A Special Homotopy Continuation Method For A Class of Polynomial Systems

A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of this method is between the total degree bound and the mixed volume bound and can be easily computed. The new algorithm has been implemented as a program called LPH using C++. Our experiments show its efficiency compared to the polyhedral or other homotopies on such systems. As an application, the algorithm can be used to find witness points on each connected component of a real variety

Embryonic Mutant Huntingtin Aggregate Formation in Mouse Models of Huntington’s Disease

The role of aggregate formation in the pathophysiology of Huntington’s disease (HD) remains uncertain. However, the temporal appearance of aggregates tends to correlate with the onset of symptoms and the numbers of neuropil aggregates correlate with the progression of clinical disease. Using highly sensitive immunohistochemical methods we have detected the appearance of diffuse aggregates during embryonic development in the R6/2 and YAC128 mouse models of HD. These are initially seen in developing axonal tracts and appear to spread throughout the cerebrum in the early neonate

Certifying reality of projections

Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., square), Newton's method is locally quadratically convergent near each nonsingular solution. In such cases, Smale's alpha theory can be used to certify that a given point is in the quadratic convergence basin of some solution. This was extended to certifiably determine the reality of the corresponding solution when the polynomial system is real. Using the theory of Newton-invariant sets, we certifiably decide the reality of projections of solutions. We apply this method to certifiably count the number of real and totally real tritangent planes for instances of curves of genus 4.Comment: 9 page

MEF2 impairment underlies skeletal muscle atrophy in polyglutamine disease

Polyglutamine (polyQ) tract expansion leads to proteotoxic misfolding and drives a family of nine diseases. We study spinal and bulbar muscular atrophy (SBMA), a progressive degenerative disorder of the neuromuscular system caused by the polyQ androgen receptor (AR). Using a knock-in mouse model of SBMA, AR113Q mice, we show that E3 ubiquitin ligases which are a hallmark of the canonical muscle atrophy machinery are not induced in AR113Q muscle. Similarly, we find no evidence to suggest dysfunction of signaling pathways that trigger muscle hypertrophy or impairment of the muscle stem cell niche. Instead, we find that skeletal muscle atrophy is characterized by diminished function of the transcriptional regulator Myocyte Enhancer Factor 2 (MEF2), a regulator of myofiber homeostasis. Decreased expression of MEF2 target genes is age- and glutamine tract length-dependent, occurs due to polyQ AR proteotoxicity, and is associated with sequestration of MEF2 into intranuclear inclusions in muscle. Skeletal muscle from R6/2 mice, a model of Huntington disease which develops progressive atrophy, also sequesters MEF2 into inclusions and displays age-dependent loss of MEF2 target genes. Similarly, SBMA patient muscle shows loss of MEF2 target gene expression, and restoring MEF2 activity in AR113Q muscle rescues fiber size and MEF2-regulated gene expression. This work establishes MEF2 impairment as a novel mechanism of skeletal muscle atrophy downstream of toxic polyglutamine proteins and as a therapeutic target for muscle atrophy in these disorders

Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories

The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these short-comings. Its so-called 'embarrassing parallelizability' allows us to solve many problems and extract physical information which elude the symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.Comment: 36 page

Vaccination against Foot-and-mouth disease : do initial conditions affect its benefit?

When facing incursion of a major livestock infectious disease, the decision to implement a vaccination programme is made at the national level. To make this decision, governments must consider whether the benefits of vaccination are sufficient to outweigh potential additional costs, including further trade restrictions that may be imposed due to the implementation of vaccination. However, little consensus exists on the factors triggering its implementation on the field. This work explores the effect of several triggers in the implementation of a reactive vaccination-to-live policy when facing epidemics of foot-and-mouth disease. In particular, we tested whether changes in the location of the incursion and the delay of implementation would affect the epidemiological benefit of such a policy in the context of Scotland. To reach this goal, we used a spatial, premises-based model that has been extensively used to investigate the effectiveness of mitigation procedures in Great Britain. The results show that the decision to vaccinate, or not, is not straightforward and strongly depends on the underlying local structure of the population-at-risk. With regards to disease incursion preparedness, simply identifying areas of highest population density may not capture all complexities that may influence the spread of disease as well as the benefit of implementing vaccination. However, if a decision to vaccinate is made, we show that delaying its implementation in the field may markedly reduce its benefit. This work provides guidelines to support policy makers in their decision to implement, or not, a vaccination-to-live policy when facing epidemics of infectious livestock disease

Designing an automated clinical decision support system to match clinical practice guidelines for opioid therapy for chronic pain

