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In China, Xuan paper has been the paper of choice as artwork support and for conservation, for several centuries. However, little is known about its material properties, especially given the many grades of sized and unsized Xuan paper. In addition, there is a lack of information on its degradation. In this research, a selection of contemporary unsized Xuan papers was investigated, representing diverse raw materials. Seven out of twelve contemporary unsized Xuan papers were determined to be approximately neutral and contain > 2% alkaline reserve, indicating good durability. Viscometry was used to determine the degree of polymerisation (DP) as none of the samples gave significant reactions to the phloroglucinol spot test. The average DP of ten contemporary unsized Xuan papers is ~ 1700, excluding two papers that have presumably been sun-bleached, and that exhibit significantly lower DP. Using X-ray fluorescence, it can be demonstrated that Ca and Si are the dominant elements and interestingly, Ca content is directly correlated with ash content and with alkaline reserve. Accelerated degradation was performed at two sets of environmental conditions, i.e. 90 °C, 30% RH and 60 °C, 70% RH, and the established degradation rates agreed with the Collections Demography model of paper degradation meaning that degradation of Xuan papers proceeds in the same way as other types of paper. This research gives fundamental insights into contemporary unsized Xuan papers, which exhibit good stability during accelerated degradation despite the low starting DP in the context of the samples used in this study. Our findings may inform methods of Xuan paper production, selection of Xuan paper for conservation purposes, as well as preventive conservation of Xuan paper-based artefacts.

Based on publications related to the use of micro- and nanofibrillated cellulose (MNFC) in papermaking applications, three sets of parameters (intrinsic and extrinsic variables, furnish composition, and degree of dispersion) were proposed. This holistic approach intends to facilitate understanding and manipulation of the main factors describing the colloidal behavior in systems comprising of MNFC, pulp fibers, and additives, which directly impact paper product performance. A preliminary techno-economic assessment showed that cost reductions driven by the addition of MNFC in paper furnishes could be as high as USD 149 per ton of fiber (up to 20% fiber reduction without adverse effects on paper’s strength) depending on the cost of papermaking fibers. It was also determined that better performance in terms of strength development associated with a higher degree of MNFC fibrillation offset its high manufacturing cost. However, there is a limit from which additional fibrillation does not seem to contribute to further strength gains that can justify the increasing production cost. Further research is needed regarding raw materials, degree of fibrillation, and combination with polyelectrolytes to further explore the potential of MNFC for the reduction of weight of paper products.

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.

A lack of quality control tools limits the enforcement of fortification policies. In alignment with the World Health Organization&rsquo, s ASSURED criteria (affordable, sensitive, specific, user-friendly, rapid and robust, equipment-free, and deliverable), a paper-based assay that interfaces with a smartphone application for the quantification of iron fortificants is presented. The assay is based on the Ferrozine colorimetric method. The reaction started after deposition of the 5 &micro, L aqueous sample and drying. After developing color, pixel intensity values were obtained using a smartphone camera and image processing software or a mobile application, Nu3px. From these values, the actual iron concentration from ferrous sulfate and ferrous fumarate was calculated. The limits of detection, quantification, linearity, range, and errors (systematic and random) were ascertained. The paper-based values from real samples (wheat flour, nixtamalized corn flour, and infant formula) were compared against atomic emission spectroscopy. The comparison of several concentrations of atomic iron between the spectrophotometric and paper-based assays showed a strong positive linear correlation (y = 47.01x + 126.18, R2 = 0.9932). The dynamic range (5.0&ndash, 100 &micro, g/mL) and limit of detection (3.691 &micro, g/mL) of the paper-based assay are relevant for fortified food matrices. Random and systematic errors were 15.9% and + 8.65 &micro, g/g food, respectively. The concept can be applied to limited-resource settings to measure iron in fortified foods.

The present contribution evaluates the methods of degradation and stabilization of alum-containing paper with a focus on the alkaline environment achieved by deacidification procedures. In terms of reviewed subjects, the contribution focuses on alum-rosin sized paper, which is still used as a carrier of knowledge and information; however, it also mentions cellulose itself and other brands of paper. The contribution summarizes the results on the homogeneity of the distribution of alum and rosin in the paper mass and on the paper surface. It provides the knowledge gained in the field of alkaline hydrolysis and oxidation with special regard to transition metal species. It shows the values of alkaline reserves achieved in the main mass-deacidification processes. On the basis of the acquired knowledge, the contribution emphasizes the procedures of paper stabilization. Criteria of “increased mechanical permanence and lifetime prolongation” adopted to evaluate and compare the efficacy of individual mass-deacidification processes were applied and corresponding data are introduced. The contribution also draws attention to the existence of open issues in the area of paper degradation and stabilization.

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.

