Search

In the present work, we introduce a simple means of obtaining an analytical (i.e., grid-free) canonical polyadic (CP) representation of a multidimensional function that is expressed in terms of a set of discrete data. For this, we make use of an initial CP guess, even not fully converged, and a set of auxiliary basis functions [finite basis representation (FBR)]. The resulting CP-FBR expression constitutes the CP counterpart of our previous Tucker sum-of-products-FBR approach. However, as is well-known, CP expressions are much more compact. This has obvious advantages in high-dimensional quantum dynamics. The power of CP-FBR lies in the fact that it requires a grid much coarser than the one needed for the dynamics. In a subsequent step, the basis functions can be interpolated to any desired density of grid points. This is useful, for instance, when different initial conditions (e.g., energy content) of a system are to be considered. We show the application of the method to bound systems of increased dimensionality: H2 (3D), HONO (6D), and CH4 (9D). [ABSTRACT FROM AUTHOR]

Recent single-molecule measurements [Schoch et al., Proc. Natl. Acad. Sci. U. S. A. 118, e2113202118 (2021)] have observed dynamic lipid–lipid correlations in membranes with submicrometer spatial resolution and submillisecond temporal resolution. While short from an instrumentation standpoint, these length and time scales remain long compared to microscopic molecular motions. Theoretical expressions are derived to infer experimentally measurable correlations from the two-body diffusion matrix appropriate for membrane-bound bodies coupled by hydrodynamic interactions. The temporal (and associated spatial) averaging resulting from finite acquisition times has the effect of washing out correlations as compared to naive predictions (i.e., the bare elements of the diffusion matrix), which would be expected to hold for instantaneous measurements. The theoretical predictions are shown to be in excellent agreement with Brownian dynamics simulations of experimental measurements. Numerical results suggest that the experimental measurement of membrane protein diffusion, in complement to lipid diffusion measurements, might help to resolve the experimental ambiguities encountered for certain black lipid membranes. [ABSTRACT FROM AUTHOR]

In this work, we present an analytical model to describe atomic force microscopy force curves of standard linear solid and power-law viscoelastic materials by taking indenter geometry and finite thickness effects into account. We show that conical/pyramidal cantilevers are less susceptible to finite thickness effects than other shapes, such as spherical and flat punch indenters. This is confirmed by finite element modeling of the stress field distribution within the sample. We also perform a systematic error analysis for the cases where finite thickness samples are analyzed with an infinite thickness force model. In particular, we show that for spherical indenters and indentation depth up to 20% of sample thickness, the mechanical response of viscoelastic materials will wrongly mimic a purely elastic behavior even within timescales where viscoelastic relaxation should appear. [ABSTRACT FROM AUTHOR]

We show that the "|Δμ| big is good" principle holds at temperatures above absolute zero (the so-called "finite-T regime"). We also provide the first conditions hinting at the validity of this reactivity rule in cases where the chemical reactions involved have different signs in their chemical potential variations. [ABSTRACT FROM AUTHOR]

The Kirkwood–Buff theory is a cornerstone of the statistical mechanics of liquids and solutions. It relates volume integrals over the radial distribution function, so-called Kirkwood–Buff integrals (KBIs), to particle number fluctuations and thereby to various macroscopic thermodynamic quantities such as the isothermal compressibility and partial molar volumes. Recently, the field has seen a strong revival with breakthroughs in the numerical computation of KBIs and applications to complex systems such as bio-molecules. One of the main emergent results is the possibility to use the finite volume KBIs as a tool to access finite volume thermodynamic quantities. The purpose of this Perspective is to shed new light on the latest developments and discuss future avenues. [ABSTRACT FROM AUTHOR]

Many industrial facilities involve splitting production systems of different complexities and arrangements. The accurate and efficient evaluation of the associated performance measures is, therefore, of great importance. This challenging task can be accomplished by applying mathematical models of production system engineering at different intricacies. This paper presents the development and application of the analytical approach to splitting production systems modelling. The same problem is also addressed using the finite state method as a semi-analytical model. Several theoretical examples were considered to validate the finite state method that proved to be quite efficient and accurate. Finally, the developed modelling approach was applied in the case of a wood-processing facility. The obtained results were validated successfully against the acquired factory-floor data. [ABSTRACT FROM AUTHOR]

