We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations (...) of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed. (shrink)

This paper is devoted to Landau's concept of the problem of damping in quantum mechanics. It shows that Landau's density matrix formalism should survive in the context of modern quantum electrodynamics. The correct generalized master equation has been derived for the reduced dynamics of the charges. The recent relativistic theory of spontaneous emission becomes reproducible.

It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (“statistical mixture”) or a system that is entangled with another system (“reduced density matrix”). We point out another role, previously unnoticed in the literature, that a density matrix can play: it can be the “conditional density matrix,” conditional on the configuration of the (...) environment. A precise definition can be given in the context of Bohmian mechanics, whereas orthodox quantum mechanics is too vague to allow a sharp definition, except perhaps in special cases. In contrast to statistical and reduced density matrices, forming the conditional density matrix involves no averaging. In Bohmian mechanics with spin, the conditional density matrix replaces the notion of conditional wave function, as the object with the same dynamical significance as the wave function of a Bohmian system. (shrink)

If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie--Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for (...) which Bell [Int. J. Quantum chem. 155--159, (1980)] appears to suggest that such an interpretation is not possible. Bell’s argument is shown to be based upon a different understanding of the density matrix to that proposed here. (shrink)

In this paper, I characterize and elaborate on the “Wentaculus” theory, a new approach to time’s arrow in a quantum universe that offers a unified solution to the problems of what gives rise to the arrow of time and what the ontology of quantum mechanics is.

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. They are difficult because the fundamental dynamical laws of physics do not privilege an arrow of time, and the quantum-mechanical wave function describes a high-dimensional reality that is radically different from our ordinary experiences. -/- In this paper, I characterize and elaborate on the ``Wentaculus” theory, a new approach to time’s (...) arrow in a quantum universe that offers a unified solution to both problems. Central to the Wentaculus are (i) Density Matrix Realism, the idea that the quantum state of the universe is objective but can be impure, and (ii) the Initial Projection Hypothesis, a new law of nature that selects a unique initial quantum state. On the Wentaculus, the quantum state of the universe is sufficiently simple to be a law, and the arrow of time can be traced back to an exact boundary condition. It removes the intrinsic vagueness of the Past Hypothesis, eliminates the Statistical Postulate, provides a higher degree of theoretical unity, and contains a natural realization of “strong determinism." I end by responding to four recent objections. In a companion paper, I elaborate on Density Matrix Realism. (shrink)

The derivation of the expression for the density matrix of scattered particles in terms of that of the incident ones, taking different impact parameters into account, shows that under well-specified and realistic conditions, the final density matrix is of the same kind as the initial one. Thus the final mixed state after a collision can be used directly as the initial mixed state in a subsequent collision. Contrary to a recent claim by Band and Park, there (...) are no “fundamental difficulties with quantum mechanical collision theory.”. (shrink)

The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this work we introduce and prove the need for a selective and non-uniform time-sampling, whose form depends on the properties of the bath. It is also applicable when an open microscopic sub-system is coupled to another finite system. By use of a time-periodic minimal coupling model between (...) these two systems, we present detailed quantitative consequences of time coarsening, which include initial state independence of equilibration, deviations from long term averages, their environment size dependence and the approach to classicality, as measured by a Leggett–Garg type inequality. An interacting multiple qubit model affords comparison between the time integrating procedure and the more conventional environment tracing method. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

The density matrix ρ describing a decaying system can be expressed in terms of correlations among observables belonging to the subsystems. Due to this structure and to the difficulties in measuring higher rank tensors of decay products for a single decay event, it is found that the mean value of ρ cannot be determined, in general, from measurements on the decay products. We also discuss the consequences of this conclusion as far as tests of quantum mechanics are concerned.

