Integer colorings with forbidden rainbow sums

For a set of positive integers $A \subseteq [n]$, an $r$-coloring of $A$ is rainbow sum-free if it contains no rainbow Schur triple. In this paper we initiate the study of the rainbow Erd\H{o}s-Rothchild problem in the context of sum-free sets, which asks for the subsets of $[n]$ with the maximum number of rainbow sum-free $r$-colorings. We show that for $r=3$, the interval $[n]$ is optimal, while for $r\geq8$, the set $[\lfloor n/2 \rfloor, n]$ is optimal. We also prove a stability theorem for $r\geq4$. The proofs rely on the hypergraph container method, and some ad-hoc stability analysis.Comment: 20 page

Gait phase classification for in-home gait assessment

With growing ageing population, acquiring joint measurements with sufficient accuracy for reliable gait assessment is essential. Additionally, the quality of gait analysis relies heavily on accurate feature selection and classification. Sensor-driven and one-camera optical motion capture systems are becoming increasingly popular in the scientific literature due to their portability and cost-efficacy. In this paper, we propose 12 gait parameters to characterise gait patterns and a novel gait-phase classifier, resulting in comparable classification performance with a state-of-the-art multi-sensor optical motion system. Furthermore, a novel multi-channel time series segmentation method is proposed that maximizes the temporal information of gait parameters improving the final classification success rate after gait event reconstruction. The validation, conducted over 126 experiments on 6 healthy volunteers and 9 stroke patients with handlabelled ground truth gait phases, demonstrates high gait classification accuracy

Human upper limb motion analysis for post-stroke impairment assessment using video analytics

Stroke is a worldwide healthcare problem which often causes long-term motor impairment, handicap, and disability. Optical motion analysis systems are commonly used for impairment assessment due to high accuracy. However, the requirement of equipment-heavy and large laboratory space together with operational expertise, makes these systems impractical for local clinic and home use. We propose an alternative, cost-effective and portable, decision support system for optical motion analysis, using a single camera. The system relies on detecting and tracking markers attached to subject's joints, data analytics for calculating relevant rehabilitation parameters, visualization, and robust classification based on graph-based signal processing. Experimental results show that the proposed decision support system has the potential to offer stroke survivors and clinicians an alternative, affordable, accurate and convenient impairment assessment option suitable for home healthcare and tele-rehabilitation

Shift-enabled graphs : graphs where shift-invariant filters are representable as polynomials of shift operations

In digital signal processing, a shift-invariant filter can be represented as a polynomial expansion of a shift operation, that is, the Z-transform representation. When extended to Graph Signal Processing (GSP), this would mean that a shift-invariant graph filter can be represented as a polynomial of the shift matrix of the graph. Prior work shows that this holds under the shift-enabled condition that the characteristic and minimum polynomials of the shift matrix are identical. While the shiftenabled condition is often ignored in the literature, this letter shows that this condition is essential for the following reasons. First, we prove that this condition is not just sufficient but also necessary for any shift-invariant filter to be representable by the shift matrix. Moreover, we provide a counterexample showing that given a filter that commutes with a non-shift-enabled graph, it is generally impossible to convert the graph to a shift-enabled graph with a shift matrix still commuting with the original filter. The result provides a deeper understanding of shift-invariant filters when applied in GSP and shows that further investigation of shift-enabled graphs is needed to make them applicable to practical scenarios

Electroacupuncture enhances extragonadal aromatization in ovariectomized rats

BACKGROUND: Repeated electroacupuncture (EA) stimulation is known to stimulate the activity of the hypothalamus-pituitary-adrenal axis, and to enhance the circulation level of estrogen in the ovariectomized rats. To explore the source of the increased circulation estrogen, the extragonadal aromatization was detected. METHODS: Female rats were divided into five groups: 1) intact (INT), 2) intact with EA in specific points (INT+EA), 3) ovariectomized (OVX), 4) ovariectomized with EA in specific points (OVX+EA) and 5) ovariectomized with EA in non-specific points (OVX+C). Radiometric assay, Western blot and RT-PCR were adopted to determine the extragonadal aromatization in subcutaneous abdominal (SA) adipose and liver tissues of rats. The blood concentrations of estrogen, testosterone and corticosterone were measured by radioimmunoassay. RESULTS: The aromatase activities of the SA adipose and liver tissues in the OVX+EA rats increased significantly (p < 0.01) compared with those in the INT, INT+EA and OVX rats. The 58-kDa aromatase protein and aromatase mRNA expressions normalized to β-actin in the OVX+EA rats' SA adipose tissues showed higher levels than those from corresponding tissues in the INT and INT+EA rats (p < 0.05). And the ratios of aromatase mRNA and protein to β-actin in the OVX+EA rats' liver tissues increased significantly compared with those in the OVX rats (p < 0.05). Furthermore, blood estrogen and corticosterone concentrations showed significant increase in the OVX+EA rats compared with the concentrations in the OVX and OVX+C rats (p < 0.05), but no statistical disparity occurred on the blood testosterone concentrations between the OVX+EA rats and the OVX ones. CONCLUSION: Both the subcutaneous abdominal adipose and the liver tissues contributed to the effects of electroacupuncture on the extragonadal aromatization to promote the blood concentrations of estrogen in the ovariectomized rats