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Post-transcriptional modifications are intrinsic to RNA structure and function. However, methods to sequence RNA typically require a cDNA intermediate and are either not able to sequence these modifications or aretailored to sequence one specific nucleotide modification only. Interestingly, some of these modifications occur with Phe without cDNA by integrating atwo-dimensional hydrophobic RNA end-labeling strategy with an anchor-based algorithm in mass spectrometry-based sequencing (2D-HELS-AA MS Seq). The entire tRNAPhe was sequenced and the identity, location, and stoichiometry of all eleven different RNA modifications was determined, five of which were not 100% modified, including a 2'-O-methylated G (Gm) in the wobble anticodon position as well as an N2, N2-dimethylguanosine (m22G), a7-methylguanosine (m7G), a1-methyladenosine (m1A), and awybutosine (Y), suggesting numerous post-transcriptional regulations in tRNA. Two truncated isoforms at the 3'-CCA tail of the tRNAPhe (75 nt with a 3'-CC tail (80% abundance) and 74 nt with a 3'-C tail (3% abundance)) were identified in addition to the full-length 3'-CCA-tailed tRNAPhe (76 nt, 17% abundance). We discovered a new isoform with A-G transitions/editing at the 44 and 45 positions in the tRNAPhe variable loop, and discuss possible mechanisms related to the emergence and functions of the isoforms with these base transitions or editing. Our method revealed new isoforms, base modifications, and RNA editing as well as their stoichiometries in the tRNA that cannot be determined by current cDNA-based methods, opening new opportunities in the field of epitranscriptomics.

We consider the theoretical maximum extractable average power from an energy harvesting device attached to a vibrating table which provides a unidirectional displacement $$A\sin (\omega t)$$ . The total mass of moving components in the device is m. The device is assembled in a container of dimension L. The masses in the device may be interconnected in arbitrary ways. The maximum extractable average power is bounded by $$\frac{mLA\omega ^3}{\pi }$$ , for motions in 1, 2, or 3 dimensions; with both rectilinear and rotary motions as special cases; and with either single or multiple degrees of freedom. The limiting displacement profile of the moving masses for extracting maximum power is discontinuous, and not physically realizable. But smooth approximations can be nearly as good: With 15 terms in a Fourier approximation, the upper limit is 99% of the theoretical maximum. For both single-degree-of-freedom linear resonant devices and nonresonant devices where the energy extraction mimics a linear torsional damper, the maximum average power output is $$\frac{mLA\omega ^3}{4}$$ . Thirty-six experimental energy harvesting devices in the literature are found to extract power amounts ranging from 0.0036 to 29% of the theoretical maximum. Of these thirty-six, twenty achieve less than 2% and three achieve more than 20%. We suggest, as a figure of merit, that energy extraction above $$\frac{0.2 mLA\omega ^3}{\pi }$$ may be considered excellent, and extraction above $$\frac{0.3 mLA\omega ^3}{\pi }$$ may be considered challenging.

A nucleotide substitution is said to occur when a base in {A, T} is substituted for a base in {C, G}, or vice versa. Recent experiment (Heckel et al. 2019) showed that a nucleotide substitution occurs with a significantly higher probability than other substitution errors. A nucleotide edit refers to a single insertion, deletion or nucleotide substitution. In this paper, we investigate codes that corrects a single nucleotide edit and provide linear-time algorithms that encode binary messages into these codes of length n.Specifically, we provide an order-optimal encoder which corrects a single nucleotide edit with logn + loglogn + O(1) redundant bits. We also demonstrate that the codewords obey certain runlength constraints and that the code can be modified to accommodate certain GC-content constraints.

In this paper, we prove that if $2^\lambda < \kappa$ and $\mathcal A \subset [\kappa]^{\lambda}$ is a MADF then the generalized Mrowka space $\Psi (\mathcal A\setminus \mathcal B)$ has no $G_\lambda$-diagonal, where $\mathcal B \subset \mathcal A$ and $|\mathcal B|\le\lambda$. If a topological space $X$ has a regular $G_\lambda$-diagonal and a local decreasing base of cardinality $\chi(X)$ for each $x \in X$, then $|X| \le 2^{dc(X) \cdot \chi(X) \cdot \lambda}$, where $dc(X)$ is the discrete cellularity of $X$ and $\chi(X)$ is the character of $X$. As a corollary, we prove that if $X$ is a DCCC (and hence, $DC(\omega_1)$, weakly Lindelof or star Lindelof) first countable space with a regular $G_\delta$-diagonal then $|X|\le 2^\omega$, which gives a positive answer to a question in [17]. Finally, we give another counterexample to a question of Ginsburg and Woods [6], which has nicer properties than the counterexamples constructed in [15] and [16].

Let {Bn } n≥0 be the sequence of Balancing numbers defined by B 0 = 0, B 1 = 1, and B n+2 = 6B n+1 − Bn for all n ≥ 0. In this paper, we find all repdigits in base 10 which can be written as a sum of three Balancing numbers.

In this work we analyze F-theory and Type IIB orientifold compactifications to study α′-corrections to the four-dimensional, N $$ \mathcal{N} $$ = 1 effective actions. In particular, we obtain corrections to the Kählermoduli space metric and its complex structure for generic dimension originating from eight-derivative corrections to eleven-dimensional supergravity. We propose a completion of the G 2 R 3 and (∇G)2 R 2-sector in eleven-dimensions relevant in Calabi-Yau fourfold reductions. We suggest that the three-dimensional, N $$ \mathcal{N} $$ = 2 Kähler coordinates may be expressed as topological integrals depending on the first, second, and third Chern-forms of the divisors of the internal Calabi-Yau fourfold. The divisor integral Ansatz for the Kähler potential and Kähler coordinates may be lifted to four-dimensional, N $$ \mathcal{N} $$ = 1 F-theory vacua. We identify a novel correction to the Kähler potential and coordinates at order α′ 2, which is leading compared to other known corrections in the literature. At weak string coupling the correction arises from the intersection of D7-branes and O7-planes with base divisors and the volume of self-intersection curves of divisors in the base. In the presence of the conjectured novel α′-correction resulting from the divisor interpretation the no-scale structure may be broken. Furthermore, we propose a model independent scenario to achieve non-supersymmetric AdS vacua for Calabi-Yau orientifold backgrounds with negative Euler-characteristic.

