Joint distribution of the process and its sojourn time on the positive half-line for pseudo-processes governed by high-order heat equation.

Consider the high-order heat-type equation ∂u/∂t = ±∂Nu/∂xN for an integer N > 2 and introduce the related Markov pseudo-process (X(t))t≥0. In this paper, we study the sojourn time T(t) in the interval [0, +∞) up to a fixed time t for this pseudo-process. We provide explicit expressions for the joint distribution of the couple (T(t),X(t))

Joint distribution of the process and its sojourn time in a half-line [a,+∞)[a,+\infty) for pseudo-processes driven by a high-order heat-type equation.

Let (X(t))t≥0 be the pseudo-process driven by the high-order heat-type equation ∂u = ± ∂Nu , ∂t ∂xN where N is an integer greater than 2. We consider the sojourn time spent by (X(t))t≥0 in [a,+∞) (a ∈ R), up to a fixed time t > 0: Ta(t) = 0t 1l[a,+∞)(X(s)) ds. The purpose of this paper is to explicit the joint pseudo-distribution of the vector (Ta(t),X(t)) when the pseudo-process starts at a point x ∈ R at time 0. The method consists in solving a boundary value problem satisfied by the Laplace transform of the aforementioned distribution

On random flights with non-uniformly distributed directions

This paper deals with a new class of random flights $\underline{\bf X}_d(t),t>0,$ defined in the real space $\mathbb{R}^d, d\geq 2,$ characterized by non-uniform probability distributions on the multidimensional sphere. These random motions differ from similar models appeared in literature which take directions according to the uniform law. The family of angular probability distributions introduced in this paper depends on a parameter $\nu\geq 0$ which gives the level of drift of the motion. Furthermore, we assume that the number of changes of direction performed by the random flight is fixed. The time lengths between two consecutive changes of orientation have joint probability distribution given by a Dirichlet density function. The analysis of $\underline{\bf X}_d(t),t>0,$ is not an easy task, because it involves the calculation of integrals which are not always solvable. Therefore, we analyze the random flight $\underline{\bf X}_m^d(t),t>0,$ obtained as projection onto the lower spaces $\mathbb{R}^m,m<d,$ of the original random motion in $\mathbb{R}^d$. Then we get the probability distribution of $\underline{\bf X}_m^d(t),t>0.$ Although, in its general framework, the analysis of $\underline{\bf X}_d(t),t>0,$ is very complicated, for some values of $\nu$, we can provide some results on the process. Indeed, for $\nu=1$, we obtain the characteristic function of the random flight moving in $\mathbb{R}^d$. Furthermore, by inverting the characteristic function, we are able to give the analytic form (up to some constants) of the probability distribution of $\underline{\bf X}_d(t),t>0.$Comment: 28 pages, 3 figure

Vibrations and fractional vibrations of rods, plates and Fresnel pseudo-processes

Different initial and boundary value problems for the equation of vibrations of rods (also called Fresnel equation) are solved by exploiting the connection with Brownian motion and the heat equation. The analysis of the fractional version (of order $\nu$) of the Fresnel equation is also performed and, in detail, some specific cases, like $\nu=1/2$, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process $F(t)$, $t>0$ with real sign-varying density is constructed and some of its properties examined. The equation of vibrations of plates is considered and the case of circular vibrating disks $C_R$ is investigated by applying the methods of planar orthogonally reflecting Brownian motion within $C_R$. The composition of F with reflecting Brownian motion $B$ yields the law of biquadratic heat equation while the composition of $F$ with the first passage time $T_t$ of $B$ produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

Physical and optical properties of sol-gel nano-silver doped silica film on glass substrate as a function of heat-treatment temperature

Nano-silver doped silica films were deposited on glass slides using a sol-gel process and heat-treated at different temperatures. The films were characterized by ultraviolet-visible spectroscopy, x-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), Rutherford backscattering spectrometry (RBS), and transmission electron microscopy for their optical, chemical, and structural properties. The absorption peak of silver colloids (wavelength from 400 to 460 nm) was present and a blueshift and intensity reduction of the absorption peak was observed during heat-treatment. Particle size reduction and surface morphology changes in the films were observed by AFM as a function of varying heat treatment temperatures. Silver nanoparticles were formed through spontaneous reduction of silver ions. The oxidation of silver occurs during heat-treatment, causing a reduction of absorption intensity. An interdiffusion between the Ag in the film and Na in the substrate glass was observed by XPS and RBS. Sodium in the coating likely increased the stability of silver oxide at high temperature treated samples

Upper critical field and de Haas-van Alphen oscillations in KOs2_2O6_6 measured in a hybrid magnet

Magnetic torque measurements have been performed on a KOs$_2$O$_6$ single crystal in magnetic fields up to 35.3 T and at temperatures down to 0.6 K. The upper critical field is determined to be $\sim$30 T. De Haas-van Alphen oscillations are observed. A large mass enhancement of (1+$\lambda$) = $m^* / m_{band}$ = 7.6 is found. It is suggested that, for the large upper critical field to be reconciled with Pauli paramagnetic limiting, the observed mass enhancement must be of electron-phonon origin for the most part.Comment: 4 pages, 4 figures, published versio

The views and experiences of suicidal children and young people of mental health support services: A meta-ethnography.

Background: Suicide is amongst the leading causes of death in young people globally and a health priority worldwide. For children and young people (CYP) attempting or considering suicide there is no agreed treatment model. Development of treatment models should be informed by the views and experiences of CYP using services. Methods: Meta-ethnography was used to systematically identify and synthesise studies reporting the views of CYP who used mental health services following suicidal behaviour. Relevant studies were quality appraised. First order (participants) and second order (original author) data were translated to identify common and disconfirming themes and concepts. Translated findings were synthesised and led to a new hypothesis supported by additional ‘linguistic analysis’ of texts to construct a novel third order line-of-argument. Results: Four studies conducted since 2006 in three countries involving 44 young people aged 11-24 years were synthesised. Translation revealed that suicidal CYP do not know where or how to access help, they cannot access help directly and when seen by mental health practitioners they do not feel listened to. Line-of-argument synthesis identified a silence around suicidality within the conversations CYP have with mental health practitioners and within academic research reporting. Use of the term ‘self-harm’ to encompass suicidal behaviours potentially contributes to this silence by avoiding the word ‘suicide’. Conclusions: CYP who are suicidal need to have easy access to mental health services. When using services, they want to feel listened to and have suicidal feelings acknowledged. This involves professionals referring explicitly to suicide not just self-harm

Using photo-elicitation to understand reasons for repeated self-harm: a qualitative study

Background: Reasons for self-harm are not well understood. One of the reasons for this is that first-hand accounts are usually elicited using traditional interview and questionnaire methods. This study aims to explore the acceptability of using an approach (photo-elicitation) that does not rely on solely verbal or written techniques, and to make a preliminary assessment of whether people can usefully employ images to support a discussion about the reasons why they self-harm. Method: Interviews with eight participants using photo elicitation, a method in which photographs produced by the participant are used as a stimulus and guide within the interview. Results: Participants responded positively to using images to support a discussion about their self-harm and readily incorporated images in the interview. Four main themes were identified representing negative and positive or adaptive purposes of self-harm: self-harm as a response to distress, self-harm to achieve mastery, self-harm as protective and self-harm as a language or form of communication. Conclusions: Employing this novel approach was useful in broadening our understanding of self-harm