Rota-Baxter algebras and new combinatorial identities

The word problem for an arbitrary associative Rota-Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects, particularly of interest in physics, are indicated.Comment: 8 pages, improved versio

Cumulant-cumulant relations in free probability theory from Magnus' expansion

Relations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several distinct families of cumulants corresponding to different types of independences: free, Boolean and monotone. Relations among those cumulants have been studied recently. In this work we focus on the problem of expressing with a closed formula multivariate monotone cumulants in terms of free and Boolean cumulants. In the process we introduce various constructions and statistics on non-crossing partitions. Our approach is based on a pre-Lie algebra structure on cumulant functionals. Relations among cumulants are described in terms of the pre-Lie Magnus expansion combined with results on the continuous Baker-Campbell-Hausdorff formula due to A. Murua

Low-Light Image Enhancement Based on U-Net and Haar Wavelet Pooling

The inevitable environmental and technical limitations of image capturing has as a consequence that many images are frequently taken in inadequate and unbalanced lighting conditions. Low-light image enhancement has been very popular for improving the visual quality of image representations, while low-light images often require advanced techniques to improve the perception of information for a human viewer. One of the main objectives in increasing the lighting conditions is to retain patterns, texture, and style with minimal deviations from the considered image. To this direction, we propose a low-light image enhancement method with Haar wavelet-based pooling to preserve texture regions and increase their quality. The presented framework is based on the U-Net architecture to retain spatial information, with a multi-layer feature aggregation (MFA) method. The method obtains the details from the low-level layers in the stylization processing. The encoder is based on dense blocks, while the decoder is the reverse of the encoder, and extracts features that reconstruct the image. Experimental results show that the combination of the U-Net architecture with dense blocks and the wavelet-based pooling mechanism comprises an efficient approach in low-light image enhancement applications. Qualitative and quantitative evaluation demonstrates that the proposed framework reaches state-of-the-art accuracy but with less resources than LeGAN

TLR2 polymorphisms, Arg753Gln and Arg677Trp, are not associated with increased burden of tuberculosis in Indian patients

<p>Abstract</p> <p>Background</p> <p>In view of the role of TLR2 activation in host defense against mycobacteria, the present study was conducted to examine whether TLR2 polymorphisms could account for the increased prevalence of tuberculosis in Indian patients. Detection of such polymorphisms would help in assessing the risk of developing active tuberculosis among contacts or HIV positive patients and in identifying candidates for chemoprophylaxis.</p> <p>Findings</p> <p>One hundred patients with tuberculosis and 100 controls were investigated for the presence of two TLR2 polymorphisms, viz. Arg753Gln and Arg677Trp, using PCR-RFLP of a 340 bp region of the TLR2 gene, followed by DNA sequencing of a randomly selected group of 35 patients. While these polymorphisms were found to be non-existent in our study groups, we observed a novel polymorphism Phe749Tyr in 2 patients. However, this polymorphism was associated with negligible deviation in Delphi electrostatic potential and structural alignment from the wild-type TLR2 protein, making it an unlikely candidate for any significant structural or functional alteration at the protein level.</p> <p>Conclusion</p> <p>Hence we conclude that, contrary to reported associations in other populations, TLR2 polymorphisms are not responsible for the increased prevalence of TB in the Indian population.</p

Atmospheric Cold Plasma Inactivation of Salmonella and Escherichia coli on the Surface of Golden Delicious Apples

The contamination of fruits with human pathogens is a reoccurring concern in the fresh produce industry. Atmospheric cold plasma (ACP) is a potential alternate to customary approaches for non-thermal decontamination of foods. In this study, the efficacy of a dielectric barrier discharge ACP system against Salmonella (Salmonella Typhimurium, ATCC 13311; Salmonella Choleraesuis, ATCC 10708) and Escherichia coli (ATCC 25922, ATCC 11775) was explored. For each bacteria, a two-strain mixture at 8 log10 CFU/ml was spot inoculated on the surface of Golden Delicious apples, air dried, and exposed to ACP at a fixed distance of 35 mm, input power of 200 W for 30, 60, 120, 180, and 240 s. Bacterial inactivation was achieved in all treatment times with highest reduction of 5.3 log10 CFU/cm2 for Salmonella and 5.5 log10 CFU/cm2 for E. coli. Our results showed that reductions were interrelated to exposure time and ranged from 1.3 to 5.3 and 0.6 to 5.5 log10 CFU/cm2 for Salmonella and E. coli, respectively. Salmonella and E. coli significantly decreased (\u3e5.0 log) at 180 and 240 s as compared to 30, 60, and 120 s exposure. Microbial inactivation data was modeled by using Weibull distribution. These findings demonstrate the potential of ACP as a postharvest technology to effectively reduce pathogens on apples, with reference to Salmonella and E. coli

