Reflection principles for functions of Neumann and Dirichlet Laplacians on open reflection invariant subsets of Rd\mathbb{R}^d

For an open subset $\Omega$ of $\mathbb R^d$, symmetric with respect to a hyperplane and with positive part $\Omega_+$, we consider the Neumann/Dirichlet Laplacians $-\Delta_{N/D,\Omega}$ and $-\Delta_{N/D,\Omega_+}$. Given a Borel function $\Phi$ on $[0,\infty)$ we apply the spectral functional calculus and consider the pairs of operators $\Phi(-\Delta_{N,\Omega})$ and $\Phi(-\Delta_{N,\Omega_+})$, or $\Phi(-\Delta_{D,\Omega})$ and $\Phi(-\Delta_{D,\Omega_+})$. We prove relations between the integral kernels for the operators in these pairs, which in particular cases of $\Omega_+=\mathbb{R}^{d-1}\times(0,\infty)$ and $\Phi_{t}(u)=\exp(-tu)$, $u \geq 0$, $t>0$, were known as reflection principles for the Neumann/Dirichlet heat kernels. These relations are then generalized to the context of symmetry with respect to a finite number of mutually orthogonal hyperplanes.Comment: 25 page

Mobility-aware fog computing in dynamic networks with mobile nodes: A survey

Fog computing is an evolving paradigm that addresses the latency-oriented performance and spatio-temporal issues of the cloud services by providing an extension to the cloud computing and storage services in the vicinity of the service requester. In dynamic networks, where both the mobile fog nodes and the end users exhibit time-varying characteristics, including dynamic network topology changes, there is a need of mobility-aware fog computing, which is very challenging due to various dynamisms, and yet systematically uncovered. This paper presents a comprehensive survey on the fog computing compliant with the OpenFog (IEEE 1934) standardised concept, where the mobility of fog nodes constitutes an integral part. A review of the state-of-the-art research in fog computing implemented with mobile nodes is conducted. The review includes the identification of several models of fog computing concept established on the principles of opportunistic networking, social communities, temporal networks, and vehicular ad-hoc networks. Relevant to these models, the contributing research studies are critically examined to provide an insight into the open issues and future research directions in mobile fog computing research

Radiation-induced anaplastic astrocytoma following treatment of medulloblastoma

We hereby report a case of a 10-year-old girl in whom neurosurgery was performed for cerebellar vermis medulloblastoma in April 2000. After resection the patient underwent chemotherapy followed by radiotherapy, receiving 53.07 Gy to posterior fossa and 35.07 Gy to the rest of the craniospinal axis. In 2012, she was diagnosed with anaplastic astrocytoma, which was located within the high-dose region. Surgical resection of the tumour was performed. Postoperatively, the patient received radiation therapy (50.4 Gy) with concurrent temozolomide, followed by 6 cycles of adjuvant temozolomide. Five years after the diagnosis of anaplastic astrocytoma, the patient remains asymptomatic

Clinical application of 1,5-anhydroglucitol measurements in patients with hepatocyte nuclear factor-1α maturity-onset diabetes of the young

OBJECTIVE - 1,5-anhydroglucitol (1,5-AG) is a short-term marker of metabolic control in diabetes. Its renal loss is stimulated in hyperglycemic conditions by glycosuria, which results in a lowered plasma concentration. As a low renal threshold for glucose has been described in hepatocyte nuclear factor-1α (HNF-1α) maturity-onset diabetes of the young (MODY), the 1,5-AG level may be altered in these patients. The purpose of this study was to assess the 1,5-AG levels in patients with HNF-1α MODY and in type 2 diabetic subjects with a similar degree of metabolic control. In addition, we aimed to evaluate this particle as a biomarker for HNF-1α MODY. RESEARCH DESIGN AND METHODS - We included 33 diabetic patients from the Polish Nationwide Registry of MODY. In addition, we examined 43 type 2 diabetic patients and 47 nondiabetic control subjects. The 1,5-AG concentration was measured with an enzymatic assay (GlycoMark). Receiver operating characteristic (ROC) curve analysis was used to evaluate 1,5-AG as a screening marker for HNF-1α MODY. RESULTS - The mean 1,5-AG plasma concentration in diabetic HNF-1α mutation carriers was 5.9 μg/ml, and it was lower than that in type 2 diabetic patients (11.0 μg/ml, P = 0.003) and in nondiabetic control subjects (23.9 μg/ml, P < 0.00005). The ROC curve analysis revealed 85.7% sensitivity and 80.0% specificity of 1,5-AG in screening for HNF-1α MODY at the criterion of <6.5 μg/ml in patients with an A1C level between 6.5 and 9.0%. CONCLUSIONS - 1,5-AG may be a useful biomarker for differential diagnosis of patients with HNF-1α MODY with a specific range of A1C, although this requires further investigation. However, the clinical use of this particle in diabetic HNF-1α mutation carriers for metabolic control has substantial limitations

Naczyniowy czynnik wzrostu w procesie stymulacji neoangiogenezy. Rola hipoksji w procesie rozrostu komórek endotelialnych i powstawaniu krążenia obocznego

The formation of new vessels is a complex problem. In this process the key role is played by the vascular-endothelial growth factor (VEGF). It is secreted, among others, by macrophages and endothelial cells. Genes for VEGF are located on the sixth chromosome. Hypoxia is a mandatory signal for the start of the angiogenesis process. Activated through hypoxia, HIF proteins move to the cells nucleus and regulate expression of vascular-endothelial growth factor. VEGF through its receptors on endothelial cells leads to the proliferation of new vessels.Powstawanie nowych naczyń jest zagadnieniem złożonym, w którym kluczową rolę pełni naczyniowo-śródbłonkowy czynnik wzrostu (VEGF). Wydzielany między innymi przez makrofagi i komórki śródbłonka jest niezbędny do uruchomienia procesów angiogenezy. Informacja genetyczna dla tej cytokiny znajduje się w chromosomie szóstym. Sygnałem do rozpoczęcia rozrostu naczyń jest niedotlenienie tkanek. Uaktywnione w wyniku hipoksji białka pomocnicze HIF przemieszczają się do jądra komórkowego i regulują ekspresję genów dla VEGF. Wytworzony przez komórki naczyniowo-śródbłonkowy czynnik wzrostu poprzez pobudzenie receptorów na komórkach śródbłonka doprowadza do ich proliferacji i powstawania nowych naczyń

Therapeutic applications of vascular endothelial growth factor

Zazwyczaj jedyną metodą pomocy pacjentom z krytycznym niedokrwieniem jest amputacja chorej kończyny. Od kilku lat podejmuje się próby pomocy takim pacjentom poprzez stymulację rozwoju naczyń krążenia obocznego. Metody blokowania angiogenezy dają natomiast szansę na przełom w leczeniu chorób nowotworowych.Usually the only one method of treatment of the patients with critical limb ischemia is extremity amputation. Since some time we try to stimulate angiogenesis as a new method of treatment. On the other hand antyangiogenesis gives a chance for the patients with neoplasms

Kontrowersje w postępowaniu z chorymi na nasieniaka jądra w I stopniu zaawansowania klinicznego

Osiemdziesiąt procent nasieniaków sklasyfikowanych jest w I stopniu zaawansowania klinicznego, stanowiąc około40% wszystkich guzów jądra. Postępowanie z tą grupą chorych po pierwotnym leczeniu polegającym na orchiektomiijest przedmiotem kontrowersji. Rozpatrywane są trzy opcje: obserwacja, radioterapia oraz chemioterapia.Aktywna obserwacja z leczeniem wdrażanym w przypadku wznowy, uzupełniające napromienianie lub adiuwantowamonochemioterapia karboplatyną pozwalają na uzyskanie około 100% przeżyć całkowitych i są alternatywnymi,równoważnymi metodami postępowania. Na podstawie aktualnych danych z literatury przedstawiono zalety i wadykażdej z trzech omawianych opcji