506 research outputs found
Regression Depth and Center Points
We show that, for any set of n points in d dimensions, there exists a
hyperplane with regression depth at least ceiling(n/(d+1)). as had been
conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n
hyperplanes in d dimensions there exists a point that cannot escape to infinity
without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our
approach to related questions on the existence of partitions of the data into
subsets such that a common plane has nonzero regression depth in each subset,
and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure
Violator Spaces: Structure and Algorithms
Sharir and Welzl introduced an abstract framework for optimization problems,
called LP-type problems or also generalized linear programming problems, which
proved useful in algorithm design. We define a new, and as we believe, simpler
and more natural framework: violator spaces, which constitute a proper
generalization of LP-type problems. We show that Clarkson's randomized
algorithms for low-dimensional linear programming work in the context of
violator spaces. For example, in this way we obtain the fastest known algorithm
for the P-matrix generalized linear complementarity problem with a constant
number of blocks. We also give two new characterizations of LP-type problems:
they are equivalent to acyclic violator spaces, as well as to concrete LP-type
problems (informally, the constraints in a concrete LP-type problem are subsets
of a linearly ordered ground set, and the value of a set of constraints is the
minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006;
author spelling fixe
Exploring the integration of artificial intelligence (AI) and augmented reality (AR) in maritime medicine
This narrative literature review has analyzed the integration of artificial intelligence (AI) and augmented reality (AR) in the field of maritime medicine. A comprehensive search was conducted in academic databases using relevant search terms, resulting in the identification of 257 records. After screening for relevance and quality, a final review was conducted on 17 papers. This review highlights the potential applications and benefits of AI and AR in enhancing medical practices and safety measures for seafarers. The integration of AI and AR technologies in maritime medicine shows promise in providing real-time medical assistance, remote consultations, augmented training, and improved diagnostic capabilities. Additionally, AI-driven predictive models can aid in early detection of health issues and support proactive health management onboard ships. Challenges related to data privacy, connectivity at sea, and the need for regulatory frameworks are also discussed. The data analysis reported in this review contributes to a better understanding of the current state and future potential of AI and AR in maritime medicine and provide insights into opportunities for further research and implementation in the maritime industry
A Multi-signal Variant for the GPU-based Parallelization of Growing Self-Organizing Networks
Among the many possible approaches for the parallelization of self-organizing
networks, and in particular of growing self-organizing networks, perhaps the
most common one is producing an optimized, parallel implementation of the
standard sequential algorithms reported in the literature. In this paper we
explore an alternative approach, based on a new algorithm variant specifically
designed to match the features of the large-scale, fine-grained parallelism of
GPUs, in which multiple input signals are processed at once. Comparative tests
have been performed, using both parallel and sequential implementations of the
new algorithm variant, in particular for a growing self-organizing network that
reconstructs surfaces from point clouds. The experimental results show that
this approach allows harnessing in a more effective way the intrinsic
parallelism that the self-organizing networks algorithms seem intuitively to
suggest, obtaining better performances even with networks of smaller size.Comment: 17 page
Construction and Analysis of Projected Deformed Products
We introduce a deformed product construction for simple polytopes in terms of
lower-triangular block matrix representations. We further show how Gale duality
can be employed for the construction and for the analysis of deformed products
such that specified faces (e.g. all the k-faces) are ``strictly preserved''
under projection. Thus, starting from an arbitrary neighborly simplicial
(d-2)-polytope Q on n-1 vertices we construct a deformed n-cube, whose
projection to the last dcoordinates yields a neighborly cubical d-polytope. As
an extension of thecubical case, we construct matrix representations of
deformed products of(even) polygons (DPPs), which have a projection to d-space
that retains the complete (\lfloor \tfrac{d}{2} \rfloor - 1)-skeleton. In both
cases the combinatorial structure of the images under projection is completely
determined by the neighborly polytope Q: Our analysis provides explicit
combinatorial descriptions. This yields a multitude of combinatorially
different neighborly cubical polytopes and DPPs. As a special case, we obtain
simplified descriptions of the neighborly cubical polytopes of Joswig & Ziegler
(2000) as well as of the ``projected deformed products of polygons'' that were
announced by Ziegler (2004), a family of 4-polytopes whose ``fatness'' gets
arbitrarily close to 9.Comment: 20 pages, 5 figure
Prodsimplicial-Neighborly Polytopes
Simultaneously generalizing both neighborly and neighborly cubical polytopes,
we introduce PSN polytopes: their k-skeleton is combinatorially equivalent to
that of a product of r simplices. We construct PSN polytopes by three different
methods, the most versatile of which is an extension of Sanyal and Ziegler's
"projecting deformed products" construction to products of arbitrary simple
polytopes. For general r and k, the lowest dimension we achieve is 2k+r+1.
