Lie symmetries of (1+2) nonautonomous evolution equations in Financial Mathematics

We analyse two classes of $(1+2)$ evolution equations which are of special interest in Financial Mathematics, namely the Two-dimensional Black-Scholes Equation and the equation for the Two-factor Commodities Problem. Our approach is that of Lie Symmetry Analysis. We study these equations for the case in which they are autonomous and for the case in which the parameters of the equations are unspecified functions of time. For the autonomous Black-Scholes Equation we find that the symmetry is maximal and so the equation is reducible to the $(1+2)$ Classical Heat Equation. This is not the case for the nonautonomous equation for which the number of symmetries is submaximal. In the case of the two-factor equation the number of symmetries is submaximal in both autonomous and nonautonomous cases. When the solution symmetries are used to reduce each equation to a $(1+1)$ equation, the resulting equation is of maximal symmetry and so equivalent to the $(1+1)$ Classical Heat Equation.Comment: 15 pages, 1 figure, to be published in Mathematics in the Special issue "Mathematical Finance

Ion yields and erosion rates for Si1−xGex(0x1) ultralow energy O2+ secondary ion mass spectrometry in the energy range of 0.25–1 keV

We report the SIMS parameters required for the quantitative analysis of Si1−xGex across the range of 0 ≤ x ≤ 1 when using low energy O2+ primary ions at normal incidence. These include the silicon and germanium secondary ion yield [i.e., the measured ion signal (ions/s)] and erosion rate [i.e., the speed at which the material sputters (nm/min)] as a function of x. We show that the ratio Rx of erosion rates, Si1−xGex/Si, at a given x is almost independent of beam energy, implying that the properties of the altered layer are dominated by the interaction of oxygen with silicon. Rx shows an exponential dependence on x. Unsurprisingly, the silicon and germanium secondary ion yields are found to depart somewhat from proportionality to (1−x) and x, respectively, although an approximate linear relationship could be used for quantification across around 30% of the range of x (i.e., a reference material containing Ge fraction x would give reasonably accurate quantification across the range of ±0.15x). Direct comparison of the useful (ion) yields [i.e., the ratio of ion yield to the total number of atoms sputtered for a particular species (ions/atom)] and the sputter yields [i.e., the total number of atoms sputtered per incident primary ion (atoms/ions)] reveals a moderate matrix effect where the former decrease monotonically with increasing x except at the lowest beam energy investigated (250 eV). Here, the useful yield of Ge is found to be invariant with x. At 250 eV, the germanium ion and sputter yields are proportional to x for all x

Echoes of multiple outbursts of Sagittarius A* revealed by Chandra

The relatively rapid spatial and temporal variability of the X-ray radiation from some molecular clouds near the Galactic center shows that this emission component is due to the reflection of X-rays generated by a source that was luminous in the past, most likely the central supermassive black hole, Sagittarius A*. Studying the evolution of the molecular cloud reflection features is therefore a key element to reconstruct Sgr A*'s past activity. The aim of the present work is to study this emission on small angular scales in order to characterize the source outburst on short time scales. We use Chandra high-resolution data collected from 1999 to 2011 to study the most rapid variations detected so far, those of clouds between 5' and 20' from Sgr A* towards positive longitudes. Our systematic spectral-imaging analysis of the reflection emission, notably of the Fe Kalpha line at 6.4 keV and its associated 4-8 keV continuum, allows us to characterize the variations down to 15" angular scale and 1-year time scale. We reveal for the first time abrupt variations of few years only and in particular a short peaked emission, with a factor of 10 increase followed by a comparable decrease, that propagates along the dense filaments of the Bridge cloud. This 2-year peaked feature contrasts with the slower 10-year linear variations we reveal in all the other molecular structures of the region. Based on column density constraints, we argue that these two different behaviors are unlikely to be due to the same illuminating event. The variations are likely due to a highly variable active phase of Sgr A* sometime within the past few hundred years, characterized by at least two luminous outbursts of a few-year time scale and during which the Sgr A* luminosity went up to at least 10^39 erg/s.Comment: 17 pages, 16 figures, Accepted for publication in Astronomy & Astrophysic

Barriers to reporting non-motor symptoms to health-care providers in people with Parkinson's