We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on $n$ vertices, on each turn Proposer proposes a potential edge and Decider simultaneously decides (without knowing Proposer's choice) whether to add it to the graph. Proposer cannot propose an edge which would create a triangle in the graph. The game ends when Proposer has no legal moves remaining, and Proposer wins if the final graph has independence number at least $s$. We prove a threshold phenomenon exists for this game by exhibiting randomized strategies for both players that are optimal up to constants. Namely, there exist constants $0B\sqrt{n}\log{n}$. This is a factor of $\Theta(\sqrt{\log{n}})$ larger than the lower bound coming from the off-diagonal Ramsey number $r(3,s)$.

In this short article, we mainly give some examples to prove that the main results of Section 4 of the paper [W. S. Liao and J. Wu, Ann. Func. Anal. 6 (2015), no. 3, 191–202] are not true. Then we give the corrected matrix inequalities.

N-benzylphenethylamines derivatives, such as NBOMe and NBOH series, are potent hallucinogen drugs that are usually sold in the illicit market as blotter papers containing “legal” LSD alternatives. The identification of these drugs is mainly performed by liquid or gas chromatography coupled with mass spectrometry, but there is a lack of a rapid screening methods to identify samples containing or not drugs of these series. For this purpose, this work offers a fast and non-destructive method applying a handheld NIR spectrometer for discrimination of drugs absorbed in blotter papers using PLS-DA and SIMCA. The method was developed in a two-stage approach: Model A for identification of samples containing or not drugs and model B for identification of samples containing NBOMe or NBOH drugs. PLS-DA models have provided efficiency rates higher 97% in both training and validation phases. Robustness of model B was evaluated with a random permutation of samples among training and validation phases, given mean efficiency rates higher than 89%. SIMCA models presented equivalent efficiency for model A, but lower efficiency for model B comparing to PLS-DA results. However, SIMCA showed a higher efficiency to deal with samples containing drugs not included in the training phase. Results support use of this method for in loco forensic analysis and as a screening method prior the chromatographic and mass spectrometry analysis.

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 design and testing of a novel vermicomposting system, acronymed FLUVTS ─ FLippable Units Vermireactor Train System ─ is presented. It enables rapid vermicomposting of paper waste without the need of pre-composting and requires animal manure supplementation to the extent of only 10:1 paper: manure mass ratio in contrast to reported systems which must have 50% or more of the feed mass as animal manure. Moreover, the system enables the vermicomposting to be accomplished at a high rate, achieving near-total convertion of feed to vermicast at solid retention times of just 30 days in comparison to conventional systems which take 90–120 days for the same process. Uninterrupted vermireactor operation for 6 months, during which the feed was put in and its vermicompost harvested once in 30 days, demonstrates the robustness and the consistency of the system. The suitability of the paper-waste vermicompost as an organic fertilizer was then tested in terms of it's effect on seed germination and early growth of four food plants chilly (Capsicum annuum), ladies finger, (Abelmoschus esculentus), cucumber (Cucumis sativus), and tomato (Lycopersicon esculentum). In general, the paper waste vermicompost when applied at levels

In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some of their theorems and we present alternative proofs. Moreover, we extend the definition of approximately pseudo-dissipative in the setting of metrizable topological vector spaces.

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.

We give an overview of our critiques of "proofs" of security and a guide to our papers on the subject that have appeared over the past decade and a half. We also provide numerous additional examples and a few updates and errata.

The paper alluded to in the title contains the following striking result: Let $I$ be the unit interval and $\Delta$ the Cantor set. If $X$ is a quasi Banach space containing no copy of $c_0$ which is isomorphic to a closed subspace of a space with a basis and $C(I, X)$ is linearly homeomorphic to $C(\Delta, X)$, then $X$ is locally convex, i.e., a Banach space. It is shown that Kalton result is sharp by exhibiting non locally convex quasi Banach spaces X with a basis for which $C(I, X)$ and $C(\Delta, X)$ are isomorphic. Our examples are rather specific and actually in all cases X is isomorphic to $C(\Delta, X)$ if $K$ is a metric compactum of finite covering dimension., Comment: 4 pages

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.

P values linked to null hypothesis significance testing (NHST) is the most widely (mis)used method of statistical inference. Empirical data suggest that across the biomedical literature (1990–2015)...

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 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

What can be learned from data about human survival at extreme age? In this rejoinder we give our views on some of the issues raised in the discussion of our paper Rootzen and Zholud (Extremes 20(4), 713–728, 2017).

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

In a recent paper referred to in the title, the author used the concept of quasi self-adjointness to obtain conservation laws for a system of the ( 2 + 1 ) -dimensional Bogoyavlensky–Konopelchenko equation. Apart from the adjoint system of equations, all the results on the quasi self-adjointness and the subsequent conservation laws obtained are inaccurate. In this comment, we clarify these inaccuracies and also generate conservation laws for a potential form of the underlying equation through Noether theorem.