The development of high-speed volumetric laser-induced fluorescence measurements of formaldehyde ($$\hbox {CH}_2\hbox {O}$$-LIF) using a pulse-burst laser operated at a repetition rate of $${100} \hbox { kHz}$$ is presented. A novel laser scanning system employing an acousto-optic deflector (AOD) enables quasi-4D $$\hbox {CH}_2\hbox {O}$$-LIF imaging at a scan frequency of $${10}\hbox { kHz}$$. The diagnostic capability of time-resolved volumetric imaging is demonstrated in a partially premixed DME/air lifted turbulent jet flame near the flame base. Simultaneous imaging of laser beam profiles is performed to account for the laser pulse energy fluctuation and laser sheet inhomogeneity. With the accurate registration of laser sheet positions, the volumetric reconstruction of $$\hbox {CH}_2\hbox {O}$$-LIF signals is performed within a detection volume of $$17.3 \times 11.9 \times {2.3}\, \hbox { mm}^3$$ with an average out-of-plane spatial resolution of $${250}\,\upmu \hbox {m}$$. A surface detection algorithm with adaptive thresholding is used to determine the global maximum intensity gradient by calculating gradient percentiles. The flame topology characteristics are investigated by evaluating the 3D curvatures of $$\hbox {CH}_2\hbox {O}$$ surfaces. Curvatures calculated using 2D data systematically underestimate the full 3D curvature due to the lack of out-of-plane information. The inner surfaces near the turbulent fuel jet exhibit higher probabilities of large mean curvature than the outer surfaces. The saddle and cylindrical structures are dominant on both the inner and outer surfaces and the elliptic structures occur with lower probability. The results suggest that the damping of turbulent fluctuations by the temperature increase through the $$\hbox {CH}_2\hbox {O}$$ region reduces the curvature, but the local structure topology remains self-similar.

M dwarf stars are currently the main targets in searches for potentially habitable planets. However, their winds have been suggested to be harmful to planetary atmospheres. Here, in order to better understand the winds of M dwarfs and also infer their physical properties, we perform a one-dimensional magnetohydrodynamic parametric study of winds of M dwarfs that are heated by dissipation of Alfv��n waves. These waves are triggered by sub-surface convective motions and propagate along magnetic field lines. Here, we vary the magnetic field strength and density at the wind base (chromosphere), while keeping the same relative wave amplitude ($0.1 B_0$) and dissipation lenghtscale. We find that our winds very quickly reach isothermal temperatures with mass-loss rates proportional to base density square. We compare our results with Parker wind models and find that, in the high-beta regime, both models agree. However, in the low-beta regime, the Parker wind underestimates the terminal velocity by around one order of magnitude and mass-loss rate by several orders of magnitude. We also find that M dwarfs could have chromospheres extending to 18% to 180% of the stellar radius. We apply our model to the planet-hosting star GJ 436 and find, from X-ray observational constraints, $\dot{M}, 12 pages, 11 figures

The ESS$\nu$SB project proposes to base a neutrino ''Super Beam'' of unprecedented luminosity at the European Spallation Source. The original proposal identified the second peak of the oscillation probability as the optimal to maximize the discovery potential to leptonic CP violation. However this choice reduces the statistics at the detector and penalizes other complementary searches such as the determination of the atmospheric oscillation parameters, particularly the octant of $\theta_{23}$ as well as the neutrino mass ordering. We explore how these shortcomings can be alleviated by the combination of the beam data with the atmospheric neutrino sample that would also be collected at the detector. We find that the combination not only improves very significantly these drawbacks, but also enhances both the CP violation discovery potential and the precision in the measurement of the CP violating phase, for which the facility was originally optimized, by lifting parametric degeneracies. We then reassess the optimization of the ESS$\nu$SB setup when the atmospheric neutrino sample is considered, with an emphasis in performing a measurement of the CP violating phase as precise as possible. We find that for the presently preferred value of $\delta \sim -\pi/2$, shorter baselines and longer running time in neutrino mode would be optimal. In these conditions, a measurement better than $14^\circ$ would be achievable for any value of the $\theta_{23}$ octant and the mass ordering. Conversely, if present and next generation facilities were not able to discover CP violation, longer baselines and more even splitting between neutrino and neutrino modes would be preferable. These choices would allow a $5 \sigma$ discovery of CP violation for around a $60\%$ of the possible values of $\delta$ and to determine its value with a precision around $6^\circ$ if it is close to $0$ or $\pi$., Comment: Several comments and references added; matches published version in EPJ C

QuickXsort is a highly efficient in-place sequential sorting scheme that mixes Hoare’s Quicksort algorithm with X, where X can be chosen from a wider range of other known sorting algorithms, like Heapsort, Insertionsort and Mergesort. Its major advantage is that QuickXsort can be in-place even if X is not. In this work we provide general transfer theorems expressing the number of comparisons of QuickXsort in terms of the number of comparisons of X. More specifically, if pivots are chosen as medians of (not too fast) growing size samples, the average number of comparisons of QuickXsort and X differ only by o(n)-terms. For median-of-k pivot selection for some constant k, the difference is a linear term whose coefficient we compute precisely. For instance, median-of-three QuickMergesort uses at most $$n \lg n - 0.8358n + {\mathcal {O}}(\log n)$$ comparisons. Furthermore, we examine the possibility of sorting base cases with some other algorithm using even less comparisons. By doing so the average-case number of comparisons can be reduced down to $$n \lg n - 1.4112n + o(n)$$ for a remaining gap of only 0.0315n comparisons to the known lower bound (while using only $${\mathcal {O}}(\log n)$$ additional space and $${\mathcal {O}}(n\log n)$$ time overall). Implementations of these sorting strategies show that the algorithms challenge well-established library implementations like Musser’s Introsort.

