Harold Martin - Academia.edu (original) (raw)

Papers by Harold Martin

Proceedings of the 1990 ACM annual conference on Cooperation - CSC '90

2017 IEEE Signal Processing in Medicine and Biology Symposium (SPMB), 2017

Electrocardiograms (EKGs) are the most common diagnosis tools used for the detection and diagnosi... more Electrocardiograms (EKGs) are the most common diagnosis tools used for the detection and diagnosis of cardiovascular diseases and abnormalities. In this paper, we proposed a method that uses independent component analysis (ICA) for the real-time detection of the most distinct component of the cardiac electrical signal, the R-peak. This approach will open the door to real-time analysis and decomposition of the complete cardiac signal and the online diagnosis of cardiac abnormalities. The potential benefits of such real-time implementation are far reaching, from the online diagnosis of diseases and abnormalities to its use in tracking heart functioning during the testing and development of cutting edge research and treatments, such as transcranial magnetic stimulation (TMS).

IEEE Sensors Journal, 2018

This study integrates a time of flight sensor (ToF) to a high-resolution CCD camera in a new and ... more This study integrates a time of flight sensor (ToF) to a high-resolution CCD camera in a new and fully automated book reader design for individuals with visual impairment and blindness. This cost-effective and portable book reader design integrates, in a unique way, a 3-D map extracted by a low-resolution ToF sensor and a high-resolution image as means to correct the page curvature of bound books. This is achieved by a seamless registration process of two imaging modalities, so that the low resolution (160 × 120 pixels) depth map accurately reflects the entire book spread as captured by the high resolution camera (3072 × 2304 pixels). As part of the automated registration process, the book reader will give the user a warning message if the book is misplaced within its field of view. The reading accuracy is further improved by a mathematical framework formulating the flattening and extension operations, which together optimally dewarp the book spread images. This correction process is resilient to potential misplacement of the book within the book-reader platform. The testing phase led to a reading accuracy of over 95%, involving an unprecedented acquisition and processing of 200 pages. A database consisting of all the 200 high resolution book spread images together with their respective extracted depth maps are made available to the research community for further developments.

Transactions of the American Mathematical Society, 1976

Several weak base (in the sense of A. V. Arhangel’skiĭ) metrization theorems are established, inc... more Several weak base (in the sense of A. V. Arhangel’skiĭ) metrization theorems are established, including a weak base generalization of the Nagata-Smirnov Metrization Theorem.

Rocky Mountain Journal of Mathematics, 1976

Proceedings of the American Mathematical Society, 1973

Proceedings of the American Mathematical Society, 1972

A symmetric d for a topological space R is said to be coherent if whenever { x ( n ) } \{ x(n)\} ... more A symmetric d for a topological space R is said to be coherent if whenever { x ( n ) } \{ x(n)\} and { y ( n ) } \{ y(n)\} are sequences in R with d ( x ( n ) , y ( n ) ) → 0 d(x(n),y(n)) \to 0 and d ( x ( n ) , x ) → 0 d(x(n),x) \to 0 , then d ( y ( n ) , x ) → 0 d(y(n),x) \to 0 . V. Niemytzki and W. A. Wilson have essentially shown that a topological space R is metrizable if and only if R is symmetrizable via a coherent symmetric. Conditions on a symmetric d which are equivalent to d being coherent are established. As a consequence, a theorem of A. Arhangel’skiĭ may be refined by showing that if f : R → Y f:R \to Y is a quotient map from a metrizable space R onto a T 0 {T_0} -space y, then Y is metrizable if and only if f is a regular map.

Pacific Journal of Mathematics, 1987

Telgarsky calls a topological space C-scattered when each of its non-empty closed sets contains a... more Telgarsky calls a topological space C-scattered when each of its non-empty closed sets contains a compact set with non-empty relative interior. With respect to infinite products, hyperspaces, and the partially ordered set of compactifications, we study the class of paracompact C-scattered spaces and two of its subclasses, MacDonald and Willard's A'-spaces and Λ-spaces. 0. Introduction. All spaces are Hausdorff spaces. A space X is said to be C-scattered [16] provided that each of its non-empty closed subspaces contains a compact set with non-empty relative interior. The notion of C-scatteredness seems a simple simultaneous generalization of scattered (Ξ= each non-empty set has a relative isolated point) and of local compactness. However, the class of paracompact C-scattered spaces is most interesting because [19] it contains its perfect pre-images, it is closed under finite products, it contains all closed continuous images of paracompact locally compact spaces, and for each of its members X, X X Y is paracompact iff Y is paracompact. Presently we study this class and two of its subclasses. Section 1 is due to the third author and § §2 and 3 are due to the first two authors. In §1 of our paper, we show that each countable product of paracompact C-scattered spaces is paracompact. This result improves upon the same theorem, due to Rudin and Watson [18], for paracompact scattered spaces, and answers the question raised for Λ'-spaces by the first two authors of this paper. As a corollary, we find that each countable product of Lindelof C-scattered spaces is Lindelof, a result due to Alster [2]. In the second section, we investigate hyperspaces of paracompact C-scattered spaces-a situation so complex that we limit our attention to A '-spaces. An A'-space is a space whose set of accumulation points is compact [10]. Thus, an ^I'-space is paracompact C-scattered. It is known [12] that the compact-set hyperspace ^(X) is locally compact (metrizable) iff X is locally compact (respectively, metrizable). Here we present an example of a Lindelof scattered A '-space X such that ^(X) is neither C-scattered or normal. Further, we prove that ^(X) is an A '-space 277 278

Pacific Journal of Mathematics, 1975

Journal of Mathematical Analysis and Applications, 1980

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Let n denote a positive integer relatively prime to 10. Let the period of 1/n be a · b with b &gt... more Let n denote a positive integer relatively prime to 10. Let the period of 1/n be a · b with b > 1. Break the repeating block of a · b digits up into b sub blocks, each of length a, and let B(n,a,b) denote the sum of these b blocks. In 1836, E. Midy proved that if p is a prime greater than 5, and the period of 1/p is 2 · a, then B(p,a,2) = 10a ! 1. In 2004, B. Ginsberg (2) showed that if p is a prime greater than 5, and the period of 1/p is 3 · a, then B(p,a,3) = 10a ! 1. In 2005, A. Gupta and B. Sury (3) showed that if p is a prime greater than 5, and the period of 1/p is a·b with b > 1, then B(p,a,b) = k·(10a! 1). (The results of Midy and Ginsberg follow quickly from this). In this paper we examine the case in which p is not necessarily prime. Define two positive integers u and v to be period compatible provided that there exist odd integers r and t and a positive integer s such that the periods of 1/u and 1/v are of the form r · 2s and t · 2s respectively. Let n be a positiv...

American Journal of Physics, 2004

Parrondo’s paradox is the proposition that two losing strategies can, by alternating randomly, pr... more Parrondo’s paradox is the proposition that two losing strategies can, by alternating randomly, produce a winner. R. D. Astumian has recently created a simple board game to illustrate this counterintuitive phenomenon. We prove that the inherent symmetry of Astumian’s game prevents it from achieving its purpose, and suggest amended versions that do. We also display the additional paradoxical effect of two slow, losing games combining into a fast, winning one.

$Research paper thumbnail of A note on the metrization of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma </annotation></semantics></math>γ-spaces$

Proceedings of the American Mathematical Society, 1976

The class of quasi Nagata spaces, which strictly includes the class of wN-spaces, is defined. A c... more The class of quasi Nagata spaces, which strictly includes the class of wN-spaces, is defined. A closely related class of spaces, pseudo Nagata spaces, are also defined. It is shown that a Hausdorff γ \gamma -space is metrizable if and only if it is either a quasi Nagata space or a pseudo Nagata space.

Proceedings of the American Mathematical Society, 1977

A metric d is strongly rigid if and only if d(x,y) J= d(w,z) whenever the doubleton {x,y} is not ... more A metric d is strongly rigid if and only if d(x,y) J= d(w,z) whenever the doubleton {x,y} is not equal to the doubleton {w, z). It is shown that a nonempty metrizable space X admits a compatible strongly rigid metric if X has covering dimension zero and has cardinality equal to or less than that of the real line.

Proceedings of the American Mathematical Society, 1978

A subset B of a metric space (X, d) is called a d-bisector set iff there are distinct points x an... more A subset B of a metric space (X, d) is called a d-bisector set iff there are distinct points x and y in X with B = { z : d ( x , z ) = d ( y , z ) } B = \{ z:d(x,z) = d(y,z)\} . It is shown that if X is a separable metrizable space, then dim ⁡ ( X ) ⩽ n \dim (X) \leqslant n iff X has an admissible metric d for which dim ⁡ ( B ) ⩽ n − 1 \dim (B) \leqslant n - 1 whenever B is a d-bisector set. For separable metrizable spaces, another characterization of n-dimensionality is given as well as a metric dependent characterization of zero dimensionality.