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Geographically replicating objects across multiple data centers improves the performance and reliability of cloud storage systems. Maintaining consistent replicas comes with high synchronization costs, as it faces more expensive WAN transport prices and increased latency. Periodic replication is the widely used technique to reduce the synchronization costs. Periodic replication strategies in existing cloud storage systems are too static to handle traffic changes, which indicates that they are inflexible in the face of unforeseen loads, resulting in additional synchronization cost. We propose quantitative analysis models to quantify consistency and synchronization cost for periodically replicated systems, and derive the optimal synchronization period to achieve the best tradeoff between consistency and synchronization cost. Based on this, we propose a dynamic periodic synchronization method, Sync-Opt, which allows systems to set the optimal synchronization period according to the variable load in clouds to minimize the synchronization cost. Simulation results demonstrate the effectiveness of our models. Compared with the policies widely used in modern cloud storage systems, the Sync-Opt strategy significantly reduces the synchronization cost. [ABSTRACT FROM AUTHOR]

Accurately predicting the Remaining Useful Life (RUL) of lithium-ion batteries is crucial for battery management systems. Deep learning-based methods have been shown to be effective in predicting RUL by leveraging battery capacity time series data. However, the representation learning of features such as long-distance sequence dependencies and mutations in capacity time series still needs to be improved. To address this challenge, this paper proposes a novel deep learning model, the MLP-Mixer and Mixture of Expert (MMMe) model, for RUL prediction. The MMMe model leverages the Gated Recurrent Unit and Multi-Head Attention mechanism to encode the sequential data of battery capacity to capture the temporal features and a re-zero MLP-Mixer model to capture the high-level features. Additionally, we devise an ensemble predictor based on a Mixture-of-Experts (MoE) architecture to generate reliable RUL predictions. The experimental results on public datasets demonstrate that our proposed model significantly outperforms other existing methods, providing more reliable and precise RUL predictions while also accurately tracking the capacity degradation process. Our code and dataset are available at the website of github. [ABSTRACT FROM AUTHOR]

The article discusses the lack of attention given to belowground plant organs and their functions by researchers. It highlights the various functions of these organs, such as resource acquisition, clonal multiplication, and carbon sequestration, that are not well understood due to their belowground position and the difficulty of studying them. The article introduces a special issue of the journal Folia Geobotanica dedicated to belowground plant organs, featuring seven papers from four continents covering a range of topics. These include the role of belowground bud bearing organs in response to disturbance and competition, the diversity of belowground storage and bud bearing organs in different regions, methods for manipulating root architecture, and the discovery of rare and interesting morphological traits. The article concludes by expressing hope that the special issue will inspire further research and interest in belowground plant organs. [Extracted from the article]

This study empirically investigated the influence of freeze–thaw cycling on the dynamic splitting tensile properties of steel fiber reinforced concrete (SFRC). Brazilian disc splitting tests were conducted using four loading rates (0.002, 0.02, 0.2, and 2 mm/s) on specimens with four steel fiber contents (0%, 0.6%, 1.2%, and 1.8%) subjected to 0 and 50 freeze–thaw cycles. The dynamic splitting tensile damage characteristics were evaluated using acoustic emission (AE) parameter analysis and Fourier transform spectral analysis. The results quantified using the freeze–thaw damage factor defined in this paper indicate that the degree of damage to SFRC caused by freeze–thaw cycling was aggravated with increasing loading rate but mitigated by increasing fiber content. The percentage of low-frequency AE signals produced by the SFRC specimens during loading decreased with increasing loading rate, whereas that of high-frequency AE signals increased. Freeze–thaw action had little effect on the crack types observed during the early and middle stages of the loading process; however, the primary crack type observed during the later stage of loading changed from shear to tensile after the SFRC specimens were subjected to freeze–thaw cycling. Notably, the results of this study indicate that the freeze–thaw damage to SFRC reduces AE signal activity at low frequencies. [ABSTRACT FROM AUTHOR]

Roads are exposed to various degradation mechanisms during their lifetime. The pavement deterioration caused by the surrounding environment is particularly severe in winter when the humidity and subfreezing temperatures prevail. Frost heave-induced damage is one of the winter-related pavement deterioration. It occurs when the porewater in the soil is exposed to freezing temperatures. The study of frost heave requires conducting a multiphysics analysis, considering the thermal, mechanical, and hydraulic fields. This paper presents the use of a coupled thermo-mechanical approach to simulate frost heave in saturated soils. A function predicting porosity evolution is implemented to couple the thermal and mechanical field analyses. This function indirectly considers the effect of the water seepage inside the soil. Different frost heave scenarios with uniform and non-uniform boundary conditions are considered to demonstrate the capabilities of the method. The results of the simulations indicate that the thermo-mechanical model captures various processes involved in the frost heave phenomenon, such as water fusion, porosity variation, cryogenic suction force generation, and soil expansion. The characteristics and consequences of each process are determined and discussed separately. Furthermore, the results show that non-uniform thermal boundaries and presence of a culvert inside the soil result in uneven ground surface deformations. [ABSTRACT FROM AUTHOR]

