A Cauchy Integral Related to a Robot-safety Device System

We introduce a robot-safety device system attended by two different repairmen. The twin system is characterized by the natural feature of cold standby and by an admissible “risky” state. In order to analyse the random behaviour of the entire system (robot, safety device, repair facility) we employ a stochastic process endowed with probability measures satisfying general Hokstad-type differential equations. The solution procedure is based on the theory of sectionally holomorphic functions, characterized by a Cauchy-type integral defined as a Cauchy principal value in double sense. An application of the Sokhotski-Plemelj formulae determines the long-run availability of the robot-safety device. Finally, we consider the particular but important case of deterministic repair

On Gaver's parallel system

Gaver’s parallel system (and its variants) has received considerable attention in the literature. The Laplace-transform (LT) of the survival function, corresponding to the underlying systems, has been derived by various (alternative) methods. Unfortunately, little-to-no attention has been paid to invert the corresponding transform. First, we present a general reliability analysis of Gaver’s basic parallel system (valid for an arbitrary repair time distribution). Then, we formulate some general hints to obtain the numerical inverse. Finally, we propose a tangible methodology to derive the exact inverse in some particular but important cases of non-rotational transforms.Gaver se parallelsisteem (en variante daarvan) is reeds dikwels behandel in die literatuur. Die Laplacetransformasie van die oorlewingsfunksie van die onderliggende sisteme is reeds afgelei op verskillende uiteenlopende wyses. Ongelukkigerwys is min aandag gegee aan die ooreenstemmende inverse transformasie. Ten aanvang word 'n algemene betroubaarheidsontleding van Gaver se basiese parallelsisteem voorgehou (geldig vir 'n arbitrêre hersteltyd-verdeling). Dit word gevolg deur wenke vir bepaling van die numeriese inverse. Ten slotte word 'n tasbare metodologie vir die afleiding van die presiese inverse vir sekere belangrike nie-rotasionele transformasies voorgestel.http://sajie.journals.ac.z

Static solitons with non-zero Hopf number

We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We explicitly compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons.Comment: 13 pages, RevTeX, 7 Postscript figures, minor changes have been made, a reference has been corrected and a figure replace

31st Annual Meeting and Associated Programs of the Society for Immunotherapy of Cancer (SITC 2016) : part two

Background The immunological escape of tumors represents one of the main ob- stacles to the treatment of malignancies. The blockade of PD-1 or CTLA-4 receptors represented a milestone in the history of immunotherapy. However, immune checkpoint inhibitors seem to be effective in specific cohorts of patients. It has been proposed that their efficacy relies on the presence of an immunological response. Thus, we hypothesized that disruption of the PD-L1/PD-1 axis would synergize with our oncolytic vaccine platform PeptiCRAd. Methods We used murine B16OVA in vivo tumor models and flow cytometry analysis to investigate the immunological background. Results First, we found that high-burden B16OVA tumors were refractory to combination immunotherapy. However, with a more aggressive schedule, tumors with a lower burden were more susceptible to the combination of PeptiCRAd and PD-L1 blockade. The therapy signifi- cantly increased the median survival of mice (Fig. 7). Interestingly, the reduced growth of contralaterally injected B16F10 cells sug- gested the presence of a long lasting immunological memory also against non-targeted antigens. Concerning the functional state of tumor infiltrating lymphocytes (TILs), we found that all the immune therapies would enhance the percentage of activated (PD-1pos TIM- 3neg) T lymphocytes and reduce the amount of exhausted (PD-1pos TIM-3pos) cells compared to placebo. As expected, we found that PeptiCRAd monotherapy could increase the number of antigen spe- cific CD8+ T cells compared to other treatments. However, only the combination with PD-L1 blockade could significantly increase the ra- tio between activated and exhausted pentamer positive cells (p= 0.0058), suggesting that by disrupting the PD-1/PD-L1 axis we could decrease the amount of dysfunctional antigen specific T cells. We ob- served that the anatomical location deeply influenced the state of CD4+ and CD8+ T lymphocytes. In fact, TIM-3 expression was in- creased by 2 fold on TILs compared to splenic and lymphoid T cells. In the CD8+ compartment, the expression of PD-1 on the surface seemed to be restricted to the tumor micro-environment, while CD4 + T cells had a high expression of PD-1 also in lymphoid organs. Interestingly, we found that the levels of PD-1 were significantly higher on CD8+ T cells than on CD4+ T cells into the tumor micro- environment (p < 0.0001). Conclusions In conclusion, we demonstrated that the efficacy of immune check- point inhibitors might be strongly enhanced by their combination with cancer vaccines. PeptiCRAd was able to increase the number of antigen-specific T cells and PD-L1 blockade prevented their exhaus- tion, resulting in long-lasting immunological memory and increased median survival

Long-run availability of a priority system: a numerical approach

We consider a two-unit cold standby system attended by two repairmen and subjected to a priority rule. In order to describe the random behavior of the twin system, we employ a stochastic process endowed with state probability functions satisfying coupled Hokstad-type differential equations. An explicit evaluation of the exact solution is in general quite intricate. Therefore, we propose a numerical solution of the equations. Finally, particular but important repair time distributions are involved to analyze the long-run availability of the T-system. Numerical results are illustrated by adequate computer-plotted graphs