On log concavity for order-preserving and order-non-reversing maps of partial orders

Stanley used the Aleksandrov-Fenchel inequalities from the theory of nixed volumes to prove the following result. Let P be a partially ordered set with n elements, and let x ∊ P. If Ni* is the number of linear extensions , ⋋ : P + (1 , 2,...,n) satisfying ⋋ (x) = i, then the sequence N*1,…,N*n is log concave (and therefore unimodal). Here the analogous results for both order-preserving and order-non-reversing maps are proved using an explicit injection. Further, if vc is the number of order-preserving maps of P into a chain of length c, then vc is shown to be 1-og concave, and the corresponding result is established for order-non-reversing maps

Combinatorics of unique maximal factorization families (UMFFs)

Suppose a set W of strings contains exactly one rotation (cyclic shift) of every primitive string on some alphabet Σ. Then W is a circ-UMFF if and only if every word in Σ+ has a unique maximal factorization over W. The classic circ-UMFF is the set of Lyndon words based on lexicographic ordering (1958). Duval (1983) designed a linear sequential Lyndon factorization algorithm; a corresponding PRAM parallel algorithm was described by J. Daykin, Iliopoulos and Smyth (1994). Daykin and Daykin defined new circ-UMFFs based on various methods for totally ordering sets of strings (2003), and further described the structure of all circ-UMFFs (2008). Here we prove new combinatorial results for circ-UMFFs, and in particular for the case of Lyndon words. We introduce Acrobat and Flight Deck circ-UMFFs, and describe some of our results in terms of dictionaries. Applications of circ-UMFFs pertain to structured methods for concatenating and factoring strings over ordered alphabets, and those of Lyndon words are wide ranging and multidisciplinary

PDV/MPDV APPs: Modeling Tools to Predict System Performance for Design and Experimentation

Author Institution: National Security Technologies, LLCSlides presented at the 2016 Photonic Doppler Velocimetry (PDV) unclassified program, Bankhead Theater, Livermore, California, June 7 - 9, 2016. Morning program, June 8, 2016

Novelty, distillation, and federation in machine learning for medical imaging

The practical application of deep learning methods in the medical domain has many challenges. Pathologies are diverse and very few examples may be available for rare cases. Where data is collected it may lie in multiple institutions and cannot be pooled for practical and ethical reasons. Deep learning is powerful for image segmentation problems but ultimately its output must be interpretable at the patient level. Although clearly not an exhaustive list, these are the three problems tackled in this thesis. To address the rarity of pathology I investigate novelty detection algorithms to find outliers from normal anatomy. The problem is structured as first finding a low-dimension embedding and then detecting outliers in that embedding space. I evaluate for speed and accuracy several unsupervised embedding and outlier detection methods. Data consist of Magnetic Resonance Imaging (MRI) for interstitial lung disease for which healthy and pathological patches are available; only the healthy patches are used in model training. I then explore the clinical interpretability of a model output. I take related work by the Canon team — a model providing voxel-level detection of acute ischemic stroke signs — and deliver the Alberta Stroke Programme Early CT Score (ASPECTS, a measure of stroke severity). The data are acute head computed tomography volumes of suspected stroke patients. I convert from the voxel level to the brain region level and then to the patient level through a series of rules. Due to the real world clinical complexity of the problem, there are at each level — voxel, region and patient — multiple sources of “truth”; I evaluate my results appropriately against these truths. Finally, federated learning is used to train a model on data that are divided between multiple institutions. I introduce a novel evolution of this algorithm — dubbed “soft federated learning” — that avoids the central coordinating authority, and takes into account domain shift (covariate shift) and dataset size. I first demonstrate the key properties of these two algorithms on a series of MNIST (handwritten digits) toy problems. Then I apply the methods to the BraTS medical dataset, which contains MRI brain glioma scans from multiple institutions, to compare these algorithms in a realistic setting