The macroscopic magnetic properties and microscopic magnetic structure of ${\mathrm{Rb}}_{2}{\mathrm{Mn}}_{3}{({\mathrm{MoO}}_{4})}_{3}{(\mathrm{OH})}_{2}$ (space group $Pnma)$ are investigated by magnetization, heat capacity, and single-crystal neutron diffraction measurements. The compound's crystal structure contains bond-alternating ${[{\mathrm{Mn}}_{3}{\mathrm{O}}_{11}]}^{\ensuremath{\infty}}$ chains along the $b$ axis, formed by isosceles triangles of Mn ions occupying two crystallographically nonequivalent sites (the Mn1 site on the base and Mn2 site on the vertex). These chains are only weakly linked to each other by nonmagnetic oxyanions. Both superconducting quantum interference device magnetometry and neutron diffraction experiments show two successive magnetic transitions as a function of temperature. On cooling, it transitions from a paramagnetic phase into an incommensurate phase below 4.5 K with a magnetic wave vector near ${\mathbf{k}}_{1}=(0,\phantom{\rule{0.16em}{0ex}}0.46,\phantom{\rule{0.16em}{0ex}}0)$. An additional commensurate antiferromagnetically ordered component arises with ${\mathbf{k}}_{2}=(0,\phantom{\rule{0.16em}{0ex}}0,\phantom{\rule{0.16em}{0ex}}0)$, forming a complex magnetic structure below 3.5 K with two different propagation vectors of different stars. On further cooling, the incommensurate wave vector undergoes a lock-in transition below 2.3 K. The experimental results suggest that the magnetic superspace group is $Pnma.{1}^{\ensuremath{'}}(0b0)s0ss$ for the single-$\mathbf{k}$ incommensurate phase and is $P{n}^{\ensuremath{'}}ma(0b0)00s$ for the two-$\mathbf{k}$ magnetic phase. We propose a simplified magnetic structure model taking into account the major ordered contributions, where the commensurate ${\mathbf{k}}_{2}$ defines the ordering of the $c$-axis component of the Mn1 magnetic moment, while the incommensurate ${\mathbf{k}}_{1}$ describes the ordering of the $ab$-plane components of both Mn1 and Mn2 moments into elliptical cycloids.

A central ZF3 molecule (Z = P, As, Sb, Bi) is allowed to interact with a number of nucleophiles exemplified by NCH, NH3, and NC- anion. The Z···N pnicogen bond (ZB) to a single base grows stronger for heavier Z atom: P < A < Sb < Bi and follows the NCH < NH3 < NC- order for the three bases. The maximum number of ZBs depends on both the nature of the base and pnicogen atom. PF3 and AsF3 can pnicogen bond with only a single CN-; SbF3 and BiF3 can interact with two anions but only weakly. The weak NCH nucleophile can engage in a maximum of two ZBs, while three ZBs occur for NH3. The latter NH3 maximum can be extended to four ZBs but only for BiF3. The fourth ZB is somewhat longer and weaker than the others, and the entire (H3N)4···BiF3 complex relies partially on secondary interactions for its stability.

In this paper, using the asymptotic expansion of $$\left( \left( \sin x\right) /x\right) ^{2/5}$$ we obtain some new bounds for Sinc function in terms of $$(1-ax^{2})^{b}$$ and $$(1-ax^{2}-px^{6})^{b}$$. Then we find some better bounds by using simultaneous approximation of the base function and exponential function. Finally, we come to the conclusion that the new lower bound is better than those in the previous literature.

In this paper, we explicitly construct the smooth compact base threefold for the elliptic Calabi-Yau fourfold with the largest known $h^{1,1}=303\,148$. It is generated by blowing up a smooth toric "seed" base threefold with $(E_8,E_8,E_8)$ collisions. The 4d F-theory compactification model over it has the largest geometric gauge group, $E_8^{2\,561}\times F_4^{7\,576}\times G_2^{20\,168}\times SU(2)^{30\,200}$, and the largest number of axions, $181\,820$, in the known 4d $\mathcal{N}=1$ supergravity landscape. We also prove that there are at least $1100^{15\,048}\approx 7.5\times 10^{45\,766}$ different flip and flop phases of this base threefold. Moreover, we find that many other base threefolds with large $h^{1,1}$ in the 4d F-theory landscape can be constructed in a similar way as well., v4, 32 pages

We investigate the structure of $N$ -length discrete signals $h$ satisfying $h*h=h$ that vanish on a given set of indices. We motivate this problem from examples in sampling, Fuglede's conjecture, and orthogonal interpolation of bandlimited signals. When $N=p^M$ is a prime power, we characterize all such $h$ with a prescribed zero set in terms of base- $p$ expansions of nonzero indices in $\mathcal{F}^{-1}h$ .

We use coupling ideas introduced in \cite{levine2018long} to show that an IDLA process on a cylinder graph $G\times \mathbb{Z}$ forgets a typical initial profile in $\mathcal{O}( N\sqrt{\tau_N} (\log \! N)^2 )$ steps for large $N$, where $N$ is the size of the base graph $G$, and $\tau_N$ is the total variation mixing time of a simple random walk on $G$. The main new ingredient is a maximal fluctuations bound for IDLA on $G\times \mathbb{Z}$ which only relies on the mixing properties of the base graph $G$ and the Abelian property., Comment: 15 pages. Removed the Markovian assumption on the coupling

We provide a new large class of countable icc groups $\mathcal A$ for which the product rigidity result from [CdSS15] holds: if $\Gamma_1,\dots,\Gamma_n\in\mathcal A$ and $\Lambda$ is any group such that $L(\Gamma_1\times\dots\times\Gamma_n)\cong L(\Lambda)$, then there exists a product decomposition $\Lambda=\Lambda_1\times\dots\times \Lambda_n$ such that $L(\Lambda_i)$ is stably isomorphic to $L(\Gamma_i)$, for any $1\leq i\leq n$. Class $\mathcal A$ consists of groups $\Gamma$ for which $L(\Gamma)$ admits an s-malleable deformation in the sense of Sorin Popa and it includes all non-amenable groups $\Gamma$ such that either (a) $\Gamma$ admits an unbounded 1-cocycle into its left regular representation, or (b) $\Gamma$ is an arbitrary wreath product group with amenable base. As a byproduct of these results, we obtain new examples of W$^*$-superrigid groups and new rigidity results in the C$^*$-algebra theory., Comment: To appear as such in Communications in Mathematical Physics

We solve the three-particle multichannel Coulomb scattering problem with rearrangement channels without partial wave decomposition on the base of Faddeev-Merkuriev equations. Highly efficient numerical approach allowed us to perform the detailed calculations of all possible S-wave cross-sections in systems \(e^+e^-\bar{p}\) and \(e^+e^-\text{ He }^{++}\) for low-energy binary collisions.