Renormalization: a quasi-shuffle approach

In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs, with values in a Rota-Baxter algebra of amplitudes. We associate in this paper to any such algebra a universal semi-group (different in nature from the Connes-Marcolli "cosmical Galois group"). Its action on the physical amplitudes associated to Feynman graphs produces the expected operations: Bogoliubov's preparation map, extraction of divergences, renormalization. In this process a key role is played by commutative and noncommutative quasi-shuffle bialgebras whose universal properties are instrumental in encoding the renormalization process

Exponential renormalization

Moving beyond the classical additive and multiplicative approaches, we present an "exponential" method for perturbative renormalization. Using Dyson's identity for Green's functions as well as the link between the Faa di Bruno Hopf algebra and the Hopf algebras of Feynman graphs, its relation to the composition of formal power series is analyzed. Eventually, we argue that the new method has several attractive features and encompasses the BPHZ method. The latter can be seen as a special case of the new procedure for renormalization scheme maps with the Rota-Baxter property. To our best knowledge, although very natural from group-theoretical and physical points of view, several ideas introduced in the present paper seem to be new (besides the exponential method, let us mention the notions of counterfactors and of order n bare coupling constants).Comment: revised version; accepted for publication in Annales Henri Poincar

Cycle-Consistent Adversarial Networks and Fast Adaptive Bi-Dimensional Empirical Mode Decomposition for Style Transfer

Recently, research endeavors have shown the potentiality of Cycle-Consistent Adversarial Networks (CycleGAN) in style transfer. In Cycle-Consistent Adversarial Networks, the consistency loss is introduced to measure the difference between the original images and the reconstructed in both directions, forward and backward. In this work, the combination of Cycle-Consistent Adversarial Networks with Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD) is proposed to perform style transfer on images. In the proposed approach the cycle-consistency loss is modified to include the differences between the extracted Intrinsic Mode Functions (BIMFs) images. Instead of an estimation of pixel-to-pixel difference between the produced and input images, the FABEMD is applied and the extracted BIMFs are involved in the computation of the total cycle loss. This method enriches the computation of the total loss in a content-to-content and style-to-style comparison by connecting the spatial information to the frequency components. The experimental results reveal that the proposed method is efficient and produces qualitative results comparable to state-of-the-art methods

UV-C treatment on the safety of skim milk: Effect on microbial inactivation and cytotoxicity evaluation

The efficacy of UV-C irradiation as a nonthermal processing method for skim milk (SM) was investigated. SM inoculated with two surrogate viruses (MS2 and T1UV), and three bacteria (Escherichia coli ATCC 25922, Salmonella enterica serovar Typhimurium ATCC 13311, and Listeria monocytogenes ATCC 19115) was treated with Deanflow UV-C irradiation, a spiral reactor with the fluid pumped around a central low-pressure mercury UV lamp (40 W) emitting at 254 nm wave-length. A series of known UV doses (0–168.33 mJ·cm2) were delivered to the samples. The microbial loads of MS2, T1UV, E. coli, Salmonella, and Listeria were reduced by more than 5 log10. The inactivation kinetics of all microorganisms were best described by log linear models with a low RMSE and higher coefficient of determination (R2 \u3e 0.95). This study demonstrated that high levels of inactivation of pathogenic particles can be achieved in SM. Practical applications This scientific study provides evidence based data on the advantages of UV-C light in achieving microbial reduction in skim milk. The irradiated skim milk did not show any toxicity on mice liver and intestinal cells. UV-C irradiation is an efficient food preservation technology and offers opportunities for dairy and food processing industries to meet the growing demand from consumers for safer foods. This exploration would provide methodological evidence for commercialization of UV-C processing of milk and dairy based beverages

Time-ordering and a generalized Magnus expansion

Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including however directly a non-trivial initial condition. As a by-product we recover a variant of the time ordering operation, known as T*-ordering. Eventually, placing our results in the general context of Rota-Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations