Projection Rule Research Articles

Judicial System and Public Policy: Strategy for Expeditious Disposal of Backlog

This study aims to identify the causes of delayed justice in Karachi district courts and analyse the critical causes of delay that the Pakistani judicial and legal system is confronting daily. Article 37 (d) of the Constitution of the Islamic Republic of Pakistan emphasise speedy, expeditious and inexpensive justice. World Justice Project Rule of Law Index has ranked Pakistan 130 out of 139 countries on various parameters, including civil and criminal courts. This research makes a comprehensive analysis of civil and criminal litigation in Pakistan for delay reduction. Unfortunately, less has been done previously in Pakistan and especially equal to none of quantitative. This research will focus on the quantitative aspect regarding the rule of law. Moreover, this study used factor analysis to identify the top contributing factors that cause subordinate courts delays. The linear regression model is used to determine and test the directions of the independent variables. This research measures significance of these factors to reject the null hypothesis at a 5% interval level. Similarly, linear regression is used for the cost of litigation to identify the relationship between independent and dependent variables, which is the ”cost of each hearing”. The results show that unnecessary adjournments on frivolous grounds are the most contributing factor of the delayed justice and filing of the miscellaneous applications on frivolous grounds, lack of skills and standardised level of training of both advocates as well as learned judges.

L$\ddot {u}$der Rule, Von Neumann Rule and Cirelson’s Bound of Bell CHSH Inequality

In [PRL, 113, 050401 (2014)] the authors have shown that instead of L$\ddot{u}$der rule, if degeneracy breaking von Neumann projection rule is adopted for state reduction, the quantum value of three-time Leggett-Garg inequality can exceed it's L$\ddot{u}$ders bound. Such violation of L$\ddot{u}$ders bound may even approach algebraic maximum of the inequality in the asymptotic limit of system size. They also claim that for Clauser-Horne-Shimony-Holt (CHSH) inequality such violation of L$\ddot{u}$ders bound (known as Cirelson's bound) cannot be obtained even when the measurement is performed sequentially first by Alice followed by Bob. In this paper, we have shown that if von Neumann projection rule is used, quantum bound of CHSH inequality exceeds it's Cirelson's bound and may also reach its algebraic maximum four. This thus provide a strong objection regarding the viability of von Neumann rule as a valid state reduction rule. Further, we pointed out that the violation of Cirelson's bound occurs due to the injection of additional quantum non-locality by the act of implementing von Neumann measurement rule.

Storage Capacity of Quaternion-Valued Hopfield Neural Networks With Dual Connections.

A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model. A quaternion-valued Hopfield neural network (QHNN) with a twin-multistate activation function was proposed to reduce the number of weight parameters of CHNN. Dual connections (DCs) are introduced to the QHNNs to improve the noise tolerance. The DCs take advantage of the noncommutativity of quaternions and consist of two weights between neurons. A QHNN with DCs provides much better noise tolerance than a CHNN. Although a CHNN and a QHNN with DCs have the samenumber of weight parameters, the storage capacity of projection rule for QHNNs with DCs is half of that for CHNNs and equals that of conventional QHNNs. The small storage capacity of QHNNs with DCs is caused by projection rule, not the architecture. In this work, the ebbian rule is introduced and proved by stochastic analysis that the storage capacity of a QHNN with DCs is 0.8 times as many as that of a CHNN.

Noise Robust Projection Rule for Klein Hopfield Neural Networks

Multistate Hopfield models, such as complex-valued Hopfield neural networks (CHNNs), have been used as multistate neural associative memories. Quaternion-valued Hopfield neural networks (QHNNs) reduce the number of weight parameters of CHNNs. The CHNNs and QHNNs have weak noise tolerance by the inherent property of rotational invariance. Klein Hopfield neural networks (KHNNs) improve the noise tolerance by resolving rotational invariance. However, the KHNNs have another disadvantage of self-feedback, a major factor of deterioration in noise tolerance. In this work, the stability conditions of KHNNs are extended. Moreover, the projection rule for KHNNs is modified using the extended conditions. The proposed projection rule improves the noise tolerance by a reduction in self-feedback. Computer simulations support that the proposed projection rule improves the noise tolerance of KHNNs.

Event-Based Formation Coordinated Control for Multiple Spacecraft Under Communication Constraints

This paper addresses the relative position coordinated control problem for spacecraft formation flying under an undirected communication graph, whilst considering mass uncertainties, external disturbances, and limited communication resources. A new event-triggered information transmission mechanism is first presented, where each spacecraft only requires accessing to the states of neighbors intermittently. Subsequently, a novel event-based coordinated control scheme is proposed by combining a smooth adaptive projection rule that confines the parameter estimations to well-defined bounded convex hypercubes. Under the proposed control framework, the information exchange among spacecraft occurs only when the specified event is triggered, thereby significantly reducing the communication load and saving the onboard resources. Furthermore, a positive lower bound on interevent time intervals is guaranteed to exclude Zeno behavior. By virtue of Lyapunov stability analysis and graph theory, it is proved that the relative position tracking errors can converge to small invariant sets around the origin, and that all closed-loop signals are bounded, even in the presence of mass uncertainties and external disturbances. Finally, numerical simulations are given to evaluate the effectiveness and highlight the advantages of the developed control algorithm.

