Measure valued solutions of sub-linear diffusion equations with a drift term

In this paper we study nonnegative, measure valued solutions of the initial value problem for one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing $C^1$ function $\beta$ with $\lim_{r\to +\infty} \beta(r)<+\infty$. By using tools of optimal transport, we will show that this kind of problems is well posed in the class of nonnegative Borel measures with finite mass $m$ and finite quadratic momentum and it is the gradient flow of a suitable entropy functional with respect to the so called $L^2$-Wasserstein distance. Due to the degeneracy of diffusion for large densities, concentration of masses can occur, whose support is transported by the drift. We shall show that the large-time behavior of solutions depends on a critical mass ${m}_{\rm c}$, which can be explicitely characterized in terms of $\beta$ and of the drift term. If the initial mass is less then ${m}_{\rm c}$, the entropy has a unique minimizer which is absolutely continuous with respect to the Lebesgue measure. Conversely, when the total mass $m$ of the solutions is greater than the critical one, the steady state has a singular part in which the exceeding mass ${m} - {m}_{\rm c}$ is accumulated.Comment: 30 page

Gradient flows for non-smooth interaction potentials

none3mixedJ.A. Carrillo;S. Lisini;E. MaininiJ. A., Carrillo; S., Lisini; Mainini, Edoard

UNIQUENESS FOR KELLER-SEGEL-TYPE CHEMOTAXIS MODELS

We prove uniqueness in the class of integrable and bounded non- negative solutions in the energy sense to the Keller-Segel (KS) chemotaxis system. Our proof works for the fully parabolic KS model, it includes the classical parabolic-elliptic KS equation as a particular case, and it can be gen- eralized to nonlinear diffusions in the particle density equation as long as the diffusion satisfies the classical McCann displacement convexity condition. The strategy uses Quasi-Lipschitz estimates for the chemoattractant equation and the above-the-tangent characterizations of displacement convexity. As a con- sequence, the displacement convexity of the free energy functional associated to the KS system is obtained from its evolution for bounded integrable initial data

Exploiting Intrinsic Kinematic Null Space for Supernumerary Robotic Limbs Control

Supernumerary robotic limbs (SRLs) gained increasing interest in the last years for their applicability as healthcare and assistive technologies. These devices can either support or augment human sensorimotor capabilities, allowing users to complete tasks that are more complex than those feasible for their natural limbs. However, for a successful coordination between natural and artificial limbs, intuitiveness of interaction and perception of autonomy are key enabling features, especially for people suffering from motor disorders and impairments. The development of suitable human-robot interfaces is thus fundamental to foster the adoption of SRLs.With this work, we describe how to control an extra degree of freedom by taking advantage of what we defined the Intrinsic Kinematic Null Space, i.e. the redundancy of the human kinematic chain involved in the ongoing task. Obtained results demonstrated that the proposed control strategy is effective for performing complex tasks with a supernumerary robotic finger, and that practice improves users' control ability

Uniform convergence to equilibrium for granular media

We study the long time asymptotics of a nonlinear, nonlocal equation used in the modelling of granular media. We prove a uniform exponential convergence to equilibrium for degenerately convex and non convex interaction or confinement potentials, improving in particular results by J. A. Carrillo, R. J. McCann and C. Villani. The method is based on studying the dissipation of the Wasserstein distance between a solution and the steady state

Discovery of a 0.42-s pulsar in the ultraluminous X-ray source NGC 7793 P13

NGC 7793 P13 is a variable (luminosity range ~100) ultraluminous X-ray source (ULX) proposed to host a stellar-mass black hole of less than 15 M$_{\odot}$ in a binary system with orbital period of 64 d and a 18-23 M$_{\odot}$ B9Ia companion. Within the EXTraS project we discovered pulsations at a period of ~0.42 s in two XMM-Newton observations of NGC 7793 P13, during which the source was detected at $L_{\mathrm{X}}\sim2.1\times10^{39}$ and $5\times10^{39}$ erg s$^{-1}$ (0.3-10 keV band). These findings unambiguously demonstrate that the compact object in NGC 7793 P13 is a neutron star accreting at super-Eddington rates. While standard accretion models face difficulties accounting for the pulsar X-ray luminosity, the presence of a multipolar magnetic field with $B$ ~ few $\times$ 10$^{13}$ G close to the base of the accretion column appears to be in agreement with the properties of the system.Comment: 5 pages, 5 figures, 2 tables; Version accepted for publication in MNRAS Letter

Haptic Guidance in Dynamic Environments Using Optimal Reciprocal Collision Avoidance

Human guidance in situations where the users cannot rely on their main sensory modalities, such as assistive or search-and-rescue scenarios, is a challenging task. In this letter, we address the problem of guiding users along collision-free paths in dynamic environments, assuming that they cannot rely on their main sensory modalities. In order to safely guide the subjects, we adapt the optimal reciprocal collision avoidance to our specific problem. The proposed algorithm takes into account the stimuli which can be displayed to the users and the motion uncertainty of the users when reacting to the provided stimuli. The proposed algorithm was evaluated in three different dynamic scenarios. A total of 18 blindfolded human subjects were asked to follow haptic cues in order to reach a target area while avoiding real static obstacles and moving users. Three metrics such as time to reach the goal, length of the trajectories, and minimal distance from the obstacles are considered to compare results obtained using this approach and experiments performed without visual impairments. Experimental results reveal that blindfolded subjects are successfully able to avoid collisions and safely reach the targets in all the performed trials. Although in this letter we display directional cues via haptic stimuli, we believe that the proposed approach can be general and tuned to work with different haptic interfaces and/or feedback modalities

Automated Large-Scale Production of Paclitaxel Loaded Mesenchymal Stromal Cells for Cell Therapy Applications

Mesenchymal stromal cells (MSCs) prepared as advanced therapies medicinal products (ATMPs) have been widely used for the treatment of different diseases. The latest developments concern the possibility to use MSCs as carrier of molecules, including chemotherapeutic drugs. Taking advantage of their intrinsic homing feature, MSCs may improve drugs localization in the disease area. However, for cell therapy applications, a significant number of MSCs loaded with the drug is required. We here investigate the possibility to produce a large amount of Good Manufacturing Practice (GMP)-compliant MSCs loaded with the chemotherapeutic drug Paclitaxel (MSCs-PTX), using a closed bioreactor system. Cells were obtained starting from 13 adipose tissue lipoaspirates. All samples were characterized in terms of number/viability, morphology, growth kinetics, and immunophenotype. The ability of MSCs to internalize PTX as well as the antiproliferative activity of the MSCs-PTX in vitro was also assessed. The results demonstrate that our approach allows a large scale expansion of cells within a week; the MSCs-PTX, despite a different morphology from MSCs, displayed the typical features of MSCs in terms of viability, adhesion capacity, and phenotype. In addition, MSCs showed the ability to internalize PTX and finally to kill cancer cells, inhibiting the proliferation of tumor lines in vitro. In summary our results demonstrate for the first time that it is possible to obtain, in a short time, large amounts of MSCs loaded with PTX to be used in clinical trials for the treatment of patients with oncological diseases

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

In vitro biosafety profile evaluation of multipotent mesenchymal stem cells derived from the bone marrow of sarcoma patients.

BACKGROUND: In osteosarcoma (OS) and most Ewing sarcoma (EWS) patients, the primary tumor originates in the bone. Although tumor resection surgery is commonly used to treat these diseases, it frequently leaves massive bone defects that are particularly difficult to be treated. Due to the therapeutic potential of mesenchymal stem cells (MSCs), OS and EWS patients could benefit from an autologous MSCs-based bone reconstruction. However, safety concerns regarding the in vitro expansion of bone marrow-derived MSCs have been raised. To investigate the possible oncogenic potential of MSCs from OS or EWS patients (MSC-SAR) after expansion, this study focused on a biosafety assessment of MSC-SAR obtained after short- and long-term cultivation compared with MSCs from healthy donors (MSC-CTRL). METHODS: We initially characterized the morphology, immunophenotype, and differentiation multipotency of isolated MSC-SAR. MSC-SAR and MSC-CTRL were subsequently expanded under identical culture conditions. Cells at the early (P3/P4) and late (P10) passages were collected for the in vitro analyses including: the sequencing of genes frequently mutated in OS and EWS, evaluation of telomerase activity, assessment of the gene expression profile and activity of major cancer pathways, cytogenetic analysis on synchronous MSC, and molecular karyotyping using a comparative genomic hybridization (CGH) array. RESULTS: MSC-SAR displayed comparable morphology, immunophenotype, proliferation rate, differentiation potential, and telomerase activity to MSC-CTRL. Both cell types displayed signs of senescence in the late stages of culture with no relevant changes in cancer gene expression. However, cytogenetic analysis detected chromosomal anomalies in the early and late stages of MSC-SAR and MSC-CTRL after culture. CONCLUSIONS: Our results demonstrated that the in vitro expansion of MSC does not influence or favor malignant transformation since MSC-SAR were not more prone than MSC-CTRL to deleterious changes during culture. However, the presence of chromosomal aberrations supports rigorous phenotypic, functional and genetic evaluation of the biosafety of MSCs, which is important for clinical applications