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We prove that the integral operators associated with the layer heat potentials depend smoothly upon a parametrization of the support of integration. The analysis is carried out in the optimal H\"older setting.

We consider a linearly elastic material with a periodic set of voids. On the boundaries of the voids we set a Robin-type traction condition. Then we investigate the asymptotic behavior of the displacement solution as the Robin condition turns into a pure traction one. To wit, there will be a matrix function {$b[k](\cdot)$ that depends analytically on a real parameter $k$ and vanishes for $k=0$ and we multiply the Dirichlet-like part of the Robin condition by $b[k](\cdot)$}. We show that the displacement solution can be written in terms of power series of $k$ that converge for $k$ in a whole neighborhood of $0$. For our analysis we use the Functional Analytic Approach.

In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the solution can be written as the sum of a single layer potential, a constant function and a linear function of the space variable. The density of the periodic single layer potential and the constant are identified as the unique solutions of a certain integral equation., arXiv admin note: substantial text overlap with arXiv:1306.6177

We show that there are harmonic functions on a ball ${\mathbb{B}_n}$ of $\mathbb{R}^n$, $n\ge 2$, that are continuous up to the boundary (and even H\"older continuous) but not in the Sobolev space $H^s(\mathbb{B}_n)$ for any $s$ sufficiently big. The idea for the construction of these functions is inspired by the two-dimensional example of a harmonic continuous function with infinite energy presented by Hadamard in 1906. To obtain examples in any dimension $n\ge 2$ we exploit certain series of spherical harmonics. As an application, we verify that the regularity of the solutions that was proven for a class of boundary value problems with nonlinear transmission conditions is, in a sense, optimal., Comment: 19 pages

We consider a Neumann problem for the Laplace equation in a periodic domain. We prove that the solution depends real analytically on the shape of the domain, on the periodicity parameters, on the Neumann datum, and on its boundary integral.

We lay down the preliminary work to apply the Functional Analytic Approach to quasi-periodic boundary value problems for the Helmholtz equation. This consists in introducing a quasi-periodic fundamental solution and the related layer potentials, showing how they are used to construct the solutions of quasi-periodic boundary value problems, and how they behave when we perform a singular perturbation of the domain. To show an application, we study a nonlinear quasi-periodic Robin problem in a domain with a set of holes that shrink to points.

We show that there are harmonic functions on a ball ${\mathbb{B}_n}$ of $\mathbb{R}^n$, $n\ge 2$, that are continuous up to the boundary (and even Hölder continuous) but not in the Sobolev space $H^s(\mathbb{B}_n)$ for any $s$ sufficiently big. The idea for the construction of these functions is inspired by the two-dimensional example of a harmonic continuous function with infinite energy presented by Hadamard in 1906. To obtain examples in any dimension $n\ge 2$ we exploit certain series of spherical harmonics. As an application, we verify that the regularity of the solutions that was proven for a class of boundary value problems with nonlinear transmission conditions is, in a sense, optimal., 19 pages

Supplementary Video 1

BACKGROUND: The tumor microenvironment plays a major tumor-supportive role in glioma. In particular, tumor-associated macrophages (TAMs), which can make up to one-third of the tumor mass, actively support tumor growth, invasion, and angiogenesis. Predominantly alternatively activated (M2-polarized) TAMs are found in late-stage glioma in both human and mouse tumors, as well as in relapse samples from patients. However, whether tumor-educated M2 TAMs can actively contribute to the emergence and growth of relapse is currently debated. METHODS: To investigate whether tumor-educated stromal cells remaining in the brain after surgical removal of the primary tumor can be long-lived and retain their tumor-supporting function, we developed a transplantation mouse model and performed lineage-tracing. RESULTS: We discovered that macrophages can survive transplantation and stay present in the tumor much longer than previously suggested, while sustaining an M2-polarized protumorigenic phenotype. Transplanted tumors showed a more aggressive growth and faster polarization of the TAMs toward an M2 phenotype compared with primary tumors, a process dependent on the presence of few cotransplanted macrophages. CONCLUSIONS: Overall, we propose a new way for tumor-educated TAMs to contribute to glioma aggressiveness by long survival and stable protumorigenic features. These properties could have a relapse-supporting effect. ispartof: NEURO-ONCOLOGY ADVANCES vol:2 issue:1 ispartof: location:England status: published

One of the most challenging issues in Mediterranean ecosystems to date has been to understand the emergence of discontinuous changes or catastrophic shifts. In the era of the 2030 Sustainable Development Goals, which encompass ideas around Land Degradation Neutrality, advancing this understanding has become even more critical and urgent. The aim of this paper is to synthesise insights into the drivers, processes and management of catastrophic shifts to highlight ways forward for the management of Mediterranean ecosystems. We use a multidisciplinary approach that extends beyond the typical single site, single scale, single approach studies in the current literature. We link applied and theoretical ecology at multiple scales with analyses and modelling of human-environment-climate relations and stakeholder engagement in six field sites in Mediterranean ecosystems to address three key questions: i) How do major degradation drivers affect ecosystem functioning and services in Mediterranean ecosystems? ii) What processes happen in the soil and vegetation during a catastrophic shift? iii) How can management of vulnerable ecosystems be optimized using these findings? Drawing together the findings from the use of different approaches allows us to address the whole pipeline of changes from drivers through to action. We highlight ways to assess ecosystem vulnerability that can help to prevent ecosystem shifts to undesirable states; identify cost-effective management measures that align with the vision and plans of land users; and evaluate the timing of these measures to enable optimization of their application before thresholds are reached. Such a multidisciplinary approach enables improved identification of early warning signals for discontinuous changes informing more timely and cost-effective management, allowing anticipation of, adaptation to, or even prevention of, undesirable catastrophic ecosystem shifts.

One of the most challenging issues in Mediterranean ecosystems to date has been to understand the emergence of discontinuous changes or catastrophic shifts. In the era of the 2030 Sustainable Development Goals, which encompass ideas around Land Degradation Neutrality, advancing this understanding has become even more critical and urgent. The aim of this paper is to synthesise insights into the drivers, processes and management of catastrophic shifts to highlight ways forward for the management of Mediterranean ecosystems. We use a multidisciplinary approach that extends beyond the typical single site, single scale, single approach studies in the current literature. We link applied and theoretical ecology at multiple scales with analyses and modelling of human-environment-climate relations and stakeholder engagement in six field sites in Mediterranean ecosystems to address three key questions: i) How do major degradation drivers affect ecosystem functioning and services in Mediterranean ecosystems? ii) What processes happen in the soil and vegetation during a catastrophic shift? iii) How can management of vulnerable ecosystems be optimized using these findings? Drawing together the findings from the use of different approaches allows us to address the whole pipeline of changes from drivers through to action. We highlight ways to assess ecosystem vulnerability that can help to prevent ecosystem shifts to undesirable states; identify cost-effective management measures that align with the vision and plans of land users; and evaluate the timing of these measures to enable optimization of their application before thresholds are reached. Such a multidisciplinary approach enables improved identification of early warning signals for discontinuous changes informing more timely and cost-effective management, allowing anticipation of, adaptation to, or even prevention of, undesirable catastrophic ecosystem shifts.

Additional file 2: Table S2. Prognosis Model for all cases.

Additional file 5: Table S5. Event-free Survival (EFS) Prognosis Model including molecular data for grade I pilocytic and grade II diffuse intramedullary astrocytomas.

Additional file 1: Table S1. List of genes, copy number variations (CNV) and KIAA1549-BRAF fusions tested.

Additional file 4: Table S4. Prognosis Model including molecular data for all cases.

Additional file 3: Table S3. Event-Free Survival (EFS) Prognosis Model for LG cases (grade I and grade II only).

Figure S1: A) Far UV CD spectra of 10 µM nmRec and 300 µM EGTA (black), after sequential additions of 1 mM free Ca2+ (red), 15 µM GRK1 peptide (blue) and 4.2 mM free EGTA (green). B) Far UV CD spectra of 10 µM nmRec and 300 µM EGTA (black), after sequential additions of 15 µM GRK1 peptide (red), 1 mM free Ca2+ (blue) and 4.2 mM free EGTA (green). C) Far UV CD spectra of 10 µM mRec and 300 µM EGTA (black), after sequential additions of 1 mM free Ca2+ (red), 15 µM GRK1 peptide (blue) and 4.2 mM free EGTA (green). D) Far UV CD spectra of 10 µM mRec and 300 µM EGTA (black), after sequential additions of 15 µM GRK1 peptide (red), 1 mM free Ca2+ (blue) and 4.2 mM free EGTA (green).; Figure S2: Hydrodynamic diameter estimation of 15 nM LP monitored by A) DLS and B) Nanoparticle Tracking Analysis.; Figure S3: Near UV CD spectra of 7 µM mRec in the presence of 5 nM LP and 300 µM EGTA (black) or 1 mM Ca2+ (red). B) Near UV CD spectra of 7 µM mRec in the presence of 5 nM LP, 10.5 µM GRK1 peptide and 300 µM EGTA (black) or 1 mM Ca2+.

info:eu-repo/semantics/published

ispartof: Proc. Intl. Soc. Mag. Reson. Med. vol:27 ispartof: Annual Meeting of the International Society for Magnetic Resonance in Medicine location:Montreal date:11 May - 16 May 2019 status: published

The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper we focus on the mapping properties of the volume potentials with weakly singular periodic kernels. Our main result is to prove that the map which takes a density function and a periodic kernel to a (suitable restriction of the) volume potential is bilinear and continuous with values in a Roumieu class of analytic functions. Such result extends to the periodic case some previous results obtained by the authors for non periodic potentials and it is motivated by the study of perturbation problems for the solutions of boundary value problems for elliptic differential equations in periodic domains.

We present a limiting property and a local uniqueness result for converging families of solutions of a singularly perturbed nonlinear traction problem in an unbounded periodic domain with small holes.

ispartof: ITOC location:Prague date:20 Mar - 22 Mar 2017 status: published

Given a non-trivial automorphism (resp. anti-automorphism) of a semigroup, we study its homomorphic (resp. anti-homomorphic) extensions to a larger semigroup by considering the images of the absorbing elements. Then we exhibit some examples to show the application of the results obtained.

Objective: intracranial collateral circulation performance is emerging as a strong outcome determinant in both human and experimental ischemic stroke. The aim of this study was to investigate and compare the effects of two putative strategies, which might actively modulate intracranial collateral flow in the setting of acute cerebral ischemia: intravascular volume load using polygeline and cerebro-selective vasodilatation using acetazolamide. Materials and methods: MCA was transiently occluded (90 min) by intraluminal filament in adult male Wistar rats. 10 rats were left untreated; 30 rats were treated after 30 min of ischemia with intravenous administration of either saline solution (n=10), polygeline (n=10) or acetazolamide (n =10). Intracranial collateral flow was studied in terms of perfusion deficit using multi-site laser Doppler monitoring, functional deficit was assessed using a sensory-motor score and infarct volume was calculated on consecutive sections stained with Cresyl violet, performed 24 hours after ischemia induction. Blood pressure, heart and respiratory rate were continuously monitored by a pressure transducer placed in femoral artery. Results: post-ischemic administration of both polygeline and acetazolamide significantly increased intracranial collateral flow in the territory of leptomeningeal branches during MCA occlusion and reduced infarct size as well as functional deficit, compared to untreated and saline-treated rats. No significant effect on blood pressure was observed. Conclusions: therapeutic modulation of intracranial collateral flow is feasible and is associated with a better outcome after transient MCA occlusion in rats. “Collateral therapeutics” may represent an simple tissue-saving strategy in the hyper-acute phase of ischemic stroke prior to recanalization therapy.

Question: Provide a topographical and morphological characterization of post-reperfusion molecular penumbra in the rat stroke model of transient middle cerebral artery (MCA) occlusion Methods: Young adult male Wistar rats (n=25) underwent 90 minutes of transient intraluminal MCA occlusion, followed by 24 hours of reperfusion. Immunohistochemistry for Heat Shock Protein 70 (HSP70) and Microtubule-Associated Protein 2 (MAP2), TUNEL staining and Cresyl violet staining were performed in the same or adjacent brain coronal sections within the entire vascular territory supplied by MCA. Results: Peri-lesional regions showed multiple areas of HSP70 immunostaining of variable extent and localization in the neocortex, mostly in superficial cortical layers. HSP70-positive cells were qualified as neurons (both morphologically and by MAP2 staining) and apparently maintained a tissue organization. We interpreted such regions as ‘mini-penumbras’, likely saved by reperfusion, hypothesis supported by lack of TUNEL staining. ‘Mini-penumbras’ surrounded spots or boundaries of low density marked cells interpreted as ‘mini-cores’, penumbra which has progressed to infarction in spite of reperfusion. Within the ischemic lesion, infarcted cortical and subcortical areas presented a large number of TUNEL-positive cells and a low density of regularly distributed HSP70 marked cells, mainly identified as endothelial cells and rarely as neurons. Conclusions: Qualitative assessment of residual molecular penumbra after 24 hours of reperfusion demonstrated a high variability in staining topography, pattern and extension, along with the emerging concept of heterogeneous penumbra. The preferential localization of “mini-penumbras” in the superficial cortical areas might reflect the variable contribution of leptomeningeal collateral circulation during the ischemic phase.

Let n\ge 3. Let \Omega^i and \Omega^o be open bounded connected subsets of R^n containing the origin. Let \epsilon_0>0 be such that \Omega^o contains the closure of \epsilon\Omega^i for all \epsilon\in]-\epsilon_0,\epsilon_0[. Then, for a fixed \epsilon\in]-\epsilon_0,\epsilon_0[\{0} we consider a Dirichlet problem for the Laplace operator in the perforated domain \Omega^o\\epsilon\Omega^i. We denote by u_\epsilon the corresponding solution. If p\in\Omega^o and p\neq 0, then we know that under suitable regularity assumptions there exist \epsilon_p>0 and a real analytic operator U_p from ]-\epsilon_p,\epsilon_p[ to R such that u_\epsilon(p)=U_p[\epsilon] for all \epsilon\in]0,\epsilon_p[. Thus it is natural to ask what happens to the equality u_\epsilon(p)=U_p[\epsilon] for \epsilon

We construct of a family of fundamental solutions for elliptic partial differential operators with real constant coefficients. The elements of such a family are expressed by means of jointly real analytic functions of the coefficients of the operators and of the spatial variable. We show regularity properties in the frame of Schauder spaces for the corresponding single layer potentials.

Intracranial collaterals provide residual blood flow to penumbral tissue in acute ischemic stroke and contribute to infarct size variability in humans. In the present study, hemodynamic monitoring of the borderzone territory between the leptomeningeal branches of middle cerebral artery and anterior cerebral artery was compared to lateral middle cerebral artery territory, during common carotid artery occlusion and middle cerebral artery occlusion in rats. The functional performance of intracranial collaterals, shown by perfusion deficit in the territory of leptomeningeal branches either during common carotid artery occlusion or middle cerebral artery occlusion, showed significant variability among animals and consistently predicted infarct size and functional deficit. Our findings indicate that leptomeningeal collateral flow is a strong predictor of stroke severity in rats, similarly to humans. Monitoring of collateral blood flow in experimental stroke is essential for reducing variability in neuroprotection studies and accelerating the development of collateral therapeutics. © 2011 Elsevier Inc.

Wildfires have always been a part of the history of Mediterranean forests. However, forests are not always certain to regenerate after a wildfire. Whether they do depends on many factors, some of which may be influenced by land management activities. Failure to regenerate will cause a regime shift in the ecosystem, reducing the provision of ecosystem services and ultimately leading to desertification. How can we increase the resilience of Mediterranean forests to fire? Our approach to answering this question was twofold: first, we reviewed the literature to investigate chains of processes that allowed forests to regenerate (which we label Regeneration Mechanisms, or RMs); and second, we assessed the impact of selected management practices documented in the WOCAT database on these RMs. For the assessment, we evaluated the relation between the benefits and disadvantages of the land management practices on the one hand, and the hindering and supporting factors of the RMs on the other. We identified three distinct RMs that enable Mediterranean forests to recover, as well as the time frame before and after a fire in which they are at work, and factors that can hinder or support resilience. The three RMs enabling a forest to regenerate after a fire consist of regeneration (1) from a seed bank; (2) from resprouting individuals; and (3) from unburned plants that escaped the fire. Management practices were grouped into four categories: (1) fuel breaks; (2) fuel management; (3) afforestation; and (4) mulching. We assessed how and under what conditions land management modifies the ecosystem’s resilience. The results show that land management influences resilience by interacting with resilience mechanisms before and after the fire, and not just by modifying the fire regime. Our analysis demonstrates a need for adaptive—i.e., context- and time-specific—management strategies.