A hinting pseudorandom generator (PRG) is a potentially stronger variant of PRG with a “deterministic” form of circular security with respect to the seed of the PRG (Koppula and Waters, in: Boldyreva and Micciancio (eds) CRYPTO 2019, Part II, volume 11693 of LNCS, pp 671-700, Springer, Heidelberg, 2019). Hinting PRGs enable many cryptographic applications, most notably CCA-secure public-key encryption and trapdoor functions. In this paper, we study cryptographic primitives with the hinting property, yielding the following results: We present a novel and conceptually simpler approach for designing hinting PRGs from certain decisional assumptions over cyclic groups or isogeny-based group actions, which enables simpler security proofs as compared to the existing approaches for designing such primitives. We also show that the same design approach yields a generic construction of hinting PRGs from a simple cryptographic primitive with algebraic structure, namely a key-homomorphic weak PRF. We introduce hinting pseudorandom functions (PRFs) and hinting weak PRFs, which are natural extensions of the hinting property to PRFs and weak PRFs. We show how to realize circular/KDM-secure symmetric-key encryption from any hinting weak PRF. We demonstrate that our simple approach for building hinting PRGs can be extended to realize hinting weak PRFs from the same set of decisional assumptions. We also show a generic construction of hinting (weak) PRF from any hinting PRG with certain structural properties, thus yielding the first constructions of symmetric-key encryption with full-fledged circular/KDM-security from such hinting PRGs. We propose a stronger version of the hinting property, which we call the functional hinting property, that guarantees security even in the presence of hints about functions of the secret seed/key. We show how to instantiate functional hinting PRGs/weak PRFs for certain (families of) functions by building upon our simple techniques for realizing plain hinting PRGs/weak PRFs. We also demonstrate the applicability of a functional hinting weak PRF with certain algebraic properties in realizing KDM-secure public-key encryption in a black-box manner. We show the first black-box separation between hinting PRFs (and hence, hinting PRGs) from public-key encryption using simple realizations of these primitives given only a random oracle. [ABSTRACT FROM AUTHOR]

We study the maximum number of limit cycles that bifurcate from the periodic annulus of the isochronous cubic centre of discontinuous and continuous piecewise differential systems with three zones formed by the discontinuity set Σ = { (x , y) ∈ R 2 : (y = 0) ∨ (x = 0 ∧ y ≥ 0) } . More precisely, we consider the following perturbed systems x ˙ = - y + x 2 y + ϵ p i (x , y) , y ˙ = x + x y 2 + ϵ q i (x , y) , i = 1 , 2 , 3 , where p i and q i are polynomials of degree m. Using the averaging theory of first order, we prove that for m = 1 , 2 , 3 , at most 3, 9 and 15 limit cycles bifurcate from the periodic annulus of the isochronous cubic centre in the discontinuous case, respectively. While for the continuous case, it can appear 1, 5 and 6 limit cycles from the periodic orbits of these centres, respectively. Furthermore, we extend our study when p i and q i are homogeneous polynomials with 1 ≤ m ≤ 3 , obtaining respectively for m = 1 , 2 , 3 at most one, seven and at least twelve limit cycles, which bifurcate from the periodic orbits of the isochronous cubic centre. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cauchy problem for the nonlinear Schrödinger equation with focusing inverse-power potential and the Sobolev critical nonlinearity. By considering the corresponding local minimization problem, we show that the existence of ground state solutions. Then, we prove that the solution of this equation exists globally when the initial data φ sufficiently close to the ground states. Based on these results, we show that the set of ground states is orbitally stable. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following quasilinear Schrödinger equation involving Stein–Weiss type nonlinearity: - Δ u + V (x) u - Δ (u 2) u = 1 | x | α ∫ R N G (u (y)) | y - x | μ | y | α d y g (u (x)) , in R N , where N ≥ 3 , 0 < μ < N , α ≥ 0 and 2 α + μ < min { N + 2 2 , 4 } and G is the primitive of function g. The potential V : R N → R may decay to zero at infinity. By using variational methods, penalization technique and L ∞ -estimates, we obtain the existence of a positive solution for the above quasilinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

Combining the spectral radius of matrix with the generalized Banach fixed point theory and some properties of exponential contraction, we prove periodic solution and almost periodic solution of a neutral delay multispecies logarithmic population model with piecewise constant argument is existent and unique in appropriate conditions. The results have generalized and improved some results of literature on logarithmic population model. Finally, one example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

