Search

Rewinding machines are used in the paper converting industrial sector to unroll paper veils from large source reels and wind them around smaller rolls, for the production of paper logs to be used in household activities. Many different types of rewinding machine exist, and they are mostly based on stapling devices which automatically unroll a large coil of paper, roll it up around a new log, stop the veil allowing it to be torn off, unload the completed paper log, and reload a new paper core to be rolled up. Winding units generally include a primary and a secondary roller, supplying the desired rotational speed for winding, and a pressure unit consisting of a pressure roller in contact with the paper log being rolled up, which assures adequate containment and avoids the paper log to escape. All known systems have some mechanical limitations, mainly due to the contact of the pressure roller with the paper log, causing instabilities and vibrations, particularly when working with soft paper veils. This limits the maximum possible winding speed. The aim of this paper is it to present a detailed kinematic analysis of a novel pressure unit which overcomes the aforementioned limitation.

We present a metapopulation dynamic model for the diffusively-coupled rock-paper-scissors (RPS) game with mutation in scale-free hierarchical networks. We investigate how the RPS game changes by mutation in scale-free networks. Only the mutation from rock to scissors (R-to-S) occurs with rate μ. In the network, a node represents a patch where the RPS game is performed. RPS individuals migrate among nodes by diffusion. The dynamics are represented by the reaction-diffusion equations with the recursion formula. We study where and how species coexist or go extinct in the scale-free network. We numerically obtained the solutions for the metapopulation dynamics and derived the transition points. The results show that, with increasing mutation rate μ, the extinction of P species occurs and then the extinction of R species occurs, and finally only S species survives. Thus, the first and second dynamical phase transitions occur in the scale-free hierarchical network. We also show that the scaling law holds for the population dynamics which suggests that the transition points approach zero in the limit of infinite size.

To facilitate better interpretation of dielectric response measurements—thereby directing numerical evidence for condition assessments of oil-paper-insulated equipment in high-voltage alternating current (HVAC) transmission systems—a novel approach is presented to estimate the parameters in the extended Debye model (EDM) using wideband frequency domain spectroscopy (FDS). A syncretic algorithm that integrates a genetic algorithm (GA) and the Levenberg-Marquardt (L-M) algorithm is introduced in the present study to parameterize EDM using the FDS measurements of a real-life 126 kV oil-impregnated paper (OIP) bushing under different controlled temperatures. As for the uncertainty of the EDM structure due to variable branch quantity, Akaike’s information criterion (AIC) is employed to determine the model orders. For verification, comparative analysis of FDS reconstruction and results of FDS transformation to polarization–depolarization current (PDC)/return voltage measurement (RVM) are presented. The comparison demonstrates good agreement between the measured and reconstructed spectroscopies of complex capacitance and tan δ over the full tested frequency band (10−4 Hz–103 Hz) with goodness of fit over 0.99. Deviations between the tested and modelled PDC/RVM from FDS are then discussed. Compared with the previous studies to parameterize the model using time domain dielectric responses, the proposed method solves the problematic matching between EDM and FDS especially in a wide frequency band, and therefore assures a basis for quantitative insulation condition assessment of OIP-insulated apparatus in energy systems.

In this note we offer some criticism on the paper “On an identity for zeros of Bessel functions” by Baricz et al. [3] . The paper gives identities of type Stieltjes–Calogero for the sums of reciprocals of differences of fourth powers of zeros of Bessel functions. Although interesting in principle, by containing one too many sums of similar complexity the identities fail to convey the true spirit of the work of Stieltjes and Calogero. We rectify this by providing what we think is the correct type of identity for the above-said sums, in the general setup of entire functions of order

The analysis of dielectric response function obtained from the power transformer is a well-accepted technique in insulation diagnosis. A convenient way of analysing time-domain dielectric response φ(t) is the formulation of simple resistance−capacitance-based circuits like the conventional Debye model (CDM) or the modified Debye model (MDM) that are capable of modelling φ(t). However, available techniques do not guarantee unique branch parameters of such circuits for a given φ(t). In fact, the branch parameters are known to depend on the curve-fitting procedure opted during model formulation. This makes accuracy of CDM and MDM parameter-based diagnosis techniques less reliable. Furthermore, it seems logical to analyse the time-domain dielectric response of oil-paper insulation using a model containing time-varying parameters. In this study, a methodology is proposed using which such an insulation model (containing time-varying parameters) is formulated using time-domain insulation response. Related analysis presented suggests that the proposed model is immune to problems associated with available insulation models (containing time-invariant parameters). The performance of the proposed model in indicating insulation condition is tested on data obtained from several real-life power transformers.

Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. © 2019 Howison et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E 2019). By using both dimensional analysis and data fitting, a universal scaling law of a paper spring is formulated. The scaling law shows that origami spring force obeys power square law of spring extension, however strong nonlinear to the total twist angle. The study has also successfully generalized the scaling law from the Poisson ratio 0.3 to an arbitrary Poisson's ratio with the help of dimensional analysis., Comment: 3 pages, 3 figues and 1 table

We investigate a modified spatial stochastic Lotka-Volterra formulation of the rock-paper-scissors model using off-lattice stochastic simulations. In this model one of the species moves preferentially in a specific direction -- the level of preference being controlled by a noise strength parameter $\eta \in [0, 1]$ ($\eta = 0$ and $\eta = 1$ corresponding to total preference and no preference, respectively) -- while the other two species have no referred direction of motion. We study the behaviour of the system starting from random initial conditions, showing that the species with asymmetric mobility has always an advantage over its predator. We also determine the optimal value of the noise strength parameter which gives the maximum advantage to that species. Finally, we find that the critical number of individuals, below which the probability of extinction becomes significant, decreases as the noise level increases, thus showing that the addition of a preferred mobility direction studied in the present paper does not favour coexistence., Comment: 5 pages, 7 figures

We correct a mistake in a lemma in the paper cited in the title and show that it did not affect any of the other results of the paper. To this end, we prove results on linearly disjoint field extensions that do not seem to be commonly known. We give an example to show that a separability assumption in one of these results cannot be dropped (doing so had led to the mistake). Further, we discuss recent generalizations of the original classification of defect extensions.

This comment is devoted to the paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation” (Symmery, 2020, vol.12, 170), in which several results are either incorrect, or incomplete, or misleading.

We investigate the problem of the predominance and survival of "weak" species in the context of the simplest generalization of the spatial stochastic rock-paper-scissors model to four species by considering models in which one, two, or three species have a reduced predation probability. We show, using lattice based spatial stochastic simulations with random initial conditions, that if only one of the four species has its probability reduced then the most abundant species is the prey of the "weakest" (assuming that the simulations are large enough for coexistence to prevail). Also, among the remaining cases, we present examples in which "weak" and "strong" species have similar average abundances and others in which either of them dominates -- the most abundant species being always a prey of a "weak" species with which it maintains a unidirectional predator-prey interaction. However, in contrast to the three-species model, we find no systematic difference in the global performance of "weak" and "strong" species, and we conjecture that the same result will hold if the number of species is further increased. We also determine the probability of single species survival and coexistence as a function of the lattice size, discussing its dependence on initial conditions and on the change to the dynamics of the model which results from the extinction of one of the species., Comment: 7 pages, 6 figures. arXiv admin note: text overlap with arXiv:1907.11280

We revisit the problem of the predominance of the 'weakest' species in the context of Lotka-Volterra and May-Leonard implementations of a spatial stochastic rock-paper-scissors model in which one of the species has its predation probability reduced by $0 < \mathcal{P}_w < 1$. We show that,despite the different population dynamics and spatial patterns, these two implementations lead to qualitatively similar results for the late time values of the relative abundances of the three species (as a function of $\mathcal{P}_w$), as long as the simulation lattices are sufficiently large for coexistence to prevail --- the 'weakest' species generally having an advantage over the others (specially over its predator). However, for smaller simulation lattices, we find that the relatively large oscillations at the initial stages of simulations with random initial conditions may result in a significant dependence of the probability of species survival on the lattice size and total simulation time., 7 pages and 6 figures

We give a comprehensive account of Chern's Theorem that S^6 admits no omega-compatible almost complex structures. No claim to originality is being made, as the paper is mostly an expanded version of material already in the literature. This article extends the talks that both authors gave in Marburg during the conference "(Non)existence of complex structures on S^6" in April 2017., Misprints corrected

The purpose of this comment paper is to show that the results of the paper (Cui, 2021) are incorrect.