Hyperbolic-valued Hopfield neural networks in hybrid mode

A complex-valued Hopfield neural network (CHNN) has been applied as a multistate neural associative memory. Although synchronous mode accelerates the recall process, a CHNN with a projection rule may be trapped at a cycle of length two. A hyperbolic-valued Hopfield neural network (HHNN) with a conventional projection rule converges to a fixed point in synchronous mode. A noise robust projection rule improves the noise tolerance of HHNN, though it is not able to be applied to an HHNN in synchronous mode. In this work, we proposed hybrid mode, that is, asynchronous mode after synchronous mode. The conventional projection rule is employed in synchronous mode, and the noise robust projection rule is employed in asynchronous mode. Thus, the HHNN in hybrid mode converges in both modes. The HHNN in hybrid mode is expected to provide better noise tolerance than an HHNN in synchronous mode and faster recall than an HHNN in asynchronous mode. Computer simulations imply that our expectations are achieved.

Volunteer tourism fields: spaces of altruism and unsustainability

ABSTRACT Drawing upon research from six volunteer projects in Cambodia, this paper explores the volunteer host community as a ‘space’ that has its own rules and normalized ways of behaving that influences the assistance prospective beneficiaries receive. Underpinned by Bourdieu’s theory of field’s, qualitative interviews and participant observation is conducted with both volunteers and hosts. This paper concludes that volunteer project rules are not homogeneous and that normalized ways of behaving can lead to unregulated and unsustainable practice but also integrated and productive outcomes. This suggests a more regulative and structured approach to volunteer tourism led by media and volunteers themselves may enhance the sustainable foundation of the sector.

Quaternion Projection Rule for Rotor Hopfield Neural Networks.

A rotor Hopfield neural network (RHNN) is an extension of a complex-valued Hopfield neural network (CHNN) and has excellent noise tolerance. The RHNN decomposition theorem says that an RHNN decomposes into a CHNN and a symmetric CHNN. For a large number of training patterns, the projection rule for RHNNs generates large self-feedbacks, which deteriorates the noise tolerance. To remove self-feedbacks, we propose a projection rule using quaternions based on the decomposition theorem. Using computer simulations, we show that the quaternion projection rule improves noise tolerance.

Stability Conditions of Bicomplex-Valued Hopfield Neural Networks.

Hopfield neural networks have been extended using hypercomplex numbers. The algebra of bicomplex numbers, also referred to as commutative quaternions, is a number system of dimension 4. Since the multiplication is commutative, many notions and theories of linear algebra, such as determinant, are available, unlike quaternions. A bicomplex-valued Hopfield neural network (BHNN) has been proposed as a multistate neural associative memory. However, the stability conditions have been insufficient for the projection rule. In this work, the stability conditions are extended and applied to improvement of the projection rule. The computer simulations suggest improved noise tolerance.

A Scale-Invariant Generalization of the Rényi Entropy, Associated Divergences and Their Optimizations Under Tsallis’ Nonextensive Framework

Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization of the entropy and the minimization of the cross entropy or relative entropy (divergence), are essential for general logical inference in our physical world. In this paper, we discuss a two parameter generalization of the popular R\'{e}nyi entropy and associated optimization problems. We derive the desired entropic characteristics of the new generalized entropy measure including its positivity, expandability, extensivity and generalized (sub-)additivity. More importantly, when considered over the class of sub-probabilities, our new family turns out to be scale-invariant. We also propose the corresponding cross entropy and relative entropy measures and discuss their geometric properties including generalized Pythagorean results over $\beta$-convex sets. The maximization of the new entropy and the minimization of the corresponding cross or relative entropy measures are carried out explicitly under the non-extensive (`third-choice') constraints given by the Tsallis' normalized $q$ expectations which also correspond to the $\beta$-linear family of probability distributions. Important properties of the associated forward and reverse projection rules are discussed along with their existence and uniqueness. In this context, we have come up with, for the first time, a class of entropy measures -- a subfamily of our two-parameter generalization -- that leads to the classical (extensive) exponential family of MaxEnt distributions under the non-extensive constraints. Other members of the new entropy family, however, lead to the power-law type generalized $q$-exponential MaxEnt distributions which is in conformity with Tsallis' nonextensive theory.

Complex-valued Hopfield neural networks with real weights in synchronous mode

A complex-valued Hopfield neural network with a multistate activation function converges in asynchronous mode, whereas it converges or is trapped at a cycle of length two in synchronous mode. For parallel processing, convergence in synchronous mode is necessary. In particular, a complex-valued Hopfield neural network (CHNN) is the most widely used multistate Hopfield model, and it is desirable that a CHNN converges in synchronous mode. In this work, a real-weight CHNN (RWCHNN) is proposed. An RWCHNN restricts the weights of a CHNN to real numbers and has half weight parameters of a CHNN. We provide the stability conditions of an RWCHNN in synchronous mode and prove that the projection rule satisfies them. The RWCHNN is the first model such that it converges in synchronous mode and has half weight parameters of a CHNN. Computer simulations show that the average update count until convergence is far less than those of the hypercomplex-valued Hopfield neural networks with the same number of weight parameters of an RWCHNN.

Noise-Robust Projection Rule for Rotor and Matrix-Valued Hopfield Neural Networks.

A complex-valued Hopfield neural network (CHNN) has weak noise tolerance due to rotational invariance. Some alternatives of CHNN, such as a rotor Hopfield neural network (RHNN) and a matrix-valued Hopfield neural network (MHNN), resolve rotational invariance and improve the noise tolerance. However, the RHNN and MHNN with projection rules have a different problem of self-feedbacks. If the self-feedbacks are reduced, the noise tolerance is expected to be improved further. For reduction in the self-feedbacks, the noise-robust projection rules are introduced. The stability conditions are extended, and the self-feedbacks are reduced based on the extended stability conditions. Computer simulations support that the noise tolerance is improved. In particular, the noise tolerance is more robust against an increase in the number of training patterns.

Bicomplex Projection Rule for Complex-Valued Hopfield Neural Networks.

A complex-valued Hopfield neural network (CHNN) with a multistate activation function is a multistate model of neural associative memory. The weight parameters need a lot of memory resources. Twin-multistate activation functions were introduced to quaternion- and bicomplex-valued Hopfield neural networks. Since their architectures are much more complicated than that of CHNN, the architecture should be simplified. In this work, the number of weight parameters is reduced by bicomplex projection rule for CHNNs, which is given by the decomposition of bicomplex-valued Hopfield neural networks. Computer simulations support that the noise tolerance of CHNN with a bicomplex projection rule is equal to or even better than that of quaternion- and bicomplex-valued Hopfield neural networks. By computer simulations, we find that the projection rule for hyperbolic-valued Hopfield neural networks in synchronous mode maintains a high noise tolerance.

Hyperbolic-Valued Hopfield Neural Networks in Synchronous Mode.

For most multistate Hopfield neural networks, the stability conditions in asynchronous mode are known, whereas those in synchronous mode are not. If they were to converge in synchronous mode, recall would be accelerated by parallel processing. Complex-valued Hopfield neural networks (CHNNs) with a projection rule do not converge in synchronous mode. In this work, we provide stability conditions for hyperbolic Hopfield neural networks (HHNNs) in synchronous mode instead of CHNNs. HHNNs provide better noise tolerance than CHNNs. In addition, the stability conditions are applied to the projection rule, and HHNNs with a projection rule converge in synchronous mode. By computer simulations, we find that the projection rule for HHNNs in synchronous mode maintains a high noise tolerance.

A Projection Rule for Complex‐Valued Associative Memory with Partial Connections

Projection rule is a powerful learning scheme for embedding patterns onto Hopfield‐type associative memories, but this cannot be used for non‐fully connected networks, such as bidirectional associative memory. This paper presents a novel type of Projection rule that can embed patterns onto partially connected networks. The applicability and performances of the proposed Projection rule are evaluated through numerical experiments. From experimental results, it is confirmed that the proposed scheme actually works on partially connected networks, though the embedding capability is not high with compared to the one in fully connected networks. It is also shown that gray‐scaled images can be embedded and retrieved in the networks. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

ON THE ASSESSMENT OF MATHEMATICAL COMPETENCIES FOR SOLVING NON-LINEAR EQUATION S

The process of learning and acquiring mathematics by students is inextricably linked with the need to measure the achieved level of their knowledge and skills at each stage of education. The aim of the study is to propose a methodological approach for evaluating students’ mathematics competencies in engineering degrees, developed in accordance with the results of the European Erasmus+ project Rules_Math. A competency assessment model is presented that includes three main components: multiple-choice test, tasks to solve and a small practical project on a topic from the curriculum for first-year students. The multiple-choice test aims to assess students' understanding of the basic notions, concepts, and methods in the field. Solving problems should measure the level of knowledge and skills acquired. The practical project could evaluate the students’ ability to apply what has been learned to solve practice-oriented tasks. It is recommended to use mathematical software. The approach is demonstrated with a specific example of assessing mathematical competencies for solving non-linear equations of a single variable. Answers and solutions are also provided. The presented methodology can be used by professors and tutors in higher education institutions to update the assessment of students' competencies in mathematics.

Conditions for macrorealism for systems described by many-valued variables

Macrorealism (MR) is the view that a system evolving in time possesses definite properties independent of past or future measurements and is traditionally tested for systems described at each time by a single dichotomic variable $Q$. A number of necessary and sufficient conditions for macrorealism have been derived for a dichtomic variable using sets of Leggett-Garg (LG) inequalities, or the stronger no-signaling in time (NSIT) conditions, or a combination thereof. Here, we extend this framework by establishing necessary and sufficient conditions for macrorealism for measurements made at two and three times for systems described by variables taking three or more values at each time. Our results include a generalization of Fine's theorem to many-valued variables for measurements at three pairs of times and we derive the corresponding complete set of LG inequalities. We find that LG inequalities and NSIT conditions for many-valued variables do not enjoy the simple hierarchical relationship exhibited by the dichotomic case. This sheds light on some recent experiments on three-level systems which exhibit a LG inequality violation even though certain NSIT conditions are satisfied. Under measurements of dichotomic variables using the Luders projection rule the three-time LG inequalities cannot be violated beyond the Luders bound (which coincides numerically with the Tsirelson bound obeyed by correlators in Bell experiments), but this bound can be violated in LG tests using degeneracy-breaking (von Neumann) measurements. We identify precisely which MR conditions are violated under these circumstances.

Split Quaternion-Valued Twin-Multistate Hopfield Neural Networks

Complex-valued Hopfield neural networks have been extended to 4-dimensional models using quaternions and commutative quaternions. The algebra of split quaternions is another 4-dimensional hypercomplex number system. In this work, a split quaternion-valued Hopfield neural network is defined. By the computer simulations using the twin-multistate activation function and projection rule, we evaluate the noise tolerance.

Japan: An Overview of Constitution & Judicial System

Japan was the first country in Asia to have a written constitution in late nineteenth century. The Japanese constitution is the oldest unamended constitution in the world. In 2020, Japan ranked 15th in the World Justice Project's Rule of Law Index, a middling among G7 countries. It has not had any amendments to its text in more than 70 years. It is a short constitution with only 5000 words, compared to the average constitution with 21,000 words. At the highest of the Japanese legal system is the current Constitution of Japan. Promulgated on November 3, 1946, it entered into force on May 3, 1947. The progressive constitution granted universal suffrage, stripped Emperor Hirohito of all but symbolic power, stipulated a bill of rights, abolished peerage, and outlawed Japan’s right to make war. The necessity and practical extent of Article 9 has been debated in Japan since its enactment, particularly following the establishment of the Japan Self-Defense Forces (JSDF), a de facto post-war Japanese military force that substitutes for the pre-war Armed Forces, since 1 July 1954. Some lower courts have found the JSDF unconstitutional, but the Supreme Court never ruled on this issue.Three Articles are particularly important with regard to the juridical system: the Article on legislative power provides for the Diet as the sole law-making organ of the State; the Article on executive power provides that this authority is vested in the Cabinet; and the Article on judicial power provides that the whole of judicial power is vested in the Supreme Court and in such lower courts as are established by law. Taken together, these constitutional provisions create a governmental structure in Japan that is based on the separation of powers, and provide for checks and balances among the three organs of the State. There are five types of courts in Japan: The Supreme Court, High Courts, District Courts, Family Courts and Summary Courts. Japan adopts a three tiered judicial system and a summary, family, or district court will be the court of first instance depending on the nature of the matter. The Supreme Court is the highest court in the land and has been furnished with the power of judicial review.

A Bus Arrival Time Prediction Method Based on Position Calibration and LSTM

Bus arrival time prediction not only provides convenience for passengers, but also helps to improve the efficiency of intelligent transportation system. Unfortunately, the low precision of bus-mounted GPS system, lack of real-time traffic information and poor performance of prediction model lead to low estimation accuracy - greatly influence bus service performance. Hence, in this paper, a GPS calibration method is put forward, while projection rules of specific road shapes are discussed. Moreover, two traffic factors, travel factor and dwelling factor, are defined to express real-time traffic state. Then, considering both historic data and real-time traffic condition, a hybrid dynamic BAT prediction factor, which achieves accuracy enhancement by taking into account traffic flow evaluation results and GPS position calibration, is defined. A LSTM training model is construct to realize BAT prediction. Experiment results demonstrate that our technique can provide a higher level of accuracy compared to methods based on traditional time-of-arrival techniques, especially in the accuracy of multi-stops BAT prediction.