A Multipartite Hajnal-Szemer\'edi Theorem

The celebrated Hajnal-Szemer\'edi theorem gives the precise minimum degree threshold that forces a graph to contain a perfect K_k-packing. Fischer's conjecture states that the analogous result holds for all multipartite graphs except for those formed by a single construction. Recently, we deduced an approximate version of this conjecture from new results on perfect matchings in hypergraphs. In this paper, we apply a stability analysis to the extremal cases of this argument, thus showing that the exact conjecture holds for any sufficiently large graph.Comment: Final version, accepted to appear in JCTB. 43 pages, 2 figure

Counterculture

Counterculture is a creative thesis written to earn the degree of Master of Arts at the University of Maine in spring of 2001. The short novel tells the story of Cannister Barnes, a young man who goes to England in the late summer for study and briefly catches a glimpse of a young woman while he’s lost in the winding streets and paths of Eton. His trip is also marred by a dreadful experience in the London Underground, in which he sees an indigent man in a wheelchair roll himself into the path of an oncoming train. Before returning to the States, however, Cannister finds that the man has left behind a little red book, and Cannister claims it as his own. He carries the memory of this trauma, the image of the young woman, and the red book all back with him to America. Back at home, Cannister finds himself being forced to confront problems in his life he’d rather do without-namely, the relationship with his partner, Amelia, seems to be f&g apart. Things are made worse by the fact that instead of taking action to either help or hinder these problems, Cannister would rather read the red book he absconded with back at the Underground. It appears to be a fictional account of shady scientific experiments, strange goings on, and other odd events. Cannister is drawn again and again to the book’s narrative. His life at the University, as well, begins to falter; absorption in the book‘s story Ieads to a few missed classes, to procrastination and un- graded papers. A close friend he made in England comes to visit him and expresses interest in the red book and its meaning. Upon the friend’s departure, Cannister, continuing to read onward, discovers that the book details his own young life, and he finally decides to travel back to England in search of his own history, and in fact, his own humanity. Counterculture explores a number of themes, many of them related to the reality of identity, and what shapes it. Cannister Barnes represents a peculiar icon of a mad society that has lost any sort of hold on what it means to be what we are. His personal search is representative in its commonality, but antithetical in the unique character of Cannister’s past

Authority in liberal catholic Anglicanism

The Anglican view of authority, set out in her more recent official documents, owes much to the influence of liberal Catholicism; more especially to that of the generation younger than Gore who had themselves been influenced by the concept of authority espoused by certain Roman Catholic modernists. Radical movements in philosophy, literature, and science during the eighteenth and early nineteenth centuries created a climate of suspicion and doubt. By the mid-nineteenth century the accepted view of authority within Anglicanism could no longer sustain the weight placed upon it by the effects of these movements. Liberal Catholicism emerged in the l880's with a view of authority which allowed a certain liberality for the exploration of new ideas without compromise to the historic and catholic basis of Anglicanism. Within Roman Catholicism the modernist Tyrrell was opposing the official concept of authority which imposed upon the faithful dogmas defined by the hierarchy. Tyrrell maintained that the faithful themselves, in their collective spiritual experience, guaranteed the authority of dogma. The importance of spiritual experience, and hence of the consensus fidelium, was siezed upon by the younger generation of liberal catholic Anglicans, Incorporating the modernist view of authority they produced a neo-liberal Catholicism as catholic as Gore's, but with a greater degree of liberality. The emergence of neo-liberal Catholicism was catalysed by a ' period of crisis within Anglicanism immediately prior to the Great War. The Doctrine Commission, appointed in 1922, included a number of neo-liberal Catholics. Amongst them was A.E.J.Rawlinson and Will Spens, Rawlinson, as Bishop of Derby, also participated in the 1948 Lambeth Conference. In so far as they deal with authority both the report of the Doctrine Commission and the report of Lambeth 1948 show a marked dependence upon the neo-liberal catholic view of authority