Composition of processes and related partial differential equations

In this paper different types of compositions involving independent fractional Brownian motions B^j_{H_j}(t), t>0, j=1,$ are examined. The partial differential equations governing the distributions of I_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|), t>0 and J_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|^{1/H_1}), t>0 are derived by different methods and compared with those existing in the literature and with those related to B^1(|B^2_{H_2}(t)|), t>0. The process of iterated Brownian motion I^n_F(t), t>0 is examined in detail and its moments are calculated. Furthermore for J^{n-1}_F(t)=B^1_{H}(|B^2_H(...|B^n_H(t)|^{1/H}...)|^{1/H}), t>0 the following factorization is proved J^{n-1}_F(t)=\prod_{j=1}^{n} B^j_{\frac{H}{n}}(t), t>0. A series of compositions involving Cauchy processes and fractional Brownian motions are also studied and the corresponding non-homogeneous wave equations are derived.Comment: 32 page

Time-Changed Poisson Processes

We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson processes where the the time-change is inverse Gaussian, or its hitting time process, and discuss the governing DDE's. The stable subordinator, inverse stable subordinator and their iterated versions are also considered as time-changes. DDE's corresponding to probability mass functions of these time-changed processes are obtained. Finally, we obtain a new governing partial differential equation for the tempered stable subordinator of index $0<\beta<1,$ when $\beta$ is a rational number. We then use this result to obtain the governing DDE for the mass function of Poisson process time-changed by tempered stable subordinator. Our results extend and complement the results in Baeumer et al. \cite{B-M-N} and Beghin et al. \cite{BO-1} in several directions.Comment: 18 page

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

Subdiffusive transport in intergranular lanes on the Sun. The Leighton model revisited

In this paper we consider a random motion of magnetic bright points (MBP) associated with magnetic fields at the solar photosphere. The MBP transport in the short time range [0-20 minutes] has a subdiffusive character as the magnetic flux tends to accumulate at sinks of the flow field. Such a behavior can be rigorously described in the framework of a continuous time random walk leading to the fractional Fokker-Planck dynamics. This formalism, applied for the analysis of the solar subdiffusion of magnetic fields, generalizes the Leighton's model.Comment: 7 page

Low-lying GT(+) strength in Co-64 studied via the Ni-64(d,He-2)Co-64 reaction

The Ni-64(d,He-2)Co-64 reaction was studied at the AGOR cyclotron of KVI, Groningen, with the Big-Bite Spectrometer and the EuroSuperNova detector using a 171-MeV deuteron beam. An energy resolution of about 110 keV was achieved. In addition to the J(pi) = 1(+) ground state, several other 1(+) states could be identified in Co-64 and the strengths of the corresponding Gamow-Teller transitions were determined. The obtained strength distribution was compared with theoretical predictions and former (n,p) experimental results and displayed a good agreement. Due to the good energy resolution, detailed spectroscopic information was obtained, which supplements the data base needed for network calculations for supernova scenarios

Spectromicroscopic insights for rational design of redox-based memristive devices

The demand for highly scalable, low-power devices for data storage and logic operations is strongly stimulating research into resistive switching as a novel concept for future non-volatile memory devices. To meet technological requirements, it is imperative to have a set of material design rules based on fundamental material physics, but deriving such rules is proving challenging. Here, we elucidate both switching mechanism and failure mechanism in the valence-change model material SrTiO3, and on this basis we derive a design rule for failure-resistant devices. Spectromicroscopy reveals that the resistance change during device operation and failure is indeed caused by nanoscale oxygen migration resulting in localized valence changes between Ti4+ and Ti3+. While fast reoxidation typically results in retention failure in SrTiO3, local phase separation within the switching filament stabilizes the retention. Mimicking this phase separation by intentionally introducing retention-stabilization layers with slow oxygen transport improves retention times considerably

Fractional Cauchy problems on bounded domains: survey of recent results

In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by \citet{nigmatullin}, and \citet{zaslavsky} in $\mathbb R^d$ for modeling some physical phenomena. The fractional derivative models time delays in a diffusion process. We will give a survey of the recent results on the fractional Cauchy problem and its generalizations on bounded domains D\subset \rd obtained in \citet{m-n-v-aop, mnv-2}. We also study the solutions of fractional Cauchy problem where the first time derivative is replaced with an infinite sum of fractional derivatives. We point out a connection to eigenvalue problems for the fractional time operators considered. The solutions to the eigenvalue problems are expressed by Mittag-Leffler functions and its generalized versions. The stochastic solution of the eigenvalue problems for the fractional derivatives are given by inverse subordinators