The oil-paper compound insulation plays a vital role in the insulation structure of power transformer. To obtain the characteristics of the transformer's insulation system, it is of great importance to study the dielectric response of oil-paper compound insulation. In this study, fractional calculus is applied to model the oil-paper compound insulation. Both low-frequency and broadband high-frequency models are proposed and then they are verified by fitting the measured data of different insulation papers. Finally they are applied to two different cases: (i) the low-frequency model for fitting polarity reversal property; (ii) the broadband high-frequency model for studying the influence of the parameters variations on the frequency domain spectroscopy (FDS). The results demonstrate the advantages of the proposed models when compared with traditional ones.

A popular physics legend holds that scissors can cut paper with a speed faster than light. Here this counter-intuitive myth is investigated theoretically using four simple examples of scissors. For simplicity, all cases will involve a static lower scissors blade that remains horizontal just under the paper. In the first case, the upper blade will be considered perfectly rigid as it rotates around and through the paper, while in the second case, a rigid upper blade will drop down to cut the paper like a guillotine. In the third case, the paper is cut with a laser rotating with a constant angular speed that is pointed initially perpendicular to the paper at the closest point, while in the fourth case, the uniformly rotating laser is pointed initially parallel to the paper. Although details can be surprising and occasionally complex, all cases allow sections of the paper to be cut faster than light without violating special relativity. Therefore, the popular legend is confirmed, in theory, to be true., 6 pages, 9 figures, accepted for publication in Physics Education (un-copyedited version)

Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state.

In 1903, Epstein published his proof of meromorphic continuation and a functional equation for Dirichlet series associated with quadratic forms, now called Epstein zeta-functions. However, already in 1889 (or even earlier) Hurwitz was aware of these results as his mathematical diaries and some unpublished notes (in an almost final form) found in his estate at the ETH Zurich show. In this article we present and analyze Hurwitz's notes and compare his reasoning with Epstein's paper in detail.

A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.

We correct an error in the paper of Z. Shen, S. Li, and J. Zhang published in [4]. In addition, we give an answer to a question posed by the authors.

We study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We introduce an unevenness in the system, by considering that one of the species is weaker because of a lower selection probability. The simulation results show that the pattern formation is drastically affected by the presence of the weaker species, with no spiral waves arising immediately from random initial conditions. Instead, single-species spatial domains cyclically dominate the entire territory until a region occupied by the weaker species is sufficiently narrow to be crossed by individuals without being selected. This leads to the appearance of spatial patterns responsible for the species coexistence. We verify that the asymmetry in the selection probabilities leads to different spatial autocorrelation function and average relative species abundances. Finally, we investigate the coexistence probability and show that the surviving species depends on the level of unevenness of the model and the mobility of individuals., 6 pages, 7 figures

Does non-transitivity in information theory have an analog in thermodynamics? A non-transitive game, “Swap”, is used as a toy thermodynamic model to explore concepts such as temperature, heat flow, equilibrium and entropy. These concepts, found to be inadequate for non-transitive thermodynamic, need to be generalized. Two kinds of temperatures, statistical and kinetic, are distinguished. Statistical temperature is a parameter in statistical distributions. Kinetic temperature is proportional to the expected kinetic energy based on its distribution. Identical for Maxwell-Boltzmann statistics, these temperatures differ in non-Maxwellian statistics when a force is present. Fourier’s law of conduction and entropy should be expressed using statistical temperature, not kinetic temperature. Kinetic temperature is always scalar but statistical temperature and statistical entropy in non-transitive systems have circulation, thereby allowing continuous and circular heat flow. Entropy is relative to underlying statistics, in analogy to the Kullback-Leibler divergence in information theory. The H-theorem, limited by assumptions of homogeneity and indistinguishability, only covers statistically homogeneous systems. The theorem does not cover non-transitive, statistically heterogeneous systems combining different distributions such as Maxwell-Boltzmann, biased half-Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. The second law can be preserved if generalized by expressing it in terms of statistical temperature and statistical entropy.

Inspired by the article “Anomalous relaxation model based on the fractional derivative with a Prabhakar-like kernel” (Z. Angew. Math. Phys. (2019) 70:42) whose authors Zhao and Sun studied the integro-differential equation with the kernel given by the Prabhakar function $$e^{-\gamma }_{\alpha , \beta }(t, \lambda )$$ , we provide the solution to this equation which is complementary to that obtained up to now. Our solution is valid for effective relaxation times whose admissible range extends the limits given in Zhao and Sun (Z Angew Math Phys 70:42, 2019, Theorem 3.1) to all positive values. For special choices of parameters entering the equation itself and/or characterizing the kernel, the solution comprises to known phenomenological relaxation patterns, e.g., to the Cole–Cole model (if $$\gamma = 1, \beta =1-\alpha $$ ) or to the standard Debye relaxation.