Recently a full-shape analysis of large-scale structure (LSS) data was employed to provide new constraints on a class of Early Dark Energy (EDE) models. In this note, we derive similar constraints on New Early Dark Energy (NEDE) using the publicly available PyBird code, which makes use of the effective field theory of LSS. We study the NEDE base model with the fraction of NEDE and the trigger field mass as two additional parameters allowed to vary freely while making simplifying assumptions about the decaying fluid sector. Including the full-shape analysis of LSS together with measurements of the cosmic microwave background (CMB), baryonic acoustic oscillations (BAO) and supernovae (SN) data, we report $ H_0= 71.2 \pm 1.0~\textrm{km}\, \textrm{s}^{-1}\, \textrm{Mpc}^{-1}$ ($68 \%$ C.L.) together with a $\simeq 4 \, \sigma$ evidence for a non-vanishing fraction of NEDE. This is an insignificant change to the value previously found without full-shape LSS data, $ H_0= 71.4 \pm 1.0~\textrm{km}\, \textrm{s}^{-1}\, \textrm{Mpc}^{-1} $ ($68 \%$ C.L.). As a result, while the NEDE fit cannot be improved upon the inclusion of additional LSS data, it is also not adversely affected by it, making it compatible with current constraints from LSS data. In fact, we find evidence that the effective field theory of LSS acts in favor of NEDE., Comment: 15 pages, 4 figures, v2: added detailed discussion on linear and EFT-corrected power spectrum, added references, improvements to manuscript

Recently, Few-Shot Learning (FSL), or learning from very few (typically 1 or 5) examples per novel class (unseen during training), has received a lot of attention and significant performance advances. While number of techniques have been proposed for FSL, several factors have emerged as most important for FSL performance, awarding SOTA even to the simplest of techniques. These are: the backbone architecture (bigger is better), type of pre-training (meta-training vs multi-class), quantity and diversity of the base classes (the more the merrier), and using auxiliary self-supervised tasks (a proxy for increasing the diversity). In this paper we propose TAFSSL, a simple technique for improving the few shot performance in cases when some additional unlabeled data accompanies the few-shot task. TAFSSL is built upon the intuition of reducing the feature and sampling noise inherent to few-shot tasks comprised of novel classes unseen during pre-training. Specifically, we show that on the challenging miniImageNet and tieredImageNet benchmarks, TAFSSL can improve the current state-of-the-art in both transductive and semi-supervised FSL settings by more than \(5\%\), while increasing the benefit of using unlabeled data in FSL to above \(10\%\) performance gain.

We find that the degeneracies and many peculiarities of the DNA genetic code may be described thanks to two closely related (fivefold symmetric) finite groups. The first group has signature G=Z5⋊H where H=Z2.S4&cong, 2O is isomorphic to the binary octahedral group 2O and S4 is the symmetric group on four letters/bases. The second group has signature G=Z5⋊GL(2,3) and points out a threefold symmetry of base pairings. For those groups, the representations for the 22 conjugacy classes of G are in one-to-one correspondence with the multiplets encoding the proteinogenic amino acids. Additionally, most of the 22 characters of G attached to those representations are informationally complete. The biological meaning of these coincidences is discussed.

We present the data concerning the clustering of sense and antisense amino acid pairs into polar, nonpolar and neutral groups, as measured using hydrophobicity parameter—logarithmic equilibrium constants (Log10 Kw>c)—at 25 °C and 100 °C (Wolfenden et al., 2015). The Log10 Kw>c, values, of the complementary amino acid pairs are strongly correlated to the central (2nd) purine base of the mRNA codon and the complementary pyrimidine base of the tRNA anticodon. Clustering of amino acids is temperature independent with regard to the direction of translation (3′ → 5′ or 5′ → 3′). The Log10 Kw>c discriminate between artificial Hecht α- and β-protein datasets at 25 °C and 100 °C. Interpretation of this data may be found in the research article entitled “Determining amino acid scores of the genetic code table: complementarity, structure, function and evolution” (Stambuk and Konjevoda, 2020).

We consider a rational map $\phi: \mathbb{P}_k^{m} \dashrightarrow \mathbb{P}_k^n$ that is a parameterization of an $m$-dimensional variety. Our main goal is to study the $(m-1)$-dimensional fibers of $\phi$ in relation to the $m$-th local cohomology modules of the Rees algebra of its base ideal., Comment: 13 Pages

In this article, the existence of Ulrich bundles on projective bundles $\mathbb P(E) \to X$ is discussed. In the case, that the base variety $X$ is a curve or surface, a close relationship between Ulrich bundles on $X$ and those on $\mathbb P(E)$ is established for specific polarisations. This yields the existence of Ulrich bundles on a wide range of projective bundles over curves and surfaces., Comment: 13 pages, minor changes to improve the article. Same content as published version

