Zero Forcing, Linear and Quantum Controllability for Systems Evolving on Networks

We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Our main result says that controllability in the quantum sense, expressed by the Lie algebra rank condition, and controllability in the sense of linear systems, expressed by the controllability matrix rank condition, are equivalent conditions. We also investigate how the graph theoretic concept of a zero forcing set impacts the controllability property; if a set of vertices is a zero forcing set, the associated dynamical system is controllable. These results open up the possibility of further exploiting the analogy between networks, linear control systems theory, and quantum systems Lie algebraic theory. This study is motivated by several quantum systems currently under study, including continuous quantum walks modeling transport phenomena

Logic circuits from zero forcing

We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices to encode each logical bit, we obtain universal computation. We also highlight a phenomenon of “back forcing” as a property of each function. Such a phenomenon occurs in a circuit when the input of gates which have been already used at a given time step is further modified by a computation actually performed at a later stage. Finally, we show that zero forcing can be also used to implement reversible computation. The model introduced here provides a potentially new tool in the analysis of Boolean functions, with particular attention to monotonicity. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits

Biogenic synthesis of gold nanoparticles using red and green pear fruit extracts

>Magister Scientiae - MScThere has been a growing interest in the design of biocompatible and environmentally affable nanoparticles (NPs) among scientists to develop novel and safe biomaterials for use in various biomedical applications. This can be obtained through the use of plant and/ or fruit-derived phytochemicals that are capable of reducing gold ions into gold nanoparticles (AuNPs). Several studies have shown that different plant and fruit extracts possess different pharmacological properties as a result of their phytochemical profile and are capable of synthesising AuNPs with potential applications in medicine. Pears possess a unique phytochemical profile and these phytochemicals vary in the different parts of the pear and allows pears to exhibit beneficial pharmacological activities such as antioxidant, antimicrobial, anticarcinogenic as well as anti-inflammatory properties. Anthocyanins are important pigments responsible for the colouration of fruits but also have multiple uses in traditional Chinese medicine. Anthocyanins are strong antioxidants and since these molecules are present in pears, they could possibly be able to reduce gold (III) chloride to form NPs. The red-coloured ‘Bon Rouge’ pear contains higher levels of anthocyanins in comparison to the green-coloured ‘Williams Bon Chretien’ pear of which it is a mutant bud. A comprehensive study of the capability of the ‘Williams Bon Chretien’ and ‘Bon Rouge’ pears as the novel materials for the biogenic synthesis of AuNPs was conducted. Differences in the physicochemical properties of these AuNPs and potential biological applications based on the influence of anthocyanins and other phytochemicals within the pears were also explored. In addition, the effect of reaction temperature and extract concentration as well as kinetics as a function of time on the synthesis of AuNPs were conducted. The synthesized AuNPs were characterised for their size, polydispersity, morphology, crystallinity, active functional groups and in vitro stability

ResearchFanshawe Magazine Issue 5

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The Effectiveness of Exercise Interventions Supported by Telerehabilitation For Recently Hospitalized Adult Medical Patients: A Systematic Review

Objective: To evaluate the effectiveness of exercise interventions delivered via telerehabilitation (via videoconference) for recently hospitalized adult medical patients. Data sources: A search was undertaken across six databases for English language publications from inception to May 2020. Methods: Studies were selected if they included an exercise intervention for recently hospitalized adults, delivered by a physiotherapist via videoconference. Two reviewers independently screened 1,122 articles (21 full text screening) and assessed methodological quality using the Downs and Black Checklist. A narrative synthesis of the included studies was undertaken. Results: Three studies met eligibility criteria involving 201 participants with chronic heart failure or chronic obstructive pulmonary disease. Findings demonstrated limited evidence supporting the effectiveness of exercise delivered via telerehabilitation in improving physical function and patient reported quality of life outcomes in recently hospitalized medical patients. Telerehabilitation in this setting was also associated with high attendance rates and patient satisfaction. Conclusions: Findings provide preliminary support for the benefits of exercise interventions delivered via telerehabilitation for recently hospitalized medical patients. Results do need to be interpreted with caution as further high-quality studies specific to this method of exercise intervention delivery are needed

Detrended fluctuation analysis of gait dynamics when entraining to music and metronomes at different tempi in persons with multiple sclerosis

In persons with multiple sclerosis (PwMS), synchronizing walking to auditory stimuli such as to music and metronomes have been shown to be feasible, and positive clinical effects have been reported on step frequency and perception of fatigue. Yet, the dynamic interaction during the process of synchronization, such as the coupling of the steps to the beat intervals in music and metronomes, and at different tempi remain unknown. Understanding these interactions are clinically relevant, as it reflects the pattern of step intervals over time, known as gait dynamics. 28 PwMS and 29 healthy controls were instructed to walk to music and metronomes at 6 tempi (0-10% in increments of 2%). Detrended fluctuation analysis was applied to calculate the fractal statistical properties of the gait time-series to quantify gait dynamics by the outcome measure alpha. The results showed no group differences, but significantly higher alpha when walking to music compared to metronomes, and when walking to both stimuli at tempi+8,+10% compared to lower tempi. These observations suggest that the precision and adaptation gain differ during the coupling of the steps to beats in music compared to metronomes (continuous compared to discrete auditory structures) and at different tempi (different inter-beat-intervals)

The Herschel Virgo Cluster Survey - XIII. Dust in early-type galaxies

Aims. We study the dust content of a large optical input sample of 910 early-type galaxies (ETG) in the Virgo cluster, extending also to the dwarf ETG, and examine the results in relation with those on the other cold ISM components. Methods. We searched for far-infrared emission in all galaxies of the input sample using the 250 micron image of the Herschel Virgo Cluster Survey (HeViCS). This image covers a large fraction of the cluster. For the detected ETG we measured fluxes in 5 bands from 100 to 500 micron, and estimated the dust mass and temperature with modified black-body fits. Results. Dust is detected above the completeness limit of 25.4 mJy at 250 micron in 46 ETG, 43 of which are in the optically complete part of the input sample. In addition dust is present at fainter levels in another 6 ETG. We detect dust in the 4 ETG with synchrotron emission, including M 87. Dust appears to be much more concentrated than stars and more luminous ETG have higher dust temperatures. Dust detection rates down to the 25.4 mJy limit are 17% for ellipticals, about 40% for lenticulars (S0 + S0a) and around 3% for dwarf ETG. Dust mass does not correlate clearly with stellar mass and is often much more than that expected for a passive galaxy in a closed-box model. The dust-to-stars mass ratio anticorrelates with galaxy luminosity, and for some dwarf ETG reaches values as high as for dusty late-type galaxies. In the Virgo cluster slow rotators appear more likely to contain dust than fast ones. Comparing the dust results with those on HI from ALFALFA, there are only 8 ETG detected both in dust and in HI in the HeViCS area; 39 have dust but only an upper limit on HI, and 8 have HI but only an upper limit on dust. The locations of these galaxies in the cluster are different, with the dusty ETG concentrated in the densest regions, while the HI rich ETG are at the periphery.Comment: Accepted by Astronomy and Astrophysics; modified to reflect the on-line forthcoming version on the A&A web sit

ResearchFanshawe Magazine Issue 6

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