Bounds on the Speed and on Regeneration Times for Certain Processes on Regular Trees

We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic (2002) prove an upper bound of the form $b/(b+\delta)$ for the speed on the $b$-ary tree, where $\delta$ is the reinforcement parameter. For $\delta>1$ we provide a lower bound of the form $\gamma^2 b/(b+\delta)$, where $\gamma$ is the survival probability of an associated branching process.Comment: 21 page

Bounds on the speed and on regeneration times for certain processes on regular trees

We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic [11] prove an upper bound of the form b/(b + d) for the speed on the b-ary tree, where d is the reinforcement parameter. For d > 1 we provide a lower bound of the form g^2b/(b + d), where g is the survival probability of an associated branching process.Random walk in a random environment; once edge-reinforced random walk; lower bound on the speed; regeneration times; regular trees.

Effects of subthalamic nucleus deep brain stimulation on emotional working memory capacity and mood in patients with Parkinson's disease

Background: In Parkinson’s disease (PD), cognitive symptoms and mood changes may be even more distressing for the patient than motor symptoms. Objective: Our aim was to determine the effects of bilateral subthalamic nucleus deep brain stimulation (STN-DBS) on working memory (WM) and mood. Methods: Sixteen patients with PD were assessed with STN-DBS switched on (DBS-ON) and with dopaminergic treatment (Med-ON) compared to switched off (DBS-OFF) and without dopaminergic treatment (Med-OFF). The primary outcome measures were a Visual Analog Mood Scale (VAMS) and an emotional 2-back WM task at 12 months after DBS in the optimal DBS-ON/Med-ON setting compared to DBS-OFF/Med-OFF. Results: Comparison of DBS-OFF/Med-OFF to DBS-ON/Med-ON revealed a significant increase in alertness (meanoff/off =51.59±24.54; meanon/on =72.75; P=0.016) and contentedness (meanoff/off =38.73±24.41; meanon/on =79.01±17.66; P=0.001, n=16), and a trend for reduction in sedation (P=0.060), which was related to stimulation as shown in a subgroup of seven patients. The N-back task revealed a significant increase in accuracy with DBS-ON/Med-ON compared to DBS-OFF/Med- OFF (82.0% vs 76.0%, respectively) (P=0.044), regardless of stimulus valence. Conclusion: In line with previous studies, we found that patients rated themselves subjectively as more alert, content, and less sedated during short- term DBS-ON. Accuracy in the WM task increased with the combination of DBS and medication, possibly related to higher alertness of the patients. Our results add to the currently mixed results described for DBS on WM and suggest that there are no deleterious DBS effects on this specific cognitive domain

Revolution again in Kyrgyzstan: forward to the past?

Kyrgyzstan's presidential election and constitutional referendum on 10 January 2021 represent the provisional endpoint of a series of violent episodes that has gripped the country since October 2020. The victory of the populist Sadyr Japarov and approval for his plan to reintroduce a presidential system of government prepares the ground for a dismantling of democratic principles and rule of law, so that politically Kyrgyz­stan is set to look more like its Central Asian neighbours. A new constitution is in preparation. The draft bears the portents of a neo-traditional roll-back that rebuffs a young generation demanding more democracy and rule of law, and has the potential to deeply polarise the nation. (author's abstract

Religious policy in Uzbekistan: between liberalisation, state ideology and Islamisation

The religious policy innovations that Uzbekistan's President Mirziyoyev has initiated in the name of liberalisation and reform continue the policies of his predecessor in key aspects. Under the motto "enlightenment against ignorance", state influence over the religious knowledge taught in educational and research institutions has been strengthened. The country's Islamic heritage is proactively used for representative purposes and held up as an integral part of national culture. The religious policy measures that amount to a "secularisation" of Islam through scientification and musealisation do not reach large sections of society. For the ordinary believer, Islam is not a science but a matter of belief, a system of rules and convictions that guides the way they live. The liberalisation of the media landscape means that religious advice is available in abundance. It often includes propaganda transporting illiberal ideas, but the state intervenes only selectively. The liberalisation of religious policy has resulted in a growing Islamisation of the population. The authoritarian state headed by President Mirziyoyev is thus being consolidated. Repression remains the means of choice should Islamic milieus seriously challenge the secular state. (author's abstract

Tajikistan on the road to totalitarianism

Rather overshadowed by ongoing violence in Afghanistan and an unexpected political opening in Uzbekistan, Tajikistan is witnessing the emergence of a totalitarian system focused entirely on the president. Alongside legal moves and key appointments, ideological propaganda plays a central role. Two main trends are involved: the presentation of President Emomali Rahmon as bringer of peace and guarantor of national unity, and the establishment of a canon of "national" norms and values designed to enforce social and ideological homogeneity. The spectre of Islamic fundamentalism is instrumentalised to consolidate the ruling ideology, while surveillance and sanctioning enforce behavioural conformity