Three‐coordinate cationic bismuth compounds [Bi(diaryl)(EPMe3)][SbF6] have been isolated and fully characterized (diaryl=[(C6H4)2C2H2]2−, E=S, Se). They represent rare examples of molecular complexes with Bi⋅⋅⋅EPR3 interactions (R=monoanionic substituent). The 31P NMR chemical shift of EPMe3 has been found to be sensitive to the formation of LA⋅⋅⋅EPMe3 Lewis acid/base interactions (LA=Lewis acid). This corresponds to a modification of the Gutmann–Beckett method and reveals information about the hardness/softness of the Lewis acid under investigation. A series of organobismuth compounds, bismuth halides, and cationic bismuth species have been investigated with this approach and compared to traditional group 13 and cationic group 14 Lewis acids. Especially cationic bismuth species have been shown to be potent soft Lewis acids that may prefer Lewis pair formation with a soft (S/Se‐based) rather than a hard (O/N‐based) donor. Analytical techniques applied in this work include (heteronuclear) NMR spectroscopy, single‐crystal X‐ray diffraction analysis, and DFT calculations., Cationic bismuth species [Bi(diaryl)]+ show significant bonding interactions with soft donors EPMe3 (E=S, Se). The 31P NMR chemical shifts of EPMe3 are sensitive to Lewis pair formation and are suggested as an easily accessible experimental parameter for the evaluation of the soft character of a Lewis acid. Using this method, a range of neutral and cationic bismuth species have been investigated and compared to more traditional group 13 and 14 Lewis acids.

This article discusses the synthesis of algorithms for fuzzy control of the polymer temperature during its extrusion in a worm extruder based on the classical principle of deviation control and fuzzy control algorithm. The complexity of building control algorithms based on the analytical model of this process is shown. To obtain a mathematical model of the fuzzy control algorithm, basic term sets of input and output variables are introduced, and a fuzzy inference system based on fuzzy linguistic statements in the form “\( \beta_{i} \,it\,is\,\tau_{Ti} \)” is used. The base of temperature control rules is written in the form of a multidimensional matrix \( \left\| {L_{iklr} } \right\| \), which ensures sufficient efficiency of the control process. A block diagram of the developed system based on the principle of deviation control is given.

We consider the problem of computing the Lyapunov exponents of reversible cellular automata (CA). We show that the class of reversible CA with right Lyapunov exponent $2$ cannot be separated algorithmically from the class of reversible CA whose right Lyapunov exponents are at most $2-\delta$ for some absolute constant $\delta>0$. Therefore there is no algorithm that, given as an input a description of an arbitrary reversible CA $F$ and a positive rational number $\epsilon>0$, outputs the Lyapunov exponents of $F$ with accuracy $\epsilon$. We also compute the average Lyapunov exponents (with respect to the uniform measure) of the CA that perform multiplication by $p$ in base $pq$ for coprime $p,q>1$., Comment: 19 pages, 6 figures, submitted to Natural Computing

Transfer covariance function, which can model domain similarity and adaptively control the knowledge transfer across domains, is widely used in transfer learning. In this paper, we concentrate on Gaussian process (GP) models using a transfer covariance function for regression problems in a black-box learning scenario. Precisely, we investigate a family of rather general transfer covariance functions, T*, that can model the heterogeneous sub-similarities of domains through multiple kernel learning. A necessary and sufficient condition to obtain valid GPs using T* (GPT* ) for any data is given. This condition becomes specially handy for practical applications as (i) it enables semantic interpretations of the sub-similarities and (ii) it can readily be used for model learning. In particular, we propose a computationally inexpensive model learning rule that can explicitly capture different sub-similarities of domains. We propose two instantiations of GPT* , one with a set of predefined constant base kernels and one with a set of learnable parametric base kernels. Extensive experiments on 36 synthetic transfer tasks and 12 real-world transfer tasks demonstrate the effectiveness of GPT* on the sub-similarity capture and the transfer performance. Nanyang Technological University National Research Foundation (NRF) Accepted version This research is partially supported by the National Research Foundation (NRF), Singapore, under the Singapore Data Science Consortium (SDSC) International Research Collaboration Grant No. SDSC-2020-004. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of NRF and SDSC. Yew- Soon Ong acknowledges the support of the Singtel Cognitive and Artificial Intelligence Lab for Enterprises (SCALE@NTU), which is a collaboration between Singapore Telecommunications Limited (Singtel) and Nanyang Technological University (NTU) that is funded by the Singapore Government through the Industry Alignment Fund - Industry Collaboration Projects Grant.

In the paper, we investigate (scattered) compact spaces with a P -base for some poset P . More specifically, we prove that any compact space with an ω ω -base is metrizable and any scattered compact space with an ω ω -base is countable under the assumption ω 1 b . These give positive solutions to Problems 8.6.9 and 8.7.7 in Banakh (2019). Using forcing, we also prove that in a model of ω 1 b , there is a non-first-countable compact space with a P -base for some poset P with calibre ω 1 .

There are introduced three methods for defining finite 6-dimensional associative algebras over the ground finite field GF(p), every one of which contains a set of the global right-sided units. Formulas describing the set of the global units are presented for every of the considered three algebras that contain \(p^s\) global units, where \(s=2,3,4.\) The algebras are used as carriers of the hidden discrete logarithm problem that is used as the base cryptographic primitive of the post-quantum digital signature algorithms.

We propose coding techniques that simultaneously limit the length of homopolymers runs, ensure the ${\tt G}{\tt C}$ -content constraint, and are capable of correcting a single edit error in strands of nucleotides in DNA-based data storage systems. In particular, for given $\ell, \epsilon >0$ , we propose simple and efficient encoders/decoders that transform binary sequences into DNA base sequences (codewords), namely sequences of the symbols ${\tt A}, {\tt T}, {\tt C}$ and ${\tt G}$ , that satisfy all of the following properties: 1) runlength constraint: the maximum homopolymer run in each codeword is at most $\ell $ ; 2) ${\tt G}{\tt C}$ -content constraint: the ${\tt G}{\tt C}$ -content of each codeword is within $[0.5-\epsilon,0.5+\epsilon]$ ; 3) error-correction: each codeword is capable of correcting a single deletion, or single insertion, or single substitution error. While various combinations of these properties have been considered in the literature, this work provides generalizations of codes constructions that satisfy all the properties with arbitrary parameters of $\ell $ and $\epsilon $ . Furthermore, for practical values of $\ell $ and $\epsilon $ , we show that our encoders achieve higher rates than existing results in the literature and approach capacity. Our methods have low encoding/decoding complexity and limited error propagation.

