Some additive results on Drazin inverse

In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ba, we show that a + b is Drazin invertible if and only if aa^D(a+b) is Drazin invertible, where the superscript D means the Drazin inverse. Furthermore we find an expression of (a + b)^D. As an application we give some new representations for the Drazin inverse of a 2 × 2 block matrix.Supported by the National Natural Science Foundation of China (11361009), the Guangxi Provincial Natural Science Foundation of China (2013GXNSFAA019008), and Science Research Project 2013 of the China-ASEAN Study Center (Guangxi Science Experiment Center) of Guangxi University for Nationalities.Liu, X.; Qin, X.; Benítez López, J. (2015). Some additive results on Drazin inverse. Applied Mathematics - A Journal of Chinese Universities. 30(4):479-490. https://doi.org/10.1007/s11766-015-3333-4S479490304A Ben-Israel, T N E Greville. Generalized Inverses, Theory and Applications, 2nd edition, Springer-Verlag, 2003.S L Campbell, C D Meyer. Generalized Inverses of Linear Transformations, Pitman (Advanced Publishing Program), Boston, MA, 1979.N Castro-González, J J Koliha. Additive perturbation results for the Drazin inverse, Linear Algebra Appl, 2005, 397: 279–297.N Castro-González, E Dopazo, M F Martínez-Serrano. On the Drazin inverse of the sum of two operators and its application to operator matrices, J Math Anal Appl, 2008, 350: 207–215.N Castro-González, M F Martínez-Serrano. Expressions for the g-Drazin inverse of additive perturbed elements in a Banach algebra, Linear Algebra Appl, 2010, 432: 1885–1895.N Castro-González, J J Koliha. New additive results for the Drazin inverse, Proc Roy Soc Edinburgh Sect A, 2004, 134: 1085–1097.M Catral, D D Olesky, P van den Driessche. Block representations of the Drazin inverse of a bipartite matrix, Electron J Linear Algebra, 2009, 18: 98–107.J L Chen, G F Zhuang, Y Wei. The Drazin inverse of a sum of morphisms, Acta Math Sci Ser A Chin Ed, 2009, 29(3): 538–552.D S Cvetković-Ilić, D S Djordjević, Y Wei. Additive results for the generalized Drazin inverse in a Banach algebra, Linear Algebra Appl, 2006, 418, 53–61.D S Cvetković-Ilić. A note on the representation for the Drazin inverse of 2 × 2 block matrices, Linear Algebra Appl, 2008, 429: 242–248.C Deng. The Drazin inverses of sum and difference of idempotents, Linear Algebra Appl, 2009, 430: 1282–1291.C Deng, Y Wei. Characterizations and representations of the Drazin inverse of idempotents, Linear Algebra Appl, 2009, 431: 1526–1538.C Deng, Y Wei. New additive results for the generalized Drazin inverse, J Math Anal Appl, 2010, 370: 313–321.D S Djordjević, P S Stanimirović. On the generalized Drazin inverse and generalized resolvent, Czechoslovak Math J, 2001, 51(126): 617–634.D S Djordjević, Y Wei. Additive results for the generalized Drazin inverse, J Aust Math Soc, 2002, 73: 115–125.D S Djordjević, V Rakočević. Lectures on Generalized inverses, University of Niš, 2008.E Dopazo, M F Martínez-Serrano. Further results on the representation of the Drazin inverse of a 2 × 2 block matrices, Linear Algebra Appl, 2010, 432: 1896–1904.M P Drazin. Pseudo-inverses in associative rings and semiproup, Amer Math Monthly, 1958, 65: 506–514.R E Hartwig, G R Wang, Y Wei. Some additive results on Drazin inverse, Linear Algebra Appl, 2001, 322: 207–217.R E Hartwig, X Li, Y Wei. Representations for the Drazin inverse of a 2×2 block matrix, SIAM J Matrix Anal Appl, 2006, 27: 757–771.Y Liu, C G Cao. Drazin inverse for some partitioned matrices over skew fields, J Nat Sci Heilongjiang Univ, 2004, 24: 112–114.J Ljubisavljević, D S Cvetković-Ilić. Additive results for the Drazin inverse of block matrices and applications, J Comput Appl Math, 2011, 235: 3683–3690.C D Meyer ffixJr, N J Rose. The index and the Drazin inverse of block triangular matrices, SIAM J Appl Math, 1977, 33(1): 1–7.L Wang, H H Zhu, X Zhu, J L Chen. Additive property of Drazin invertibility of elements, arXiv: 1307.1816v1 [math.RA], 2013.H Yang, X Liu. The Drazin inverse of the sum of two matrices and its applications, J Comput Appl Math, 2011, 235: 1412–1417

