Dichotomies for Lp spaces

AbstractAssume that (X,Σ,μ) is a measure space and p1,…,pn, r>0. We prove that {(f1,…,fn)∈Lp1×⋯×Lpn:f1⋯fn∈Lr} is either Lp1×⋯×Lpn or a σ-porous subset of Lp1×⋯×Lpn. This dichotomy depends on properties of μ and the sign of the number 1r−1p1−⋯−1pn

Rehabilitacja poudarowa metodą PNF, z zastosowaniem i bez zastosowania toksyny botulinowej : opisy przypadków

One of the most common diseases of the nervous system is stroke. Its most frequently occuring kinetic symptoms are paresis or paralysis accompanied by an increase in muscular tension called spasticity. For patients and their carers these disturbances become a problem in many aspects of their everyday life, especially in locomotion. New ways need to be looked for to create therapies that could decrease or remove spasticity and restore the function which was disrupted. Therapy by botulinum toxin has been used as a method of decreasing spasticity to treat children with cerebral palsy having equines-varus foot, and it proves to be a breakthrough in the treatment of diseases with increased muscular tension. Owing to it, a range of mobility increases, for example in an ankle and knee joints, which facilitates locomotion. This improvement is caused by both pharmacological action, and assisted kinesitherapy. Proproceptive Neuromuscular Facilitation (PNF) is considered to be especially effective rehabilitation method based on neuro-physiological mechanisms. This method in the therapy of adults, along with the application of botulinum toxin, seems to facilitate physical activity of the patient after stroke, which may be very important for secondary stroke prevention. The aim of the research was to assess the influence of the therapy by PNF method associated with a botulinum toxin application on the patients after stroke with spasticity in lower limbs. During gait the patients had the flexion of ankle and knee joints measured by means of VICON system with the special focus on the amplitude of angular values. All patients presented in this description of cases showed an improvement in most of the measured parameters, in both a four-week and a three-month period after the therapy. The results show a necessity to carry out further randomized control studies of larger groups.Jedną z częściej spotykanych chorób układu nerwowego jest udar mózgu. Do najczęstszych objawów ruchowych należą niedowłady bądź porażenia kończyn, z towarzyszącym wzrostem napięcia mięśniowego, zwanym spastycznością. Dla pacjentów oraz ich opiekunów zaburzenia te stają się problemem w wielu aspektach życia codziennego, między innymi w lokomocji. Wymaga to poszukiwania nowych dróg w tworzeniu terapii mogących zmniejszyć bądź znieść spastyczność i przywrócić zaburzoną funkcję. Terapia toksyną botulinową jako metoda obniżająca spastyczność, jest stosowana do tej pory w terapii dzieci z mózgowym porażeniem dziecięcym ze stopą końsko-szpotawą i przynosi przełom w leczeniu schorzeń przebiegających z nadmiernym napięciem mięśniowym. Uzyskuje się poprawę zakresu ruchomości, miedzy innymi w stawie skokowym, a poprzez to ułatwia lokomocję. Poprawa ta uzyskiwana jest zarówno poprzez oddziaływanie farmakologiczne, jak i prowadzoną równolegle kinezyterapię. Szczególnie skuteczne wydają się metody rehabilitacyjne oparte na mechanizmach neurofizjologicznych. Jedną z takich metod jest PNF. Zastosowanie terapii metodą PNF połączone z zastosowaniem toksyny botulinowej u dorosłych wydaje się ułatwiać aktywność ruchową pacjenta po udarze mózgu, co może być bardzo ważne w profilaktyce wtórnej udaru mózgu. Celem pracy było przedstawienie możliwości połączenia i wpływu terapii metodą PNF skojarzoną z podaniem toksyny botulinowej u pacjentów po udarze mózgu ze spastyczną kończyna dolną. Dokonano w trakcie chodu pomiaru kąta ugięcia w stawie skokowym i kolanowym biorąc pod uwagę amplitudę ruchu, wykorzystując system VICON. U wszystkich przebadanych w niniejszym doniesieniu pacjentów odnotowano poprawę większości analizowanych parametrów, zarówno w okresie czterotygodniowym, jak i czteromiesięcznym. Przeprowadzone pomiary wskazują na konieczność wykonania randomizowanych, kontrolowanych badań na dużych grupach