We report on quantum dynamical simulations of inter-chain exciton transport in a model of regioregular poly(3-hexylthiophene), rr-P3HT, at finite temperature using the Multi-Layer Multi-Configuration Time-Dependent Hartree method for a system of up to 63 electronic states and 180 vibrational modes. A Frenkel Hamiltonian of HJ aggregate type is used along with a reduced H-aggregate representation; electron–phonon coupling includes local high-frequency modes as well as anharmonic intermolecular modes. The latter are operative in mediating inter-chain transport by a mechanism of transient localization type. Strikingly, this mechanism is found to be of quantum coherent character and involves non-adiabatic effects. Using periodic boundary conditions, a normal diffusion regime is identified from the exciton mean-squared displacement, apart from early-time transients. Diffusion coefficients are found to be of the order of 3 × 10−3 cm2/s, showing a non-linear increase with temperature. [ABSTRACT FROM AUTHOR]

High harmonic spectra for H2 and H 2 + are simulated by solving the time-dependent Kohn–Sham equation in the presence of a strong laser field using an atom-centered Gaussian representation of the density and a complex absorbing potential. The latter serves to mitigate artifacts associated with the finite extent of the basis functions, including spurious reflection of the outgoing electronic wave packet. Interference between the outgoing and reflected waves manifests as peak broadening in the spectrum as well as the appearance of spurious high-energy peaks after the harmonic progression has terminated. We demonstrate that well-resolved spectra can be obtained through the use of an atom-centered absorbing potential. As compared to grid-based algorithms, the present approach is more readily extensible to larger molecules. [ABSTRACT FROM AUTHOR]

The buffer allocation problem in production lines is an NP-hard combinatorial optimisation problem. This paper proposes a new hybrid optimisation approach (using simulation) relying on genetic algorithm (GA) and finite perturbation analysis (FPA). Unlike the infinitesimal perturbation analysis, which deals with small (infinitesimal variation) perturbations for estimating gradients of the performance measure, FPA deals with larger (finite) or more lasting perturbations. It is an extension specifically dedicated to discrete decision variables and applicable to most discrete-event dynamic systems. The proposed method allows a global search using GA, with refinement in specific solution-space regions using FPA. The main objective is to maximise the average production rate of a production line with unreliable machines, by allocating the total buffer capacity in locations between machines. Extensive numerical experiments show that: (1) the proposed hybrid GA-FPA method clearly outperforms the state-of-the-art methods from the literature; (2) combining FPA and GA is beneficial when compared to employing GA or FPA independently. [ABSTRACT FROM AUTHOR]

We use a degenerated Ising model to describe nucleation and crystallization from solution in a confined two-component system. The free energy is calculated using metadynamics simulation with coordination numbers as the reaction coordinates. We deploy nudged elastic band simulation to determine the minimum energy path and give properties of the crystallization path. In this confined system, depletion effects, which could also be caused by slow material transport in the solution, prevent the post-critical cluster from further growth, and the crystalline state would only be stable at larger cluster sizes. Fluctuation of the higher coupling strength of the crystalline state enables further growth until the crystalline cluster is in equilibrium with the solvent, and this way, a second barrier is crossed. From the parameters and setup, we find necessary conditions for the occurrence of two-step nucleation in our system. These findings can be adapted to real systems as biomineralization, colloidal crystallization, and the solidification of metals. [ABSTRACT FROM AUTHOR]

Finite size artifacts arise in molecular simulations of nucleation when critical nuclei are too close to their periodic images. A rigorous determination of what constitutes too close is, however, a major challenge. Recently, we devised rigorous heuristics for detecting such artifacts based on our investigation of how system size impacts the rate of heterogeneous ice nucleation [S. Hussain and A. Haji-Akbari, J. Chem. Phys. 154, 014108 (2021)]. We identified the prevalence of critical nuclei spanning across the periodic boundary, and the thermodynamic and structural properties of the liquid occupying the inter-image region as indicators of finite size artifacts. Here, we further probe the performance of such heuristics by examining the dependence of homogeneous crystal nucleation rates in the Lennard-Jones (LJ) liquid on system size. The rates depend non-monotonically on system size and vary by almost six orders of magnitude for the range of system sizes considered here. We confirm that the prevalence of spanning critical nuclei is the primary indicator of finite size artifacts and almost fully explains the observed variations in rate. Proximity, or structuring of the inter-image liquid, however, is not as strong of an indicator due to the fragmented nature of crystalline nuclei. As a result, the dependence of rate on system size is subtle for the systems with a minuscule fraction of spanning critical nuclei. These observations indicate that our heuristics are universally applicable to different modes of nucleation (homogeneous and heterogeneous) in different systems even if they might be overly stringent for homogeneous nucleation, e.g., in the LJ system. [ABSTRACT FROM AUTHOR]

The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg–Kohn theorem is found void, in general, while many insights into the topological structure of the density-potential mapping can be won. We give precise conditions for a ground state to be uniquely v-representable and are able to prove that this property holds for almost all densities. A set of examples illustrates the theory and demonstrates the non-convexity of the pure-state constrained-search functional. [ABSTRACT FROM AUTHOR]

The field of topological photonics has made great strides in the past decade with many new designs based on bandgap and band inversion structures that provide robust, unidirectional, and reflection-free propagation of energy. The topological invariant or Chern number of a metamaterial guarantees the existence of topologically protected edge modes. However, its mathematical application to real systems is not always straightforward and can be greatly simplified by reducing the dimensional complexity of the problem by the calculation of a Zak phase that determines the topological phase in just one dimension. This work explores two methods of creating interface modes with finite height dielectric slabs: (1) transverse resonance through variable edge truncation of a photonic crystal (PhC) or cell sliding and (2) a uni-axial topological phase by means of scaling the internal features of a unit cell. The proposed metamaterial devices use the same C 4 v symmetric unit cell structure on both sides of the interface and are finite in all three dimensions, allowing for easy fabrication, excitation, and implementation in real-world applications. The all-dielectric design also enables an easy transition to and from conventional PhC waveguides and lends itself well to operation in frequencies spanning across the microwave and optical spectrum without concerns of additional metallic losses in the THz region. [ABSTRACT FROM AUTHOR]

Distribution-free control charts have been proposed in recent years to monitor processes with insufficient information about the distribution of observations. A promising field of application of these charts is the small production of finite batches of products, where the number of scheduled inspections is limited to a few tens. Following the machine reconfiguration after a process set-up, the quality practitioner cannot rely on past production runs to get knowledge about the distribution of the observations: this scenario can be referred to as the Case U (Unknown) condition in statistical process monitoring. Here, we investigate the issues related to the implementation of Mann–Whitney (MW) type control charts for monitoring the location in a finite horizon production (FHP) process. The practitioner-to-practitioner variability is considered while designing the control limits. The in-control and out-of-control chart performances are investigated over a wide set of scenarios and some graphical tools are proposed to help practitioners during the decision-making process. A comparison with the Shewhart Sign control chart for FHP processes is also presented. An illustrative example is provided to demonstrate the implementation of the proposed chart on a real industrial dataset. [ABSTRACT FROM AUTHOR]

We introduce a thermofield-based formulation of the multilayer multiconfigurational time-dependent Hartree (MCTDH) method to study finite temperature effects on non-adiabatic quantum dynamics from a non-stochastic, wave function perspective. Our approach is based on the formal equivalence of bosonic many-body theory at zero temperature with a doubled number of degrees of freedom and the thermal quasi-particle representation of bosonic thermofield dynamics (TFD). This equivalence allows for a transfer of bosonic many-body MCTDH as introduced by Wang and Thoss to the finite temperature framework of thermal quasi-particle TFD. As an application, we study temperature effects on the ultrafast internal conversion dynamics in pyrazine. We show that finite temperature effects can be efficiently accounted for in the construction of multilayer expansions of thermofield states in the framework presented herein. Furthermore, we find our results to agree well with existing studies on the pyrazine model based on the ρMCTDH method. [ABSTRACT FROM AUTHOR]