In this paper, we initiate the study of the 2d F-theory landscape based on compact elliptic Calabi-Yau fivefolds. In particular, we determine the boundary models of the landscape using Calabi-Yau fivefolds with the largest known Hodge numbers $h^{1,1}$ and $h^{4,1}$. The former gives rise to the largest geometric gauge group in the currently known 2d (0,2) supergravity landscape, which is $E_8^{482\,632\,421}\times F_4^{3\,224\,195\,728}\times G_2^{11\,927\,989\,964}\times SU(2)^{25\,625\,222\,180}$. Besides that, we systematically study the hypersurfaces in weighted projective spaces with small degrees, and check the gravitational anomaly cancellation. Moreover, we also initiate the study of singular bases in 2d F-theory. We find that orbifold singularities on the base fourfold have non-zero contributions to the gravitational anomaly., Comment: 42 pages, 6 figures

The Collatz process is defined on natural numbers by iterating the map \(T(x) = T_0(x) = x/2\) when \(x\in \mathbb {N}\) is even and \(T(x)=T_1(x) =(3x+1)/2\) when x is odd. In an effort to understand its dynamics, and since Generalised Collatz Maps are known to simulate Turing Machines [Conway, 1972], it seems natural to ask what kinds of algorithmic behaviours it embeds. We define a quasi-cellular automaton that exactly simulates the Collatz process on the square grid: on input \(x\in \mathbb {N}\), written horizontally in base 2, successive rows give the Collatz sequence of x in base 2. We show that vertical columns simultaneously iterate the map in base 3. This leads to our main result: the Collatz process embeds an algorithm that converts any natural number from base 3 to base 2. We also find that the evolution of our automaton computes the parity of the number of 1s in any ternary input. It follows that predicting about half of the bits of the iterates \(T^i(x)\), for \(i = O(\log x)\), is in the complexity class NC\(^1\) but outside AC\(^0\). These results show that the Collatz process is capable of some simple, but non-trivial, computation in bases 2 and 3, suggesting an algorithmic approach to thinking about prediction and existence of cycles in the Collatz process.

In this paper we investigate that most of plants have the symmetric property. In addition, the human body is also symmetric and contains the DNA symmetric base complementarity. We can see the logarithm helices in Fibonacci series and helices of plants. The sunflower has a shape of circle. A circle is circular symmetric because the shapes are same when it is shifted on the center. Einstein’s spatial relativity is the relation of time and space conversion by the symmetrically generalization of time and space conversion over the spacial. The left and right helices of plants are the symmetric and have element-wise inverse relationships each other. The weight of center weight Hadamard matrix is 2 and is same as the base 2 of natural logarithm. The helix matrices are symmetric and have element-wise inverses matrics base on the finite group theory A B = B A = \( I_{N} \). Also, we present human a DNA-RNA genetic code with symmetric base complements A = T = U = 30%, C = G = 20% and C + U = G + A. E. Chargaff discovered yeast and octopus DNA base complement [C T; A G] of four componentry A = T = U = 33% and C = G = 17% of the experimental results. This strongly hinted towards the base pair makeup of DNA, although Chargaff did not explicitly state this connection himself. However, it has not been proved in a mathematical analysis view yet. In this paper, we have a simple proof of this problem based on information theory as the doubly stochastic matrix.

We present our final orbit for the late-type spectroscopic binary HD 1. Employed are 553 spectra from 13 years of observations with our robotic STELLA facility and its high-resolution echelle spectrograph SES. Its long-term radial-velocity stability is $\approx$50m/s . A single radial velocity of HD 1 reached a rms residual of 63m/s, close to the expected precision. Spectral lines of HD 1 are rotationally broadened with $v\sin i$ of 9.1$\pm$0.1 km/s . The overall spectrum appears single-lined and yielded an orbit with an eccentricity of 0.5056$\pm$0.0005 and a semi-amplitude of 4.44km/s . We constrain and refine the orbital period based on the SES data alone to 2318.70$\pm$0.32d, compared to 2317.8$\pm$1.1d when including the older data set published by DAO and Cambridge/Coravel. Owing to the higher precision of the SES data, we base the orbit calculation only on the STELLA/SES velocities in order not to degrade its solution. We redetermine astrophysical parameters for HD 1 from spectrum synthesis and, together with the new {\it Gaia} DR-2 parallax, suggest a higher luminosity than published previously. We conclude that HD 1 is a slightly metal-deficient K0 III-II giant 217 times more luminous than the Sun. The secondary remains invisible at optical wavelengths. We present evidence for the existence of a third component.

A hypergraph $\mathcal H$ is super-pancyclic if for each $A \subseteq V(\mathcal H)$ with $|A| \geq 3$, $\mathcal H$ contains a Berge cycle with base vertex set $A$. We present two natural necessary conditions for a hypergraph to be super-pancyclic, and show that in several classes of hypergraphs these necessary conditions are also sufficient for this. In particular, they are sufficient for every hypergraph $\mathcal H$ with $ \delta(\mathcal H)\geq \max\{|V(\mathcal H)|, \frac{|E(\mathcal H)|+10}{4}\}$. We also consider super-cyclic bipartite graphs: those are $(X,Y)$-bigraphs $G$ such that for each $A \subseteq X$ with $|A| \geq 3$, $G$ has a cycle $C_A$ such that $V(C_A)\cap X=A$. Such graphs are incidence graphs of super-pancyclic hypergraphs, and our proofs use the language of such graphs., Comment: 17 pages

A Cantor series expansion for a real number $x$ with respect to a basic sequence $Q=(q_1,q_2,\dots)$, where $q_i \geq 2$, is a representation of the form $x=a_0 + \sum_{i=1}^\infty \frac{a_i}{q_1q_2\cdots q_i}$ where $0 \leq a_i, Comment: 22 pages

The work in this chapter follows from the results shown in Chap. 3, where nuclear demagnetisation of on-chip copper refrigerant was proven to be a viable cooling technique for nanoelectronic devices, and from Chap. 4, where it was shown that using this technique on a wet dilution refrigerator, with a lower base temperature and larger magnetic field, has promise for breaking the \(1\,\mathrm {mK}\) electron temperature barrier. The electron temperature results in Chap. 4 were, however, inconclusive due to the CBT being used outside the weak Coulomb blockade regime. This chapter describes the attempts at further on-chip cooling using a different CBT which was optimised for operation at much lower temperatures, and hence allowed a minimum electron temperature of \(1.20 \pm 0.03\,\mathrm {mK}\) to be recorded. These results were presented in the publication [1], which was drafted by the author of this thesis.

