Optimal space-time adaptive wavelet methods for degenerate parabolic PDEs

We analyze parabolic PDEs with certain type of weakly singular or degenerate time-dependent coefficients and prove existence and uniqueness of weak solutions in an appropriate sense. A localization of the PDEs to a bounded spatial domain is justified. For the numerical solution a space-time wavelet discretization is employed. An optimality result for the iterative solution of the arising systems can be obtained. Finally, applications to fractional Brownian motion models in option pricing are presente

Wavelet solution of variable order pseudodifferential equations

Sobolev spaces H m(x)(I) of variable order 0<m(x)<1 on an interval I⊂ℝ arise as domains of Dirichlet forms for certain quadratic, pure jump Feller processes X t∈ℝ with unbounded, state-dependent intensity of small jumps. For spline wavelets with complementary boundary conditions, we establish multilevel norm equivalences in H m(x)(I) and prove preconditioning and wavelet matrix compression results for the variable order pseudodifferential generators A of X. Sufficient conditions on A to satisfy a Gårding inequality in H m(x)(I) and time-analyticity of the semigroup T t associated with the Feller process X t are established. As application, wavelet-based algorithms of log-linear complexity are obtained for the valuation of contingent claims on pure jump Feller-Lévy processes X t with state-dependent jump intensity by numerical solution of the corresponding Kolmogoroff equation

The Effective Potential of the N=0* Yang-Mills Theory

We study the \N=4 SYM theory with SU(N) gauge group in the large N limit, deformed by giving equal mass to the four adjoint fermions. With this modification, a potential is dynamically generated for the six scalars in the theory, \phi^i. We show that the resulting theory is stable (perturbatively in the 't Hooft coupling), and that there are some indications that =0 is the vacuum of the theory. Using the AdS/CFT correspondence, we compare the results to the corresponding supergravity computation, i.e. brane probing a deformed AdS_5 x S^5 background, and we find qualitative agreement.Comment: 12 pages, 2 figures, version to appear in JHE

A Fermi Surface Model for Large Supersymmetric AdS_5 Black Holes

We identify a large family of 1/16 BPS operators in N=4 SYM that qualitatively reproduce the relations between charge, angular momentum and entropy in regular supersymmetric AdS_5 black holes when the main contribution to their masses is given by their angular momentum.Comment: 32 pages, 6 figures, LaTeX uses JHEP3 class; ver 2- added acknowledgment, minor change

Expanding the scope of Cu(I) Catalyzed “Click Chemistry” with abnormal NHCs: three-fold click to Tris-Triazoles

Ho NKT, Reichmann SO, Rottschäfer D, Herbst-Irmer R, Ghadwal R. Expanding the scope of Cu(I) Catalyzed “Click Chemistry” with abnormal NHCs: three-fold click to Tris-Triazoles. Catalysts. 2017;7(9): 262.Cationic copper(I) complexes [Cu(aIPrPh)(IPr)]I (3) and [Cu(aIPrPh)2]I (4) featuring an abnormal N-heterocyclic carbene (aNHC) (aIPrPh = 1,3-bis(2,6-diisopropylphenyl)-2-phenyl- imidazol-4-ylidene) and/or an NHC (IPr = 1,3-Bis(2,6-diisopropylphenyl)imidazol-2-ylidene) ligand(s) are reported. Treatment of Cu(aIPrPh)I (2) with IPr affords complex 3. Reaction of (IPrPh)I (1) (IPrPh = 1,3-bis(2,6-diisopropylphenyl)-2-phenyl-imidazolium) with CuI in the presence of K{N(SiMe3)2} leads to the formation of 4. Complexes 3 and 4 represent rare examples of mixed aNHC-NHC and bis-aNHC metal complexes, respectively. They are characterized by elemental analysis, NMR spectroscopic, and mass spectrometric studies. The solid-state molecular structures of 3 and 4 have been determined by single crystal X-ray diffraction analyses. The catalytic activity of 2, 3, and 4 has been investigated in the [3+2] cycloaddition of alkynes and organic azides, affording triazole derivatives in an almost quantitative yield. Notably, complexes 2, 3, and 4 are excellent catalysts for the three-fold cycloaddition of a tris-azide with various alkynes. This catalytic protocol offers a high yield access to tris-triazoles in a shorter reaction time and considerably reduces the experimental work-up compared to the classical synthetic method

Thermal AdS(3), BTZ and competing winding modes condensation

We study the thermal physics of AdS(3) and the BTZ black hole when embedded in String theory. The exact calculation of the Hagedorn temperature in TAdS(3) is reinterpreted as the appearance of a winding tachyon both in AdS(3) and BTZ. We construct a dual framework for analyzing the phases of the system. In this dual framework, tachyon condensation and geometric capping appear on the same footing, bridging the usual gap of connecting tachyon condensation to modifications of geometry. This allows us to construct in a natural way a candidate for the unstable phase, analogous to a small black hole in higher dimensions. Additional peculiar effects associated with the Hagedorn temperature and the Hawking-Page transition, some to do with the asymptotic structure of AdS(3) and some with strong curvature effects, are analyzed and explained.Comment: 40 pages, 5 figures, JHEP3 format. v2: added references, minor corrections and clarification

Skin swabbing is a refined technique to collect DNA from model fish species

Model fish species such as sticklebacks and zebrafish are frequently used in studies that require DNA to be collected from live animals. This is typically achieved by fin clipping, a procedure that is simple and reliable to perform but that can harm fish. An alternative procedure to sample DNA involves swabbing the skin to collect mucus and epithelial cells. Although swabbing appears to be less invasive than fin clipping, it still requires fish to be netted, held in air and handled—procedures that can cause stress. In this study we combine behavioural and physiological analyses to investigate changes in gene expression, behaviour and welfare after fin clipping and swabbing. Swabbing led to a smaller change in cortisol release and behaviour on the first day of analysis compared to fin clipping. It also led to less variability in data suggesting that fewer animals need to be measured after using this technique. However, swabbing triggered some longer term changes in zebrafish behaviour suggesting a delayed response to sample collection. Skin swabbing does not require the use of anaesthetics and triggers fewer changes in behaviour and physiology than fin clipping. It is therefore a more refined technique for DNA collection with the potential to improve fish health and welfare

Ruthenium polypyridyl complexes and their modes of interaction with DNA : is there a correlation between these interactions and the antitumor activity of the compounds?

Various interaction modes between a group of six ruthenium polypyridyl complexes and DNA have been studied using a number of spectroscopic techniques. Five mononuclear species were selected with formula [Ru(tpy) L1L2](2-n)?, and one closely related dinuclear cation of formula [{Ru(apy)(tpy)}2{l-H2N(CH2)6NH2}]4?. The ligand tpy is 2,20:60,200-terpyridine and the ligand L1 is a bidentate ligand, namely, apy (2,20-azobispyridine), 2-phenylazopyridine, or 2-phenylpyridinylmethylene amine. The ligand L2 is a labile monodentate ligand, being Cl-, H2O, or CH3CN. All six species containing a labile L2 were found to be able to coordinate to the DNA model base 9-ethylguanine by 1H NMR and mass spectrometry. The dinuclear cationic species, which has no positions available for coordination to a DNA base, was studied for comparison purposes. The interactions between a selection of four representative complexes and calf-thymus DNA were studied by circular and linear dichroism. To explore a possible relation between DNA-binding ability and toxicity, all compounds were screened for anticancer activity in a variety of cancer cell lines, showing in some cases an activity which is comparable to that of cisplatin. Comparison of the details of the compound structures, their DNA binding, and their toxicity allows the exploration of structure–activity relationships that might be used to guide optimization of the activity of agents of this class of compounds

On Field Theory Thermalization from Gravitational Collapse

Motivated by its field theory interpretation, we study gravitational collapse of a minimally coupled massless scalar field in Einstein gravity with a negative cosmological constant. After demonstrating the accuracy of the numerical algorithm for the questions we are interested in, we investigate various aspects of the apparent horizon formation. In particular, we study the time and radius of the apparent horizon formed as functions of the initial Gaussian profile for the scalar field. We comment on several aspects of the dual field theory picture.Comment: 31 pages, 17 figures; V2 Some figures corrected, minor revision. arXiv admin note: substantial text overlap with arXiv:1106.233

Roles of residues in the interface of transient protein-protein complexes before complexation

Transient protein-protein interactions play crucial roles in all facets of cellular physiology. Here, using an analysis on known 3-D structures of transient protein-protein complexes, their corresponding uncomplexed forms and energy calculations we seek to understand the roles of protein-protein interfacial residues in the unbound forms. We show that there are conformationally near invariant and evolutionarily conserved interfacial residues which are rigid and they account for ∼65% of the core interface. Interestingly, some of these residues contribute significantly to the stabilization of the interface structure in the uncomplexed form. Such residues have strong energetic basis to perform dual roles of stabilizing the structure of the uncomplexed form as well as the complex once formed while they maintain their rigid nature throughout. This feature is evolutionarily well conserved at both the structural and sequence levels. We believe this analysis has general bearing in the prediction of interfaces and understanding molecular recognition