In this paper the generalization of the converse of Baer's theorem for two-nilpotent variety of class row (n,m) is carried out. Baer proved that finiteness of G/Zn(G) implies that γn+1(G) is finite. Hekster proved the converse of the Baer's theorem with the assumption that G can be finitely generated. The Baer's theorem can be considered as a result of a classical theorem by Schur denoting that finiteness of G/Z(G) leads to the finiteness of G ′. The converse of the Baer's theorem has been proved conditionally by Taghavi et al. (2019), as well. In the Main Theorem, we prove that, if γm,n(G) ∩ Zn,m(G) = 1 and γm,n+i(G) is finite for some n, i,m ≥ 0. Then G/Zn,m(G) is finite in which γm,n(G) and Zn,m(G) denote verbal and marginal subgroups with respect to two-nilpotent variety of class row (n,m). Thus the generalization of the converse of Baer's theorem for two-nilpotent variety of groups valids by considering i = 0. In this article some other results are attained by the converse of the Baer's theorem. It is also concluded that when n = m = 1. Similar results are obtained for variety of the soluble groups. In addition, the converse of the Schur's theorem which proved by Halasi and Podoski is concluded in this paper, for two-nilpotent variety. We have also obtained some similar results of Chakaneh et al. (2019) for (n,m)-isoclinic family of groups and (1,m)-stem groups. [ABSTRACT FROM AUTHOR]

Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay for extended reservoir simulations, where relaxation maintains a bias or temperature drop across the system. Our analysis begins in the non-interacting limit, where we parameterize different discretizations to compare them on an even footing. For many-body systems, we develop a method to estimate the relaxation that best approximates the continuum by controlling virtual transitions in Kramers turnover for the current. While some discretizations are more efficient for calculating currents, there is little benefit with regard to the overall state of the system. Any gains become marginal for many-body, tensor network simulations, where the relative performance of discretizations varies when sweeping other numerical controls. These results indicate that typical reservoir discretizations have little impact on numerical costs for certain computational tools. The choice of a relaxation parameter is nonetheless crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs. [ABSTRACT FROM AUTHOR]

The complete-active-space (CAS) extended Koopmans theorem (EKT) method is defined as a special case of the EKT in which the reference state is a CAS configuration interaction (CI) expansion and the electron removal operator acts only on the active orbitals. With these restrictions, the EKT is equivalent to the CI procedure involving all hole-state configurations derived from the active space of the reference wavefunction and has properties analogous to those of the original Koopmans theorem. The equivalence is used to demonstrate in a transparent manner that the first ionization energy predicted by the EKT is in general not exact, i.e., not equal to the difference between the full CI energies of the neutral and the ion, but can approach the full CI result with arbitrary precision even within a finite basis set. The findings also reconcile various statements about the EKT found in the literature. [ABSTRACT FROM AUTHOR]

We extend the finite-temperature Keldysh non-equilibrium coupled cluster theory (Keldysh-CC) [A. F. White and G. K.-L. Chan, J. Chem. Theory Comput. 15, 6137–6253 (2019)] to include a time-dependent orbital basis. When chosen to minimize the action, such a basis restores local and global conservation laws (Ehrenfest's theorem) for all one-particle properties while remaining energy conserving for time-independent Hamiltonians. We present the time-dependent Keldysh orbital-optimized coupled cluster doubles method in analogy with the formalism for zero-temperature dynamics, extended to finite temperatures through the time-dependent action on the Keldysh contour. To demonstrate the conservation property and understand the numerical performance of the method, we apply it to several problems of non-equilibrium finite-temperature dynamics: a 1D Hubbard model with a time-dependent Peierls phase, laser driving of molecular H2, driven dynamics in warm-dense silicon, and transport in the single impurity Anderson model. [ABSTRACT FROM AUTHOR]