Using topological obstructions similar to those introduced by Sanyal to bound
the number of vertices of Minkowski sums, we show that this dimension is
minimal if we additionally require that the PSN polytope is obtained as a
projection of a polytope that is combinatorially equivalent to the product of r
simplices, when the dimensions of these simplices are all large compared to k.Comment: 28 pages, 9 figures; minor correction
Bounding Helly numbers via Betti numbers
We show that very weak topological assumptions are enough to ensure the
existence of a Helly-type theorem. More precisely, we show that for any
non-negative integers and there exists an integer such that
the following holds. If is a finite family of subsets of such that for any
and every
then has Helly number at most . Here
denotes the reduced -Betti numbers (with singular homology). These
topological conditions are sharp: not controlling any of these first Betti numbers allow for families with unbounded Helly number.
Our proofs combine homological non-embeddability results with a Ramsey-based
approach to build, given an arbitrary simplicial complex , some well-behaved
chain map .Comment: 29 pages, 8 figure
Artificial Intelligence Models in the Diagnosis of Adult-Onset Dementia Disorders: A Review
Background: The progressive aging of populations, primarily in the industrialized western world, is accompanied by the increased incidence of several non-transmittable diseases, including neurodegenerative diseases and adult-onset dementia disorders. To stimulate adequate interventions, including treatment and preventive measures, an early, accurate diagnosis is necessary. Conventional magnetic resonance imaging (MRI) represents a technique quite common for the diagnosis of neurological disorders. Increasing evidence indicates that the association of artificial intelligence (AI) approaches with MRI is particularly useful for improving the diagnostic accuracy of different dementia types. Objectives: In this work, we have systematically reviewed the characteristics of AI algorithms in the early detection of adult-onset dementia disorders, and also discussed its performance metrics. Methods: A document search was conducted with three databases, namely PubMed (Medline), Web of Science, and Scopus. The search was limited to the articles published after 2006 and in English only. The screening of the articles was performed using quality criteria based on the Newcastle-Ottawa Scale (NOS) rating. Only papers with an NOS score ≥ 7 were considered for further review. Results: The document search produced a count of 1876 articles and, because of duplication, 1195 papers were not considered. Multiple screenings were performed to assess quality criteria, which yielded 29 studies. All the selected articles were further grouped based on different attributes, including study type, type of AI model used in the identification of dementia, performance metrics, and data type. Conclusions: The most common adult-onset dementia disorders occurring were Alzheimer's disease and vascular dementia. AI techniques associated with MRI resulted in increased diagnostic accuracy ranging from 73.3% to 99%. These findings suggest that AI should be associated with conventional MRI techniques to obtain a precise and early diagnosis of dementia disorders occurring in old age
Conflicting phylogenomic signals reveal a pattern of reticulate evolution in a recent high‐Andean diversification (Asteraceae: Astereae: Diplostephium)
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137610/1/nph14530_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137610/2/nph14530.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137610/3/nph14530-sup-0001-SupInfo.pd
On the use of cartographic projections in visualizing phylo-genetic tree space
Phylogenetic analysis is becoming an increasingly important tool for biological research. Applications include epidemiological studies, drug development, and evolutionary analysis. Phylogenetic search is a known NP-Hard problem. The size of the data sets which can be analyzed is limited by the exponential growth in the number of trees that must be considered as the problem size increases. A better understanding of the problem space could lead to better methods, which in turn could lead to the feasible analysis of more data sets. We present a definition of phylogenetic tree space and a visualization of this space that shows significant exploitable structure. This structure can be used to develop search methods capable of handling much larger data sets
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