Finite Number Of States Research Articles

DUALITY: DETECTABILITY VERSUS STABILIZABILITY IN THE STOCHASTIC CONTEXT

The aim of this paper is to extend to the stochastic framework the well known duality relation between the detectability property and the stabilizability property of a finite dimensional, linear time invariant, deterministic system. We consider continuous time linear stochastic systems having the state space representation described by a system of Itˆo differential equations with periodic coefficients possibly subject to some stochastic perturbations modeled by a standard homogeneous Markov process with a finite number of states. It will be seen that in the case when the given system is affected by jump Markov perturba tions a state space representation of the dual triple may be rigorously defined if and only if the transition probability matrix of the Markov process is double stochastic (in the sense that the sums of all elements from its each row and each column are equal 1).

Optimal filtering of an information process depended on noninformative parameters described by Marcovian chain when radio signals are receiving

In radio navigation and radio location tasks tracking systems on radio signals parameters often operate when object acceleration has stepwise changing. If we synthesize various tracking systems using optimal filtering theory it is necessary to represent the estimated process as a multidimensional Marcovian process. But such representation for stepwise changed acceleration is a rough approximation that lead to estimates accuracy degradation. One of possible approach to such disambiguation is to describe acceleration as Marcovian chain with finite number of states. This approach is developed in the article. Objective. To synthesize an optimal filtering algorithm of information process depended on noninformative parameters described by Marcovian chain using the observation grouping method when receiving radio signals and to implement simulation for an illustrative task.

Modeling and Estimation of Continuous Flexible Structure Using Theory of Functional Connections

This paper presents a novel method for modeling and estimating the dynamics of a continuous structure based on a limited number of noisy measurements. The goal is reached using a Kalman filter in synergy with the recently developed mathematical framework known as the Theory of Functional Connections (TFC). The TFC allows deriving a functional expression capable of representing the entire space of the functions that satisfy a given set of linear and, in some cases, nonlinear constraints. The proposed approach exploits the possibilities offered by the TFC to derive an approximated dynamical model for the flexible system using the Lagrangian mechanics. The result is a representation of the structural dynamics using a finite number of states, in contrast to the infinite-dimensional model that would be obtained by application of the traditional continuum mechanics models that are based on sets of partial differential equations. The limited number of states enables the application of the well-known Kalman filter framework to improve the estimation of the displacements and displacement velocities. In addition, the continuous displacement field of the structure can be reconstructed with high fidelity. The theoretical development of the method is presented in relation to the case of an Euler–Bernoulli beam. Finally, the obtained model is used to carry out a simulation campaign aimed at assessing the accuracy, efficiency, and robustness of the proposed method.

Image segmentation with Cellular Automata

Image segmentation is a computer vision technique that involves dividing an image into distinct and meaningful regions or segments. The objective was to partition the image into areas that share similar visual characteristics. Noise and undesirable artifacts introduce inconsistencies and irregularities in image data. These inconsistencies severely affect the ability of most segmentation algorithms to distinguish between true image features, leading to less reliable and lower-quality results. Cellular Automata (CA) is a computational concept that consists of a grid of cells, each of which can be in a finite number of states. These cells evolve over discrete time steps based on a set of predefined rules that dictate how a cell's state changes according to its own state and the states of its neighboring cells. In this paper, a new segmentation approach based on the CA model was introduced. The proposed approach consisted of three phases. In the initial two phases of the process, the primary objective was to eliminate noise and undesirable artifacts that can interfere with the identification of regions exhibiting similar visual characteristics. To achieve this, a set of rules is designed to modify the state value of each cell or pixel based on the states of its neighboring elements. In the third phase, each element is assigned a state that is chosen from a set of predefined states. These states directly represent the final segmentation values for the corresponding elements. The proposed method was evaluated using different images, considering important quality indices. The experimental results indicated that the proposed approach produces better-segmented images in terms of quality and robustness.

Factorisation in the semiring of finite dynamical systems

Finite dynamical systems (FDSs) are commonly used to model systems with a finite number of states that evolve deterministically and at discrete time steps. Considered up to isomorphism, those correspond to functional graphs. As such, FDSs have a sum and product operation, which correspond to the direct sum and direct product of their respective graphs; the collection of FDSs endowed with these operations then forms a semiring. The algebraic structure of the product of FDSs is particularly interesting. For instance, an FDS can be factorised if and only if it is composed of two sub-systems running in parallel. In this work, we further the understanding of the factorisation, division, and root finding problems for FDSs. Firstly, an FDS A is cancellative if one can divide by it unambiguously, i.e. AX=AY implies X=Y. We prove that an FDS A is cancellative if and only if it has a fixed point. Secondly, we prove that if an FDS A has a k-th root (i.e. B such that Bk=A), then it is unique. Thirdly, unlike integers, the monoid of FDS product does not have unique factorisation into irreducibles. We instead exhibit a large class of monoids of FDSs with unique factorisation. To obtain our main results, we introduce the unrolling of an FDS, which can be viewed as a space-time expansion of the system. This allows us to work with (possibly infinite) trees, where the product is easier to handle than its counterpart for FDSs.

Design of Smart Traffic Signal using Verilog

Traffic light control can be designed as synchronous sequential machine with finite number of states. Explicit finite state model is used to design the necessary coding for control system using Verilog HDL. The machine is modeled with only six states necessary delay is provided and for that particular delay the necessary traffic lights are set ON and OFF. For illustration just only two roads Chosen and control algorithm controls the traffic lights of that roads proposes a flexible framework which provides a particular delaying particular using click divider, also discusses the issues of modeling the state machine in a synthes is friendly manner. The proposed system aims to optimize traffic flow and reduce congestion by dynamically adjusting signal timings based on real-time traffic data. The design includes modules for vehicle detection, data processing, and signal control. By utilizing Verilog's capabilities, the system achieves efficient and accurate signal management, enhancing over all traffic management and contributing to safer and more stream lined urban mobility..

Study: Medical cannabis did not reduce opioid pain prescriptions

State laws that allow medical cannabis to be prescribed and dispensed did not result in the reduced treatment of chronic noncancer pain, researchers have found. In the study, “Effects of U.S. State Medical Cannabis Laws on Treatment of Chronic Noncancer Pain,” lead author Emma E. McGinty, Ph.D., and colleagues found that the availability of medical cannabis did not reduce opioid prescriptions or non‐opioid procedures for pain. Proponents of cannabis legalization have long used the opioid epidemic as an argument for making the cannabis more available, but this study, published in the July issue of the Annals of Internal Medicine, said cannabis did not have any effect. The study looked at 583,820 commercially insured adults with chronic noncancer pain and reported that the availability of medical cannabis did not change their practices. The researchers used data from 12 states that implemented medical cannabis laws and compared that data to 17 other states. The study found that medical cannabis laws led to an average difference of 0.05 percentage points in the proportion of patients who received any opioid prescription. The study looked at the first three years of the law implementation. The researchers were able to predict what would have happened had the law not been implemented. Their study limitations included assumptions involving parallel trends, a finite number of states, and the possible lack of generalizability to non‐commercially insured populations, each of which could not be validated by testing.

A Two-Stage PBFT Architecture With Trust and Reward Incentive Mechanism

Consensus algorithm is an essential ingredient of any blockchain system. Many different consensus mechanisms such as Practical Byzantine Fault Tolerance (PBFT), Proof-of-Work (PoW), Proof-of-Stake (PoS), and their many derivatives have been proposed over the years, but the complementary problems of performance and resilience to malicious behavior of the nodes have yet to be resolved in a satisfactory manner. In this work, we propose a consensus mechanism that integrates PoS with PBFT, which can effectively deal with dishonest nodes, both individual validators and leaders, whilst maintaining high performance. Our model incentivized truthful behavior by using trust score and reward mechanisms as crucial components of the block validation and ordering processes. The performance of the proposed scheme is evaluated using an analytical model that employs a semi-Markov process, defined by an ergodic multidimensional Markov chain with a finite number of states. The results show the efficiency of the proposed model in consensus-based decision making, even under a high likelihood of dishonest node behavior.

METODE MARKOV CHAIN DALAM PENGENDALIAN PERSEDIAAN UNTUK PERENCANAAN BIAYA PERSEDIAAN BAHAN BAKU PADA TOKO AIRIN BAKERY & CAKE SHOP

Airin Bakery & Cake Shop produces various kinds of cakes and bread. This shop is often faced with problems that occur, namely the supply of raw materials that are insufficient or excess so that the production process does not go well. This study aims to determine the ordering capacity and the right time to order raw materials to minimize the total cost of raw material inventory using the silver meal method. The total inventory cost is Rp. 14,637,947.4 less than the cost set by the company. Inventory control, which is a stochastic process, can also be carried out without regard to safety stock, lead time, and reorder points. The stochastic process of total inventory can be described by a finite number of states. The probability of transitions between these states is described by a markov chain. The markov chain method can predict future raw material inventory costs. After making several states on the amount of raw material inventory, a prediction of the future raw material inventory costs of Rp.31.747.932,98 is obtained