We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-04 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein's approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways., Comment: 22 pages, submitted to JSP

In Fritz John's famous paper (1979), he discovered that for the wave equation $\Box u=|u|^p$, where $1, Comment: 11 pages, 3 figures

The problem of grabbing a non-tumbling satellite, addressed in this paper, is split into two subproblems, the first of determining a minimum distance collision-free path from the starting stowed pose of the space manipulator to the grabbing pose, and the second of determining a minimum time motion along this path, subject to speed and torque constraints of the manipulator. The first problem is solved using the well known A∗ algorithm, after posing path planning as a graph search problem. Different types of heuristic functions are used for the graph search, and their influence in finding the solution is discussed. The non-smooth path generated using A∗ algorithm is smoothened, and then minimum time motion subject to constraints is determined by posing it as a nonlinear programming problem and solved using an SQP algorithm. Solutions obtained for three different target satellite poses are discussed.

Dirty paper codes are a powerful tool for combating known interference. However, there is a significant difference between knowing the transmitted interference sequence and knowing the received interference sequence, especially when the channel modifying the interference is uncertain. We present an upper bound on the capacity of a compound vector dirty paper channel where although an additive Gaussian sequence is known to the transmitter, the channel matrix between the interferer and receiver is uncertain but known to lie within a bounded set. Our bound is tighter than previous bounds in the low-SIR regime for the scalar version of the compound dirty paper channel and employs a construction that focuses on the relationship between the dimension of the message-bearing signal and the dimension of the additive state sequence. Additionally, a bound on the high-SNR behavior of the system is established., Comment: to be presented at ISIT 2013

We characterize functions of finite energy in the plane in terms of their traces on the lines that make up "graph paper" with squares of side length $mn$ for all $n$, and certain $\12-$order Sobolev norms on the graph paper lines. We also obtain analogous results for functions of finite energy on two classical fractals: the Sierpinski gasket and the Sierpinski carpet.

In this short note, it is shown that there is a gap in the proof of Theorem 11 in the paper of Meyer and Neutsch (J. of Algebra, 1993). We prove, nevertheless, that the statement of the theorem is true and fix the proof by using a certain extremal property of idempotents which has an independent interest., 6 pages, submitted 2017

Assume that A and G are finite groups of coprime orders such that A acts on G via automorphisms. Let p be a prime. The following coprime action version of a well-known theorem of Ito about the structure of a minimal non-p-nilpotent groups is proved: if every maximal A-invariant subgroup of G is p-nilpotent, then G is p-soluble. If, moreover, G is not p-nilpotent, then G must be soluble. Some earlier results about coprime action are consequences of this theorem.

Let [Formula: see text] be a projective variety of dimension [Formula: see text] over an algebraically closed field of arbitrary characteristic. We prove a Fujiki–Lieberman type theorem on the structure of the automorphism group of [Formula: see text]. Let [Formula: see text] be a group of zero entropy automorphisms of [Formula: see text] and [Formula: see text] the set of elements in [Formula: see text] which are isotopic to the identity. We show that after replacing [Formula: see text] by a suitable finite-index subgroup, [Formula: see text] is a unipotent group of the derived length at most [Formula: see text]. This result was first proved by Dinh et al. for compact Kähler manifolds.

RD is absent from the dimensional Eqs. (1)–(6) in Ref. [1], which we included in Ref. [1] as reference to the study of the related flow behaviors of the nanofluid. These equations constitute the governing flow equations of nanofluid over a stretching sheet in Ref. [1], and these dimensional equations are independent from the entropy generation Eq. (1) from Ref. [1] with RD as mentioned above. Entropy generation measures the degree or level of available (existing) irreversibilities within a process. The entropy generation equation is an extension from the governing flow Eqs. (1)–(6).

In this note we show that the presented proof of [1, th. 12] , being based on a false statement appearing in this proof, is not viable for all of the proclaimed values of the involved parameters. We also determine necessary and sufficient conditions for those parameters, which provides that the considered statement, and therefore [1, th. 12] itself, still remains valid.