Morbidity, outcomes and cost-benefit analysis of wildlife rehabilitation in Catalonia (Spain)

Background There are few studies of careful examination of wildlife casualties in Wildlife Rehabilitation Centers. These studies are essential for detecting menaces to wild species and providing objective criteria about cost-benefit of treatments in those centers. The release rate is considered the main outcome indicator, but other parameters such as length of stay at the center and a cost-benefit index expressed as number of released animals per euro and day, could be used as reliable estimators of the rehabilitation costs. Methodology A retrospective study based on 54772 admissions recorded from 1995-2013 in the database of the Wildlife Rehabilitation Center of Torreferrussa (Catalonia, NW Spain) assessed the morbidity, outcomes and cost-benefits of the rehabilitation practices. Results Three hundred and two species were included: 232 birds (n = 48633), 37 mammals (n = 3293), 20 reptiles (n = 2705) and 13 amphibians (n = 141). The most frequent causes of admission were: 39.8% confiscation of protected species (89.4% passerines), 31.8% orphaned young animals (35.3% swifts, 21.7% diurnal raptors and owls) and 17.4% trauma casualties (46.7% raptors and owls). The highest proportion of releases was found in the captivity confiscation category [87.4% passerines (median time of stay: 12 days)], followed by the orphaned category [78% owls (66 days), 76.5% diurnal birds of prey (43 days), 75.6% hedgehogs (49 days), 52.7% swifts (19 days) and 52% bats (55 days)]. For the trauma group, 46.8% of releases were hedgehogs (44 days) and 25.6% owls (103 days). As regards the cost-benefit index, the trauma casualties and infectious diseases had the worse values with 1.3 and 1.4 released animals/euro/day respectively, and were particularly low in raptors, waders, marine birds and chiroptera. On the contrary, captivity (4.6) and misplacement (4.1) had the best index, particulary in amphibian, reptiles and passerines. Conclusions/significance Cost-benefit studies including the release rate, the time of stay at the center and the costbenefit index should be implemented for improving management efficiency of the Wildlife Rehabilitation Centers

The effect of single-pulse transcranial magnetic stimulation and peripheral nerve stimulation on complexity of EMG signal: fractal analysis

The aim of this study was to examine whether single-pulse transcranial magnetic stimulation (spTMS) affects the pattern of corticospinal activity once voluntary drive has been restored after spTMS-induced EMG silence. We used fractal dimension (FD) to explore the 'complexity' of the electromyography (EMG) signal, and median frequency of the spectra (MDF) to examine changes in EMG spectral characteristics. FD and MDF of the raw EMG epochs immediately before were compared with those obtained from epochs after the EMG silence. Changes in FD and MDF after spTMS were examined with three levels of muscle contraction corresponding to weak (20-40 %), moderate (40-60 %) and strong (60-80 % of maximal voluntary contraction) and three intensities of stimulation set at 10, 20 and 30 % above the resting motor threshold. FD was calculated using the Higuchi fractal dimension algorithm. Finally, to discern the origin of FD changes between the CNS and muscle, we compared the effects of spTMS with the effects of peripheral nerve stimulation (PNS) on FD and MDF. The results show that spTMS induced significant decrease in both FD and MDF of EMG signal after stimulation. PNS did not have any significant effects on FD nor MDF. Changes in TMS intensity did not have any significant effect on FD or MDF after stimulation nor had the strength of muscle contraction. However, increase in contraction strength decreased FD before stimulation but only between weak and moderate contraction. The results suggest that the effects of spTMS on corticospinal activity, underlying voluntary motor output, outlast the TMS stimulus. It appears that the complexity of the EMG signal is reduced after spTMS, suggesting that TMS alters the dynamics of the ongoing corticospinal activity most likely temporarily synchronizing the neural network activity. Further studies are needed to confirm whether observed changes after TMS occur at the cortical level

Scaling analysis of bilateral hand tremor movements in essential tremor patients

Recent evidence suggests that the dynamic-scaling behavior of the time-series of signals extracted from separate peaks of tremor spectra may reveal existence of multiple independent sources of tremor. Here, we have studied dynamic characteristics of the time-series of hand tremor movements in essential tremor (ET) patients using the detrended fluctuation analysis method. Hand accelerometry was recorded with (500 g) and without weight loading under postural conditions in 25 ET patients and 20 normal subjects. The time-series comprising peak-to-peak (PtP) intervals were extracted from regions around the first three main frequency components of power spectra (PwS) of the recorded tremors. The data were compared between the load and no-load condition on dominant (related to tremor severity) and non-dominant tremor side and with the normal (physiological) oscillations in healthy subjects. Our analysis shows that, in ET, the dynamic characteristics of the main frequency component of recorded tremors exhibit scaling behavior. Furthermore, they show that the two main components of ET tremor frequency spectra, otherwise indistinguishable without load, become significantly different after inertial loading and that they differ between the tremor sides (related to tremor severity). These results show that scaling, a time-domain analysis, helps revealing tremor features previously not revealed by frequency-domain analysis and suggest that distinct oscillatory central circuits may generate the tremor in ET patients

Scaling analysis of the effects of load on hand tremor movements in essential tremor

In this paper we have used the Wavelet Transform (WT) and the Detrended Fluctuation Analysis (DFA) methods to analyze hand tremor movements in essential tremor (ET), in two different recording conditions (before and after the addition of wrist-cuff load). We have analyzed the time series comprised of peak-to-peak (PtP) intervals, extracted from regions around the first three main frequency components of the power spectra (PwS) of the recorded tremors, in order to substantiate results related to the effects of load on ET, to distinguish between multiple sources of ET, and to separate the influence of peripheral factors on ET. Our results show that, in ET, the dynamical characteristics, that is, values of respective scaling exponents, of the main frequency component of recorded tremors change after the addition of load. Our results also show that in all the observed cases the scaling behavior of the calculated functions changes as well the calculated WT scalegrams and DFA functions display a shift in the position of the crossover when the load is added. We conclude that the difference in behavior of the WT and DFA functions between different conditions in ET could be associated with the expected pathology in ET, or with some additional mechanism that controls movements in ET patients, and causes the observed changes in scaling behavior

Retinal ganglion cell/inner plexiform layer thickness in patients with Parkinson's disease

Introduction: The aim of the paper was to analyze the changes in the macular ganglion cell layer and inner plexiform layer (GCL-IPL) thickness in patients with Parkinson's disease. Material and methods: The study enrolled 46 patients with established diagnosis of Parkinson's disease and 46 healthy subjects. Both groups were age- and gender-matched. An OCT protocol, namely standardized Ganglion Cell Analysis algorithm was used to measure the thickness of the macular GCL-IPL layer. The average, minimum, and six sectoral (superotemporal, superior, superonasal, inferonasal, inferior, inferotemporal) GCL-IPL thicknesses were measured from the elliptical annulus centered on the fovea. Results: The mean value of the clinical severity of Parkinson's disease was between 2 and 3, according to the Hoehn and Yahr scale. Statistically significant thinning of the GCL-IPL layer was registered in average and minimum GCLIPL thickness, as well as in the sectoral layer thicknesses in patients with Parkinson's disease in comparison to the controls. There was no correlation between structural changes in the retina and disease duration or severity. A statistically significant difference in thickness between the different stages of the disease was registered only in the inferior sector. Conclusions: Parkinson's disease is accompanied by thinning of the GCL-IPL complex of macula even in the earliest stages. This may indicate a possible retinal dopaminergic neurodegeneration. There is no correlation between duration or severity of Parkinson's disease with thinning of the GCL-IPL complex