Binary hidden Markov models and varieties

The technological applications of hidden Markov models have been extremely diverse and successful, including natural language processing, gesture recognition, gene sequencing, and Kalman filtering of physical measurements. HMMs are highly non-linear statistical models, and just as linear models are amenable to linear algebraic techniques, non-linear models are amenable to commutative algebra and algebraic geometry. This paper closely examines HMMs in which all the hidden random variables are binary. Its main contributions are (1) a birational parametrization for every such HMM, with an explicit inverse for recovering the hidden parameters in terms of observables, (2) a semialgebraic model membership test for every such HMM, and (3) minimal defining equations for the 4-node fully binary model, comprising 21 quadrics and 29 cubics, which were computed using Grobner bases in the cumulant coordinates of Sturmfels and Zwiernik. The new model parameters in (1) are rationally identifiable in the sense of Sullivant, Garcia-Puente, and Spielvogel, and each model's Zariski closure is therefore a rational projective variety of dimension 5. Grobner basis computations for the model and its graph are found to be considerably faster using these parameters. In the case of two hidden states, item (2) supersedes a previous algorithm of Schonhuth which is only generically defined, and the defining equations (3) yield new invariants for HMMs of all lengths $\geq 4$. Such invariants have been used successfully in model selection problems in phylogenetics, and one can hope for similar applications in the case of HMMs

Canadian Association of Gastroenterology Clinical Practice Guideline for the Medical Management of Pediatric Luminal Crohn's Disease

Background & Aims: We aim to provide guidance for medical treatment of luminal Crohn's disease in children. Methods: We performed a systematic search of publication databases to identify studies of medical management of pediatric Crohn's disease. Quality of evidence and strength of recommendations were rated according to the GRADE (Grading of Recommendation Assessment, Development, and Evaluation) approach. We developed statements through an iterative online platform and then finalized and voted on them. Results: The consensus includes 25 statements focused on medical treatment options. Consensus was not reached, and no recommendations were made, for 14 additional statements, largely due to lack of evidence. The group suggested corticosteroid therapies (including budesonide for mild to moderate disease). The group suggested exclusive enteral nutrition for induction therapy and biologic tumor necrosis factor antagonists for induction and maintenance therapy at diagnosis or at early stages of severe disease, and for patients failed by steroid and immunosuppressant induction therapies. The group recommended against the use of oral 5-aminosalicylate for induction or maintenance therapy in patients with moderate disease, and recommended against thiopurines for induction therapy, corticosteroids for maintenance therapy, and cannabis in any role. The group was unable to clearly define the role of concomitant immunosuppressants during initiation therapy with a biologic agent, although thiopurine combinations are not recommended for male patients. No consensus was reached on the role of aminosalicylates in treatment of patients with mild disease, antibiotics or vedolizumab for induction or maintenance therapy, or methotrexate for induction therapy. Patients in clinical remission who are receiving immunomodulators should be assessed for mucosal healing within 1 year of treatment initiation. Conclusions: Evidence-based medical treatment of Crohn's disease in children is recommended, with thorough ongoing assessments to define treatment success

Towards a risk model for the Northern Baltic maritime winter navigation system

The implementation of the Finnish-Swedish winter navigation system has managed to increase the safe passage of merchant vessels in the Baltic Sea. However, there will always be risk associated with Baltic Sea winter navigation. Based upon IMO\u92s Formal Safety Assessment; steps zero through two, this report will aim to provide a system description of the Finnish-Swedish winter navigation system outlining the main elements used to ensure safe passage for merchant vessels, and based upon a literature survey, discussion with Finnish icebreaker crew and the results of an exploratory hazard session this report will determine the hazards associated with Baltic Sea winter navigation, the preliminary results of a risk analysis and the icebreaking operations which are linked to the winter navigation accidents. This work will lay out the preliminary work towards a risk model for preventing oil spills in the Northern Baltic

Machine learning classification of multiple sclerosis patients based on raw data from an instrumented walkway

Background Using embedded sensors, instrumented walkways provide clinicians with important information regarding gait disturbances. However, because raw data are summarized into standard gait variables, there may be some salient features and patterns that are ignored. Multiple sclerosis (MS) is an inflammatory neurodegenerative disease which predominantly impacts young to middle-aged adults. People with MS may experience varying degrees of gait impairments, making it a reasonable model to test contemporary machine leaning algorithms. In this study, we employ machine learning techniques applied to raw walkway data to discern MS patients from healthy controls. We achieve this goal by constructing a range of new features which supplement standard parameters to improve machine learning model performance. Results Eleven variables from the standard gait feature set achieved the highest accuracy of 81%, precision of 95%, recall of 81%, and F1-score of 87%, using support vector machine (SVM). The inclusion of the novel features (toe direction, hull area, base of support area, foot length, foot width and foot area) increased classification accuracy by 7%, recall by 9%, and F1-score by 6%. Conclusions The use of an instrumented walkway can generate rich data that is generally unseen by clinicians and researchers. Machine learning applied to standard gait variables can discern MS patients from healthy controls with excellent accuracy. Noteworthy, classifications are made stronger by including novel gait features (toe direction, hull area, base of support area, foot length and foot area)

Biliary Atresia: The Canadian Experience

To determine the outcomes of Canadian children with biliary atresia. Health records of infants born in Canada between January 1, 1985 and December 31, 1995 (ERA I) and between January 1, 1996 and December 31, 2002 (ERA II) who were diagnosed with biliary atresia at a university center were reviewed. 349 patients were identified. Median patient age at time of the Kasai operation was 55 days. Median age at last follow-up was 70 months. The 4-year patient survival rate was 81% (ERA I = 74%; ERA II = 82%; P = not significant [NS]). Kaplan-Meier survival curves for patients undergoing the Kasai operation at age ≤30, 31 to 90, and >90 days showed 49%, 36%, and 23%, respectively, were alive with their native liver at 4 years ( P < .0001). This difference continued through 10 years. The 2- and 4-year post-Kasai operation native liver survival rates were 47% and 35% for ERA I and 46% and 39% for ERA II ( P = NS). A total of 210 patients (60%) underwent liver transplantation; the 4-year transplantation survival rate was 82% (ERA I = 83%, ERA II = 82%; P = NS). This is the largest outcome series of North American children with biliary atresia at a time when liver transplantation was available. Results in each era were similar. Late referral remains problematic; policies to ensure timely diagnosis are required. Nevertheless, outcomes in Canada are comparable to those reported elsewhere