We solve open problems concerning the Kleene star L* of a finite set L of words over an alphabet Σ. The Frobenius monoid problem is the question for a given finite set of words L, whether the language L* is cofinite. We show that it is PSPACE-complete. We also exhibit an infinite family of sets L such that the length of the longest words not in L* (when L* is cofinite) is exponential in the length of the longest words in L and subexponential in the sum of the lengths of words in L. The factor universality problem is the question for a given finite set of words L, whether every word over Σ is a factor (substring) of some word from L*. We show that it is also PSPACE-complete. Besides that, we exhibit an infinite family of sets L such that the length of the shortest words not being a factor of any word in L* is exponential in the length of the longest words in L and subexponential in the sum of the lengths of words in L. This essentially settles in the negative the longstanding Restivo's conjecture (1981) and its weak variations. All our solutions are based on one shared construction, and as an auxiliary general tool, we introduce the concept of set rewriting systems. Finally, we complement the results with upper bounds. [ABSTRACT FROM AUTHOR]

For a semigroup S, the covering number of S with respect to semigroups, σs (S), is the minimum number of proper subsemigroups of S whose union is S. This article investigates covering numbers of semigroups and analogously defined covering numbers of inverse semigroups and monoids. Our three main theorems give a complete description of the covering number of finite semigroups, finite inverse semigroups, and monoids (modulo groups and infinite semigroups). For a finite semigroup that is neither monogenic nor a group, its covering number is two. For all n ≥ 2, there exists an inverse semigroup with covering number n, similar to the case of loops. Finally, a monoid that is neither a group nor a semigroup with an identity adjoined has covering number two as well. [ABSTRACT FROM AUTHOR]

Discussions of supererogation usually focus on cases in which the agent can choose among a finite number of options. However, Daniel Muñoz has recently shown that cases in which the agent faces an infinite chain of increasingly less good options make trouble for existing definitions of supererogation. Muñoz proposes a promising new definition as a solution to the problem of infinite cases. I argue that any acceptable account of supererogation must (1) enable us to accurately identify supererogatory acts in both finite and infinite option cases. It must also (2) include a suitably related account of what makes one act more supererogatory than another for finite, infinite, single-choice (one agent choosing among several supererogatory options) and inter-choice (two different agents, each choosing a supererogatory option) cases. I further argue that the best current account of supererogation for finite cases works well for finite cases, but cannot handle infinite cases. However, Muñoz's proposal cannot handle inter-choice cases in either finite or infinite cases. I conclude we still need an account for infinite cases, and may have to settle for separate definitions of supererogation for finite and infinite cases. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to analyze the morality's role in one of the most important promises professed by transhumanism, the promise of human immortality. This purpose will be carried out through the interpretation of the short tale: The Immortal by Jorge Luis Borges. This in order to unveil the close relationship that exists between the moral dimension of man - the question of what should I do - and the recognition of his finitude, of his becoming, as a being that forms his own narrative in the world. [ABSTRACT FROM AUTHOR]

Copyright of ANAFORA is the property of Anafora and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required. [ABSTRACT FROM AUTHOR]

We investigate the viability of the phaseless finite-temperature auxiliary-field quantum Monte Carlo (ph-FT-AFQMC) method for ab initio systems using the uniform electron gas as a model. Through comparisons with exact results and FT coupled cluster theory, we find that ph-FT-AFQMC is sufficiently accurate at high to intermediate electronic densities. We show, both analytically and numerically, that the phaseless constraint at FT is fundamentally different from its zero-temperature counterpart (i.e., ph-ZT-AFQMC), and generally, one should not expect ph-FT-AFQMC to agree with ph-ZT-AFQMC in the low-temperature limit. With an efficient implementation, we are able to compare exchange-correlation energies to the existing results in the thermodynamic limit and find that the existing parameterizations are highly accurate. In particular, we found that ph-FT-AFQMC exchange-correlation energies are in better agreement with a known parameterization than is restricted path-integral MC in the regime of Θ ≤ 0.5 and rs ≤ 2, which highlights the strength of ph-FT-AFQMC. [ABSTRACT FROM AUTHOR]

Transfer entropy in information theory was recently demonstrated [Basak et al., Phys. Rev. E 102, 012404 (2020)] to enable us to elucidate the interaction domain among interacting elements solely from an ensemble of trajectories. Therefore, only pairs of elements whose distances are shorter than some distance variable, termed cutoff distance, are taken into account in the computation of transfer entropies. The prediction performance in capturing the underlying interaction domain is subject to the noise level exerted on the elements and the sufficiency of statistics of the interaction events. In this paper, the dependence of the prediction performance is scrutinized systematically on noise level and the length of trajectories by using a modified Vicsek model. The larger the noise level and the shorter the time length of trajectories, the more the derivative of average transfer entropy fluctuates, which makes the identification of the interaction domain in terms of the position of global minimum of the derivative of average transfer entropy difficult. A measure to quantify the degree of strong convexity at the coarse-grained level is proposed. It is shown that the convexity score scheme can identify the interaction distance fairly well even while the position of the global minimum of the derivative of average transfer entropy does not. We also derive an analytical model to explain the relationship between the interaction domain and the change in transfer entropy that supports our cutoff distance technique to elucidate the underlying interaction domain from trajectories. [ABSTRACT FROM AUTHOR]

We propose a formalism for deriving force–elongation and elongation–force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality to the numerical evaluation of Marko and Siggia's variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests that our analytical finite chain length corrections achieve a comparable accuracy. As an application of our results, we discuss the possibility of inferring the time-dependent number of nicks in single-molecule stretching experiments on double-stranded DNA from the accompanying changes in the effective chain length. [ABSTRACT FROM AUTHOR]

Computational studies of crystal nucleation can be impacted by finite size effects, primarily due to unphysical interactions between crystalline nuclei and their periodic images. It is, however, not always feasible to systematically investigate the sensitivity of nucleation kinetics and mechanism to system size due to large computational costs of nucleation studies. Here, we use jumpy forward flux sampling to accurately compute the rates of heterogeneous ice nucleation in the vicinity of square-shaped model structureless ice nucleating particles (INPs) of different sizes and identify three distinct regimes for the dependence of rate on the INP dimension, L. For small INPs, the rate is a strong function of L due to the artificial spanning of critical nuclei across the periodic boundary. Intermediate-sized INPs, however, give rise to the emergence of non-spanning "proximal" nuclei that are close enough to their periodic images to fully structure the intermediary liquid. While such proximity can facilitate nucleation, its effect is offset by the higher density of the intermediary liquid, leading to artificially small nucleation rates overall. The critical nuclei formed at large INPs are neither spanning nor proximal. Yet, the rate is a weak function of L, with its logarithm scaling linearly with 1/L. The key heuristic emerging from these observations is that finite size effects will be minimal if critical nuclei are neither spanning nor proximal and if the intermediary liquid has a region that is structurally indistinguishable from the supercooled liquid under the same conditions. [ABSTRACT FROM AUTHOR]

Open-system simulations of quantum transport provide a platform for the study of true steady states, Floquet states, and the role of temperature, time dynamics, and fluctuations, among other physical processes. They are rapidly gaining traction, especially techniques that revolve around "extended reservoirs," a collection of a finite number of degrees of freedom with relaxation that maintains a bias or temperature gradient, and have appeared under various guises (e.g., the extended or mesoscopic reservoir, auxiliary master equation, and driven Liouville–von Neumann approaches). Yet, there are still a number of open questions regarding the behavior and convergence of these techniques. Here, we derive general analytical solutions, and associated asymptotic analyses, for the steady-state current driven by finite reservoirs with proportional coupling to the system/junction. In doing so, we present a simplified and unified derivation of the non-interacting and many-body steady-state currents through arbitrary junctions, including outside of proportional coupling. We conjecture that the analytic solution for proportional coupling is the most general of its form for isomodal relaxation (i.e., relaxing proportional coupling will remove the ability to find compact, general analytical expressions for finite reservoirs). These results should be of broad utility in diagnosing the behavior and implementation of extended reservoir and related approaches, including the convergence to the Landauer limit (for non-interacting systems) and the Meir–Wingreen formula (for many-body systems). [ABSTRACT FROM AUTHOR]

This paper examines serial production lines with unreliable non-identical parallel machines at each workstation and intermediate buffers with finite capacities. All machines are assumed to have exponential service times, times to failure and repair times. An efficient decomposition technique is introduced for the performance evaluation of such lines. Rather than replacing each parallel-machine workstation with an equivalent single-server workstation, the main contribution of this paper is the presentation of a direct approach to derive and apply decomposition equations directly for every parallel machine at each workstation. Experimental results indicate that such a method can provide a computationally efficient algorithm to analyse large serial unreliable multi-server production lines with a good accuracy compared against simulation and other available methods. [ABSTRACT FROM AUTHOR]

Although there is a broad literature on capacity management, there has been only limited attention on how to support short-term capacity control decisions, especially in high-variety make-to-order shops. While finite loading has been identified as a potential means of guiding capacity adjustments, the actual performance impact of this solution has not been adequately assessed. Using a simulation model of a make-to-order job shop, we compare the performance impact of four different forward and backward finite loading methods and a load trigger method recently presented in the literature. Results confirm the potential of finite loading to improve performance when compared to a general capacity increase. Yet all four methods are outperformed by the load trigger method. The capacity adjustments made under finite loading methods are determined by individual jobs and their properties. This may lead to no adjustments despite an overload period (e.g. if a job has a long due date but only one overload station in its routing) or to unnecessary adjustments when there is no overload (e.g. if a large job has a tight due date). This finding draws into question the use of finite loading altogether and reinforces the importance of the load trigger method. [ABSTRACT FROM AUTHOR]

This is a survey on a group construction in connection with the non-abelian tensor square of groups. We report on the developments obtained in the last decade emphasizing the results from a commutator point of view. [ABSTRACT FROM AUTHOR]

This paper will deal with differentiability properties of the class of Hellinger–Kantorovich distances HK Λ , Σ (Λ , Σ > 0) which was recently introduced on the space M (R d) of finite nonnegative Radon measures. The derivatives of t ↦ HK Λ , Σ (μ t , ν t) 2 , for absolutely continuous curves (μ t) t , (ν t) t in (M (R d) , HK Λ , Σ) , will be computed L 1 -a.e.. The characterization of absolutely continuous curves in (M (R d) , HK Λ , Σ) will be refined. [ABSTRACT FROM AUTHOR]

The well-posedness and dynamic properties of solutions to a class of fourth order parabolic equations with mean curvature nonlinearity are studied. More specifically, we first prove the existence and uniqueness of strong solutions by semigroup method. Then, we establish conditions for the global existence and finite time blow-up of solutions with subcritical, critical and supercritical initial energies. At the same time, we study the exponential decay and $ \omega $-limit set of the global solutions, and the upper bound of the blow-up time of the blow-up solutions. In addition, we also study the existence and regularity of ground state solutions for the steady state problems. [ABSTRACT FROM AUTHOR]

In this article, we investigate the asymptotic behavior of solutions for a non-autonomous regularized magnetohydrodynamics equations on 3D bounded domains. More precisely, the upper bounds on the number of determining modes and determining nodes for the system are established. The results show that the asymptotic behavior of the weak solution can be determined completely by its first finite number of Fourier modes and the large time behavior of the strong solution can be determined by its values on a finite number of points. [ABSTRACT FROM AUTHOR]

Visual search can be accelerated according to the properties of information stored in memory and prior knowledge of the upcoming work. This helps the searcher direct their attention to (or avoid) items that match these properties. Meanwhile, different functional areas where these properties exist become attentional templates. Compared with neutral conditions, the use of attentional templates significantly benefits reaction time (RT). However, previous studies might have confounded the memory-driven and cue-driven effects. Thus, it is less clear which factor influences the template benefits. Modeled on previous research, this study employed a new design to explore the independent effects of textual cues, thus finding an inverse effect. More specifically, positively cueing an item retained in memory did not improve behavioral performance, whereas negatively cueing an item did achieve such an enhancement. Moreover, positive cueing even resulted in some damage to attentional searching under some conditions, thus indicating that the advantages of positive cueing reported in previous studies may be driven by working memory, while the effects of negative cueing are driven by prior knowledge. [ABSTRACT FROM AUTHOR]

Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes. This enables simple and efficient implementation, but in turn, restricts the representation capability of the deformation, often leading to unsatisfactory warping results. We present a novel, flexible polygonal finite element (poly-FEM) method for content-aware image warping. Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image. This allows highly adaptive meshes and smoother warping with fewer degrees of freedom, thus significantly extending the flexibility and capability of the warping representation. Benefiting from the continuous formulation of image deformation, our poly-FEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations. We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with global solvability of a fully parabolic system of Keller–Segel-type involving non-monotonic signal-dependent motility. First, we prove global existence of classical solutions to our problem with generic positive motility function under a certain smallness assumption at infinity, which however permits the motility function to be arbitrarily large within a finite region. Then uniform-in-time boundedness of classical solutions is established whenever the motility function has strictly positive lower and upper bounds in any dimension N ≥ 1 , or decays at a certain slow rate at infinity for N ≥ 2. Our results remove the crucial non-increasing requirement on the motility function in some recent work [10,13,16] and hence allow for both chemo-attractive and chemo-repulsive effect, or their co-existence in applications. The key ingredient of our proof lies in an important improvement of the comparison method developed in [10,16,18]. [ABSTRACT FROM AUTHOR]

The critical exponent E(\mathbf u) of an infinite sequence \mathbf u over a finite alphabet expresses the maximal repetition of a factor in \mathbf u. By the famous Dejean's theorem, E(\mathbf u) \geq 1+\frac 1{d-1} for every d-ary sequence \mathbf u. We define the asymptotic critical exponent E^*(\mathbf u) as the upper limit of the maximal repetition of factors of length n. We show that for any d>1 there exists a d-ary sequence \mathbf u having E^*(\mathbf u) arbitrarily close to 1. Then we focus on the class of d-ary balanced sequences. In this class, the values E^*(\mathbf u) are bounded from below by a threshold strictly bigger than 1. We provide a method which enables us to find a d-ary balanced sequence with the least asymptotic critical exponent for 2\leq d\leq 10. [ABSTRACT FROM AUTHOR]

We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients. The methods fitting into this framework combine line searches and suitably decaying step lengths. A key issue is a two-step sampling at each iteration, which allows us to control the error present in the line-search procedure. Stationarity of limit points is proved in the almost-sure sense, while almost-sure convergence of the sequence of approximations to the solution holds with the additional hypothesis that the functions are strongly convex. Numerical experiments, including comparisons with state-of-the art stochastic optimization methods, show the efficiency of our approach. [ABSTRACT FROM AUTHOR]

We use Constraint Satisfaction Methods to construct and enumerate finite L-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the combinatorial Yang–Baxter equation. There are 377,322,225 isomorphism classes of L-algebras of size eight. The database constructed suggests the existence of bijections between certain classes of L-algebras and well-known combinatorial objects. We prove that Bell numbers enumerate isomorphism classes of finite linear L-algebras. We also prove that finite regular L-algebras are in bijective correspondence with infinite-dimensional Young diagrams. [ABSTRACT FROM AUTHOR]

Years ago Zeev Rudnick defined the \lambda-Poisson generic sequences as the infinite sequences of symbols in a finite alphabet where the number of occurrences of long words in the initial segments follow the Poisson distribution with parameter \lambda. Although almost all sequences, with respect to the uniform measure, are Poisson generic, no explicit instance has yet been given. In this note we give a construction of an explicit \lambda-Poisson generic sequence over any alphabet and any positive \lambda, except for the case of the two-symbol alphabet, in which it is required that \lambda be less than or equal to the natural logarithm of 2. Since \lambda-Poisson genericity implies Borel normality, the constructed sequences are Borel normal. The same construction provides explicit instances of Borel normal sequences that are not \lambda-Poisson generic. [ABSTRACT FROM AUTHOR]

Suppose that a finite solvable group G acts faithfully, irreducibly and quasi-primitively on a finite vector space V , and G is not metacyclic. Then G always has a regular orbit on V except for a few "small" cases. We completely classify these cases in this paper. [ABSTRACT FROM AUTHOR]

We aim to study Morita theory for tensor triangulated categories. For two finite tensor categories having no projective simple objects, we prove that their stable equivalence induced by an exact \Bbbk \text {-}linear monoidal functor can be lifted to a tensor equivalence under some certain conditions. [ABSTRACT FROM AUTHOR]