A G -strand is an evolutionary map g (t , s) : R × R → G into a Lie group G that follows from the Hamilton's principle for a certain class of G -invariant Lagrangians defined on the Lie algebra of the group G . t and s are independent variables associated to a G -invariant Lagrangian. The G -strand equations comprises a system of integrable partial differential equations obtained from the Euler–Poincaré variational equations coupled to an auxiliary zero curvature equation. Some of these integrable partial differential equations include the Hunter–Saxton equation that arises in the study of nematic liquid crystals and the Camassa–Holm equation that arises in modeling waves in shallow water including solitons and peakons. However, nonlocal integrable systems have attracted significant attention in recent years. In this study, we use a higher-order nonlocal operator approach to study nonlocal Hunter–Saxton type peakons. Peakons-antipeakons collision on Lie group is also analyzed and discussed. It was observed that the system of "two-peakon" collisions exhibits a kind of disordered behavior which is observed in various integrable and non-integrable nonlinear evolution dynamical systems. [ABSTRACT FROM AUTHOR]

Studying the transformation mechanisms of soliton solutions of some high-dimensional equations can aid in comprehending the physical phenomena of the relevant nonlinear wave interactions. Therefore, the transitions and mechanisms of nonlinear waves in the (2+1)-dimensional sine-Gordon and (2+1)-dimensional modified Boussinesq equations are investigated for the first time by means of characteristic line and phase shift analysis, and the dynamic behavior of various nonlinear transformed waves is analyzed. Firstly, we derive the N-soliton solution by applying the Hirota bilinear method, from which the breather solution is constructed by changing the parameters into a complex form in pairs. In addition, via the characteristic-line analysis, we present the mechanism for the transformation of the breather solution, which is composed of the nonlinear superposition of a solitary wave and periodic wave. When the characteristic lines of the two parts are parallel, we find that various transformed nonlinear wave structures can be obtained, such as M-type solitons, oscillating M-type solitons, multi-peak solitons, quasi-sine waves and so on. Finally, we demonstrate that the geometric properties of the characteristic lines vary with time essentially resulting in the time-varying properties of nonlinear waves, which have never been found in (1+1)-dimensional systems. Overall, the study of breath-wave transitions in the (2+1)-dimensional sine-Gordon equation and the modified Boussinesq equation provides valuable insights into the bahavior of nonlinear systems and wave propagation. [ABSTRACT FROM AUTHOR]

The global attractor of a dissipative dynamical system provides the necessary information to understand the asymptotic dynamics of all the system’s solutions. A crucial question consists in finding the structure of this set. In this paper we provide a full characterization of the structure of attractors for a planar non-autonomous Lotka–Volterra cooperative system. We show sufficient conditions for the existence of forward attractors and give a full description of them by proving the existence of such bounded global solutions that all bounded global solutions join them, i.e. converge towards them when time tends to plus and minus infinity. These results generalize those known in an autonomous framework. The case of particular interest in our work is the situation where globally forward-stable non-autonomous solutions have both coordinates strictly positive. We study this case in detail and obtain sufficient conditions that the problem parameters must satisfy in order to obtain various structures of non-autonomous attractors. This allows us to understand different paths of the solutions towards the unique globally stable one. [ABSTRACT FROM AUTHOR]

A hierarchy of nonlocal nonlinear Schrödinger equations is derived by using the Lenard gradients and the zero-curvature equation. According to the Lax matrix of the nonlocal nonlinear Schrödinger equations, we introduce a hyperelliptic Riemann surface K n of genus n, from which Dubrovin-type equations, meromorphic function, and Baker–Akhiezer function are established. By the theory of algebraic curves, the corresponding flows are straightened by resorting to the Abel–Jacobi coordinates. Finally, we obtain the explicit Riemann theta function representations of the Baker–Akhiezer function, specifically, that of solutions for the hierarchy of nonlocal nonlinear Schrödinger equations in regard to the asymptotic properties of the Baker–Akhiezer function. [ABSTRACT FROM AUTHOR]

In this paper we study the generalized Lagrangian system with a small perturbation. We assume the main term in the system to have a maximum, but do not suppose any condition for perturbation term. Then we prove the existence of a periodic solution via Ekeland’s principle. Moreover, we prove a convergence theorem for periodic solutions of perturbed systems. [ABSTRACT FROM AUTHOR]

This study is centered on addressing the complexities of the nonlinear time-fractional Harry Dym equation through a combined application of analytical and numerical methodologies. The principal objective is to establish a comprehensive framework for solving this intricate fractional partial differential equation. The introduction of the Khater II method as an analytical technique presents a novel approach specifically designed to handle such equations. In tandem, the utilization of numerical schemes-cubic-B-spline, quantic-B-spline, and septic-B-spline methods-further refines the accuracy and efficiency of the solutions. The outcomes underscore the efficacy of these proposed methods in effectively resolving the challenges posed by the Harry Dym equation. Emphasis is placed on the dual facets of analytical insights and numerical precision. The significance of this study lies in its contribution to advancing comprehension of nonlinear time-fractional equations while offering practical tools for their resolution. The conclusions drawn from this research provide valuable insights into the practical applicability of the Khater II method and B-spline schemes in navigating complex mathematical models. The novelty of this work lies in the amalgamation of an innovative analytical approach with established numerical techniques, signifying a noteworthy contribution to this field of study. [ABSTRACT FROM AUTHOR]

