Canonical Representatives of Morphic Permutations

An infinite permutation can be defined as a linear ordering of the set of natural numbers. In particular, an infinite permutation can be constructed with an aperiodic infinite word over $\{0,\ldots,q-1\}$ as the lexicographic order of the shifts of the word. In this paper, we discuss the question if an infinite permutation defined this way admits a canonical representative, that is, can be defined by a sequence of numbers from [0, 1], such that the frequency of its elements in any interval is equal to the length of that interval. We show that a canonical representative exists if and only if the word is uniquely ergodic, and that is why we use the term ergodic permutations. We also discuss ways to construct the canonical representative of a permutation defined by a morphic word and generalize the construction of Makarov, 2009, for the Thue-Morse permutation to a wider class of infinite words.Comment: Springer. WORDS 2015, Sep 2015, Kiel, Germany. Combinatorics on Words: 10th International Conference. arXiv admin note: text overlap with arXiv:1503.0618

Photophysical properties of halide perovskite CsPb(Br1-xIx)3 thin films and nanowires

This is an accepted manuscript of an article published by Elsevier in Journal of Luminescence on 26/12/2019, available online: https://doi.org/10.1016/j.jlumin.2019.116985 The accepted version of the publication may differ from the final published version.© 2019 Thin films and nanowires based on lead halide perovskites are promising objects for the design of various optoelectronic devices as well as nano- and microlasers. One of the main advantages of such materials is their absorption and photoluminescence spectra tuning across the visible range via the change in their chemical composition, for instance, by substitution of one halide atom (Br) for another one (I) in the crystal lattice of CsPb(Br1-xIx)3. However, this approach gives materials showing unstable photoluminescence behavior caused by light-induced perovskite phase separation under high-intensity excitation at room temperature. In this work, CsPb(Br1-xIx)3 thin films and nanowires are obtained by chemical vapor anion exchange method from their CsPbBr3 counterparts fabricated by improved wet chemical methods. Spontaneous and stimulated emission from the mixed-halide and pristine bromide samples are studied. Tribromide nanowires exhibit lasing with relatively low thresholds (10–100 μJ/cm2) and high Q-factor of the laser mode up to 3500. The temperature dependence of the photoinitiated phase separation in CsPbBr1.5I1.5 samples is investigated, showing that light-induced phase instability of the mixed-halide nanowires can be suppressed at the somewhat higher temperature (250 K) than the value observed for the thin films having a similar chemical composition. The results obtained are important for the optimization of the functioning of optoelectronic devices based on considered perovskite materials.S.V.M. and A.A.Z. thank the Russian Science Foundation (grant 17-73-20336) for the financial support of study of nanostructures. S.V.M. acknowledges funding from the Ministry of Science and Higher Education of the Russian Federation (project 14.Y26.31.0010). M.V. acknowledges funding from the European Regional Development Fund according to the supported activity ‘Research Projects Implemented by World-class Researcher Groups’ under Measure No. 01.2.2-LMT-K-718, grant No. 01.2.2-LMT-K-718-01-0014. G.H. acknowledges ITMO Fellowship Program.Accepted versio

Computer-aided synthesis of dapsone-phytochemical conjugates against dapsone-resistant Mycobacterium leprae

Abstract: Leprosy continues to be the belligerent public health hazard for the causation of high disability and eventual morbidity cases with stable prevalence rates, even with treatment by the on-going multidrug therapy (MDT). Today, dapsone (DDS) resistance has led to fear of leprosy in more unfortunate people of certain developing countries. Herein, DDS was chemically conjugated with five phytochemicals independently as dapsone-phytochemical conjugates (DPCs) based on azo-coupling reaction. Possible biological activities were verified with computational chemistry and quantum mechanics by molecular dynamics simulation program before chemical synthesis and spectral characterizations viz., proton-HNMR, FTIR, UV and LC-MS. The in vivo antileprosy activity was monitored using the ‘mouse-foot-pad propagation method’, with WHO recommended concentration 0.01% mg/kg each DPC for 12 weeks, and the host-toxicity testing of the active DPC4 was seen in cultured-human-lymphocytes in vitro. One-log bacilli cells in DDS-resistant infected mice footpads decreased by the DPC4, and no bacilli were found in the DDS-sensitive mice hind pads. Additionally, the in vitro host toxicity study also confirmed that the DCP4 up to 5,000 mg/L level was safety for oral administration, since a minor number of dead cells were found in red color under a fluorescent microscope. Several advanced bioinformatics tools could help locate the potential chemical entity, thereby reducing the time and resources required for in vitro and in vitro tests. DPC4 could be used in place of DDS in MDT, evidenced from in vivo antileprosy activity and in vitro host toxicity study

Development of 100^{100}Mo-containing scintillating bolometers for a high-sensitivity neutrinoless double-beta decay search

We report recent achievements in the development of scintillating bolometers to search for neutrinoless double-beta decay of $^{100}$Mo. The presented results have been obtained in the framework of the LUMINEU, LUCIFER and EDELWEISS collaborations, and are now part of the R\&D activities towards CUPID (CUORE Update with Particle IDentification), a proposed next-generation double-beta decay experiment based on the CUORE experience. We have developed a technology for the production of large mass ($\sim$1 kg), high optical quality, radiopure zinc and lithium molybdate crystal scintillators (ZnMoO$_4$ and Li$_2$MoO$_4$, respectively) from deeply purified natural and $^{100}$Mo-enriched molybdenum. The procedure is applied for a routine production of enriched crystals. Furthermore, the technology of a single detector module consisting of a large-volume ($\sim 100$~cm$^3$) Zn$^{100}$MoO$_4$ and Li$_2$$^{100}$MoO$_4$ scintillating bolometer has been established, demonstrating performance and radiopurity that are close to satisfy the demands of CUPID. In particular, the FWHM energy resolution of the detectors at 2615 keV --- near the $Q$-value of the double-beta transition of $^{100}$Mo (3034~keV) --- is $\approx$ 4--10~keV. The achieved rejection of $\alpha$-induced dominant background above 2.6~MeV is at the level of more than 99.9\%. The bulk activity of $^{232}$Th ($^{228}$Th) and $^{226}$Ra in the crystals is below 10 $\mu$Bq/kg. Both crystallization and detector technologies favor Li$_2$MoO$_4$, which was selected as a main element for the realization of a CUPID demonstrator (CUPID-0/Mo) with $\sim$7 kg of $^{100}$Mo

Cancer Biomarker Discovery: The Entropic Hallmark

Background: It is a commonly accepted belief that cancer cells modify their transcriptional state during the progression of the disease. We propose that the progression of cancer cells towards malignant phenotypes can be efficiently tracked using high-throughput technologies that follow the gradual changes observed in the gene expression profiles by employing Shannon's mathematical theory of communication. Methods based on Information Theory can then quantify the divergence of cancer cells' transcriptional profiles from those of normally appearing cells of the originating tissues. The relevance of the proposed methods can be evaluated using microarray datasets available in the public domain but the method is in principle applicable to other high-throughput methods. Methodology/Principal Findings: Using melanoma and prostate cancer datasets we illustrate how it is possible to employ Shannon Entropy and the Jensen-Shannon divergence to trace the transcriptional changes progression of the disease. We establish how the variations of these two measures correlate with established biomarkers of cancer progression. The Information Theory measures allow us to identify novel biomarkers for both progressive and relatively more sudden transcriptional changes leading to malignant phenotypes. At the same time, the methodology was able to validate a large number of genes and processes that seem to be implicated in the progression of melanoma and prostate cancer. Conclusions/Significance: We thus present a quantitative guiding rule, a new unifying hallmark of cancer: the cancer cell's transcriptome changes lead to measurable observed transitions of Normalized Shannon Entropy values (as measured by high-throughput technologies). At the same time, tumor cells increment their divergence from the normal tissue profile increasing their disorder via creation of states that we might not directly measure. This unifying hallmark allows, via the the Jensen-Shannon divergence, to identify the arrow of time of the processes from the gene expression profiles, and helps to map the phenotypical and molecular hallmarks of specific cancer subtypes. The deep mathematical basis of the approach allows us to suggest that this principle is, hopefully, of general applicability for other diseases