Let $G$ be a finite primitive permutation group on a set $\Omega$ with nontrivial point stabilizer $G_{\alpha}$. We say that $G$ is extremely primitive if $G_{\alpha}$ acts primitively on each of its orbits in $\Omega \setminus \{\alpha\}$. These groups arise naturally in several different contexts and their study can be traced back to work of Manning in the 1920s. In this paper, we determine the almost simple extremely primitive groups with socle an exceptional group of Lie type. By combining this result with earlier work of Burness, Praeger and Seress, this completes the classification of the almost simple extremely primitive groups. Moreover, in view of results by Mann, Praeger and Seress, our main theorem gives a complete classification of all finite extremely primitive groups, up to finitely many affine exceptions (and it is conjectured that there are no exceptions). Along the way, we also establish several new results on base sizes for primitive actions of exceptional groups, which may be of independent interest., Comment: 64 pages; to appear in IMRN

The Schubert varieties on a flag manifold G/P give rise to a cell decomposition on G/P whose Kronecker duals, known as the Schubert classes on G/P, form an additive base of the integral cohomology \(H^{*}(G/P)\). The Schubert’s problem of characteristics asks to express a monomial in the Schubert classes as a linear combination in the Schubert basis. We present a unified formula expressing the characteristics of a flag manifold G/P as polynomials in the Cartan numbers of the group G. As application we develop a direct approach to our recent works on the Schubert presentation of the cohomology rings of flag manifolds G/P.

Invariable generation is a topic that has predominantly been studied for finite groups. In 2014, Kantor, Lubotzky, and Shalev produced extensive tools for investigating invariable generation for infinite groups. Since their paper, various authors have investigated the property for particular infinite groups or families of infinite groups. A group is invariably generated by a subset $S$ if replacing each element of $S$ with any of its conjugates still results in a generating set for $G$. In this paper we investigate how this property behaves with respect to wreath products. Our main work is to deal with the case where the base of $G\wr_X H$ is not invariably generated. We see both positive and negative results here depending on $H$ and its action on $X$., Comment: 11 pages; to appear in J. Group Theory

It was recently discovered that a conductive, metallic state is formed on the surface of some insulating oxides. Firstly observed on SrTiO$_3$(001), it was then found in other compounds as diverse as anatase TiO$_2$, KTaO$_3$, BaTiO$_3$, ZnO, and also on different surfaces of SrTiO$_3$ (or other oxides) with different symmetries. The spatial extension of the wave function of this electronic state is of only a few atomic layers. Experiments indicate its existence is related to the presence of oxygen vacancies induced at or near the surface of the oxide. In this article we present a simplified model aimed at describing the effect of its small spatial extension on measurements of its 3D electronic structure by angular resolved photoemission spectroscopy (ARPES). For the sake of clarity, we base our discussion on a simple tight binding scheme plus a confining potential that is assumed to be induced by the oxygen vacancies. Our model parameters are, nevertheless, obtained from density functional calculations. With this methodology we can explain from a very simple concept of selective interference the "wobbling", i.e., the photoemission intensity modulation and/or apparent dispersion of the Fermi surface and spectra along the out-of-plane ($k_z$) direction, and the "mixed 2D/3D" characteristics observed in some experiments. We conclude that the critical model parameters for such an effect are the relative strength of the electronic hopping of each band and the height/width aspect ratio of the surface confining potential. By considering recent photoemission measurements under the light of our findings, we can get relevant information on the electronic wave functions and of the nature of the confining potential., Comment: Accepted to Physical Review B

We report atomic structures and chemical compositions of defects associated to planar faults in a creep deformed Co-base superalloy and discuss their formation and contribution to plastic deformation. The multinary single crystalline Co-base superalloy was creep deformed under tension along \( \left[ {001} \right] \)-direction at 850 °C and 400 MPa. The creep microstructure comprises a high density of planar defects. Solute segregation to superlattice intrinsic stacking faults (SISF) is characterized via EDXS analysis of a statistically relevant number of faults and compared at different creep stages. The amount of solute segregation shows negligible difference at different creep stages indicating that segregation directly occurs during planar fault formation and does not significantly evolve afterward. Based on the observation and analysis of Frank partial dislocations with \( {\raise0.7ex\hbox{$a$} \!\mathord{\left/ {\vphantom {a 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}{\langle111\rangle} \) Burgers vectors terminating SISF, we discuss a new route to SISF formation via dislocation climb. Additionally, two more complex fault structures are analyzed, and potential formation mechanisms are discussed. The first of these structures is a terminating end of an SISF where an \( {\raise0.7ex\hbox{$a$} \!\mathord{\left/ {\vphantom {a 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}{\langle112\rangle} \) partial dislocation splits up into two closely spaced \( {\raise0.7ex\hbox{$a$} \!\mathord{\left/ {\vphantom {a 6}}\right.\kern-0pt} \!\lower0.7ex\hbox{$6$}}{\langle112\rangle} \) partials separated by an SESF. The second structure consists of two parallel SISFs connected by an anti-phase boundary (APB). All deformation mechanisms described in this study show an involvement of solute segregation directly affecting formation and propagation of creep defects by changing planar fault energies and chemical environments of dislocations. Solute segregation is therefore expected to be a key to future alloy design by enabling control of creep deformation mechanisms in specific temperature and stress regimes.

