Atomic walk counts (awc's) of order k (k > or = 1) are the number of all possible walks of length k which start at a specified vertex (atom) i and end at any vertex j separated by m (0 < or = m < or = k) edges from vertex i. The sum of atomic walk counts of order k is the molecular walk count (mwc) of order k. The concept of atomic and molecular walk counts was extended to zero and negative orders by using a backward algorithm based on the usual procedure used to obtain the values of mwc's. The procedure can also be used in cases in which the adjacency matrix A related to the actual structure is singular and therefore A(-1) does not exist. awc's and mwc's of negative order may assume noninteger and even negative values. If matrix A is singular, atomic walk counts of zero order may not be equal to one.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1021/ci025655t | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Association of Preoperative Walking Speed With 1-Year Outcomes After Hip Arthroscopy for Femoroacetabular Impingement Syndrome.
Sports Health
January 2025
Section of Young Adult Hip Surgery, Division of Sports Medicine, Department of Orthopaedic Surgery, Rush Medical College of Rush University, Rush University Medical Center, Chicago, Illinois.
Background: Previous studies have identified demographic, radiographic, and intraoperative predictors of outcomes after hip arthroscopy for femoroacetabular impingement syndrome, yet few studies have identified whether preoperative gait metrics can predict outcomes.
Hypothesis: Increased preoperative step count, walking speed, step length, and gait symmetry will be associated with better outcomes after surgery.
Study Design: Retrospective cohort study.
Continuous high-soy protein soymilk intake affects ordinary walking speed in the Japanese pre-frail and frail elderly: a randomized controlled trial.
BMC Geriatr
January 2025
Geroscience Research Center, Research Institute, National Center for Geriatrics and Gerontology, Obu, Aichi, 474-8511, Japan.
Background: To investigate whether continuous intervention using soymilk containing high soy protein improves physical frailty, a randomized controlled trial was conducted among the Japanese pre-frail and frail elderly.
Methods: Japanese pre-frail and frail elderly participants (n = 73) were randomly assigned to the high-soy protein and control groups, who then ingested soymilk containing 14.5 g/200 ml and 3.
Associations of daily step count with all-cause mortality and cardiovascular mortality in hypertensive US adults: a cohort study from NHANES 2005-2006.
BMC Public Health
January 2025
Department of Emergency Medicine, The Second Xiangya Hospital, Central South University, Changsha, Hunan Province, China.
Background: The health benefits of physical activity, including walking, are well-established, but the relationship between daily step count and mortality in hypertensive populations remains underexplored. This study investigates the association between daily step count and both all-cause and cardiovascular mortality in hypertensive American adults.
Methods: We used data from the National Health and Nutrition Examination Survey 2005-2006, including 1,629 hypertensive participants with accelerometer-measured step counts.
Dr David Sabgir and Walk with a Doc-every step counts.
Br J Sports Med
December 2024
PM&R/Sports Medicine, Westchester Medical Center, Hawthorne, New York, USA.
Oral Frailty and Its Relationship with Physical Frailty in Older Adults: A Longitudinal Study Using the Oral Frailty Five-Item Checklist.
Nutrients
December 2024
Division of General Medicine, Department of Internal Medicine, Hyogo Medical University, Nishinomiya 663-8501, Hyogo, Japan.
Background/objectives: Oral frailty, first identified in Japan in 2014, refers to a state between healthy oral function and severe decline, marked by minor issues, such as tooth loss and chewing difficulties. The oral frailty five-item checklist (OF-5) enables non-dental professionals to evaluate oral frailty using five key indicators: remaining teeth count, chewing difficulties, swallowing difficulties, dry mouth, and articulatory oral skills. Limited studies exist.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!