Abstract Background Opioid prescribing for chronic pain is common and controversial, but recommended clinical practices are followed inconsistently in many clinical settings. Strategies for increasing adherence to clinical practice guideline recommendations are needed to increase effectiveness and reduce negative consequences of opioid prescribing in chronic pain patients. Methods Here we describe the process and outcomes of a project to operationalize the 2003 VA/DOD Clinical Practice Guideline for Opioid Therapy for Chronic Non-Cancer Pain into a computerized decision support system (DSS) to encourage good opioid prescribing practices during primary care visits. We based the DSS on the existing ATHENA-DSS. We used an iterative process of design, testing, and revision of the DSS by a diverse team including guideline authors, medical informatics experts, clinical content experts, and end-users to convert the written clinical practice guideline into a computable algorithm to generate patient-specific recommendations for care based upon existing information in the electronic medical record (EMR), and a set of clinical tools. Results The iterative revision process identified numerous and varied problems with the initially designed system despite diverse expert participation in the design process. The process of operationalizing the guideline identified areas in which the guideline was vague, left decisions to clinical judgment, or required clarification of detail to insure safe clinical implementation. The revisions led to workable solutions to problems, defined the limits of the DSS and its utility in clinical practice, improved integration into clinical workflow, and improved the clarity and accuracy of system recommendations and tools. Conclusions Use of this iterative process led to development of a multifunctional DSS that met the approval of the clinical practice guideline authors, content experts, and clinicians involved in testing. The process and experiences described provide a model for development of other DSSs that translate written guidelines into actionable, real-time clinical recommendations.http://deepblue.lib.umich.edu/bitstream/2027.42/78267/1/1748-5908-5-26.xmlhttp://deepblue.lib.umich.edu/bitstream/2027.42/78267/2/1748-5908-5-26.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/78267/3/1748-5908-5-26-S3.TIFFhttp://deepblue.lib.umich.edu/bitstream/2027.42/78267/4/1748-5908-5-26-S2.TIFFhttp://deepblue.lib.umich.edu/bitstream/2027.42/78267/5/1748-5908-5-26-S1.TIFFPeer Reviewe

Anorexia nervosa and Wernicke-Korsakoff syndrome: a case report

<p>Abstract</p> <p>Introduction</p> <p>Wernicke's encephalopathy is an acute, potentially fatal, neuropsychiatric syndrome resulting from thiamine deficiency. The disorder is still greatly under-diagnosed, and failure to promptly identify and adequately treat the condition can lead to death or to the chronic form of the encephalopathy - Korsakoff's syndrome. Wernicke's encephalopathy has traditionally been associated with alcoholism but, in recent years, there has been an increase in the number of clinical settings in which the disorder is observed.</p> <p>Case presentation</p> <p>We report the case of a 45-year-old Caucasian woman who arrived at the emergency room presenting signs of marked malnutrition and mental confusion, ataxic gait and ophthalmoplegia. Main laboratory test findings included low serum magnesium and megaloblastic anemia. Brain magnetic resonance imaging revealed increased T2 signal in the supratentorial paraventricular region, the medial regions of the thalamus and the central and periaqueductal midbrain. The diagnosis of Wernicke's encephalopathy was made at once and immediate reposition of thiamine and magnesium was started. The patient had a long history of recurrent thoughts of being overweight, severe self-imposed diet restrictions and self-induced vomiting. She had also been drinking gin on a daily basis for the last eight years. One day after admittance the acute global confusional state resolved, but she presented severe memory deficits and confabulation. After six months of outpatient follow-up, memory deficits remained unaltered.</p> <p>Conclusion</p> <p>In this case, self-imposed long-lasting nutritional deprivation is thought to be the main cause of thiamine deficiency and subsequent encephalopathy, but adjunct factors, such as magnesium depletion and chronic alcohol misuse, might have played an important role, especially in the development of Korsakoff's syndrome. The co-morbidity between eating disorders and substance abuse disorders has emerged as a significant health issue for women, and the subgroup of patients with anorexia nervosa who also misuse alcohol is probably at a particular risk of developing Wernicke-Korsakoff syndrome. The present case report highlights this relevant issue.</p

Tissue-engineered tracheal replacement in a child: a 4-year follow-up study

In 2010, a tissue-engineered trachea was transplanted into a 10-year-old child using a decellularized deceased donor trachea repopulated with the recipient's respiratory epithelium and mesenchymal stromal cells. We report the child's clinical progress, tracheal epithelialization and costs over the 4 years. A chronology of events was derived from clinical notes and costs determined using reference costs per procedure. Serial tracheoscopy images, lung function tests and anti-HLA blood samples were compared. Epithelial morphology and T cell, Ki67 and cleaved caspase 3 activity were examined. Computational fluid dynamic simulations determined flow, velocity and airway pressure drops. After the first year following transplantation, the number of interventions fell and the child is currently clinically well and continues in education. Endoscopy demonstrated a complete mucosal lining at 15 months, despite retention of a stent. Histocytology indicates a differentiated respiratory layer and no abnormal immune activity. Computational fluid dynamic analysis demonstrated increased velocity and pressure drops around a distal tracheal narrowing. Cross-sectional area analysis showed restriction of growth within an area of in-stent stenosis. This report demonstrates the long-term viability of a decellularized tissue-engineered trachea within a child. Further research is needed to develop bioengineered pediatric tracheal replacements with lower morbidity, better biomechanics and lower costs