Ground state in the energy super-critical Gross-Pitaevskii equation with a harmonic potential

The energy super-critical Gross--Pitaevskii equation with a harmonic potential is revisited in the particular case of cubic focusing nonlinearity and dimension d > 4. In order to prove the existence of a ground state (a positive, radially symmetric solution in the energy space), we develop the shooting method and deal with a one-parameter family of classical solutions to an initial-value problem for the stationary equation. We prove that the solution curve (the graph of the eigenvalue parameter versus the supremum) is oscillatory for d = 13. Compared to the existing literature, rigorous asymptotics are derived by constructing three families of solutions to the stationary equation with functional-analytic rather than geometric methods.Comment: 42 page

PeptiCKDdb-peptide- and protein-centric database for the investigation of genesis and progression of chronic kidney disease

The peptiCKDdb is a publicly available database platform dedicated to support research in the field of chronic kidney disease (CKD) through identification of novel biomarkers and molecular features of this complex pathology. PeptiCKDdb collects peptidomics and proteomics datasets manually extracted from published studies related to CKD. Datasets from peptidomics or proteomics, human case/control studies on CKD and kidney or urine profiling were included. Data from 114 publications (studies of body fluids and kidney tissue: 26 peptidomics and 76 proteomics manuscripts on human CKD, and 12 focusing on healthy proteome profiling) are currently deposited and the content is quarterly updated. Extracted datasets include information about the experimental setup, clinical study design, discovery-validation sample sizes and list of differentially expressed proteins (P-value < 0.05). A dedicated interactive web interface, equipped with multiparametric search engine, data export and visualization tools, enables easy browsing of the data and comprehensive analysis. In conclusion, this repository might serve as a source of data for integrative analysis or a knowledgebase for scientists seeking confirmation of their findings and as such, is expected to facilitate the modeling of molecular mechanisms underlying CKD and identification of biologically relevant biomarkers.Database URL: www.peptickddb.com

Two COVID-19-related video-accompanied cases of severe ataxia-myoclonus syndrome

Aim of the study. The pandemic state of COVID-19 has resulted in new neurological post-infection syndromes. Recently, several papers have reported ataxia-myoclonus syndrome following SARS-CoV-2 infection. The aim of this study was to present our two cases and compare them to previously reported cases. Materials and methods. We present two video-accompanied new cases with ataxia-myoclonus syndrome following SARS-CoV-2 infection and discuss the studies published so far. Results. Ataxia-myoclonus syndrome, isolated myoclonus, opsoclonus-myoclonus syndrome as post-COVID-19 syndrome following infection have been described in 16 patients (including our two cases). Patients have been treated with intravenous immunoglobulins and/or steroids except for 4 patients, which resulted in a significant improvement within 1–8 weeks. Conclusions and clinical implications. The increasing number of patients with a similar symptomatology shows a significant relationship between COVID-19 infection and ataxia-myoclonus syndrome. The subacute onset of neurological symptoms after a resolved COVID-19 infection and prominent response to immunotherapy may suggest that the neurological manifestations are immune-mediated. Although recovery is highly possible, it may take several weeks/months, and clinicians should be aware of this diagnosis and the beneficial effects of immunological treatment administered as soon as possible

Identification of novel molecular signatures of IgA nephropathy through an integrative -omics analysis