A Preliminary Study and Implementing Algorithm Using Finite State Automaton for Remote Identification of Drones

Electronic remote identification (ER-ID) is a new radio frequency (RF) technology that is initiated by the Federal Aviation Authorities (FAA). For security reasons, traffic control, and so on, ER-ID has been applied for drones by the FAA to enable them to transmit their unique identification and location so that unauthorized drones can be identified. The current limitation of the existing ER-ID algorithms is that the application is limited to the Wi-Fi and Bluetooth wireless controllers, which results in a maximum range of 10–20 m for Bluetooth and 50–100 m for Wi-Fi. In this study, a mathematical computing technique based on finite state automaton (FSA) is introduced to expand the range of the ER-ID RF system and reduce the energy required by the drone to use the technology. A finite number of states have been designed to include a larger range of wireless network techniques, enabling the drones to be recognized while they are further away and in remote areas. This is achieved by including other means of RF channels, such as 4G/5G, Automatic Dependent Surveillance-Broadcast (ADS-B), long range Internet of things (IoT), and satellite communications, in the suggested ER-ID algorithm of this study. The introduced algorithm is tested via a case study. The results showed the ability to detect drones using all types of available radio frequency communication systems (RF-CS) while also minimizing the consumed energy. Hence, the authorities can control the licensed drones by using available RF-CS devices, such as Bluetooth and Wi-Fi, which are already widely used for mobile phones, as an example.

Veneziano variations: how unique are string amplitudes?

String theory offers an elegant and concrete realization of how to consistently couple states of arbitrarily high spin. But how unique is this construction? In this paper we derive a novel, multi-parameter family of four-point scattering amplitudes exhibiting i) polynomially bounded high-energy behavior and ii) exchange of an infinite tower of high-spin modes, albeit with a finite number of states at each resonance. These amplitudes take an infinite-product form and, depending on parameters, exhibit mass spectra that are either unbounded or bounded, thus corresponding to generalizations of the Veneziano and Coon amplitudes, respectively. For the bounded case, masses converge to an accumulation point, a peculiar feature seen in the Coon amplitude but more recently understood to arise naturally in string theory [1]. Importantly, our amplitudes contain free parameters allowing for the customization of the slope and offset of the spin-dependence in the Regge trajectory. We compute all partial waves for this multi-parameter class of amplitudes and identify unitary regions of parameter space. For the unbounded case, we apply similar methods to derive new deformations of the Veneziano and Virasoro-Shapiro amplitudes.

A Concurrent Switching Model for Traffic Congestion Control

We introduce a new conservation-based approach for traffic coordination modeling and control in a network of interconnected roads (NOIR) with switching movement phase rotations at every NOIR junction. For modeling of traffic evolution, we first assume that the movement phase rotation is cyclic at every NOIR junction, but the duration of each movement phase can be arbitrarily commanded by traffic signals. Then, we propose a novel concurrent switching dynamics (CSD) with deterministic transitions among a finite number of states, representing the NOIR movement phases. We define the CSD control as a cyclic receding horizon optimization problem with periodic quadratic cost and constraints. More specifically, the cost is defined so that the traffic density is minimized and the boundary inflow is uniformly distributed over the boundary inlet roads, whereas the cost parameters are periodically changed with time. The constraints are linear and imposed by a trapezoidal fundamental diagram at every NOIR road so that traffic feasibility is assured and traffic over-saturation is avoided.

Protocols with constant local storage and unreliable communication

Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication occurs nondeterministically, allowing the involved agents to change their states based on each other's states.In the present paper we study unreliable models based on population protocols and their variations from the point of view of expressive power. We model the effects of message loss. We show that for a general definition of protocols with unreliable communication with constant-storage agents such protocols can only compute predicates computable by immediate observation (IO) population protocols (sometimes also called one-way protocols). Immediate observation population protocols are inherently tolerant to unreliable communication and keep their expressive power under a wide range of fairness conditions. We also prove that a large class of message-based models that are generally more expressive than IO becomes strictly less expressive than IO in the unreliable case.

An improved estimator of Shannon entropy with applications to systems with memory

We investigate the memory properties of discrete sequences built upon a finite number of states. We find that the block entropy can reliably determine the memory for systems modeled as Markov chains of arbitrary finite order. Further, we provide an entropy estimator that remarkably gives accurate results when correlations are present. To illustrate our findings, we calculate the memory of daily precipitation series at different locations. Our results are in agreement with existing methods being at the same time valid in the undersampled regime and independent of model selection.