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

This paper discusses the development of a near infrared (NIR) spectroscopic method coupled with multivariate analysis to characterise historical paper. Specifically, partial least squares (PLS) regression was used to predict one of the most important properties of paper as a condition indicator – degree of polymerisation (DP). Supported by a set of model cellulose samples, the NIR-PLS method for DP prediction was validated and the modelling approach that led to the best prediction of DP of paper was established. The coefficient of variation of the NIR-PLS models were found to be approximately 8% and 20% of the DP of model cellulose and historical paper, respectively. The variance of the reference DP, the variance of the predicted DP, and the model bias were identified as the main sources of the total expected generalisation error of prediction. For both model cellulose and historical paper, the variance of the predicted DP by the NIR-PLS models contributed the most to the total error of prediction. This suggests that improving the instrumentation and the operation procedure is essential to improve model performance. Furthermore, the effect of water content of the samples on model performance was investigated. The model for historical paper was proven to be robust to relative humidity fluctuations between 30% and 70%, indicating the applicability of the model for collection surveys in a range of environments.

In this short review note we show that the new proof of theorem 1.1 given by Zheng Jie Sun and Ling Zhu in the paper Simple proofs of the Cusa-Huygens-type and Becker-Stark-type inequalities is logically incorrect and present another simple proof of the same.

We congratulate the authors Bertsimas, Pauphilet and van Parys (hereafter BPvP) and Hastie, Tibshirani and Tibshirani (hereafter HTT) for providing fresh and insightful views on the problem of variable selection and prediction in linear models. Their contributions at the fundamental level provide guidance for more complex models and procedures.

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

These notes aim to provide a deeper insight on the specifics of two articles dealing with chemotaxis models with nonlinear production. More precisely, we are referring to the papers “Boundedness of solutions to a quasilinear parabolic–parabolic chemotaxis model with nonlinear signal production” by Tao et al. (2019) [2] and “Boundedness for a fully parabolic Keller–Segel model with sublinear segregation and superlinear aggregation” by Frassu and Viglialoro (2021) [1] . These works, independently published in these last years, present results leaving open room for further improvement. Indeed, in the first a gap in the proof of the main claim appears, whereas the cornerstone assumption in the second is not sharp. In these pages we give a more complete picture to the relative underlying comprehension.

We thank Holger Rootzen and Dmitrii Zholud’s for their stimulating work, that led us to further investigate the problem of best fitting the human life span distribution. Their assertion “human life is unlimited but short” is based on their conclusion that the exponential model is the best to fit. We provide results based on standard Extreme Value approaches, the Block Maxima and Peaks-over-Threshold, and on the whole data available in the IDL database (IDL A, B validations and GRG). We verify that negative values for the extreme value index are more likely, supporting the conclusion that models with finite endpoint seem better to fit to the human life span distribution.

O. Einstein (2008) proved Bollob\'as-type theorems on intersecting families of ordered sets of finite sets and subspaces. Unfortunately, we report that the proof of a theorem on ordered sets of subspaces had a mistake. We prove two weaker variants., Comment: 6 pages. Improved bound for Theorem 4

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.

The aim of this paper is the development of a mathematical model to compute the optimal inventory mix to face stochastic demand at minimum cost in a two-level supply chain. The paper addresses a multi-product dynamic lot-sizing problem under stochastic demand subject to capacity and service level constraints. This model is executed to compare a Make To Order (MTO) strategy to a Vendor Managed Inventory (VMI) partnership between the supplier and their customers. Both strategies provide the demand order to be produced. A schedule of production orders is determined over the planning horizon in order to minimize the inventory holding costs of the supply chain, taking into consideration that the supplier is also responsible of initiating the replenishment orders and deliveries of their customers according to the VMI partnership. The simulation model is illustrated empirically using a real case study: a paper manufacturing company that pursues to improve customer service level and supply chain inventory costs through a proper production planning of their paper machines and a suitable VMI order replenishment schedule.

The translation into English of Aleksandr Yakovlevich Khinchin's (1894–1959) 1926 paper entitled ‘Ideas of intuitionism and the struggle for a subject matter in contemporary mathematics’ is made available for the first time. Here, Khinchin presented the famous foundational debate between L.E.J. Brouwer and David Hilbert of the 1920s in terms of a search for a mathematics with content. His main aim seems to have been to make intuitionism ideologically acceptable to his audience at the Communist Academy by means of the claim that insofar as Brouwer's intuitionism had a clear ‘subject matter’ and Hilbert's new program was a concession to intuitionism, the alleged victory of intuitionism not only implied the defeat of ‘empty’ formalism, but also showed the compatibility and affinity of Marxism with the newest developments in modern mathematics. This introduction provides a tentative exploration of the issue of what was tactical (or due to ideological pressure) and what was real scientific interest (or due to ignorance) (or what was both) in Khinchin's 1926 paper in the form of a detailed commentary, especially, on the tactical side of his presentation of the positions of Brouwer and Hilbert.