In this article, the phase portraits, chaotic patterns, and traveling wave solutions of the stochastic Sasa–Satsuma equation are investigated. Firstly, the stochastic Sasa–Satsuma equation is transformed into an ordinary differential equation through traveling wave transformation. Secondly, two-dimensional planar dynamical system is presented by using the theory of planar dynamical systems. Then, the three-dimensional and two-dimensional phase portraits of the dynamical system are drawn by using Maple software. Finally, the complete discriminant system method is used to solve the stochastic Sasa-Satsuma equation, resulting in many solutions that other methods cannot obtain, including rational, trigonometric, hyperbolic, and Jacobi elliptic function solutions. Moreover, three-dimensional-surface plots and two-dimensional-shape plots for the module length of some solutions under different parameters are drawn by using Maple software. The innovation of this article lies in introducing stochastic parameters into the Sasa–Satsuma equation, obtaining more diverse and comprehensive conclusions. [ABSTRACT FROM AUTHOR]

This study employs advanced computational methodologies to investigate the nonlinear complex fractional generalized Zakharov equations, herein referred to as NCFGZ . The primary objective is to elucidate precise and groundbreaking solitary wave solutions. These equations find wide–ranging applications in diverse domains, including plasma physics, nonlinear optics, and wave dynamics. The pursuit of highly accurate solitary wave solutions is of paramount significance, as it contributes to both theoretical comprehension and practical real-world applications. By harnessing cutting-edge computational techniques along with conformable fractional derivative (CFD) and leveraging the capabilities of Mathematica 13.1 software, this research significantly advances theoretical knowledge and provides valuable practical insights. The computational approaches employed in this research outperform conventional methods in terms of their efficacy, demonstrating a high degree of precision and efficiency in solving complex fractional differential equations. These findings underscore the pivotal role that precise solitary wave solutions play in forecasting and comprehending the behavior of nonlinear systems governed by the generalized Zakharov, or G Z , equations. Furthermore, this study yields profound implications for the symmetry theorem of solitons, enhancing our understanding of symmetry properties within the context of G Z equations and their broader influence on wave phenomena. [ABSTRACT FROM AUTHOR]

Some new criteria on existence of positive solution for a higher order elliptic problem with an eigenvalue parameter are established under some sublinear conditions, which involve the principle eigenvalues of the corresponding linear problems. New results on nonexistence and multiplicity of positive solutions are also derived. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct the general solution to a nonlocal linear differential equation of first-order, either homogeneous or inhomogeneous, together with its stability analysis. The success lies in decomposing functions into their even and odd parts, which presents an innovative approach to nonlocal equations. Our analysis also exhibits an unusual solution phenomenon occurring in nonlocal models. [ABSTRACT FROM AUTHOR]

The focus of this study lies in developing and evaluating a Caputo–Fabrizio fractional derivative model that encapsulates the dynamics of the worldwide HIV/AIDS epidemic while integrating an antiretroviral therapy component. The methodology involves employing iterative techniques alongside the fixed-point theorem to establish the existence and uniqueness solutions of the model. In particular, the model identifies equilibrium points corresponding to disease outbreaks and disease-free scenarios. Additionally, it showcases the local asymptotic stability of the disease-free equilibrium point and outlines the criteria for the presence of the endemic equilibrium point. The findings verify that as the fractional order decreases, the disease-free equilibrium point becomes more stable. To demonstrate the impact of altering the fractional order and to bolster the theoretical finding, numerical simulations are conducted over the fractional order range. [ABSTRACT FROM AUTHOR]

This paper introduces a (3 + 1)-dimensional dispersionless integrable system, utilizing a Lax pair involving contact vector fields, in alignment with methodologies presented by Sergyeyev in 2014. Significantly, it is shown that the proposed system serves as an integrable (3 + 1)-dimensional generalization of the well-studied (2 + 1)-dimensional dispersionless Davey–Stewartson system. This way, an interesting new example on integrability in higher dimensions is presented, with potential applications in analyzing three-dimensional nonlinear waves across various fields, including oceanography, fluid dynamics, plasma physics, and nonlinear optics. Importantly, the integrable nature of the system suggests that established techniques like the study of symmetries, conservation laws, and Hamiltonian structures could be applicable. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the approximate controllability for Hilfer fractional stochastic hemivariational inequalities of order 1 < μ < 2 in Hilbert spaces. Initially, we define the concept of a mild solution for our problem in terms of fractional calculus, cosine families, stochastic analysis, and generalized Clarke subdifferential. Then, the existence and approximate controllability for Hilfer fractional stochastic evolution hemivariational inequalities are formulated and proven under appropriate conditions using fixed point theorems for multivalued maps. Finally, an example is presented to illustrate the theory. [ABSTRACT FROM AUTHOR]

The main goal of this study is to use the ψ -Caputo fractional derivative of order ϑ ∈ (0 , 1) to construct the criteria for controllability in non-instantaneous impulsive dynamical systems. To obtain the necessary and sufficient conditions for the controllability of linear fractional systems by incorporating the positiveness of the Grammian matrices. To obtain sufficient conditions for controllability criteria for nonlinear systems, we have used Schaefer’s fixed point theorem. To enhance comprehension of the theoretical findings, several numerical examples have been provided. [ABSTRACT FROM AUTHOR]

This article primarily focuses on the single-valued and multi-valued cases of the class of nonlinear Caputo two-term fractional differential equation with three-point integral boundary conditions. In the single-valued case, we employ Schaefer’s fixed point theorem and the Banach fixed point theorem to establish results regarding the existence and uniqueness of solutions, using linear growth and Lipschitz conditions. Furthermore, we delve into the stability analysis of the single-valued problem using Ulam–Hyers and Ulam–Hyers–Rassias stabilities. In addition to the above, we address the multi-valued scenario and provide results on the existence of solutions. This is achieved by employing the Covitz–Nadler FPT and the nonlinear alternative for contractive maps. As an application of our fundamental findings, we present illustrative examples that validate our results. These examples have been implemented using MATLAB. [ABSTRACT FROM AUTHOR]

This study presents a new approach for accurately obtaining solitary wave solutions in the Boiti–Leon–Pempinelli (BLP) system, which was developed by Italian mathematicians Luca Boiti, Franco Leon, and Guido Pempinelli in the late 1980 s. The BLP system is very significant in physics and is employed in several fields. It is used to simulate the behavior of nonlinear media in electromagnetic and acoustic wave propagation, as well as to understand the features of Bose–Einstein condensates. This research thoroughly examines the acquired solutions, with a particular focus on crucial factors such as the maximum amplitude, duration, and velocity of the waves. The accurate solitary wave solutions play a crucial role in enhancing the comprehension of these physical phenomena, establishing the foundation for possible practical uses. The suggested modified exponential function approach outperforms previous numerical strategies in terms of efficacy and dependability, demonstrating the significant potential for future study in this field. The results of our investigation are graphically shown using meticulously designed graphs, providing valuable insights into the behavior of various solutions inside the (x, t) domain. This visual depiction facilitates the identification of key characteristics such as velocity, magnitude, and form, hence improving the clarity of our study findings. [ABSTRACT FROM AUTHOR]

Traveling wave solutions are a class of invariant solutions which are critical for shallow water wave equations. In this paper, traveling wave solutions for two perturbed KP-MEW equations with a local delay convolution kernel are examined. The model equation is reduced to a planar near-Hamiltonian system via geometric singular perturbation theorem, and the qualitative properties of the corresponding unperturbed system are analyzed by using dynamical system approach. The persistence of the bounded traveling wave solutions for the perturbed KP-MEW equations with delay is investigated. By using a criterion for the monotonicity of ratio of two Abelian integrals and Melnikov’s method, the existence of kink (anti-kink) wave solutions and periodic wave solutions of the model equation are established. The result shows that the delayed KP-MEW equations with positive perturbation and the one with negative perturbation exhibit completely diverse dynamical properties. These new findings greatly enrich the understanding of dynamical properties of the traveling wave solutions of perturbed nonlinear wave equations with local delay convolution kernel. Numerical experiments further confirm and illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned to studying the quasilinear Schrödinger equation: - Δ u + V (x) u - γ 2 Δ (u 2) u = | u | p - 2 u , x ∈ R N , where V(x) is a given potential, γ > 0 and either p ∈ (2 , 2 ∗) , 2 ∗ = 2 N N - 2 for N ⩾ 4 or p ∈ (2 , 4) for N = 3 . We establish the existence of arbitrary multiple nodal solutions for the above equations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the maximum number of limit cycles that can bifurcate from the periodic annulus of the linear center for discontinuous piecewise quadratic polynomial differential systems with four zones separated by two nonlinear curves y = ± x 2 . By analyzing the first order averaged function, we prove that at most 7 crossing limit cycles can produce from periodic annulus of the linear center, and the upper bound is reached. In addition, under particular conditions, we obtain that at least 8 crossing limit cycles can bifurcate from periodic annulus in this class of systems by using the second order averaged function. Our results show that multiple switching curves increase the number of crossing limit cycles in comparison with the case where there is only a single switching curve. [ABSTRACT FROM AUTHOR]

This paper is concerned with a Lotka–Volterra cooperative model with degenerate diffusion under climate change. Firstly, by constructing the appropriate upper and lower solutions to overcome the influence of the degeneracy and nonautonomous terms, and applying the monotone iteration method, we prove the existence of forced traveling waves with any speed c > 0 at which the habitat edge is shifting. Then based on the new comparison theorem for degenerate diffusion systems, we obtain the global existence of C α , β -solution to the initial value problem of this system via the compactness analysis. At the end of the paper, some numerical simulations are conducted. [ABSTRACT FROM AUTHOR]

Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as B n (x , e - n ϵ) = { y ∈ X : d (T j x , T j y) < e - n ϵ , ∀ 0 ≤ j ≤ n - 1 }. We introduce the notion of neutralized Bowen topological entropy of subsets by neutralized Bowen open ball, and establish variational principles for neutralized Bowen topological entropy of compact subsets in terms of neutralized Brin–Katok local entropy and neutralized Katok’s entropy. [ABSTRACT FROM AUTHOR]

In this paper, the minimal-speed selection mechanism to a Lotka–Volterra type of model with local versus nonlocal diffusions and cubic nonlinearity is considered. By using comparison principle and upper-lower solution method, general criteria for both linear and nonlinear selection of the minimal wave speed are derived. Based on these results, several explicit conditions for determining the linear selection of the minimal wave speed are obtained via the constructions of various upper solutions. These conditions can help us to confirm that the species will spread with the speed of a linearised system and take an insight into thresholds for different model parameters. Moreover, it is found that the model with cubic nonlinearity causes a very different mechanism compared to the one caused by quadratic nonlinearity. For example, the linear selection can be realized when the diffusion strength is in an infinite interval for the model with cubic nonlinearity. Finally, it should be pointed out that concrete conditions for nonlinear selection are not obtained due to the failure of construction of a lower solution, and are left for further work. [ABSTRACT FROM AUTHOR]

In this work, the Riemann–Hilbert (RH) problem is employed to study the Lakshmanan–Porsezian–Daniel (LPD) equation with arbitrary-order pole points under finite density initial data condition. By performing spectral analysis on Lax pairs, a suitable matrix RH problem is established. Through the residue theorem, the explicit expression of simple pole solutions is obtained by Binet–Cauchy theorem. In addition, utilizing the Wronskian form of scattering data s 11 (μ) which degenerates to zero at high-order zero points and the Taylor expansion of oscillation index e 2 i θ , the expression of the high-order pole solutions is constructed. Moreover, the detailed analysis is conducted on the dynamic behaviors of special soliton solutions, and some interesting soliton phenomena are presented by taking the influence of various parameters into consideration. [ABSTRACT FROM AUTHOR]

The density of a population in a natural state often fluctuates greatly, but it is not an unlimited change. Throughout the full text, we consider a stochastic predator–prey system with fear, Holling-II response function, distributed delay and mean-reverting Ornstein–Uhlenbeck process, which can better reflect the actual situation and provide theoretical basis for species research in the actual environment. And we drew some significant conclusions. The first step is to obtain the stability of equilibrium point. Then, the existence and uniqueness of positive solution for stochastic system is got and we also reach the stationary distribution of the stochastic system. In addition, we present an exact local expression for the density function of the random system near the unique positive equilibrium. Then we obtain the pth moment boundedness and the asymptotic behavior of the solution. At last, we give the extinction condition of the population system by the asymptotic behavior of the solution. In particular, we confirm the theoretical results by numerical simulation in the corresponding section. [ABSTRACT FROM AUTHOR]

We discuss an optimal control problem for the Kirchhoff–Poisson type controlled system. By using variational methods and embedding theorem, we obtain the existence uniqueness of solutions to the state equation and existence of an optimal control. [ABSTRACT FROM AUTHOR]

Expanding floating wind into new markets could support emission reduction targets in several national contexts. It furthers the need for adequate assessments to gain a full understanding of the technology's potential in future markets. South Africa is a prime case study as it has seen limited industry and policy developments despite its huge technical potential for floating offshore wind (FOW). This paper assessed the locational potential of floating wind in South Africa through a three-phased approach that evaluated the key technical drivers/barriers of the technology, conducted a Geographic Information System analysis (GIS) using ArcMap 10.8 to exclude unsuitable sites based on a predetermined exclusion criteria (including marine protected zones, underwater cables, major oil and gas deposits, etc.), and estimated the total harvestable capacity in the feasible sites. The study found that 2% (246,105.4 km2) of South Africa's entire Exclusive Economic Zone (EEZ) is suitable for hosting floating wind turbines, with a potential to generate a maximum of 142.61 GW of floating wind power. Although the Western Cape province holds the highest potential (80.52 GW) for floating wind in the country, the Eastern Cape region, with a locational potential of 20.04 GW, is considered most suitable for early-stage developments due to the availability of grid connection points, limited marine traffic, and proximity to appropriate port facilities. Future work can conduct techno-economic assessments to evaluate the technical and economic implications of developing floating wind in distinct sites in the country's EEZ. [ABSTRACT FROM AUTHOR]

We investigate the zero-temperature hysteresis characteristics of the diluted random field 3-state clock model under a cyclic driving field with zero frequency. This analysis is conducted in the presence of two types of quenched random fields within the mean field approximation. The influence of dilution on the hysteretic response of the model at moderate concentration levels is observed to be contingent on the particular form of disorder. Following this, simulations on a simple cubic lattice are performed for a comparative analysis with mean field predictions. [ABSTRACT FROM AUTHOR]

This work seeks to make explicit the operational connection between the preparation of two-level quantum systems with their corresponding description (as states) in a Hilbert space. This may sound outdated, but we show there is more to this connection than common sense may lead us to believe. To bridge these two separated realms—the actual laboratory and the space of states—we rely on a paradigmatic mathematical object: the Hopf fibration. We illustrate how this connection works in practice with a simple optical setup. Remarkably, this optical setup also reflects the necessity of using two charts to cover a sphere. Put another way, our experimental realization reflects the bi-dimensionality of a sphere seen as a smooth manifold. [ABSTRACT FROM AUTHOR]

Mobile Edge Computing (MEC) is a promising approach. Dynamic service migration is a key technology in MEC. In order to maintain the continuity of services in a dynamic environment, mobile users need to migrate tasks between multiple servers in real time. Due to the uncertainty of movement, frequent migration will increase delays and costs and non-migration will lead to service interruption. Therefore, it is very challenging to design an optimal migration strategy. In this paper, we investigate the multi-user task migration problem in a dynamic environment and minimizes the average service delay while meeting the migration cost. In order to optimize the service delay and migration cost, we propose an adaptive weight deep deterministic policy gradient (AWDDPG) algorithm. And distributed execution and centralized training are adopted to solve the high-dimensional problem. Experiments show that the proposed algorithm can greatly reduce the migration cost and service delay compared with the other related algorithms. [ABSTRACT FROM AUTHOR]

The use of all samples in the optimization process does not produce robust results in datasets with label noise. Because the gradients calculated according to the losses of the noisy samples cause the optimization process to go in the wrong direction. In this paper, we recommend using samples with loss less than a threshold determined during the optimization, instead of using all samples in the mini-batch. Our proposed method, Adaptive-k, aims to exclude label noise samples from the optimization process and make the process robust. On noisy datasets, we found that using a threshold-based approach, such as Adaptive-k, produces better results than using all samples or a fixed number of low-loss samples in the mini-batch. On the basis of our theoretical analysis and experimental results, we show that the Adaptive-k method is closest to the performance of the Oracle, in which noisy samples are entirely removed from the dataset. Adaptive-k is a simple but effective method. It does not require prior knowledge of the noise ratio of the dataset, does not require additional model training, and does not increase training time significantly. In the experiments, we also show that Adaptive-k is compatible with different optimizers such as SGD, SGDM, and Adam. The code for Adaptive-k is available at GitHub. [ABSTRACT FROM AUTHOR]

Learning modality-fused representations and processing unaligned multimodal sequences are meaningful and challenging in multimodal emotion recognition. Existing approaches use directional pairwise attention or a message hub to fuse language, visual, and audio modalities. However, these fusion methods are often quadratic in complexity with respect to the modal sequence length, bring redundant information and are not efficient. In this paper, we propose an efficient neural network to learn modality-fused representations with CB-Transformer (LMR-CBT) for multimodal emotion recognition from unaligned multi-modal sequences. Specifically, we first perform feature extraction for the three modalities respectively to obtain the local structure of the sequences. Then, we design an innovative asymmetric transformer with cross-modal blocks (CB-Transformer) that enables complementary learning of different modalities, mainly divided into local temporal learning, cross-modal feature fusion and global self-attention representations. In addition, we splice the fused features with the original features to classify the emotions of the sequences. Finally, we conduct word-aligned and unaligned experiments on three challenging datasets, IEMOCAP, CMU-MOSI, and CMU-MOSEI. The experimental results show the superiority and efficiency of our proposed method in both settings. Compared with the mainstream methods, our approach reaches the state-of-the-art with a minimum number of parameters. [ABSTRACT FROM AUTHOR]

Graphs that are used to model real-world entities with vertices and relationships among entities with edges, have proven to be a powerful tool for describing real-world problems in applications. In most real-world scenarios, entities and their relationships are subject to constant changes. Graphs that record such changes are called dynamic graphs. In recent years, the widespread application scenarios of dynamic graphs have stimulated extensive research on dynamic graph processing systems that continuously ingest graph updates and produce up-to-date graph analytics results. As the scale of dynamic graphs becomes larger, higher performance requirements are demanded to dynamic graph processing systems. With the massive parallel processing power and high memory bandwidth, GPUs become mainstream vehicles to accelerate dynamic graph processing tasks. GPU-based dynamic graph processing systems mainly address two challenges: maintaining the graph data when updates occur (i.e., graph updating) and producing analytics results in time (i.e., graph computing). In this paper, we survey GPU-based dynamic graph processing systems and review their methods on addressing both graph updating and graph computing. To comprehensively discuss existing dynamic graph processing systems on GPUs, we first introduce the terminologies of dynamic graph processing and then develop a taxonomy to describe the methods employed for graph updating and graph computing. In addition, we discuss the challenges and future research directions of dynamic graph processing on GPUs. [ABSTRACT FROM AUTHOR]

Learning activities interactions between small groups is a key step in understanding team sports videos. Recent research focusing on team sports videos can be strictly regarded from the perspective of the audience rather than the athlete. For team sports videos such as volleyball and basketball videos, there are plenty of intra-team and inter-team relations. In this paper, a new task named Group Scene Graph Generation is introduced to better understand intra-team relations and inter-team relations in sports videos. To tackle this problem, a novel Hierarchical Relation Network is proposed. After all players in a video are finely divided into two teams, the feature of the two teams' activities and interactions will be enhanced by Graph Convolutional Networks, which are finally recognized to generate Group Scene Graph. For evaluation, built on Volleyball dataset with additional 9660 team activity labels, a Volleyball+ dataset is proposed. A baseline is set for better comparison and our experimental results demonstrate the effectiveness of our method. Moreover, the idea of our method can be directly utilized in another video-based task, Group Activity Recognition. Experiments show the priority of our method and display the link between the two tasks. Finally, from the athlete's view, we elaborately present an interpretation that shows how to utilize Group Scene Graph to analyze teams' activities and provide professional gaming suggestions. [ABSTRACT FROM AUTHOR]

Matroid theory has been developed to be a mature branch of mathematics and has extensive applications in combinatorial optimization, algorithm design and so on. On the other hand, quantum computing has attracted much attention and has been shown to surpass classical computing on solving some computational problems. Surprisingly, crossover studies of the two fields seem to be missing in the literature. This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits (bases, flats, hyperplanes) of a matroid, and for the decision problem of deciding whether a matroid is uniform or Eulerian, by giving a uniform lower bound Ω ( ( n ⌊ n / 2 ⌋ ) ) on the query complexity of all these problems. On the other hand, for the uniform matroid decision problem, an asymptotically optimal quantum algorithm is proposed which achieves the lower bound, and for the girth problem, an almost optimal quantum algorithm is given with query complexity O (log n ( n ⌊ n / 2 ⌋ ) ) . In addition, for the paving matroid decision problem, a lower bound Ω ( ( n ⌊ n / 2 ⌋ ) / n ) on the query complexity is obtained, and an O ( ( n ⌊ n / 2 ⌋ ) ) quantum algorithm is presented. [ABSTRACT FROM AUTHOR]

Conclusion: We propose HeterMM, a versatile framework that leverages in-DRAM indexes in KV stores on heterogeneous memory. HeterMM incorporates a plug-in programming model, allowing for the integration of various types of indexes. By prioritizing the maintenance of both index and hot data in DRAM, HeterMM maximizes the utilization of the superior performance of DRAM. Our evaluation demonstrates that HeterMM outperforms existing state-of-the-art frameworks that convert in-DRAM indexes to persistent ones. Furthermore, HeterMM can surpass NVM-specific KV stores by carefully selecting the appropriate index for specific scenarios. [ABSTRACT FROM AUTHOR]

Model-based reinforcement learning is a promising direction to improve the sample efficiency of reinforcement learning with learning a model of the environment. Previous model learning methods aim at fitting the transition data, and commonly employ a supervised learning approach to minimize the distance between the predicted state and the real state. The supervised model learning methods, however, diverge from the ultimate goal of model learning, i.e., optimizing the learned-in-the-model policy. In this work, we investigate how model learning and policy learning can share the same objective of maximizing the expected return in the real environment. We find model learning towards this objective can result in a target of enhancing the similarity between the gradient on generated data and the gradient on the real data. We thus derive the gradient of the model from this target and propose the Model Gradient algorithm (MG) to integrate this novel model learning approach with policy-gradient-based policy optimization. We conduct experiments on multiple locomotion control tasks and find that MG can not only achieve high sample efficiency but also lead to better convergence performance compared to traditional model-based reinforcement learning approaches. [ABSTRACT FROM AUTHOR]

Conclusions: In this paper, we propose GSR-NTT and demonstrate that K-NTT, H-NTT, and G3-NTT are specific instances of GSR-NTT. We introduce a succinct methodology for complexity analysis, and utilize our GSR-NTT to accelerate polynomial multiplications in NTTRU and power-of-three cyclotomic rings. [ABSTRACT FROM AUTHOR]

With current success of large-scale pre-trained models (PTMs), how efficiently adapting PTMs to downstream tasks has attracted tremendous attention, especially for PTMs with billions of parameters. Previous work focuses on designing parameter-efficient tuning paradigms but needs to save and compute the gradient of the whole computational graph. In this paper, we propose Y -Tuning, an efficient yet effective paradigm to adapt frozen large-scale PTMs to specific downstream tasks. Y -Tuning learns dense representations for labels Y defined in a given task and aligns them to fixed feature representation. Without computing the gradients of text encoder at training phrase, Y -Tuning is not only parameter-efficient but also training-efficient. Experimental results show that for DeBERTaXXL with 1.6 billion parameters, Y -Tuning achieves performance more than 96% of full fine-tuning on GLUE Benchmark with only 2% tunable parameters and much fewer training costs. [ABSTRACT FROM AUTHOR]