the implanted tumor, mouse contribution, and differences between replicate PDX tumors. A unique aspect of our dataset is deep characterization of intra-tumor heterogeneity via immunofluorescence imaging, which enables investigation of variation across multiple spatial scales, from subcellular to whole tumor levels. Our study provides a benchmark data resource to investigate PDX models of metastatic CRC and serves as a template for future, quantitative investigations of spatial heterogeneity within and across PDX tumor models