IgA nephropathy (IgAN) is the most prevalent among primary glomerular diseases worldwide. Although our understanding of IgAN has advanced significantly, its underlying biology and potential drug targets are still unexplored. We investigated a combinatorial approach for the analysis of IgAN-relevant -omics data, aiming at identification of novel molecular signatures of the disease. Nine published urinary proteomics datasets were collected and the reported differentially expressed proteins in IgAN vs. healthy controls were integrated into known biological pathways. Proteins participating in these pathways were subjected to multi-step assessment, including investigation of IgAN transcriptomics datasets (Nephroseq database), their reported protein-protein interactions (STRING database), kidney tissue expression (Human Protein Atlas) and literature mining. Through this process, from an initial dataset of 232 proteins significantly associated with IgAN, 20 pathways were predicted, yielding 657 proteins for further analysis. Step-wise evaluation highlighted 20 proteins of possibly high relevance to IgAN and/or kidney disease. Experimental validation of 3 predicted relevant proteins, adenylyl cyclase-associated protein 1 (CAP1), SHC-transforming protein 1 (SHC1) and prolylcarboxypeptidase (PRCP) was performed by immunostaining of human kidney sections. Collectively, this study presents an integrative procedure for -omics data exploitation, giving rise to biologically relevant results

The effects of physiotherapy with PNF concept on gait and balance of patients with Huntington's disease : pilot study

Background and purpose Huntington's disease (HD) is a neurodegenerative, progressive disorder of the central nervous system which causes significant gait and balance disturbances. This is a pilot study which aims to determine the effects of a physiotherapy programme with use of Proprioceptive Neuromuscular Facilitation (PNF) on gait and balance in HD patients. Material and methods 30 HD patients aged 21-60 with genetically confirmed diagnosis participated in the study. Participants followed a 3-week-long PNF-based physiotherapy programme. Gait and balance were evaluated twice in each participant: first at baseline and then after the course of physiotherapy. The following methods were used for gait disturbances: Tinetti Gait Assessment Tool, Up and Go Test, Timed Walking Tests for 10m and 20m (TWT10m, TWT20m). Balance was assessed with use of Berg Balance Scale, Pastor Test and Functional Reach Test. Results There was a significant improvement in all measures of balance and gait. Conclusion PNF-based physiotherapy is effective and safe in HD patients

The effects of physiotherapy with PNF concept on gait and balance of patients with Huntington's disease – pilot study

Background and purpose Huntington's disease (HD) is a neurodegenerative, progressive disorder of the central nervous system which causes significant gait and balance disturbances. This is a pilot study which aims to determine the effects of a physiotherapy programme with use of Proprioceptive Neuromuscular Facilitation (PNF) on gait and balance in HD patients. Material and methods 30 HD patients aged 21–60 with genetically confirmed diagnosis participated in the study. Participants followed a 3-week-long PNF-based physiotherapy programme. Gait and balance were evaluated twice in each participant: first at baseline and then after the course of physiotherapy. The following methods were used for gait disturbances: Tinetti Gait Assessment Tool, Up and Go Test, Timed Walking Tests for 10m and 20m (TWT10m, TWT20m). Balance was assessed with use of Berg Balance Scale, Pastor Test and Functional Reach Test. Results There was a significant improvement in all measures of balance and gait. Conclusion PNF-based physiotherapy is effective and safe in HD patients

The influence of motor ability rehabilitation on temporal-spatial parameters of gait in Huntington's disease patients on the basis of a three-dimensional motion analysis system: An experimental trial

Objective There is no existing standard, evidence-based, scientific model for motor ability improvement in Huntington's Disease (HD) patients aimed at maintaining independent gait for as long as possible, or performing activities of daily living, the effectiveness of which would be supported by the results of studies using objective research tools. Under these circumstances, the aim of this study was to analyze the influence of motor ability rehabilitation on the spatial-temporal parameters of gait in HD patients. Design It was an experimental trial. The studied group consisted of 30 patients (17 women and 13 men) with HD. In hospital conditions, the patients participated in the 3-week motor ability l rehabilitation programme tailored to individual needs. The study group was tested using the Vicon 250 three-dimensional gait analysis system before and after the physical exercise programme. Results Walking speed after therapy increased for the left lower limb from 1.06 (SD 0.24) [m/s] to 1.21 (SD 0.23) [m/s], and for the right lower limb from 1.07 (SD 0.25) [m/s] to 1.20 (SD 0.25) [m/s]. The cycle length increased after the applied therapy for the left lower limb from 1.17 (SD 0.20) [m] to 1.23 (SD 0.19) [m]. Conclusion The three-week motor ability rehabilitation programme positively influences spatial-temporal gait parameters in HD patients