On melting for the 3D radial Stefan problem

We consider the three-dimensional radial Stefan problem which describes the evolution of a radial symmetric ice ball with free boundary \begin{equation*} \left\{\begin{aligned} &\partial_{t}u-\partial_{rr}u-\frac{2}{r}\partial_{r}u=0 \quad in\ r\geq\lambda(t),\\ &\partial_{r}u(t,\lambda(t))=-\dot{\lambda}(t),\\ &u(t,\lambda(t))=0,\\ &u(0,\cdot)=u_{0},\quad \lambda(0)=\lambda_{0}. \end{aligned}\right. \end{equation*} We prove the existence in the radial class of finite time melting with rates \begin{equation*} \lambda(t)=\left\{\begin{aligned} &4\sqrt{\pi}\frac{\sqrt{T-t}}{|\log (T-t)|}(1+o_{t\rightarrow T}(1)),\\ &c(u_{0},k)(1+o_{t\rightarrow T}(1))(T-t)^{\frac{k+1}{2}},\quad k\in{\mathbb{N}}^{*}, \end{aligned}\right. \end{equation*} which respectively correspond to the fundamental stable melting rate and a sequence of codimension $k$ unstable rates. Our analysis mainly depend on the methods developed in [17] which deals with the similar problems in two dimensions and also the construction of both stable and unstable finite time blow-up solutions for the harmonic heat flow in [49],[50]

Impaired night-time mobility in patients with Parkinson’s disease: a systematic review

Impaired bed mobility (IBM) is a symptom characteristic of patients having difficulty intentionally moving their bodies during nighttime sleep. IBM is one of the most common nocturnal symptoms of Parkinson’s disease (PD) and may lead to extreme pain and even death; it also increases the burden on the patients’ caregivers. In this systematic review, we included 19 studies involving a total of 1,407 patients with PD to observe the causes, assessment methods, and treatment options for IBM. We conclude that the extent of IBM is positively correlated with the severity of symptoms such as disease duration, dyskinesia and decreased sleep quality in patients with PD, and the evidence implies that IBM may be able to serve as a prodromal feature in the development of PD. IBM probably results from low nocturnal dopamine concentrations, reduced function of the spinal tract, torque problems in the muscles, and aging. Therefore, treatment is mostly based on continuously increasing the patient’s nocturnal dopamine concentration, while deep brain stimulation (DBS) also has a mitigating effect on IBM. Both scales and sensors are commonly used to measure the severity of IBM, the wearable device monitoring and scales being updated makes measurements easier and more accurate. The future of the advancement in this field lies in the use of more family-oriented devices (such as smart phones or watches and bracelets, etc.) to monitor IBM’s symptoms and select the appropriate therapeutic treatment according to the severity of the symptoms to relieve patients’ suffering

Independent-Set Design of Experiments for Estimating Treatment and Spillover Effects under Network Interference

Interference is ubiquitous when conducting causal experiments over networks. Except for certain network structures, causal inference on the network in the presence of interference is difficult due to the entanglement between the treatment assignments and the interference levels. In this article, we conduct causal inference under interference on an observed, sparse but connected network, and we propose a novel design of experiments based on an independent set. Compared to conventional designs, the independent-set design focuses on an independent subset of data and controls their interference exposures through the assignments to the rest (auxiliary set). We provide a lower bound on the size of the independent set from a greedy algorithm , and justify the theoretical performance of estimators under the proposed design. Our approach is capable of estimating both spillover effects and treatment effects. We justify its superiority over conventional methods and illustrate the empirical performance through simulations

Flocking control against the malicious agent

This paper investigates the flocking control of a swarm with a malicious agent that falsifies its controller parameters to cause collision, division, and escape of agents in the swarm. A novel geometric flocking condition is established by designing the configuration of the malicious agent and its neighbors, under which we propose a hierarchal geometric configuration-based flocking control method. To help detect the malicious agent, a parameter estimate mechanism is also provided. The proposed method can achieve the flocking control goal and meanwhile contain the malicious agent in the swarm without removing it. Experimental result shows the effectiveness of the theoretical result

Imaging the Centromedian Thalamic Nucleus Using Quantitative Susceptibility Mapping.

The centromedian (CM) nucleus is an intralaminar thalamic nucleus that is considered as a potentially effective target of deep brain stimulation (DBS) and ablative surgeries for the treatment of multiple neurological and psychiatric disorders. However, the structure of CM is invisible on the standard T1- and T2-weighted (T1w and T2w) magnetic resonance images, which hamper it as a direct DBS target for clinical applications. The purpose of the current study is to demonstrate the use of quantitative susceptibility mapping (QSM) technique to image the CM within the thalamic region. Twelve patients with Parkinson's disease, dystonia, or schizophrenia were included in this study. A 3D multi-echo gradient recalled echo (GRE) sequence was acquired together with T1w and T2w images on a 3-T MR scanner. The QSM image was reconstructed from the GRE phase data. Direct visual inspection of the CM was made on T1w, T2w, and QSM images. Furthermore, the contrast-to-noise ratios (CNRs) of the CM to the adjacent posterior part of thalamus on T1w, T2w, and QSM images were compared using the one-way analysis of variance (ANOVA) test. QSM dramatically improved the visualization of the CM nucleus. Clear delineation of CM compared to the surroundings was observed on QSM but not on T1w and T2w images. Statistical analysis showed that the CNR on QSM was significantly higher than those on T1w and T2w images. Taken together, our results indicate that QSM is a promising technique for improving the visualization of CM as a direct targeting for DBS surgery

Habenular Stimulation for Neurosurgery Resistant Obsessive-Compulsive Disorder: A Case Report.