In Mediterranean forests and rangelands, the supply of important ecosystem services can decrease or cease as a consequence of disturbances and climatic oscillations. Land managers can sometimes prevent or mitigate the negative effects of disturbances through appropriate land management choices. In this study, we assess the contribution of land management practices (LMPs) to the resilience of eight Mediterranean forests and rangelands to multiple disturbances. The study uses a transdisciplinary approach, involving scientists, land managers, and local administrators. Data about disturbances, ecosystem services, the role of LMPs, and the resistance of LMPs to disturbances are combined using a semiquantitative index and analysed to evaluate how the LMPs implemented are suited to the disturbances affecting each study site. Our results indicate that the practices analysed are particularly effective in improving resilience of ecosystems against wildfires and torrential rainfalls. However, droughts are more difficult to address, and the examined practices were heavily affected by their occurrence. Tree planting appears to be highly affected by disturbances. Practices that selectively reduce the amount of vegetation appear to be beneficial in fostering recovery of ecosystems. Our assessment also suggests that it is particularly difficult to increase resilience to droughts and fires simultaneously. Practices that aimed to mitigate the impact of land use did not always prove valuable in terms of resilience. Finally, study sites that included efforts to address disturbances in their management objectives also displayed practices making the biggest contribution to resilience.

One of the most challenging issues in Mediterranean ecosystems to date has been to understand the emergence of discontinuous changes or catastrophic shifts. In the era of the 2030 Sustainable Development Goals, which encompass ideas around Land Degradation Neutrality, advancing this understanding has become even more critical and urgent. The aim of this paper is to synthesize insights into the drivers, processes and management of catastrophic shifts to highlight ways forward for the management of Mediterranean ecosystems. We use a multidisciplinary approach that extends beyond the typical single site, single scale, single approach studies in the current literature. We link applied and theoretical ecology at multiple scales with analyses and modeling of human–environment–climate relations and stakeholder engagement in six field sites in Mediterranean ecosystems to address three key questions: i) How do major degradation drivers affect ecosystem functioning and services in Mediterranean ecosystems? ii) What processes happen in the soil and vegetation during a catastrophic shift? iii) How can management of vulnerable ecosystems be optimized using these findings? Drawing together the findings from the use of different approaches allows us to address the whole pipeline of changes from drivers through to action. We highlight ways to assess ecosystem vulnerability that can help to prevent ecosystem shifts to undesirable states; identify cost-effective management measures that align with the vision and plans of land users; and evaluate the timing of these measures to enable optimization of their application before thresholds are reached. Such a multidisciplinary approach enables improved identification of early warning signals for discontinuous changes informing more timely and cost-effective management, allowing anticipation of, adaptation to, or even prevention of, undesirable catastrophic ecosystem shifts.

Glioblastoma multiforme (GBM) is the most aggressive primary brain tumor with a malignant prognosis. GBM is characterized by high cellular heterogeneity and its progression relies on the interaction with the central nervous system, which ensures the immune-escape and tumor promotion. This interplay induces metabolic, (epi)-genetic and molecular rewiring in both domains. In the present study, we aim to characterize the time-related changes in the GBM landscape, using a syngeneic mouse model of primary GBM. GL261 glioma cells were injected in the right striatum of immuno-competent C57Bl/6 mice and animals were sacrificed after 7, 14, and 21 days (7D, 14D, 21D). The tumor development was assessed through 3D tomographic imaging and brains were processed for immunohistochemistry, immunofluorescence, and western blotting. A human transcriptomic database was inquired to support the translational value of the experimental data. Our results showed the dynamic of the tumor progression, being established as a bulk at 14D and surrounded by a dense scar of reactive astrocytes. The GBM growth was paralleled by the impairment in the microglial/macrophagic recruitment and antigen-presenting functions, while the invasive phase was characterized by changes in the extracellular matrix, as shown by the analysis of tenascin C and metalloproteinase-9. The present study emphasizes the role of the molecular changes in the microenvironment during the GBM progression, fostering the development of novel multi-targeted, time-dependent therapies in an experimental model similar to the human disease. ispartof: MOLECULAR NEUROBIOLOGY vol:59 issue:11 pages:6857-6873 ispartof: location:United States status: published

Purpose: We retrospectively investigated the detection rates of prostate cancer, high grade prostatic intraepithelial neoplasia and atypical glands suggestive of carcinoma by initial 18 and 12-core prostate biopsy. Materials and Methods: A total of 3,460 consecutive patients with prostate specific antigen between 2.5 and 15 ng/ml underwent 12 (1,684) or 18 (1,776) core prostate biopsy under local anesthesia at 2 departments that adopted the same indications for performing biopsy. Biopsies were evenly distributed throughout the prostate in 6 sectors. In the 12-core prostate biopsy group 2 samples were obtained from each sector and in the 18-core prostate biopsy group 1 additional core was taken from each sector. Results: The cancer detection rate in patients who underwent 18-core prostate biopsy was not different from the rate in those who underwent 12-core prostate biopsy (39.9% and 38.4%, p = 0.37), nor did the detection of atypical glands suggestive of carcinoma differ significantly between the 2 groups (2.9% and 3.3%, respectively, p = 0.33). However, 18-core prostate biopsy detected a significantly higher percent of cases of high grade prostatic intraepithelial neoplasia (20.0% vs 12.9%, p = 0.001). The cancer detection rate was higher with 18 than with 12-core prostate biopsy in patients with a prostate volume of 55 cc or greater (31.5% vs 24.8%, p = 0.01) but not in those with a prostate volume of less than 55 cc (54.3% and 53.0%, respectively, p = 0.7). Moreover, we determined that patients with positive digital rectal examination findings do not need 18-core prostate biopsy as opposed to 12-core prostate biopsy. Conclusions: Compared with 12-core prostate biopsy, 18-core prostate biopsy detects significantly more cases of high grade prostatic intraepithelial. neoplasia. However, 18-core prostate biopsy detects a significantly higher number of cancer only in patients with a prostate volume of 55 cc or greater.

Background and Purpose: Creation of an optimal retroperitoneal space is of pivotal importance in laparoscopic retroperitoneal surgery. The aim of this study was to examine the balloon dissecting technique developed at our institution, comparing the costs of our device with that of a commercially available balloon retroperitoneal expander. Patients and Methods: Twenty patients scheduled to undergo retroperitoneoscopic surgery were randomly divided in two groups. In group 1, retroperitoneal dilation was performed with the commercially available balloon expander. In group 2, we employed our balloon dilator created with two middle finger of No. 8 powder-free surgical gloves tied to a nondisposable 11-mm trocar and filled with 600 mL of saline employing two 60-mL syringes simultaneously. Subjective evaluation of the created space was performed blindly in both groups. Economic evaluation included the costs of the disposable materials and of the time required for dilation. Results: In all cases, the dilation was considered good. In group 1, the median time required to dilate the retroperitoneal space was 3.15 minutes, whereas in group 2, the median time required was 1.16 minutes, and the time required to dissect the retroperitoneal space was 4.41 minutes ( total 5.57 minutes). Considering the costs of the disposable material, the overall costs of creating the retroperitoneal space was 141.95 is an element of in group 1 and 60.27 is an element of in group 2 ( P < 0.005). Conclusion: The original dissecting balloon employed at our institution is easy and fast and offers a valid option for the proper dissection of the retroperitoneal space. Moreover, it was revealed to be cost-effective compared with the commercially available device.