The quotient Unimodular Vector group is nilpotent

Jose-Rao introduced and studied the Special Unimodular Vector group $SUm_r(R)$ and $EUm_r(R)$, its Elementary Unimodular Vector subgroup. They proved that for $r \geq 2$, $EUm_r(R)$ is a normal subgroup of $SUm_r(R)$. The Jose-Rao theorem says that the quotient Unimodular Vector group, $SUm_r(R)/EUm_r(R)$, for $r \geq 2$, is a subgroup of the orthogonal quotient group $SO_{2(r+1)}(R)/EO_{2(r + 1)}(R)$. The latter group is known to be nilpotent by the work of Hazrat-Vavilov, following methods of A. Bak; and so is the former. In this article we give a direct proof, following ideas of A. Bak, to show that the quotient Unimodular Vector group is nilpotent of class $\leq d = \dim(R)$. We also use the Quillen-Suslin theory, inspired by A. Bak's method, to prove that if $R = A[X]$, with $A$ a local ring, then the quotient Unimodular Vector group is abelian

Vertebral body versus iliac crest bone marrow as a source of multipotential stromal cells: Comparison of processing techniques, tri-lineage differentiation and application on a scaffold for spine fusion

The potential use of bone progenitors, multipotential stromal cells (MSCs) helping spine fusion is increasing, but convenient MSC sources and effective processing methods are critical factors yet to be optimised. The aim of this study was to test the effect of bone marrow processing on the MSC abundance and to compare the differentiation capabilities of vertebral body-bone marrow (VB-BM) MSCs versus iliac crest-bone marrow (IC-BM) MSCs. We assessed the effect of the red blood cell lysis (ammonium chloride, AC) and density-gradient centrifugation (Lymphoprep™, LMP), on the extracted VB-BM and IC-BM MSC numbers. The MSC abundance (indicated by colony counts and CD45lowCD271high cell numbers), phenotype, proliferation and tri-lineage differentiation of VB-BM MSCs were compared with donor-matched IC-BM MSCs. Importantly, the MSC attachment and osteogenesis were examined when VB-BM and IC-BM samples were loaded on a beta-tricalcium phosphate scaffold. In contrast to LMP, using AC yielded more colonies from IC-BM and VB-BM aspirates (p = 0.0019 & p = 0.0201 respectively). For IC-BM and VB-BM, the colony counts and CD45lowCD271high cell numbers were comparable (p = 0.5186, p = 0.2640 respectively). Furthermore, cultured VB-BM MSCs exhibited the same phenotype, proliferative and adipogenic potential, but a higher osteogenic and chondrogenic capabilities than IC-BM MSCs (p = 0.0010 and p = 0.0005 for calcium and glycosaminoglycan (GAG) levels, respectively). The gene expression data confirmed higher chondrogenesis for VB-BM MSCs than IC-BM MSCs, but osteogenic gene expression levels were comparable. When loaded on Vitoss™, both MSCs showed a similar degree of attachment and survival, but a better osteogenic ability was detected for VB-BM MSCs as measured by alkaline phosphatase activity (p = 0.0386). Collectively, the BM processing using AC had more MSC yield than using LMP. VB-BM MSCs have a comparable phenotype and proliferative capacity, but higher chondrogenesis and osteogenesis with or without using scaffold than donor-matched IC-BM MSCs. Given better accessibility, VB-BM could be an ideal MSC source for spinal bone fusion

On the Schoenberg Transformations in Data Analysis: Theory and Illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A simple distance-based discriminant algorithm illustrates the theory, intimately connected to the Gaussian kernels of Machine Learning