Synthesis for observability of logical control networks

Finite-state systems have applications in systems biology, formal verification and synthesis of infinite-state (hybrid) systems, etc. As deterministic finite-state systems, logical control networks (LCNs) consist of a finite number of nodes which can be in a finite number of states and update their states. In this paper, we investigate the synthesis problem for observability of LCNs based on state feedback with exogenous input by using the semitensor product proposed by Daizhan Cheng and the notion of observability graph (previously called weighted pair graph) proposed by us. We prove that if an unobservable LCN can be made observable by state feedback with exogenous input, then it can also be made observable by state feedback (without exogenous input, equivalent to state feedback with constant input). Furthermore, we give an upper bound on the number of state-feedback controllers that are needed to be tested in order to verify whether an unobservable LCN can be made observable by state feedback, and based on the procedure of obtaining the upper bound, we design an observability synthesis algorithm, by additionally combining the ideas of a greedy algorithm and dynamic programming. These results open the study of observability synthesis in LCNs.

Valuation of Annuity Guarantees Under a Self-Exciting Switching Jump Model

This article investigates the valuation of annuity guarantees under a regime-switching model when the dynamics of the underlying stock price follow a self-exciting switching jump-diffusion process. In this framework, we add a jump component to a regime-switching geometric Brownian for large shocks on the stock price. The intensity of shock arrivals is a Hawkes process modulated by a continuous time hidden Markov chain with a finite number of states. The interest rate used for discounting is stochastic and correlated to the stock market. In an incomplete market, we define an equivalent martingale measure to price a variable annuity contract that guarantees a minimum living or death benefit. Under this equivalent martingale measure, we propose closed-form approximation formulas using the inverse Fourier transform technique. A numerical implementation highlights the impact of self-exciting jumps and economic regimes on the valuation of guarantees.

BASIC PRINCIPLES FOR CONSTRUCTING MIXING FUNCTIONS BASED ON THE SIMPLEST LINEAR AND NONLINEAR MAPPINGS

This article is dedicated to exploring the possibility of using the simplest principles of nonlinear discrete dynamic systems theory in computer cryptography, which are characterized by their chaotic behavior. The main problem of using chaotic systems in computer calculations is that the number of possible states in a computer is finite. Therefore, computer models of chaos are only an approximation of the true chaotic behavior, and each trajectory of the approximated system is periodic. From a mathematical point of view, encryption in information systems involves transforming the space of finite messages, which is similar to the phase space in the theory of dynamical systems. The mixing function specifies such encryption. The main requirements for the mixing function are the absence of collisions, i.e., bijectivity of the mapping, good diffusion properties, and, in addition, the inverse transformation should not be more complicated than the direct one. The article demonstrates that it is possible to utilize the diffusion properties of nonlinear dynamical systems in spaces with a finite number of states by using the simplest nonlinear mapping, Tent. To enhance the diffusion properties, a superposition of the nonlinear Tent map and the linear permutation map (in the more general case of the Hill map) was used. The main advantages of the constructed functions are their simplicity of implementation, speed of calculations in mixing problems, and strong cryptographic persistence. Correlation analysis, sensitivity analysis, and analysis of the lengths of cycle periods that divide the space into non-overlapping subsets have been conducted for these functions. As a result, the expected good diffusion properties of these mixing functions are confirmed. The possibility of applying these functions to image encryption is demonstrated.

Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.

Parameterizing qudit states

Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an NN-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N){SU(N)}-invariant counterpart of the NN-level state space BN{\mathcal{B}_N}, i.e., the unitary orbit space BN/SU(N){B_N/SU(N)}. It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of BN/SU(N){B_N/SU(N)}. To illustrate the general situation, a detailed description ofBN/SU(N){B_N/SU(N)} for low-level systems: qubit (N=2{N= 2}), qutrit (N=3{N=3}), quatrit (N=4{N= 4}) - will be given.

Switching models and control of Petri Nets with shared resources under marking constraints

ABSTRACT Nowadays multi-option phenomena can generate potential problems related to industrial manufacturing systems. For instance, time and money loss are both expensive costs that should be paid when failing to make the right control choice decision, especially given the existence of various constraints. Therefore, the shared resource allocation between several processes can be transformed into a switching control problem that can be modeled using (Min, +) algebra. Due to the finite number of states and ergo of the application of this type of system, they are defined under the class of Discrete Event Systems. Accordingly, while taking into consideration modes of representation, this paper seeks to discuss a new modelling approach for competitive Timed Events Graphs under capacity constraints. The deduced switching models are then examined to solve the control problem issue of an industrial manufacturing process composed of cells of pick and place robots. To deduce the adequate control laws, an original solution based on the use of linear equations described by (Min, +) linear algebra is provided.