Convergence and Gibbs' phenomenon in cubic spline interpolation of discontinuous functions

AbstractConvergence of cubic spline interpolation for discontinuous functions are investigated. It is shown that the complete cubic spline interpolation of the Heaviside step function converges in the Lp-norm at rate O(h1p) for quasi-uniform meshes when 1⩽p<∞, and diverges in the L∞-norm when the uniform meshes are used. No matter how small the uniform mesh size is, the complete cubic spline interpolation always oscillates near the discontinuity. Although this oscillation decays exponentially away from the discontinuous point, the maximum overshoot is not decreasing. Especially, we obtain the asymptotic maximum overshoot when the uniform mesh size goes to zero. The knowledge on the Heaviside function is utilized to discuss convergence properties of cubic spline interpolation for functions with isolated discontinuous points

Short chain fatty acids potently induce latent HIV-1 in T-cells by activating P-TEFb and multiple histone modifications

AbstractHIV patients with severe periodontitis have high levels of residual virus in their saliva and plasma despite effective therapy (HAART). Multiple short chain fatty acids (SCFAs) from periodontal pathogens reactivate HIV-1 in both Jurkat and primary T-cell models of latency. SCFAs not only activate positive transcription elongation factor b (P-TEFb), which is an essential cellular cofactor for Tat, but can also reverse chromatin blocks by inducing histone modifications. SCFAs simultaneously increase histone acetylation by inhibiting class-1/2 histone deacetylases (HDACs) and decrease repressive histone tri-methylation at the proviral LTR by downregulating expression of the class-3 HDAC sirtuin-1 (SIRT1), and the histone methyltransferases enhancer of Zeste homolog 2 (EZH2) and suppressor of variegation 3–9 homolog 1 (SUV39H1). Our findings provide a mechanistic link between periodontal disease and enhanced HIV-1 replication, and suggest that treatment of periodontal disease, or blocking the activities of SCFAs, will have a therapeutic benefit for HIV patients

Identification of fungal pathogens to control postharvest passion fruit (Passiflora edulis) decays and multi-omics comparative pathway analysis reveals purple is more resistant to pathogens than a yellow cultivar

Production of passion fruit (Passiflora edulis) is restricted by postharvest decay, which limits the storage period. We isolated, identified, and characterized fungal pathogens causing decay in two passion fruit cultivars during two fruit seasons in China. Morphological characteristics and nucleotide sequences of ITS-rDNA regions identified eighteen isolates, which were pathogenic on yellow and purple fruit. Fusarium kyushuense, Fusarium concentricum, Colletotrichum truncatum, and Alternaria alternata were the most aggressive species. Visible inspections and comparative analysis of the disease incidences demonstrated that wounded and non-wounded yellow fruit were more susceptible to the pathogens than the purple fruit. Purple cultivar showed higher expression levels of defense-related genes through expression and metabolic profiling, as well as significantly higher levels of their biosynthesis pathways. We also found fungi with potential beneficial features for the quality of fruits. Our transcriptomic and metabolomics data provide a basis to identify potential targets to improve the pathogen resistance of the susceptible yellow cultivar. The identified fungi and affected features of the fruit of both cultivars provide important information for the control of pathogens in passion fruit industry and postharvest storage

DualRing: Generic Construction of Ring Signatures with Efficient Instantiations

We introduce a novel generic ring signature construction, called DualRing, which can be built from several canonical identification schemes (such as Schnorr identification). DualRing differs from the classical ring signatures by its formation of two rings: a ring of commitments and a ring of challenges. It has a structural difference from the common ring signature approaches based on accumulators or zero-knowledge proofs of the signer index. Comparatively, DualRing has a number of unique advantages. Considering the DL-based setting by using Schnorr identification scheme, our DualRing structure allows the signature size to be compressed into logarithmic size via an argument of knowledge system such as Bulletproofs. We further improve on the Bulletproofs argument system to eliminate about half of the computation while maintaining the same proof size. We call this Sum Argument and it can be of independent interest. This DL-based construction, named DualRing-EC, using Schnorr identification with Sum Argument has the shortest ring signature size in the literature without using trusted setup. Considering the lattice-based setting, we instantiate DualRing by a canonical identification based on M-LWE and M-SIS. In practice, we achieve the shortest lattice-based ring signature, named DualRing-LB, when the ring size is between 4 and 2000. DualRing-LB is also 5x faster in signing and verification than the fastest lattice-based scheme by Esgin et al. (CRYPTO\u2719)