Central Asia's Muslims and the Taliban

Afghanistan's Central Asian neighbours have generally reacted pragmatically to the Taliban's seizure of power there. For the autocratically ruled, secular states on the periphery of the former Soviet empire, economic cooperation and the stabilisation of humanitarian and political conditions in Afghanistan are at the forefront of their interests in maintaining relations with their southern neighbour. According to offi­cial discourse, Central Asia's entrenched secularism is not challenged by the Taliban's Islamism. On social media in Central Asia, however, the Islamic emirate of the Taliban is portrayed as a political counter-model; one which is more positively received in coun­tries with greater discursive freedom and under governments whose policies more openly confront the Taliban. This reveals a trend towards Islamist-inspired iden­tity formation that will be difficult to stop through censorship and repression. (author's abstract

Islam in Tajikistan: actors, discourses, conflicts

The revival of Muslim values and ideas in Central Asia is perceived primarily through the lens of security, both among local regimes and by the West. The focus on extreme forms of Islam, however, prevents a balanced assessment of the religious discourse itself and obscures the reasons for the growing attraction of Islam and its potential as a force for order in the post-Soviet states. This study explores the social and political background to the revival of Islamic discourses, networks and practices in Tajikistan since the end of the Soviet Union, identifying the central actors, and laying out the intellectual and social coordinates of the symbolic struggles they are involved in. The growing significance of Islam as a source of moral and practical guidance is associated with a differentiation and pluralisation of the landscape of actors and discourses. The interpretative monopoly of the Hanafite clergy, who cultivate a tradition of tolerance towards culture-specific ritual practice and secular lifeworlds, is now challenged by reformist and universalist doctrines that reject the pragmatic consensus of the religious establishment. The state responds by suppressing the influence of religion through increasingly pervasive surveillance, but this cannot prevent the dissemination of the unwanted teachings. Reversing the tide would demand pro-active investment in good religious education. (Autorenreferat

Uzbekistan's transformation: strategies and perspectives

The presidential transition in Uzbekistan represents a novel development in the post-Soviet space. Regime insider Shavkat Mirziyoyev has succeeded in initiating change without provoking destabilisation. His reform programme aims to liberalise the economy and society while leaving the politi­cal system largely untouched. Implementation is centrally controlled and managed, in line with the country’s long history of state planning. Uzbeks accept painful adjust­ments in the expectation of a rising standard of living. And the economic reforms are rapidly creating incontrovertible facts on the ground. Uzbekistan has also made significant moves towards political liberalisa­tion, but remains an authoritarian state whose institutional framework and presidential system are not up for discussion. Rather than democrati­sation, the outcome of the transformation is more likely to be "enlightened authoritarianism" backed by an alliance of old and new elites. Nevertheless, there are good reasons for Germany and Europe to support the reforms. Priority should be placed on the areas most relevant for fostering an open society: promoting political competition, encouraging open debate, fostering independent public engagement and enabling genuine participation. (author's abstract

Less Is More - Estimation of the Number of Strides Required to Assess Gait Variability in Spatially Confined Settings

Background: Gait variability is an established marker of gait function that can be assessed using sensor-based approaches. In clinical settings, spatial constraints and patient condition impede the execution of longer distance walks for the recording of gait parameters. Turning paradigms are often used to overcome these constraints and commercial gait analysis systems algorithmically exclude turns for gait parameters calculations. We investigated the effect of turns in sensor-based assessment of gait variability. Methods: Continuous recordings from 31 patients with movement disorders (ataxia, essential tremor and Parkinson's disease) and 162 healthy elderly (HE) performing level walks including 180° turns were obtained using an inertial sensor system. Accuracy of the manufacturer's algorithm of turn-detection was verified by plotting stride time series. Strides before and after turn events were extracted and compared to respective average of all strides. Coefficient of variation (CoV) of stride length and stride time was calculated for entire set of strides, segments between turns and as cumulative values. Their variance and congruency was used to estimate the number of strides required to reliably assess the magnitude of stride variability. Results: Non-detection of turns in 5.8% of HE lead to falsely increased CoV for these individuals. Even after exclusion of these, strides before/after turns tended to be spatially shorter and temporally longer in all groups, contributing to an increase of CoV at group level and widening of confidence margins with increasing numbers of strides. This could be attenuated by a more generous turn excision as an alternative approach. Correlation analyses revealed excellent consistency for CoVs after at most 20 strides in all groups. Respective stride counts were even lower in patients using a more generous turn excision. Conclusion: Including turns to increase continuous walking distance in spatially confined settings does not necessarily improve the validity and reliability of gait variability measures. Specifically with gait pathology, perturbations of stride characteristics before/after algorithmically excised turns were observed that may increase gait variability with this paradigm. We conclude that shorter distance walks of around 15 strides suffice for reliable and valid recordings of gait variability in the groups studied here