Information Dynamics in Living Systems: Prokaryotes, Eukaryotes, and Cancer

BACKGROUND: Living systems use information and energy to maintain stable entropy while far from thermodynamic equilibrium. The underlying first principles have not been established. FINDINGS: We propose that stable entropy in living systems, in the absence of thermodynamic equilibrium, requires an information extremum (maximum or minimum), which is invariant to first order perturbations. Proliferation and death represent key feedback mechanisms that promote stability even in a non-equilibrium state. A system moves to low or high information depending on its energy status, as the benefit of information in maintaining and increasing order is balanced against its energy cost. Prokaryotes, which lack specialized energy-producing organelles (mitochondria), are energy-limited and constrained to an information minimum. Acquisition of mitochondria is viewed as a critical evolutionary step that, by allowing eukaryotes to achieve a sufficiently high energy state, permitted a phase transition to an information maximum. This state, in contrast to the prokaryote minima, allowed evolution of complex, multicellular organisms. A special case is a malignant cell, which is modeled as a phase transition from a maximum to minimum information state. The minimum leads to a predicted power-law governing the in situ growth that is confirmed by studies measuring growth of small breast cancers. CONCLUSIONS: We find living systems achieve a stable entropic state by maintaining an extreme level of information. The evolutionary divergence of prokaryotes and eukaryotes resulted from acquisition of specialized energy organelles that allowed transition from information minima to maxima, respectively. Carcinogenesis represents a reverse transition: of an information maximum to minimum. The progressive information loss is evident in accumulating mutations, disordered morphology, and functional decline characteristics of human cancers. The findings suggest energy restriction is a critical first step that triggers the genetic mutations that drive somatic evolution of the malignant phenotype

Dietary Lipids and Cancer

For many years, epidemiological studies continued to suggest that high fat diets are linked to an increased incidence of certain cancers. However, whether the oncogenic properties of fat are associated with their quantity rather than the quality has become debatable. Epidemiological studies have been suggesting that n-6 polyunsaturated fatty acids (n-6 PUFA) and saturated fats are more likely to increase the incidence of cancer, whereas monounsaturated fatty acids (MUFA) and n-3 polyunsaturated fatty acids (n-3 PUFA) are more likely to prevent or decrease the chance of carcinogenesis. A firm conclusion cannot be drawn yet because of insufficient research. This paper reviews the current knowledge of the effects of saturated fats, different types of unsaturated fats, and fat-soluble vitamins on the etiology of cancer

Retrospective model-based inference guides model-free credit assignment

An extensive reinforcement learning literature shows that organisms assign credit efficiently, even under conditions of state uncertainty. However, little is known about credit-assignment when state uncertainty is subsequently resolved. Here, we address this problem within the framework of an interaction between model-free (MF) and model-based (MB) control systems. We present and support experimentally a theory of MB retrospective-inference. Within this framework, a MB system resolves uncertainty that prevailed when actions were taken thus guiding an MF credit-assignment. Using a task in which there was initial uncertainty about the lotteries that were chosen, we found that when participants’ momentary uncertainty about which lottery had generated an outcome was resolved by provision of subsequent information, participants preferentially assigned credit within a MF system to the lottery they retrospectively inferred was responsible for this outcome. These findings extend our knowledge about the range of MB functions and the scope of system interactions

Automated and unsupervised detection of malarial parasites in microscopic images

<p>Abstract</p> <p>Background</p> <p>Malaria is a serious infectious disease. According to the World Health Organization, it is responsible for nearly one million deaths each year. There are various techniques to diagnose malaria of which manual microscopy is considered to be the gold standard. However due to the number of steps required in manual assessment, this diagnostic method is time consuming (leading to late diagnosis) and prone to human error (leading to erroneous diagnosis), even in experienced hands. The focus of this study is to develop a robust, unsupervised and sensitive malaria screening technique with low material cost and one that has an advantage over other techniques in that it minimizes human reliance and is, therefore, more consistent in applying diagnostic criteria.</p> <p>Method</p> <p>A method based on digital image processing of Giemsa-stained thin smear image is developed to facilitate the diagnostic process. The diagnosis procedure is divided into two parts; enumeration and identification. The image-based method presented here is designed to automate the process of enumeration and identification; with the main advantage being its ability to carry out the diagnosis in an unsupervised manner and yet have high sensitivity and thus reducing cases of false negatives.</p> <p>Results</p> <p>The image based method is tested over more than 500 images from two independent laboratories. The aim is to distinguish between positive and negative cases of malaria using thin smear blood slide images. Due to the unsupervised nature of method it requires minimal human intervention thus speeding up the whole process of diagnosis. Overall sensitivity to capture cases of malaria is 100% and specificity ranges from 50-88% for all species of malaria parasites.</p> <p>Conclusion</p> <p>Image based screening method will speed up the whole process of diagnosis and is more advantageous over laboratory procedures that are prone to errors and where pathological expertise is minimal. Further this method provides a consistent and robust way of generating the parasite clearance curves.</p