BACKGROUND: Some patients suffer from persistent and severely disabling Obsessive-Compulsive Disorder (OCD) symptoms that cannot be alleviated by conventional treatments or neuroablative interventions targeting cortico-striatal loop circuits. Currently, it is unclear how to manage the clinical symptoms of these unique patients. We reasoned that deep brain stimulation (DBS) of the habenula (HB) could be a valuable subsequent treatment option for these otherwise medically intractable cases of severe OCD. The HB is an epithalamic structure critically involved in the encoding and responding to aversive stimulus events, cognitive and brain processes known to be impaired in many patients with OCD. Similarly, HB DBS can alleviate depression and anxiety, which often co-occur with OCD. Here, we explore the clinical benefits and risks of HB DBS treatment in a patient with severe and refractory OCD. CASE PRESENTATION: A 30-year-old male patient presented with persistent and severely disabling OCD symptoms that were refractory to previous psychological and pharmacological treatments as well as to neuroablative surgical interventions involving both capsulotomy and cingulotomy. After HB DBS, however, the severity of the patient's OCD symptoms was markedly reduced at 1-month follow-up, which was sustained until the final (at 12-month) follow-up. The patient also reported enduring improvements in depression, anxiety, and health-related quality of life after several months of HB DBS treatment. CONCLUSIONS: This case report provides the first clinical evidence suggesting that HB DBS could serve as a safe and effective alternative neurosurgical intervention for severe and refractory OCD. The present findings are promising and warrant further research into the role of the HB in pathophysiology and treatment of OCD

Deep Brain Stimulation-Induced Transient Effects in the Habenula

The habenula, located in the epithalamus, has been implicated in various psychiatric disorders including mood disorders and schizophrenia. This study explored the transient effects of deep brain stimulation in the habenula. Each of the four patients (two with bipolar disorder and two with schizophrenia) was tested with eight deep brain stimulation contacts. Patients were examined via transient electrical stimulation 1 month after deep brain stimulation surgery. The pulse width was 60 μs and the voltage ranged from 0 V to a maximum of 10 V, increasing in increments of 1 V. Each patient received stimulation at two frequencies, 60 and 135 Hz. A total of 221 out of 385 active trials elicited stimulation-induced effects. The three most common transient effects were numbness, heart rate changes, and pain. The incidence of numbness, heart rate changes, pain, and involuntary movements increased with the increase in stimulation voltage. Through contralateral stimulation, numbness was triggered in all parts of the body except the scalp. The obtained stimulus-response maps suggested a possible somatosensory organization of the habenula

Psychometric Properties of the Chinese version of UPPS-P Impulsive Behavior Scale.

OBJECTIVE: The present study aimed to assess the psychometric properties of a Chinese version of the UPPS-P Impulsive Behavior Scale. The associations between the UPPS-P scale and impulsivity choice, gender, smoking, and drinking status were also assessed. METHODS: A total of 127 adults ranging from 21 to 65 years old participated in the study. Participants were administered with the Chinese version of the UPPS-P Impulsive Behavior Scale, Beck Depression Inventory II (BDI-II), and State-Trait Anxiety Inventory (STAI). Impulsivity choice tasks were also tested including the Delay Discounting Task (DDT), Balloon Analogue Risk Task (BART), and Beads Task (Beads). RESULTS: A new version of the UPPS-P Impulsive Behavior Scale was formed that includes 40 items. The scores of the UPPS-P Impulsive Behavior Scale demonstrated adequate internal consistency on five subscales but less sufficient structure validity in the present sample. In addition, positive urgency was negatively related to the Beads task; negative urgency and positive urgency were positively related to the DDT and BART. Moreover, positive and negative urgency were positively correlated with depression; all five subscales were positively correlated with anxiety; sensation seeking was higher in males than females and in alcohol drinkers than non-drinkers; and lack of premeditation and lack of perseverance were higher in nonsmokers than smokers. CONCLUSIONS: The present study supports the reliability but not the structure validity of the UPPS-P Impulsive Behavior Scale. The impulsivity personality trait assessed by the UPPS-P scale was associated with impulsivity choice, depression, anxiety, gender, and drinking and smoking status. Further studies should be conducted to explore the structure of impulsivity in the Chinese population

Dynamical and individualised approach of transcranial ultrasound neuromodulation effects in non-human primates

Low-frequency transcranial ultrasound stimulation (TUS) allows to alter brain functioning with a high spatial resolution and to reach deep targets. However, the time-course of TUS effects remains largely unknown. We applied TUS on three brain targets for three different monkeys: the anterior medial prefrontal cortex, the supplementary motor area and the perigenual anterior cingulate cortex. For each, one resting-state fMRI was acquired between 30 and 150 min after TUS as well as one without stimulation (control). We captured seed-based brain connectivity changes dynamically and on an individual basis. We also assessed between individuals and between targets homogeneity and brain features that predicted TUS changes. We found that TUS prompts heterogenous functional connectivity alterations yet retain certain consistent changes; we identified 6 time-courses of changes including transient and long duration alterations; with a notable degree of accuracy we found that brain alterations could partially be predicted. Altogether, our results highlight that TUS induces heterogeneous functional connectivity alterations. On a more technical point, we also emphasize the need to consider brain changes over-time rather than just observed during a snapshot; to consider inter-individual variability since changes could be highly different from one individual to another