In this chapter, we will take a trip around several hot-spots where Bohmian mechanics and its capacity to describe the microscopic reality, even in the absence of measurements, can be harnessed as computational tools, in order to help in the prediction of phenomenologically accessible information (also useful for the followers of the Copenhagen theory). As a first example, we will see how a Stochastic Schrödinger Equation, when used to compute the reduced density matrix of a non-Markovian open (...) quantum system, necessarily seems to employ the Bohmian concept of a conditional wavefunction. We will see that by dressing these conditional wavefunctions with an interpretation, the Bohmian theory can prove to be a useful tool to build general quantum simulation frameworks, such as a high-frequency electron transport model. As a second example, we will explain how a Copenhagen “observable operator” can be related to numerical properties of the Bohmian trajectories, which within Bohmian mechanics, are well-defined even for an “unmeasured” system. Most importantly in practice, even if these numbers are given no ontological meaning, not only we will be able to simulate (thus, predict and talk about) them, but we will see that they can be operationally determined in a weak value experiment. Therefore, they will be practical numbers to characterize a quantum system irrespective of the followed quantum theory. (shrink)

The paper investigates the type of realism that best suits the framework of decoherence taken at face value without postulating a plurality of worlds, or additional hidden variables, or non-unitary dynamical mechanisms. It is argued that this reading of decoherence leads to an extremely radical type of perspectival realism, especially when cosmological decoherence is considered.

What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave function and (...) theories with a fundamental density matrix. The Past Hypothesis is compatible with infinitely many initial wave functions, none of which seems to be particularly natural. However, once we turn to density matrices, the Past Hypothesis provides a natural choice---the normalized projection onto the Past Hypothesis subspace in the Hilbert space. Nevertheless, the two types of theories can be empirically equivalent. To provide a concrete understanding of the empirical equivalence, I provide a novel subsystem analysis in the context of Bohmian theories. Given the empirical equivalence, it seems empirically underdetermined whether the universe is in a pure state or a mixed state. Finally, I discuss some theoretical payoffs of the density-matrix theories and present some open problems for future research. (Bibliographic note: the thesis was submitted for the Master of Science in mathematics at Rutgers University.). (shrink)

This note, in rejoinder to a paper by Newton critical of our analysis of certain limitations of quantum scattering theory, seeks to acknowledge and to clarify the disparate interests of the two conflicting articles.

It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence effects are essentially Gaussian wave packets that form continua of non-orthogonal states. Hence they are not a discrete set of orthogonal basis states to which finite probabilities can be assigned by the usual rules. The natural way to get an orthogonal basis without going outside (...) the Schroedinger dynamics is to use the eigenstates of the reduced density matrix, and this idea is the basis of some recent attempts by many-worlds proponents to solve the basis problem. But these eigenstates do not enjoy the locality and quasi-classicality properties of the states defined by environmental decoherence effects, and hence are not satisfactory preferred basis states. This core problem is obscured by approaches that treat the universe as a quantum computer, but it needs to be addressed and resolved before a many-worlds-type interpretation can be said to exist. (shrink)

The role of the environment in producing the correct classical limit in the Bohm interpretation of quantum mechanics is investigated, in the context of a model of quantum Brownian motion. One of the effects of the interaction is to produce a rapid approximate diagonalisation of the reduced density matrix in the position representation. This effect is, by itself, insufficient to produce generically quasi-classical behaviour of the Bohmian trajectory. However, it is shown that, if the system particle is (...) initially in an approximate energy eigenstate, then there is a tendency for the Bohmian trajectory to become approximately classical on a longer time-scale. The relationship between this phenomenon and the behaviour of the Wigner function post-decoherence is discussed. (shrink)

Density matrices for mixed state qubits, parametrized by the Bloch vector in the open unit ball of the Euclidean 3-space, are well known in quantum computation theory. We bring the seemingly structureless set of all these density matrices under the umbrella of gyrovector spaces, where the Bloch vector is treated as a hyperbolic vector, called a gyrovector. As such, this article catalizes and supports interdisciplinary research spreading from mathematical physics to algebra and geometry. Gyrovector spaces are mathematical objects (...) that form the setting for the hyperbolic geometry of Bolyai and Lobachevski just as vector spaces form the setting for Euclidean geometry. It is thus interesting, in geometric quantum computation, to realize that the set of all qubit density matrices has rich structure with strong link to hyperbolic geometry. Concrete examples for the use of the gyro-structure to derive old and new, interesting identities for qubit density matrices are presented. (shrink)

We investigate the problem of “wave packet reduction” in quantum mechanics by solving the Schrödinger equation for a system composed of a model measuring apparatusM interacting with a microscopic objects. The “instrument” is intended to be somewhat more realistic than others previously proposed, but at the same time still simple enough to lead to an explicit solution for the time-dependent density matrix. It turns out that,practically, everything happens as if the wave packet reduction had occurred. This is a (...) consequence of the fact that the apparatus is made up of a very large number of microsystems interacting withs. More precisely, our model shows that the “macroscopic size” of a measuring apparatus can lead by itself to a density matrix for the systemM + s which is physically equivalent to the density matrix of a statistical mixture corresponding to the reduced wave packet. (shrink)

The partial ordering of Medvedev reducibility restricted to the family of Π0 1 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π0 1 class, which we call a ``c.e. separating class''. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.

Abstract.The partial ordering of Medvedev reducibility restricted to the family of Π01 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π01 class, which we call a ``c.e. separating class''. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.

The core structures of d 111 ¢ screw dislocations in bcc metals are studied using density functional theory in the local-density approximation. For Mo and Fe, direct calculations of the core structures show the cores to be symmetric with respect to 180° rotations around an axis perpendicular to the dislocation line. The magnetic moment in the Fe core is shown to be reduced relative to the bulk value. Calculations of n surfaces and the elastic constants B , (...) C ' and c 44 are reported for Fe and all group VB and VIB metals. Using a criterion suggested by Vitek and Duesbery the calculations point to symmetric core structures for all the studied metals. (shrink)

Motivated by a recent proof of free choices in linking equations to the experiments they describe, I clarify some relations among purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and operator-valued measures), thereby allowing applications of these entities to the modeling of a wider variety of physical situations. I relate conditional probabilities associated with projection-valued measures to conditional density operators identical, in some cases but not in others, to the usual reduced density (...) operators. While a fatal obstacle precludes associating conditional density operators with general non-projective measures, tensor products of general positive operator-valued measures (POVMs) are associated with conditional density operators. This association together with the free choice of probe particles allows a postulate of state reductions to be replaced by a theorem. An application shows an equivalence between one form of quantum key distribution and another with respect to certain eavesdropping attacks. (shrink)

Concerning Post's problem for Kleene degrees and its relativization, Hrbacek showed in [1] and [2] that if V = L, then Kleene degrees of coanalytic sets are dense, and then for all K ⊆ωω, there are N1 sets which are Kleene semirecursive in K and not Kleene recursive in each other and K. But the density of Kleene semirecursive in K Kleene degrees is not obtained from these theorems. In this note, we extend these theorems by showing that if (...) V = L, then for all K ⊆ ωω, Kleene semirecursive in K Kleene degrees are dense above K. (shrink)

It is shown that the matrix models which give non-perturbative definitions of string and M theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their entries are the non-local hidden variables. This is shown by studying the bosonic matrix model at finite temperature, with T taken to scale as 1/N, with N the rank of the matrices. For large N the eigenvalues of the matrices undergo Brownian (...) motion due to the interaction of the diagonal elements with the off diagonal elements, giving rise to a diffusion constant that remains finite as N goes to infinity. The resulting probability density and current for the eigenvalues are then found to evolve in agreement with the Schroedinger equation, to leading order in 1/N, with hbar proportional to the thermal diffusion constant for the eigenvalues. The quantum uctuations and uncertainties in the eigenvalues are then consequences of ordinary statistical uctuations in the values of the off-diagonal matrix elements. Furthermore, this formulation of the quantum theory is background independent, as the definition of the thermal ensemble makes no use of a particular classical solution. The derivation relies on Nelson's stochastic formulation of quantum theory, which is expressed in terms of a variational principle. (shrink)

We study the effects of density dependent migrations on the stability of a predator-prey model in a patchy environment which is composed with two sites connected by migration. The two patches are different. On the first patch, preys can find resource but can be captured by predators. The second patch is a refuge for the prey and thus predators do not have access to this patch. We assume a repulsive effect of predator on prey on the resource patch. Therefore, (...) when the predator density is large on that patch, preys are more likely to leave it to return to the refuge. We consider two models. In the first model, preys leave the refuge to go to the resource patch at constant migration rates. In the second model, preys are assumed to be in competition for the resource and leave the refuge to the resource patch according to the prey density. We assume two different time scales, a fast time scale for migration and a slow time scale for population growth, mortality and predation. We take advantage of the two time scales to apply aggregation of variables methods and to obtain a reduced model governing the total prey and predator densities. In the case of the first model, we show that the repulsive effect of predator on prey has a stabilizing effect on the predator-prey community. In the case of the second model, we show that there exists a window for the prey proportion on the resource patch to ensure stability. (shrink)

The class Matr(C) of all matrices for a prepositional logic (, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matr(C) states the following. Assume C to be the consequence operation on a prepositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of C. Then Matr (C) is the least class (...) of matrices containing K and closed under m-reduced products, submatrices, matrix homomorphisms, and matrix homomorphic counter-images. (shrink)

Let ℋ be a finite-dimensional complex Hilbert space and D the set of density matrices on ℋ, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure u on D that can be regarded as the uniform distribution over D. We propose a measure on D, argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed (...) according to this measure. (shrink)

Matrix models are widely used in biology to predict the temporal evolution of stage-structured populations. One issue related to matrix models that is often disregarded is the sampling variability. As the sample used to estimate the vital rates of the models are of finite size, a sampling error is attached to parameter estimation, which has in turn repercussions on all the predictions of the model. In this study, we address the question of building confidence bounds around the predictions (...) of matrix models due to sampling variability. We focus on a density-dependent Usher model, the maximum likelihood estimator of parameters, and the predicted stationary stage vector. The asymptotic distribution of the stationary stage vector is specified, assuming that the parameters of the model remain in a set of the parameter space where the model admits one unique equilibrium point. Tests for density-dependence are also incidentally provided. The model is applied to a tropical rain forest in French Guiana. (shrink)

Various methods have been employed to investigate different aspects of the brain activity modulation related to the performance of a cycling task. In our study we examined how functional connectivity and brain network efficiency varied during an endurance cycling task. To this purpose, we reconstructed EEG signals at source level: we computed current densities in 28 anatomical regions of interest (ROIs) through the eLORETA algorithm, then we calculated the Lagged Coherence of the 28 current density signals to define the (...) adjacency matrix. To quantify changes of functional network efficiency during an exhaustive cycling task, we computed three graph theoretical indices: local efficiency (LE), global efficiency (GE) and Density (D) in two different frequency bands, Alpha and Beta bands, that indicate alertness processes and motor binding/fatigue respectively. This analysis was conducted for six different task intervals: pre-cycling, initial, intermediate and final stages of cycling, active recovery and passive recovery. Fourteen participants performed an incremental cycling task with simultaneous EEG recording and RPE monitoring to detect participants’ exhaustion. LE remained constant during the endurance cycling task in both bands. Therefore, we speculate that fatigue processes did not affect segregated neural processing. We observed an increase of GE in the Alpha band only during cycling, that could be due to greater alertness processes and preparedness to stimuli during exercise. Conversely, although D did not change significantly over time in the Alpha band, its general reduction in the Beta bands during cycling could be interpreted within the framework of the neural efficiency hypothesis, which posits a reduced neural activity for expert/automated performances. We argue that the use of graph theoretical indices represents a clear methodological advancement in studying endurance performance. (shrink)

In this paper, we analyze and calculate the crowd density in a tourist area utilizing video surveillance dynamic information analysis and divide the crowd counting and density estimation task into three stages. In this paper, novel scale perception module and inverse scale perception module are designed to further facilitate the mining of multiscale information by the counting model; the main function of the third stage is to generate the population distribution density map, which mainly consists of three (...) columns of void convolution with different void rates and generates the final population distribution density map using the feature maps of different branch regressions. Also, the algorithm uses jump connections between the top convolution and the bottom void convolution layers to reduce the risk of network gradient disappearance and gradient explosion and optimizes the network parameters using an intermediate supervision strategy. The hierarchical density estimator uses a hierarchical strategy to mine semantic features and multiscale information in a coarse-to-fine manner, and this is used to solve the problem of scale variation and perspective distortion. Also, considering that the background noise affects the quality of the generated density map, the soft attention mechanism is integrated into the model to stretch the distance between the foreground and background to further improve the quality of the density map. Also, inspired by multitask learning, this paper embeds an auxiliary count classifier in the count model to perform the count classification auxiliary task and to increase the model’s ability to express semantic information. Numerous experimental results demonstrate the effectiveness and feasibility of the proposed algorithm in solving the problems of scale variation and perspective distortion. (shrink)

In today’s era of rapid development in science and technology, the development of digital technology has increasingly higher requirements for data processing functions. The matrix signal commonly used in engineering applications also puts forward higher requirements for processing speed. The eigenvalues of the matrix represent many characteristics of the matrix. Its mathematical meaning represents the expansion of the inherent vector, and its physical meaning represents the spectrum of vibration. The eigenvalue of a matrix is the focus (...) of matrix theory. The problem of matrix eigenvalues is widely used in many research fields such as physics, chemistry, and biology. A neural network is a neuron model constructed by imitating biological neural networks. Since it was proposed, the application research of its typical models, such as recurrent neural networks and cellular neural networks, has become a new hot spot. With the emergence of deep neural network theory, scholars continue to combine deep neural networks to calculate matrix eigenvalues. This article aims to study the estimation and application of matrix eigenvalues based on deep neural networks. This article introduces the related methods of matrix eigenvalue estimation based on deep neural networks, and also designs experiments to compare the time of matrix eigenvalue estimation methods based on deep neural networks and traditional algorithms. It was found that under the serial algorithm, the algorithm based on the deep neural network reduced the calculation time by about 7% compared with the traditional algorithm, and under the parallel algorithm, the calculation time was reduced by about 17%. Experiments are also designed to calculate matrix eigenvalues with Obj and recurrent neural networks (RNNS) models, which proves that the Oja algorithm is only suitable for calculating the maximum eigenvalues of non-negative matrices, while RNNS is commonly used in general models. (shrink)

The authors of [MOC 00] conjectured that intuitionistic and classical logics are asymptotically identical. Their conjecture concerns the implicational parts of these logics over k variables and is trivially true for k = 1, because implicational parts of intuitionistic and classical logics over one variable are identical. So, it seems to be interesting to investigate the appropriate fragments of these logics for k = 2. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear (...) logic of two variables. Actually, this paper shows the existence of the density of this logic and demonstrates that the linear calculus covers a substantial part of classical propositional one. (shrink)

Abnormal behavior detection of social security funds is a method to analyze large-scale data and find abnormal behavior. Although many methods based on spectral clustering have achieved many good results in the practical application of clustering, the research on the spectral clustering algorithm is still in the early stage of development. Many existing algorithms are very sensitive to clustering parameters, especially scale parameters, and need to manually input the number of clustering. Therefore, a density-sensitive similarity measure is introduced in (...) this paper, which is obtained by introducing new parameters to transform the Gaussian function. Under this metric, the distance between data points belonging to different classes will be effectively amplified, while the distance between data points belonging to the same class will be reduced, and finally, the distribution of data will be effectively clustered. At the same time, the idea of Eigen gap is introduced into the spectral clustering algorithm, and the verified gap sequence is constructed on the basis of Laplace matrix, so as to solve the problem of the number of initial clustering. The strong global search ability of artificial bee colony algorithm is used to make up for the shortcoming of spectral clustering algorithm that is easy to fall into local optimal. The experimental results show that the adaptive spectral clustering algorithm can better identify the initial clustering center, perform more effective clustering, and detect abnormal behavior more accurately. (shrink)

The proposed article is devoted to the description of an intelligent urban passenger transport system based on unmanned electric vehicles, sequentially moving along a separate line. This system is a passenger transport system of a new urban mobility, formed under the influence of social conditions generated by high population density in cities, that suppose the development of pedestrian zones and ecological modes of transport, "transport as a service", etc. In this historical context, public transport systems acquire special relevance. The (...) described transport system belongs to intelligent systems, since it is capable of functioning in autonomous mode without human intervention, adaptively responding to changes in the dynamics of the flow of passengers during the day. Passengers are transported by electric cars, which can be combined into cassettes according to the principle of road trains based on the transportation plan drawn up by the intelligent center of the transport system according to the matrix of correspondences, filled in taking into account the incoming requests for service from passengers. When drawing up a transportation plan, the algorithms of the transport system give preference to transportation according to the "source-destination" principle, that is, when the passenger goes to the destination with a minimum number of intermediate stops, and ideally without them. The paper formulates also a criterion of arising of a conflict in the movement of vehicles, which allows to identify situations when an electric vehicle driving in front can detain vehicles following after. The work has relevance because the criterion will allow to make adjustments in the schedule of movement of vehicles and exclude the loss of time and energy that carries the transport system during braking and acceleration of electric cars, as well as to reduce waiting time and travel of passengers. (shrink)

We investigate strong versions of enumeration reducibility, the most important one being s-reducibility. We prove that every countable distributive lattice is embeddable into the local structure $L(\mathfrak D_s)$ of the s-degrees. However, $L(\mathfrak D_s)$ is not distributive. We show that on $\Delta^{0}_{2}$ sets s-reducibility coincides with its finite branch version; the same holds of e-reducibility. We prove some density results for $L(\mathfrak D_s)$ . In particular $L(\mathfrak D_s)$ is upwards dense. Among the results about reducibilities that are stronger than (...) s-reducibility, we show that the structure of the $\Delta^{0}_{2}$ bs-degrees is dense. Many of these results on s-reducibility yield interesting corollaries for Q-reducibility as well. (shrink)

Two analyzes of Spark engine performance strategies to implement the Spark technique in a matrix distributed computational algorithm, the multiplication of a sparse multiplication operational test model. The dimensions of the two input sparse matrices have been fixed to 30,000 × 30,000, and the density of the input matrix have been changed. The experimental results show that when the density reaches about 0.3, the original dense matrix multiplication performance can outperform the sparse-sparse matrix multiplication, (...) which is basically consistent with the relationship between the sparse matrix multiplication implementation in the single-machine sparse matrix test and the computational performance of the local native library. When the density of the fixed sparse matrix is 0.01, the distributed density-sparse matrix multiplication outperforms the same sparsity but uses the density matrix storage, and the acceleration ratio increases from 1.88× to 5.71× with the increase in dimension. The overall performance of distributed operations is improved. (shrink)

Ageing causes progressive decline in metabolic, behavioural, and physiological functions, leading to a reduced health span. The extracellular matrix (ECM) is the three‐dimensional network of macromolecules that provides our tissues with structure and biomechanical resilience. Imbalance between damage and repair/regeneration causes the ECM to undergo structural deterioration with age, contributing to age‐associated pathology. The ECM ‘Ageing Across the Life Course’ interdisciplinary research network (ECMage) was established to bring together researchers in the United Kingdom, and internationally, working on the (...) emerging field of ECM ageing. Here we report on a consultation at a joint meeting of ECMage and the Medical Research Council / Versus Arthritis Centre for Integrated Research into Musculoskeletal Ageing, held in January 2023, in which delegates analysed the key questions and research opportunities in the field of ECM ageing. We examine fundamental biological questions, enabling technologies, systems of study and emerging in vitro and in silico models, alongside consideration of the broader challenges facing the field. (shrink)

The susceptible-transmissible-removed (STR) model is a deterministic compartment model, based on the susceptible-infected-removed (SIR) prototype. The STR replaces 2 SIR assumptions. SIR assumes that the emigration rate (due to death or recovery) is directly proportional to the infected compartment’s size. The STR replaces this assumption with the biologically appropriate assumption that the emigration rate is the same as the immigration rate one infected period ago. This results in a unique delay differential equation epidemic model with the delay equal to the (...) infected period. Hamer’s mass action law for epidemiology is modified to resemble its chemistry precursor—the law of mass action. Constructing the model for an isolated population that exists on a surface bounded by the extent of the population’s movements permits compartment density to replace compartment size. The STR reduces to a SIR model in a timescale that negates the delay—the transmissible timescale. This establishes that the SIR model applies to an isolated population in the disease’s transmissible timescale. Cyclical social interactions will define a rhythmic timescale. It is demonstrated that the geometric mean maps transmissible timescale properties to their rhythmic timescale equivalents. This mapping defines the hybrid incidence (HI). The model validation demonstrates that the HI-STR can be constructed directly from the disease’s transmission dynamics. The basic reproduction number (R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}) is an epidemic impact property. The HI-STR model predicts that R0∝ρnB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0 \propto \root \mathfrak{B} \of {\rho_n}$$\end{document} where ρn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document} is the population density, and B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{B}}$$\end{document} is the ratio of time increments in the transmissible- and rhythmic timescales. The model is validated by experimentally verifying the relationship. R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}’s dependence on ρn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document} is demonstrated for droplet-spread SARS in Asian cities, aerosol-spread measles in Europe and non-airborne Ebola in Africa. (shrink)

The clustering of mixed-attribute data is a vital and challenging issue. The density peaks clustering algorithm brings us a simple and efficient solution, but it mainly focuses on numerical attribute data clustering and cannot be adaptive. In this paper, we studied the adaptive improvement method of such an algorithm and proposed an adaptive mixed-attribute data clustering method based on density peaks called AMDPC. In this algorithm, we used the unified distance metric of mixed-attribute data to construct the distance (...) matrix, calculated the local density based on K-nearest neighbors, and proposed the automatic determination method of cluster centers based on three inflection points. Experimental results on real University of California-Irvine datasets showed that the proposed AMDPC algorithm could realize adaptive clustering of mixed-attribute data, can automatically obtain the correct number of clusters, and improved the clustering accuracy of all datasets by more than 22.58%, by 24.25%, by 28.03%, by 22.5%, and by 10.12% for the Heart, Cleveland, Credit, Acute, and Adult datasets compared to that of the traditional K-prototype algorithm, respectively. It also outperformed a modified density peaks clustering algorithm for mixed-attribute data algorithms. (shrink)

Natural and industrial disasters are increasing in the U.S., and the terrorist threat is still with us. Our response has been proximate — remediation and protection B rather than basic B reducing our vulnerabilities. Reducing vulnerabilities will involve the deconcentration of hazardous materials, of population density in vulnerable areas, and of private centers of economic and political power. The objection that deconcentration will entail economic inefficiencies is addressed by examining four systems that are very large, highly efficient, robust, radically (...) decentralized, and innovative: the Internet, the electric power grid, networks of small firms, and, alas, terrorist networks. All are threatened, but regulation by a strong state could preserve the efficiency of the first three, and muster the tools to thwart the fourth. (shrink)

A model is proposed for the population dynamics of an annual plant (Sesbania vesicaria) with a seed bank (i.e. in which a proportion of seeds remain dormant for at least one year). A simple linear matrix model is deduced from the life cycle graph. The dominant eigenvalue of the projection matrix is estimated from demographic parameters derived from field studies. The estimated values for population growth rate () indicates that the study population should be experiencing a rapid exponential (...) increase, but this was not the case in our population.The addition of density dependent effects on seedling survivorship and adult fecundity, effects for which field studies provide evidence, considerably improves our model. Depending on the demographic parameters, the model leads to stable equilibrium, oscillations, or chaos. Study of the behaviour of this model in the parameter space shows that the existence of a seed bank allows higher among-year variation of adult fecundity, without leaving the region of demographic stability. Field data obtained over 3 years confirm this prediction. (shrink)

We study the degree structure of the ω-c.e., n-c.e., and Π10 equivalence relations under the computable many-one reducibility. In particular, we investigate for each of these classes of degrees the most basic questions about the structure of the partial order. We prove the existence of the greatest element for the ω-c.e. and n-computably enumerable equivalence relations. We provide computable enumerations of the degrees of ω-c.e., n-c.e., and Π10 equivalence relations. We prove that for all the degree classes considered, upward (...) class='Hi'>density holds and downward density fails. (shrink)

This article examines land-use changes by large-scale plantations in Ethiopia and evaluates the impacts thereof on soil organic carbon, micronutrients and bulk density. Remote sensing analysis and field research activities were undertaken at four large-scale plantation projects in Benshanguel Gumuz, Gambella, and Oromia regional states. Results show that the projects largely involved the conversion of both closed and open to closed forests and grasslands, which in turn reduced soil carbon stock and micronutrient levels and increased soil compaction. We (...) argue that unless appropriate soil management activities and impact mitigation strategies are adopted by plantation proponents, these land-use changes will pose a serious threat to the long-term economic viability and sustainability of plantation agriculture in Ethiopia. This could undermine long-term ecosystem health and national food security. (shrink)

The degree structure of functions induced by a polynomial-time reducibility first introduced in G. Miller's work on the complexity of prime factorization is investigated. Several basic results are established including the facts that the degrees restricted to the sets do not form an upper semilattice and there is a minimal degree, as well as density for the low degrees, a weak form of the exact pair theorem, the existence of minimal pairs and the decidability of the Π2 theory of (...) the low degrees. (shrink)