Regenerative partition structures

We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration after deletion of a part chosen by size-biased sampling. We associate each regenerative partition structure with a corresponding regenerative composition structure, which (as we showed in a previous paper) can be associated in turn with a regenerative random subset of the positive halfline, that is the closed range of a subordinator. A general regenerative partition structure is thus represented in terms of the Laplace exponent of an associated subordinator. We also analyse deletion properties characteristic of the two-parameter family of partition structures

Sustainable energy transition: properties and constraints of regenerative energy systems with respect to spatial planning and design

Before transforming the built environment, one must understand the characteristic of regenerative systems. The aim of this study was is to compare fossil-fuel energy systems with regenerative systems. It explores key properties and constraints of regenerative energy systems with respect to spatial organization and design of the built environment. The findings of this comparative analysis are illustrated with the help of a regional case-study in South Limburg, the Netherlands

Exponential inequalities for unbounded functions of geometrically ergodic Markov chains. Applications to quantitative error bounds for regenerative Metropolis algorithms

The aim of this note is to investigate the concentration properties of unbounded functions of geometrically ergodic Markov chains. We derive concentration properties of centered functions with respect to the square of the Lyapunov's function in the drift condition satisfied by the Markov chain. We apply the new exponential inequalities to derive confidence intervals for MCMC algorithms. Quantitative error bounds are providing for the regenerative Metropolis algorithm of [5]

Bioactive-glass in Endodontic Therapy and Associated Microsurgery

Bioactive-glass (B-G) has become a valuable adjunct to promote hard-tissue healing in many clinical situations and is of particular interest for endodontic care because of its biocompatibility, regenerative and antimicrobial properties as well as chemical composition that closely resembles the mineral make-up of human bone and dentine

Designing stem cell niches for differentiation and self-renewal

Mesenchymal stem cells, characterized by their ability to differentiate into skeletal tissues and self-renew, hold great promise for both regenerative medicine and novel therapeutic discovery. However, their regenerative capacity is retained only when in contact with their specialized microenvironment, termed the stem cell niche. Niches provide structural and functional cues that are both biochemical and biophysical, stem cells integrate this complex array of signals with intrinsic regulatory networks to meet physiological demands. Although, some of these regulatory mechanisms remain poorly understood or difficult to harness with traditional culture systems. Biomaterial strategies are being developed that aim to recapitulate stem cell niches, by engineering microenvironments with physiological-like niche properties that aim to elucidate stem cell-regulatory mechanisms, and to harness their regenerative capacity in vitro. In the future, engineered niches will prove important tools for both regenerative medicine and therapeutic discoveries

AR(1) sequence with random coefficients: Regenerative properties and its application

Let $\{X_n\}_{n\ge0}$ be a sequence of real valued random variables such that $X_n=\rho_n X_{n-1}+\epsilon_n,~n=1,2,\ldots$, where $\{(\rho_n,\epsilon_n)\}_{n\ge1}$ are i.i.d. and independent of initial value (possibly random) $X_0$. In this paper it is shown that, under some natural conditions on the distribution of $(\rho_1,\epsilon_1)$, the sequence $\{X_n\}_{n\ge0}$ is regenerative in the sense that it could be broken up into i.i.d. components. Further, when $\rho_1$ and $\epsilon_1$ are independent, we construct a non-parametric strongly consistent estimator of the characteristic functions of $\rho_1$ and $\epsilon_1$

Regenerative block empirical likelihood for Markov chains

Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical empirical likelihood method cannot be directly applied on the data but rather on blocks of consecutive data catching the dependence structure. Generalization of empirical likelihood based on the construction of blocks of increasing nonrandom length have been proposed for time series satisfying mixing conditions. Following some recent developments in the bootstrap literature, we propose a generalization for a large class of Markov chains, based on small blocks of various lengths. Our approach makes use of the regenerative structure of Markov chains, which allows us to construct blocks which are almost independent (independent in the atomic case). We obtain the asymptotic validity of the method for positive recurrent Markov chains and present some simulation results

Potential use of human periapical cyst-mesenchymal stem cells (hPCy-MSCs) as a novel stem cell source for regenerative medicine applications

Mesenchymal stem cells (MSCs) are attracting growing interest by the scientific community due to their huge regenerative potential. Thus, the plasticity of MSCs strongly suggests the utilization of these cells for regenerative medicine applications. The main issue about the clinical use of MSCs is related to the complex way to obtain them from healthy tissues; this topic has encouraged scientists to search for novel and more advantageous sources of these cells in easily accessible tissues. The oral cavity hosts several cell populations expressing mesenchymal stem cell like-features, furthermore, the access to oral and dental tissues is simple and isolation of cells is very efficient. Thus, oral-derived stem cells are highly attractive for clinical purposes. In this context, human periapical cyst mesenchymal stem cells (hPCy-MSCs) exhibit characteristics similar to other dental-derived MSCs, including their extensive proliferative potential, cell surface marker profile and the ability to differentiate into various cell types such as osteoblasts, adipocytes and neurons. Importantly, hPCy-MSCs are easily collected from the surgically removed periapical cysts; this reusing of biological waste guarantees a smart source of stem cells without any impact on the surrounding healthy tissues. In this review, we report the most interesting research topics related to hPCy-MSCs with a newsworthy discussion about the future insights. This newly discovered cell population exhibits interesting and valuable potentialities that could be of high impact in the future regenerative medicine applications

The role of ongoing dendritic oscillations in single-neuron dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as temporally local, near-instantaneous mappings from the current input of the cell to its current output, brought about by somatic summation of dendritic contributions that are generated in spatially localized functional compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations, and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought