This is a course on the fundamentals of probability geared towards first or second-year graduate students who are interested in a rigorous development of the subject. The course covers sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, and limit theorems. There is also a number of additional topics such as: language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; and deeper understanding of conditional distributions and expectations.

This is a graduate-level introduction to mathematics of information theory. We will cover both classical and modern topics, including information entropy, lossless data compression, binary hypothesis testing, channel coding, and lossy data compression.

Library Carpentry lesson: An introduction to Git. What We Will Try to Do Begin to understand and use Git/GitHub. You will not be an expert by the end of the class. You will probably not even feel very comfortable using Git. This is okay. We want to make a start but, as with any skill, using Git takes practice. Be Excellent to Each Other If you spot someone in the class who is struggling with something and you think you know how to help, please give them a hand. Try not to do the task for them: instead explain the steps they need to take and what these steps will achieve. Be Patient With The Instructor and Yourself This is a big group, with different levels of knowledge, different computer systems. This isn’t your instructor’s full-time job (though if someone wants to pay them to play with computers all day they’d probably accept). They will do their best to make this session useful. This is your session. If you feel we are going too fast, then please put up a pink sticky. We can decide as a group what to cover.

La investigación titulada: “Obligaciones tributarias y su influencia en la recaudación fiscal de las micro y pequeñas empresas” tuvo como propósito reflejar la influencia de las obligaciones tributarias en la recaudación fiscal, también busca reducir la informalidad, y ampliar la base tributaria mediante beneficios otorgados a las micro y pequeñas empresas que se acojan a los regímenes tributarios, con la finalidad de aumentar la recaudación fiscal. La estructura se desarrollado en base de cuatro capítulos, el CAPÍTULO I trata sobre el planteamiento del problema, la formulación, objetivos y justificación, CAPÍTULO II abarcó los antecedentes de estudio, bases teóricas sobre el tema de investigación, bases conceptuales, definición de términos, hipótesis, variables y la operacionalización de variables, el CAPÍTULO III contiene los materiales y métodos que se utilizó en el presente estudio finalmente el CAPÍTULO IV trató sobre la discusión de resultados, análisis de la información y la prueba de hipótesis. Como parte final del presente estudio comprende las conclusiones, recomendaciones, referencias bibliográficas y anexos.

(This case study was added to OER Commons as one of a batch of over 700. It has relevant information which may include medical imagery, lab results, and history where relevant. A link to the final diagnosis can be found at the end of the case study for review. The first paragraph of the case study -- typically, but not always the clinical presentation -- is provided below.)

The patient is a 63 year old woman with elevated calcium who, on work-up for hyperparathyroidism, was found to have a single nodule within the superior pole of the left lobe of her thyroid, measuring 0.5 cm, as well as three hypoechoic nodules of the right lobe, measuring up to 2.0 cm. The patient underwent surgical parathyroid exploration and total thyroidectomy after fine needle aspiration of the dominant right lobe nodule demonstrated a "follicular neoplasm or lesion." However, the remainder of this case will focus on a smaller right lobe nodule that was not biopsied.

(This case study was added to OER Commons as one of a batch of over 700. It has relevant information which may include medical imagery, lab results, and history where relevant. A link to the final diagnosis can be found at the end of the case study for review. The first paragraph of the case study -- typically, but not always the clinical presentation -- is provided below.)

The patient was an elderly man in his 80s who presented with dyspnea, fatigue, and subacute weight loss. Imaging identified a large left lower lobe mass with mediastinal lymphadenopathy. A CT-guided biopsy was performed, which identified a poorly differentiated adenocarcinoma (Figure 1) which was positive for CK7 and TTF-1 but negative for CK5/6 and p40, consistent with lung origin. Ancillary testing was performed, and the tumor cells were positive for PD-L1 (TPS 50%) and negative for ALK by immunohistochemistry (IHC). Fluorescence in-situ hybridization (FISH) was negative for ALK rearrangement (other targets failed). Oncomine next generation sequencing (NGS) was also performed, which identified a TP53 mutation, MET splice site mutation near codon D981, and "fusion" adjoining exons 13 and 15 of MET (Figures 2 and 3).

(This case study was added to OER Commons as one of a batch of over 700. It has relevant information which may include medical imagery, lab results, and history where relevant. A link to the final diagnosis can be found at the end of the case study for review. The first paragraph of the case study -- typically, but not always the clinical presentation -- is provided below.)

The patient is a woman in her 70s who was referred to a head and neck surgeon for evaluation of a left thyroid nodule. On ultrasound, the nodule measured 2.3 cm with calcifications. She subsequently underwent fine needle aspiration biopsy and specimens were sent for cytology, the result of which prompted molecular testing on the FNA specimen.

The applications of pattern recognition techniques to problems of machine vision is the main focus for this course. Topics covered include, an overview of problems of machine vision and pattern classification, image formation and processing, feature extraction from images, biological object recognition, bayesian decision theory, and clustering.