We give comments for the paper from Liu et al. (2019) about the Item Response Theory (IRT) model under consideration, the justification to compute Marginal likelihood, about what we learn with the data analysis performed and finally, about the computational issues in this paper.

One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described by a third-order ordinary differential equation (ODE), and typical trajectories approach each equilibrium point in turn, spending progressively longer to cycle around the three points but never stopping. This cycle has been invoked as a model of cyclic competition between populations adopting three strategies, characterised as Rock, Paper and Scissors. When spatial distribution and mobility of the populations is taken into account, waves of Rock can invade regions of Scissors, only to be invaded by Paper in turn. The dynamics is described by a set of partial differential equations (PDEs) that has travelling wave (in one dimension) and spiral (in two dimensions) solutions. In this paper, we explore how the robust heteroclinic cycle in the ODE manifests itself in the PDEs. Taking the wavespeed as a parameter, and moving into a travelling frame, the PDEs reduce to a sixth-order set of ODEs, in which travelling waves are created in a Hopf bifurcation and are destroyed in three different heteroclinic bifurcations, depending on parameters, as the travelling wave approaches the heteroclinic cycle. We explore the three different heteroclinic bifurcations, none of which have been observed in the context of robust heteroclinic cycles previously. These results are an important step towards a full understanding of the spiral patterns found in two dimensions, with possible application to travelling waves and spirals in other population dynamics models., Comment: 36 pages, 8 figures

One of the target of the above paper is the study of the entropy generation (it is included in the title). However, two serious errors exist in the study of entropy generation.

This comment concerns a rightful doubt involved in the above paper. In the reviewed article, a novel model without empirical constants was proposed to evaluate the effective thermal conductivity of three-phase soils, and such a model was claimed to be workable for soils with porosity ranging from 0.0349 to 0.4764 at all saturation degrees. However, sufficient reasons and pictorial explanations were given in this comment to prove its inapplicability for high degrees of saturation. Besides, the inapplicable range is constantly changing, depending on the porosity, i.e. the larger the porosity, the smaller the inapplicable saturation region. Similar issues were further discussed due to its great influence on the follow-up research in this field, i.e. whether can achieve a full coverage of the applicable saturation range [0,1] for a given porosity.

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.

In their celebrated paper (Furst et al., Math. Syst. Theory 17(1), 13---27 (12)), Furst, Saxe, and Sipser used random restrictions to reveal the weakness of Boolean circuits of bounded depth, establishing that constant-depth and polynomial-size circuits cannot compute the parity function. Such local restrictions have played important roles and have found many applications in complexity analysis and algorithm design over the past three decades. In this article, we give a brief overview of two intriguing applications of local restrictions: the first one is for the Isomorphism Conjecture and the second one is for moderately exponential time algorithms for the Boolean formula satisfiability problem.

We are studying topological properties of the Julia set of the map F ( z , p ) = ( ( 2 z p + 1 − 1 ) 2 , ( p − 1 p + 1 ) 2 ) F(z, p)=\left (\left (\frac {2z}{p+1}-1\right )^2, \left (\frac {p-1}{p+1}\right )^2\right ) of the complex projective plane P C 2 \mathbb {P}\mathbb {C}^2 to itself. We show a relation between this rational function and an uncountable family of “paper folding” plane filling curves.

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.

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and H\r{a}stad roved a result known as "$(2+\varepsilon)$-SAT is NP-hard" [FOCS'14/SICOMP'17]. They showed that the problem of distinguishing k-CNF formulas that are g-satisfiable (i.e. some assignment satisfies at least g literals in every clause) from those that are not even 1-satisfiable is NP-hard if $\frac{g}{k} < \frac{1}{2}$ and is in P otherwise. We study a generalisation of SAT on arbitrary finite domains, with clauses that are disjunctions of unary constraints, and establish analogous behaviour. Thus we give a dichotomy for a natural fragment of promise constraint satisfaction problems (PCSPs) on arbitrary finite domains. The hardness side is proved using the algebraic approach, via a new general NP-hardness criterion on polymorphisms of the problem, based on a gap version of the Layered Label Cover problem. We show that previously used criteria are insufficient -- the problem hence gives an interesting benchmark of algebraic techniques for proving hardness of approximation problems such as PCSPs., Comment: Full version of an ICALP 2020 paper