This paper presents the characteristics of cement-treated crushed rock material which was subjected to the multi-strain amplitudes of cyclic loads. The cyclic behaviors of cement-treated crushed rock specimens were examined by the four-point bending test adopted from the standard test for asphalt concrete. The test specimens were prepared by adding 3 and 5% cement by weight to the typical crushed rock base. The four-point bending tests were then carried out under strain-controlled mode with the strain amplitudes of 50, 100, 150, and \( 200\,\upmu \upvarepsilon \). Two different forms of strain-controlled tests were conducted in this research, which are constant-strain and multi-strain amplitude tests. For the constant-strain amplitude test, all specimens were loaded for one million cycles. The results revealed that the specimens tested with the strain amplitude of lower than \( 200\,\upmu \upvarepsilon \) were secured from fatigue failure. The multi-strain amplitude test was then employed to examine the degradation characteristics of the specimen stiffness. In this research, the multi-strain amplitude tests were conducted by employing various strain amplitudes on the individual specimen. Therefore, the test protocol with the minimum testing time and the optimum number of test specimens can be developed. More importantly, the results from multi-strain amplitude test also explored the modern knowledge on the behaviors of cement-treated crushed rock material after it is failed by the fatigue damages.

As a typical family of random partitions on \(\mathcal {P}_{n,k}\), the set of partitions of n into k parts, the conditional distribution of Pitman’s random partition, termed as the Gibbs base random partition, GBRP \((\alpha )\), is investigated. The set \(\mathcal {P}_{n,k}\) is a lattice with respect to majorization partial order with unique minimum and maximum, and GBRP \((\alpha )\) has TP2 with respect to this order. The main purpose of this paper is to study such a family of random partitions and the inference on its parameter.

A sample \( X_{1},\ldots ,X_{n} \) consisting of independent identically distributed random vectors in \( \mathbb {R}^{p} \) with zero mean and covariance matrix \( \mathbf {\Sigma }\) is considered. The recovery of spectral projectors of high-dimensional covariance matrices from a sample of observations is a key problem in statistics arising in numerous applications. This chapter describes a bootstrap procedure for constructing confidence sets for the spectral projector \( \mathbf {P}_{r} \) related to rth eigenvalue of the covariance matrix \(\mathbf {\Sigma }\) from given data on the base of corresponding spectral projector \(\widehat{\mathbf {P}}_{r}\) of the sample covariance matrix \(\widehat{\mathbf {\Sigma }}\). This approach does not use the asymptotical distribution of \( \Vert \mathbf {P}_{r} - \widehat{\mathbf {P}}_{r} \Vert _{2} \) and does not require the computation of its moment characteristics. The performance of the bootstrap approximation procedure is analyzed.

Let $V$ be a finite-dimensional vector space over a finite field, and suppose $G \leq \Gamma \mathrm{L}(V)$ is a group with a unique subnormal quasisimple subgroup $E(G)$ that is absolutely irreducible on $V$. A base for $G$ is a set of vectors $B\subseteq V$ with pointwise stabiliser $G_B=1$. If $G$ has a base of size 1, we say that it has a regular orbit on $V$. In this paper we investigate the minimal base size of groups $G$ with $E(G)/Z(E(G)) \cong \mathrm{PSL}_n(q)$ in defining characteristic, with an aim of classifying those with a regular orbit on $V$., Comment: 45 pages

To improve faster browsing and more efficient content indexing of huge video collections, video summarization has emerged as an important area of research for the multimedia community. One of the mechanisms to generate video summaries is to extract keyframes which represent the most important content of the video. However, there are still some problems like image imperfection and noise interference, which seriously affect the performance of keyframe selection. Aiming at above problems, in this paper, we propose a linear reconstruction framework to summarize the videos. The first model in our framework seeks the most informative keyframes (base vectors) using the structure sparsity of the \(\ell _{21}\) norm regularization, to represent all the frames as the linear combination of them in a video. Furthermore, we also propose another more robust model via \(\ell _{21}\) norm based loss function to suppress the outlier, and form the joint sparsity with \(\ell _{21}\) norm regularization. For the optimization, we design two efficient algorithms for two proposed models respectively. Finally the extensive experiments on real world video datesets are presented to show the effectiveness of the proposed framework.

This article describes and analyzes all existing algorithms for computing $x=a^{-1}\pmod {p^k}$ x = a - 1 ( mod p k ) for a prime $p$ p , and also introduces a new algorithm based on the exact solution of linear equations using $p$ p -adic expansions. The algorithm starts with the initial value $c=a^{-1}\pmod {p}$ c = a - 1 ( mod p ) and iteratively computes the digits of the inverse $x=a^{-1}\pmod {p^k}$ x = a - 1 ( mod p k ) in base $p$ p . The mod 2 version of the algorithm is more efficient than all existing algorithms for small values of $k$ k . Moreover, it stands out as being the only one that works for any $p$ p , any $k$ k , and digit-by-digit. While the new algorithm is asymptotically worse off, it requires the minimal number of arithmetic operations (just a single addition) per step, as compared to all existing algorithms.

The motivation for using demonic calculus for binary relations stems from the behaviour of demonic turing machines, when modelled relationally. Relational composition (; ) models sequential runs of two programs and demonic refinement ($$\sqsubseteq $$ ⊑ ) arises from the partial order given by modeling demonic choice ($$\sqcup $$ ⊔ ) of programs (see below for the formal relational definitions). We prove that the class $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) of abstract $$(\le , \circ )$$ ( ≤ , ∘ ) structures isomorphic to a set of binary relations ordered by demonic refinement with composition cannot be axiomatised by any finite set of first-order $$(\le , \circ )$$ ( ≤ , ∘ ) formulas. We provide a fairly simple, infinite, recursive axiomatisation that defines $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) . We prove that a finite representable $$(\le , \circ )$$ ( ≤ , ∘ ) structure has a representation over a finite base. This appears to be the first example of a signature for binary relations with composition where the representation class is non-finitely axiomatisable, but where the finite representation property holds for finite structures.