Epidemiology, comorbidities, and healthcare utilization of patients with chronic urticaria in Germany

Background: Comprehensive data on the epidemiology and comorbidities of chronic urticaria (CU) in Germany are either limited, or not contemporary. Objectives: To investigate the epidemiology of CU, overall comorbidities and healthcare resource utilized by patients with CU in Germany, using an anonymized statutory health insurance (SHI) database. Methods: Anonymized SHI claims research database of the Institute for Applied Health Research, Berlin [InGef] (01 January 2015-30 September 2018) was used to analyse insured individuals with a confirmed diagnosis of CU (ICD-10-GM codes). Twelve-month diagnosed prevalence and incidence, comorbidities (vs. atopic dermatitis and psoriasis), and healthcare utilization by patients with CU were investigated. Results: Of 4 693 772 individuals of all ages listed in the database, 3 538 540 were observable during 2017. Overall, 17 524 patients (˜0.5%) were diagnosed with CU; chronic spontaneous urticaria (CSU: 71.2%), chronic inducible urticaria (CIndU: 19.7%), CSU+CIndU (9.1%). Females, vs. males, had higher diagnosed prevalence (0.62% vs. 0.37%) and diagnosed incidence (0.18% vs. 0.11%) of CU among all patients. Patients most frequently visited general practitioners (41.3% of total visits). Hypertensive diseases (43.5%), lipoprotein metabolism disorders (32.1%) and affective disorders (26.0%) were the most frequently reported comorbidities of special interest. Rates of most comorbidities of special interests were similar to atopic dermatitis and psoriasis patients, and all higher vs. overall population. More than half (54.1%) of all CU patients were not prescribed any treatment. Second-generation H1 -antihistamines were the most commonly prescribed medication for adult (17.9%) and paediatric (27.9%) patients. Patients with CIndU (paediatric, 15.5%; adult, 7.8%) were more often hospitalized versus patients with CSU (paediatric, 9.9%; adult, 4.6%). Conclusions: In Germany, prevalence of CU along with multiple comorbidities may pose increased burden on the healthcare system. Awareness of adhering to treatment guidelines, and aiming for complete control of urticaria, needs to be driven and may improve outcomes

Epidemiology, comorbidities, and healthcare utilization of patients with chronic urticaria in Germany

Abstract Background Comprehensive data on the epidemiology and comorbidities of chronic urticaria (CU) in Germany are either limited, or not contemporary. Objectives To investigate the epidemiology of CU, overall comorbidities and healthcare resource utilized by patients with CU in Germany, using an anonymized statutory health insurance (SHI) database. Methods Anonymized SHI claims research database of the Institute for Applied Health Research, Berlin [InGef] (01 January 2015–30 September 2018) was used to analyse insured individuals with a confirmed diagnosis of CU (ICD‐10‐GM codes). Twelve‐month diagnosed prevalence and incidence, comorbidities (vs. atopic dermatitis and psoriasis), and healthcare utilization by patients with CU were investigated. Results Of 4 693 772 individuals of all ages listed in the database, 3 538 540 were observable during 2017. Overall, 17 524 patients (˜0.5%) were diagnosed with CU; chronic spontaneous urticaria (CSU: 71.2%), chronic inducible urticaria (CIndU: 19.7%), CSU+CIndU (9.1%). Females, vs. males, had higher diagnosed prevalence (0.62% vs. 0.37%) and diagnosed incidence (0.18% vs. 0.11%) of CU among all patients. Patients most frequently visited general practitioners (41.3% of total visits). Hypertensive diseases (43.5%), lipoprotein metabolism disorders (32.1%) and affective disorders (26.0%) were the most frequently reported comorbidities of special interest. Rates of most comorbidities of special interests were similar to atopic dermatitis and psoriasis patients, and all higher vs. overall population. More than half (54.1%) of all CU patients were not prescribed any treatment. Second‐generation H 1 ‐antihistamines were the most commonly prescribed medication for adult (17.9%) and paediatric (27.9%) patients. Patients with CIndU (paediatric, 15.5%; adult, 7.8%) were more often hospitalized versus patients with CSU (paediatric, 9.9%; adult, 4.6%). Conclusions In Germany, prevalence of CU along with multiple comorbidities may pose increased burden on the healthcare system. Awareness of adhering to treatment guidelines, and aiming for complete control of urticaria, needs to be driven and may improve outcomes