Mycobacterial catalase–peroxidase is a tissue antigen and target of the adaptive immune response in systemic sarcoidosis

Sarcoidosis is a disease of unknown etiology characterized by noncaseating epithelioid granulomas, oligoclonal CD4+ T cell infiltrates, and immune complex formation. To identify pathogenic antigens relevant to immune-mediated granulomatous inflammation in sarcoidosis, we used a limited proteomics approach to detect tissue antigens that were poorly soluble in neutral detergent and resistant to protease digestion, consistent with the known biochemical properties of granuloma-inducing sarcoidosis tissue extracts. Tissue antigens with these characteristics were detected with immunoglobulin (Ig)G or F(ab′)2 fragments from the sera of sarcoidosis patients in 9 of 12 (75%) sarcoidosis tissues (150–160, 80, or 60–64 kD) but only 3 of 22 (14%) control tissues (all 62–64 kD; P = 0.0006). Matrix-assisted laser desorption/ionization time of flight mass spectrometry identified Mycobacterium tuberculosis catalase–peroxidase (mKatG) as one of these tissue antigens. Protein immunoblotting using anti-mKatG monoclonal antibodies independently confirmed the presence of mKatG in 5 of 9 (55%) sarcoidosis tissues but in none of 14 control tissues (P = 0.0037). IgG antibodies to recombinant mKatG were detected in the sera of 12 of 25 (48%) sarcoidosis patients compared with 0 of 11 (0%) purified protein derivative (PPD)− (P = 0.0059) and 4 of 10 (40%) PPD+ (P = 0.7233) control subjects, suggesting that remnant mycobacterial catalase–peroxidase is one target of the adaptive immune response driving granulomatous inflammation in sarcoidosis

Perspectives on the scientific legacy of J. Philip Grime

Perhaps as much as any other scientist in the 20th century, J.P. Grime transformed the study of plant ecology and helped shepherd the field toward international prominence as a nexus of ideas related to global environmental change. Editors at the Journal of Ecology asked a group of senior plant ecologists to comment on Grime's scientific legacy. This commentary piece includes individual responses of 14 scientists from around the world attesting to Grime's foundational role in plant functional ecology, including his knack for sparking controversy, his unique approach to theory formulation involving clever experiments and standardized trait measurements of large numbers of species, and the continued impact of his work on ecological science and policy

Cross sections of the 144

Cross sections of the 144Sm(n,α)141Nd and 66Zn(n,α)63Ni reactions were measured at En = 4.0, 5.0 and 6.0 MeV performed at the 4.5-MV Van de Graaff Accelerator of Peking University, China. A double-section gridded ionization chamber was used to detect the alpha particles. The foil samples of 144Sm2O3 and enriched 66Zn were placed at the common cathode plate of the chamber. Monoenergetic neutrons were produced by a deuterium gas target through the 2H(d,n)3He reaction. The neutron flux was monitored by a BF3 long counter. Cross sections of the 238U(n,f) reaction were used as the standard to perform the (n,α) reaction measurement. Present results are compared with existing measurements and evaluations. They are generally in agreement with TALYS-1.6 code calculations. For the 144Sm(n,α)141Nd reaction our measurements support the data of JEF-2.2. For the 66Zn(n,α)63Ni reaction present results support the data of EAF-2010 and TENDL-2015 data

Shape transitions far from stability: The nucleus 58Cr

Abstract Excited states up to I π = 8 + in the neutron-rich nucleus 58Cr have been identified by using a new experimental setup composed of the large acceptance magnetic spectrometer PRISMA and the highly efficient γ-detector array CLARA. Interestingly, the excitation energy sequence of the ground-state band follows the one expected by the E ( 5 ) dynamical symmetry for a nucleus at the critical point of the shape phase transition from a spherical vibrator ( U ( 5 ) ) to a γ-soft rotor ( O ( 6 ) ). For the first time, in the same physical system, large scale shell-model calculations in the full fp shell are compared to the E ( 5 ) analytical model results and to the Interacting Boson Model. The theoretical results are in excellent agreement with the present data