A Classification of Minimal Sets of Torus Homeomorphisms

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.Comment: Published in Mathematische Zeitschrift, June 2013, Volume 274, Issue 1-2, pp 405-42

Patients' use of a home-based virtual reality system to provide rehabilitation of the upper limb following stroke

Background: A low cost, virtual reality system that translates movements of the hand, fingers and thumb into game play was designed to provide a flexible and motivating approach to increasing adherence to home based rehabilitation. Objective: Effectiveness depends on adherence, so did patients use the intervention to the recommended level. If not, what reasons did they give? Design: Prospective cohort study plus qualitative analysis of interviews. Methods: 17 patients recovering from stroke recruited to the intervention arm of a feasibility trial had the equipment left in their homes for eight weeks and were advised to use it three times a day for periods of no more than 20 minutes. Frequency and duration of use were automatically recorded. At the end of the intervention, participants were interviewed to determine barriers to using it in the recommended way. Results: Duration of use and how many days they used the equipment are presented for the 13 participants who successfully started the intervention. These figures were highly variable and could fall far short of our recommendations. There was a weak (p=0.053) positive correlation between duration and baseline reported activities of daily living. Participants reported familiarity with technology and competing commitments as barriers to use although appreciated the flexibility of the intervention and found it motivating

Breaking the silence of the 500-year-old smiling garden of everlasting flowers: The En Tibi book herbarium

We reveal the enigmatic origin of one of the earliest surviving botanical collections. The 16th-century Italian En Tibi herbarium is a large, luxurious book with c. 500 dried plants, made in the Renaissance scholarly circles that developed botany as a distinct discipline. Its Latin inscription, translated as “Here for you a smiling garden of everlasting flowers”, suggests that this herbarium was a gift for a patron of the emerging botanical science. We follow an integrative approach that includes a botanical similarity estimation of the En Tibi with contemporary herbaria (Aldrovandi, Cesalpino, “Cibo”, Merini, Estense) and analysis of the book’s watermark, paper, binding, handwriting, Latin inscription and the morphology and DNA of hairs mounted under specimens. Rejecting the previous origin hypothesis (Ferrara, 1542–1544), we show that the En Tibi was made in Bologna around 1558. We attribute the En Tibi herbarium to Francesco Petrollini, a neglected 16th-century botanist, to whom also belongs, as clarified herein, the controversial “Erbario Cibo” kept in Rome. The En Tibi was probably a work on commission for Petrollini, who provided the plant material for the book. Other people were apparently involved in the compilation and offering of this precious gift to a yet unknown person, possibly the Habsburg Emperor Ferdinand I. The En Tibi herbarium is a Renaissance masterpiece of art and science, representing the quest for truth in herbal medicine and botany. Our multidisciplinary approach can serve as a guideline for deciphering other anonymous herbaria, kept safely “hidden” in treasure rooms of universities, libraries and museums

TMS-Induced Central Motor Conduction Time at the Non-Infarcted Hemisphere Is Associated with Spontaneous Motor Recovery of the Paretic Upper Limb after Severe Stroke

Background: Stroke affects the neuronal networks of the non-infarcted hemisphere. The central motor conduction time (CMCT) induced by transcranial magnetic stimulation (TMS) could be used to determine the conduction time of the corticospinal tract of the non-infarcted hemisphere after a stroke. Objectives: Our primary aim was to demonstrate the existence of prolonged CMCT in the non-infarcted hemisphere, measured within the first 48 h when compared to normative data, and secondly, if the severity of motor impairment of the affected upper limb was significantly associated with prolonged CMCTs in the non-infarcted hemisphere when measured within the first 2 weeks post stroke. Methods: CMCT in the non-infarcted hemisphere was measured in 50 patients within 48 h and at 11 days after a first-ever ischemic stroke. Patients lacking significant spontaneous motor recovery, so-called non-recoverers, were defined as those who started below 18 points on the FM-UE and showed less than 6 points (10%) improvement within 6 months. Results: CMCT in the non-infarcted hemisphere was prolonged in 30/50 (60%) patients within 48 h and still in 24/49 (49%) patients at 11 days. Sustained prolonged CMCT in the non-infarcted hemisphere was significantly more frequent in non-recoverers following FM-UE. Conclusions: The current study suggests that CMCT in the non-infarcted hemisphere is significantly prolonged in 60% of severely affected, is-chemic stroke patients when measured within the first 48 h post stroke. The likelihood of CMCT is significantly higher in non-recoverers when compared to those that show spontaneous motor recovery early post stroke

Repetitive arm functional tasks after stroke (RAFTAS): a pilot randomised controlled trial

Background Repetitive functional task practise (RFTP) is a promising treatment to improve upper limb recovery following stroke. We report the findings of a study to determine the feasibility of a multi-centre randomised controlled trial to evaluate this intervention. Methods A pilot randomised controlled trial was conducted. Patients with new reduced upper limb function were recruited within 14 days of acute stroke from three stroke units in North East England. Participants were randomised to receive a four week upper limb RFTP therapy programme consisting of goal setting, independent activity practise, and twice weekly therapy reviews in addition to usual post stroke rehabilitation, or usual post stroke rehabilitation. The recruitment rate; adherence to the RFTP therapy programme; usual post stroke rehabilitation received; attrition rate; data quality; success of outcome assessor blinding; adverse events; and the views of study participants and therapists about the intervention were recorded. Results Fifty five eligible patients were identified, 4-6% of patients screened at each site. Twenty four patients participated in the pilot study. Two of the three study sites met the recruitment target of 1-2 participants per month. The median number of face to face therapy sessions received was 6 [IQR 3-8]. The median number of daily repetitions of activities recorded was 80 [IQR 39-80]. Data about usual post stroke rehabilitation were available for 18/24 (75%). Outcome data were available for 22/24 (92%) at one month and 20/24 (83%) at three months. Outcome assessors were unblinded to participant group allocation for 11/22 (50%) at one month and 6/20 (30%) at three months. Four adverse events were considered serious as they resulted in hospitalisation. None were related to study treatment. Feedback from patients and local NHS therapists about the RFTP programme was mainly positive. Conclusions A multi-centre randomised controlled trial to evaluate an upper limb RFTP therapy programme provided early after stroke is feasible and acceptable to patients and therapists, but there are issues which needed to be addressed when designing a Phase III study. A Phase III study will need to monitor and report not only recruitment and attrition but also adherence to the intervention, usual post stroke rehabilitation received, and outcome assessor blinding

A double-blinded randomised controlled trial exploring the effect of anodal transcranial direct current stimulation and uni-lateral robot therapy for the impaired upper limb in sub-acute and chronic stroke

BACKGROUND:Neurorehabilitation technologies such as robot therapy (RT) and transcranial Direct Current Stimulation (tDCS) can promote upper limb (UL) motor recovery after stroke. OBJECTIVE:To explore the effect of anodal tDCS with uni-lateral and three-dimensional RT for the impaired UL in people with sub-acute and chronic stroke. METHODS:A pilot randomised controlled trial was conducted. Stroke participants had 18 one-hour sessions of RT (Armeo®Spring) over eight weeks during which they received 20 minutes of either real tDCS or sham tDCS during each session. The primary outcome measure was the Fugl-Meyer assessment (FMA) for UL impairments and secondary were: UL function, activities and stroke impact collected at baseline, post-intervention and three-month follow-up. RESULTS:22 participants (12 sub-acute and 10 chronic) completed the trial. No significant difference was found in FMA between the real and sham tDCS groups at post-intervention and follow-up (p = 0.123). A significant ‘time’ x ‘stage of stroke’ was found for FMA (p = 0.016). A higher percentage improvement was noted in UL function, activities and stroke impact in people with sub-acute compared to chronic stroke. CONCLUSIONS:Adding tDCS did not result in an additional effect on UL impairment in stroke. RT may be of more benefit in the sub-acute than chronic phase

Українська шляхта між польським та українським етносами

Appearance and existence of the Ukrainian gentry relates to the traditions of Polish political culture, so during the whole period of its life it was between the Ukrainian and the Polish ethnic groups. Polanisation of the Ukrainian gentry begins at the date when some of the Ukrainian territories become a part of Poland and strengthens after Cossack revolution in the middle and at the end of the 16th century. Especially this process becomes effective at the beginning of the 18th century when a great part of gentry from other Polish lands migrates to Pravoberezhia (right-banked Ukraine). Nevertheless, having captured upper class and partially middle class of the Ukrainian gentry, polanisation mainly influenced consciousness and less religion of the lower class of the Ukrainian gentry. As for ethnoculture and language local gentry was mostly Ukrainian and it assimilated numerous Polish gentlemen-immigrants