The "Carbon Copy onto Dirty Paper" (CCDP) channel is the compound "writing on dirty paper" channel in which the channel output is obtained as the sum of the channel input, white Gaussian noise and a Gaussian state sequence randomly selected among a set possible realizations. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output. We study the capacity of the CCDP channel for two scenarios: (i) the state sequences are independent and identically distributed, and (ii) the state sequences are scaled versions of the same sequence. In the first scenario, we show that a combination of superposition coding, time-sharing and Gel'fand-Pinsker binning is sufficient to approach the capacity to within three bits per channel use for any number of possible state realizations. In the second scenario, we derive capacity to within four bits-per-channel-use for the case of two possible state sequences. This result is extended to the CCDP channel with any number of possible state sequences under certain conditions on the scaling parameters which we denote as "strong fading" regime. We conclude by providing some remarks on the capacity of the CCDP channel in which the state sequences have any jointly Gaussian distribution.

This work reports on two related investigations of stochastic simulations which are widely used to study biodiversity and other related issues. We first deal with the behavior of the Hamming distance under the increase of the number of species and the size of the lattice, and then investigate how the mobility of the species contributes to jeopardize biodiversity. The investigations are based on the standard rules of reproduction, mobility and predation or competition, which are described by specific rules, guided by generalization of the rock-paper-scissors game, valid in the case of three species. The results on the Hamming distance indicate that it engenders universal behavior, independently of the number of species and the size of the square lattice. The results on the mobility confirm the prediction that it may destroy diversity, if it is increased to higher and higher values., Comment: 7 pages, 9 figures. To appear in EPL

This is a continuation of our first paper in [WY16]. There are two purposes of this paper: One is to give a proof of the main result in [WY16] without going through the argument depending on numerical effectiveness. The other one is to provide a proof of our conjecture, mentioned in [TY], where the assumption of negative holomorphic sectional curvature is dropped to quasi-negative. We should note that a solution to our conjecture is also provided by Diverio-Trapani [DT]. Both proofs depend on our argument in [WY16]. But our argument here makes use of the argument given by the second author and Cheng in [CY75].

This is a mathematical commentary on Teichmuller's paper ``Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flachen" (Determination of extremal quasiconformal maps of closed oriented Riemann surfaces). This paper is among the last (and may be the last one) that Teichmuller wrote on the theory of moduli. It contains the proof of the so-called Teichmuller existence theorem for a closed surface of genus at least 2. For this proof, the author defines a mapping between a space of equivalence classes of marked Riemann surfaces (the Teichmuller space) and a space of equivalence classes of certain Fuchsian groups (the so-called Fricke space). After that, he defines a map between the latter and the Euclidean space of dimension 6g-6 Using Brouwer's theorem of invariance of domain, he shows that this map is a homeomorphism. This involves in particular a careful definition of the topologies of Fricke space, the computation of its dimension, and comparison results between hyperbolic distance and quasiconformal dilatation. The use of the invariance of domain theorem is in the spirit of Poincare and Klein's use of the so-called ``continuity principle" in their attempts to prove the uniformization theorem.

The rock-paper-scissors game is a paradigmatic model for biodiversity, with applications ranging from microbial populations to human societies. Research has shown, however, that mobility jeopardizes biodiversity by promoting the formation of spiral waves, especially if there is no conservation law in place for the total number of competing players. Firstly, we show that even if such a conservation law applies, mobility still jeopardizes biodiversity in the spatial rock-paper-scissors game if only a small fraction of links of the square lattice is randomly rewired. Secondly, we show that zealots are very effective in taming the amplitude of oscillations that emerge due to mobility and/or interaction randomness, and this regardless of whether the later is quenched or annealed. While even a tiny fraction of zealots brings significant benefits, at 5\% occupancy zealots practically destroy all oscillations regardless of the intensity of mobility, and regardless of the type and strength of randomness in the interaction structure. Interestingly, by annealed randomness the impact of zealots is qualitatively the same as by mobility, which highlights that fast diffusion does not necessarily destroy the coexistence of species, and that zealotry thus helps to recover the stable mean-field solution. Our results strengthen the important role of zealots in models of cyclic dominance, and they reveal fascinating evolutionary outcomes in structured populations that are a unique consequence of such uncompromising behavior., Comment: 6 two-column pages, 4 figures; accepted for publication in Physical Review E

We note a simple algebraic proof of Frolkina’s result that [Formula: see text] does not contain uncountably many pairwise disjoint copies of the Möbius band, and of a similar result in higher dimensions.

Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.

We consider (N,r) games of predation with N species and r < N prey and predators, acting in a cyclic way. Further basic reactions include reproduction, decay and diffusion over a regular grid, without a hard constraint on the occupation number per site, so in a "bosonic" implementation. For special combinations of N and r and appropriate parameter choices we observe games within games, that is, different coexisting games, depending on the spatial resolution. As concrete and simplest example we analyze the (6,3) game. Once the players segregate from a random initial distribution, domains emerge, which effectively play a (2,1)-game on the coarse scale of domain diameters, while agents inside the domains play (3,1) (rock-paper-scissors), leading to spiral formation with species chasing each other. As the (2,1)-game has a winner in the end, the coexistence of domains is transient, while agents inside the remaining domain coexist, until demographic fluctuations lead to extinction of all but one species in the very end. This means that we observe a dynamical generation of multiple space and time scales with emerging re-organization of players upon segregation, starting from a simple set of rules on the smallest scale and changed rules from the coarser perspective. These observations are based on Gillespie simulations. We discuss the deterministic limit derived from a van Kampen expansion. The linear stability analysis predicts the number of forming domains, their composition in terms of species; it also explains the instability of interfaces between domains, which drives their extinction; spiral patterns are identified as motion along heteroclinic cycles. The numerical solutions reproduce the observed patterns of the Gillespie simulations including even extinction events, so that the mean-field analysis here is very conclusive, which is due to the specific implementation of rules., 21 pages main text, 16 pages supplementary material (merged)

These are detailed notes on Perelman's papers "The entropy formula for the Ricci flow and its geometric applications" and "Ricci flow with surgery on three-manifolds"., 216 pages, minor corrections made

Infrared (IR) spectra of different varieties of document papers were collected with the use of attenuated total reflectance (ATR, 4000-650 cm−1, eight paper varieties) and diffuse reflectance (DRIFTS, 9000-2500 cm−1, six paper varieties) techniques. The spectral data were classified by the application of soft independent modeling of class analogies (SIMCA), using principal components analysis (PCA) to estimate the distance of separation between the different classes of paper samples and discriminant analysis (DA) to obtain a probabilistic classification. The use of DA on spectral data needed a preliminary data reduction step, either by PCA-decomposition of spectra or the selection of discrete spectral features having maximum discriminating ability. The aim of this research was to evaluate these data-reduction techniques and compare the discriminating power of these two spectral techniques (DRIFTS and ATR) by the application of PCA and DA. The use of PCA scores as DA variables provided the best resolution (100% correct classification) for the DRIFTS spectra, while PCA on the ATR spectra resulted in the best discrimination, separating 67.86% paper pairs completely with the use of cross-validation. The results of this study reemphasize that infrared spectroscopy coupled with multivariate statistical methods of analysis could provide a powerful discriminating tool for the forensic questioned document examiner.

In this paper we construct a family of circle-like continua, each admitting a finest monotone map onto S 1 such that there exists a subset of point inverses which is homeomorphic to the Cantor set cross an interval. We then show how to realize some members of this family as the boundaries ∂U of bounded irreducible local Siegel disks U . These boundaries are geometrically rigid in the following sense: there exist arbitrarily small periodic homeomorphisms of the sphere, conformal on U , which keep U invariant. The embedding portion of this paper follows a flexible construction of Herman. These results provide a partial answer to a question of Rogers and a complete answer to a question of Brechner, Guay, and Mayer.

Many results have been obtained when studying scientific papers citations databases in a network perspective. Articles can be ranked according to their current in-degree and their future popularity or citation counts can even be predicted. The dynamical properties of such networks and the observation of the time evolution of their nodes started more recently. This work adopts an evolutionary perspective and proposes an original algorithm for the construction of genealogical trees of scientific papers on the basis of their citation count evolution in time. The fitness of a paper now amounts to its in-degree growing trend and a "dying" paper will suddenly see this trend declining in time. It will give birth and be taken over by some of its most prevalent citing "offspring". Practically, this might be used to trace the successive published milestones of a research field., SCOPUS: ar.j, info:eu-repo/semantics/published