Background: Non-motor symptoms (NMS) are common in Parkinson's disease (PD) and cause significant distress. A high rate of non-declaration of NMS by patients to healthcare providers (HCP) means that many NMS remain untreated. Current understanding of the factors preventing disclosure of NMS to HCPs is limited. The present study aimed to i) further assess the prevalence of NMS and associated distress, ii) establish current rates of NMS reporting across a range of sources, and iii) explore overall and any symptom specific barriers to help-seeking for NMS. Methods: 358 PD patients completed a cross-sectional survey of NMS severity, reporting and barriers to help-seeking. A series of Generalised Estimating Equations were used to determine whether barriers were symptom specific. Results: A mean of 10.5 NMS were reported by each patient. Rates of non-reporting of NMS ranged from 15 to 72% of those experiencing distressing symptoms. The most commonly reported barriers to help-seeking were acceptance of symptoms; lack of awareness that a symptom was associated with PD, and belief that no effective treatments were available. Symptom specific barriers were found for sexual dysfunction (embarrassment), unexplained pain and urinary problems (belief about lack of treatment availability). Conclusion: A diverse range of barriers prevent PD patients reporting NMS to HCPs and these barriers differ between NMS. The study provides the foundations for developing interventions to increase reporting by targeting individual NMS. Increasing rates of help-seeking for NMS by patients to their Parkinson's healthcare providers will increase appropriate clinical care which may improve quality of life and well-being

Synaptic tagging and capture : differential role of distinct calcium/calmodulin kinases in protein synthesis-dependent long-term potentiation

Weakly tetanized synapses in area CA1 of the hippocampus that ordinarily display long-term potentiation lasting ~3 h (called early-LTP) will maintain a longer-lasting change in efficacy (late-LTP) if the weak tetanization occurs shortly before or after strong tetanization of an independent, but convergent, set of synapses in CA1. The synaptic tagging and capture hypothesis explains this heterosynaptic influence on persistence in terms of a distinction between local mechanisms of synaptic tagging and cell-wide mechanisms responsible for the synthesis, distribution, and capture of plasticity-related proteins (PRPs). We now present evidence that distinct CaM kinase (CaMK) pathways serve a dissociable role in these mechanisms. Using a hippocampal brain-slice preparation that permits stable long-term recordings in vitro for >10 h and using hippocampal cultures to validate the differential drug effects on distinct CaMK pathways, we show that tag setting is blocked by the CaMK inhibitor KN-93 (2-[N-(2-hydroxyethyl)]-N-(4-methoxybenzenesulfonyl)amino-N-(4-chlorocinnamyl)-N-methylbenzylamine) that, at low concentration, is more selective for CaMKII. In contrast, the CaMK kinase inhibitor STO-609 [7H-benzimidazo(2,1-a)benz(de)isoquinoline-7-one-3-carboxylic acid] specifically limits the synthesis and/or availability of PRPs. Analytically powerful three-pathway protocols using sequential strong and weak tetanization in varying orders and test stimulation over long periods of time after LTP induction enable a pharmacological dissociation of these distinct roles of the CaMK pathways in late-LTP and so provide a novel framework for the molecular mechanisms by which synaptic potentiation, and possibly memories, become stabilized

Optimization of the derivative expansion in the nonperturbative renormalization group

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be unambiguously implemented at order $\partial^2$ of the derivative expansion. This approach allows us to select optimized cut-off functions and to improve the accuracy of the critical exponents $\nu$ and $\eta$. The convergence of the field expansion is also analyzed. We show in particular that its optimization does not coincide with optimization of the accuracy of the critical exponents.Comment: 13 pages, 9 PS figures, published versio

The XMM-Newton view of the central degrees of the Milky Way

The deepest XMM-Newton mosaic map of the central 1.5 deg of the Galaxy is presented, including a total of about 1.5 Ms of EPIC-pn cleaned exposures in the central 15" and about 200 ks outside. This compendium presents broad-band X-ray continuum maps, soft X-ray intensity maps, a decomposition into spectral components and a comparison of the X-ray maps with emission at other wavelengths. Newly-discovered extended features, such as supernova remnants (SNRs), superbubbles and X-ray filaments are reported. We provide an atlas of extended features within +-1 degree of Sgr A*. We discover the presence of a coherent X-ray emitting region peaking around G0.1-0.1 and surrounded by the ring of cold, mid-IR-emitting material known from previous work as the "Radio Arc Bubble" and with the addition of the X-ray data now appears to be a candidate superbubble. Sgr A's bipolar lobes show sharp edges, suggesting that they could be the remnant, collimated by the circumnuclear disc, of a SN explosion that created the recently discovered magnetar, SGR J1745-2900. Soft X-ray features, most probably from SNRs, are observed to fill holes in the dust distribution, and to indicate a direct interaction between SN explosions and Galactic center (GC) molecular clouds. We also discover warm plasma at high Galactic latitude, showing a sharp edge to its distribution that correlates with the location of known radio/mid-IR features such as the "GC Lobe". These features might be associated with an inhomogeneous hot "atmosphere" over the GC, perhaps fed by continuous or episodic outflows of mass and energy from the GC region.Comment: MNRAS published online. See www.mpe.mpg.de/heg/gc/ for a higher resolution version of the figure