Set Of Possible States Research Articles

Local approximation for perfect discrimination of quantum states

Quantum state discrimination involves identifying a given state out of a set of possible states. When the states are mutually orthogonal, perfect state discrimination is alway possible using a global measurement. In the case of multipartite systems when the parties are constrained to use multiple rounds of local operations and classical communications (LOCC), perfect state discrimination is often impossible even with the use of \emph{asymptotic LOCC}, wherein an error is allowed but must vanish in the limit of an infinite number of rounds. Utilizing our recent results on asymptotic LOCC, we derive a lower bound on the error probability for LOCC discrimination of any given set of mutually orthogonal pure states. We use this lower bound to prove necessary conditions for perfect state discrimination by asymptotic LOCC. We then illustrate by example the power of these necessary conditions in significantly simplifying the determination of whether perfect discrimination of a given set of states can be accomplished arbitrarily closely using LOCC. The latter examples include a proof that perfect discrimination by asymptotic LOCC is impossible for any \emph{minimal} unextendible product basis (UPB), where minimal means that for the given multipartite system, no UPB with a smaller number of states can exist. We also give a simple proof that what has been called \emph{strong nonlocality without entanglement} is considerably stronger than had previously been demonstrated.

ANALYSIS OF MARСOVIAN SYSTEMS WITH A GIVEN SET OF SELECTED STATES

Analysis of stationary Marcovian systems is traditionally performed using systems of linear Kolmogorov differential equations. Such systems make it possible to determine the probability of the analyzed system being in each of its possible states at an arbitrary time. This standard task becomes more complicated if the set of possible states of systems is heterogeneous and some special subset can be distinguished from it, in accordance with the specifics of the system functioning. Subject of the study is technology development for such systems analysis. In accordance with this, the purpose of the work is to find the distribution law of the random duration of such a system's stay on a set of possible states until it falls into a selected subset of these states. Method for solving the problem is proposed based on splitting the entire set of possible states of the system into two subsets. The first of them contains a selected subset of states, and the second contains all the other states of the system. Now a subset of states is allocated from the second subset, from which a direct transition to the states of the first subset is possible. Next, a system of differential equations describing the transitions between the formed subsets is formed. The solution of this system of equations gives the desired result – distribution of the random duration of the system's stay until the moment of the first hit in the selected subset of states. The method allows solving a large number of practical problems, for example, in the theory of complex systems reliability with many different failure states. In particular, finding the law of the uptime duration distribution, calculating the average duration of uptime.

3d-reconstruction of destructive process models using remote sensing by a group of unmanned aerial vehicles

The paper presents a novel method of volumetric reconstruction of transient destructive processes using remote sensing by a group of unmanned aerial vehicles. The study is based on the most common class of such processes like forest fires, where a fire front is a determinant, and its propagation reflects the dynamics of the process. The effects of wind, smoke and fire, turbulence and vibration, interference, distortion, and obstacles lead to uncertainty of observations, to overcome which fuzzy sets, soft sets and gray numbers were combined. A spatial model based on a recursive eight-fold subdivision of space as well as on a hierarchical structure of virtual cells is proposed, which allowed to resolve the contradictions between the accuracy and rate of reconstruction. The set of possible states of virtual cells is determined and the algorithm of their classification based on the use of a five-channel image recognition system containing infrared, two main, and two additional optical channels is proposed. An algorithm for calculating a 3D observation vector, presented by an array of confidence vectors, is proposed, which can be used to determine the gray fuzzy state of virtual cells allowing a combination of observations from different observers and refining them sequentially. The terrain where the process evolves is represented by a soft gray fuzzy set of virtual cells, which belong to a specific state at the consideration time, allowing identification of convincing, uncertain, suspicious, and negative components. The first one defines a stable core of the fire front while the second one represents its variation caused by uncertainty. The proposed method allows the reconstruction of transient spatially distributed processes of other classes, smoothing the effects of distortions and noise and ensuring acceptable performance.

A semantic approach to nonmonotonic reasoning: Inference operations and choice

AbstractThis paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences frominfinitesets of premisses. The semantics is formulated in terms ofselection functionsand is a generalisation of thepreferential semanticsof Shoham, Kraus et al., and Makinson. A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. A proposition is anonmonotonic consequenceof a set of propositions iff holds in all the most preferred ‐states. In the literature on revealed preference theory, there are a number of well‐known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilised here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection,infinitary belief revision operations,that allow for the revision of a theory with a possibly infinite set of propositions, are introduced and characterised axiomatically. Several semantic representation theorems are proved for operations of this kind.

INFORMATION TECHNOLOGY OF FACIAL EMOTION RECOGNITION FOR VISUAL SAFETY SURVEILLANCE

Emotional expressions serve a crucial role in interpersonal communication between people while improving social life. In particular, information safety systems for visual surveillance that aim to recognize human emotional facial states are highly relevant today. In this regard, this study is devoted to the problem of identifying the main criteria for expressing the face of emotional manifestations for the possibility of recognizing without the use of specialized equipment, for example, security surveillance cameras with low resolution. In this work, we propose informational technology to define the face’s areas that reproduce the face’s emotional look. The input data from the proposed information technology is a set of videos with detected faces with the primary emotional states reproduced on them. At first, normalization of the faces of images is conducted to compare them in one base. It is executed by centering the face area and normalizing the distance between the eyes. Based on the analysis of point features moving in the set of input images, information points are then allocated (i.e., those points whose movement in the person’s emotional expression is the most significant). At the final stage, the areas of the face (with different bias thresholds) are determined, the changes of which form a visual perception of emotions. For each selected region, a set of possible states is formed. In conclusion, the behavior of point-specific features of a person under the manifestation of specific emotions is explored experimentally, and high-quality indicators for these emotions are highlighted. According to the study results, it is preferable to create a software product based on qualitative criteria for assessing the main areas of the face to determine the mimic expression of emotions.

Application of Mini-Batch Metaheuristic Algorithms in Problems of Optimization of Deterministic Systems with Incomplete Information about the State Vector

In this paper, we consider the application of the zero-order mini-batch optimization method in the problem of finding optimal control of a pencil of trajectories of nonlinear deterministic systems in the case of incomplete information about the state vector. The pencil of trajectories originates from a given set of initial states. To solve the problem, the structure of a feedback system is proposed, which contains models of the plant, measuring system, nonlinear state observer and control law of the fixed structure with unknown coefficients. The objective function proposed considers the quality of pencil of trajectories control, which is estimated by the average value of the Bolz functional over the given set of initial states. Unknown control laws of a plant and an observer are found in the form of expansions in terms of orthonormal systems of basis functions, which are specified on the set of possible states of a dynamical system. The original pencil of trajectories control problem is reduced to a global optimization problem, which is solved using the well-proven zero-order method, which uses a modified mini-batch approach in a random search procedure with adaptation. An algorithm for solving the problem is proposed. The satellite stabilization problem with incomplete information is solved.

Strategic manipulation in Bayesian dialogues.

In a Bayesian dialogue two individuals report their Bayesian updated belief about a certain event back and forth, at each step taking into account the additional information contained in the updated belief announced by the other at the previous step. Such a process, which operates through a reduction of the set of possible states of the world, converges to a commonly known posterior belief, which can be interpreted as a dynamic foundation for Aumann’s agreement result. Certainly, if two individuals have diverging interests, truthfully reporting one’s Bayesian updated belief at every step might not be optimal. This observation could lead to the intuition that always truthfully reporting one’s Bayesian updated belief were the best that two individuals could do if they had perfectly coinciding interests and these were in line with coming to know the truth. This article provides an example which shows this intuition to be wrong. In this example, at some step of the process, one individual has an incentive to deviate from truthfully reporting his Bayesian updated belief. However, not in order to hide the truth, but to help it come out at the end: to prevent the process from settling into a commonly known belief—the “Aumann conditions”—on a certain subset of the set of possible states of the world (in which the process then would be blocked), and this way make it converge to a subset of the set of possible states of the world on which it will be commonly known whether the event in question has occurred or not. The strategic movement described in this example is similar to a conversational implicature: the correct interpretation of the deviation from truthfully reporting the Bayesian updated belief thrives on it being common knowledge that the announced probability cannot possibly be the speaker’s Bayesian updated belief at this step. Finally, the argument is embedded in a game-theoretic model.

Delegation and Information Disclosure with Unforeseen Contingencies

Abstract We incorporate unawareness into the delegation problem between a financial expert and an investor, and study their pre-delegation communication. The expert has superior awareness of the possible states of the world, and decides whether to reveal some of them to the investor. We find that the expert reveals all the possible states to the investor if the investor is initially aware of a large set of possible states, but reveals partially or nothing otherwise. An investor with a higher degree of unawareness tends to delegate a larger set of projects to the expert, giving rise to a higher incentive for the expert to keep her unaware.

Comparison of guaranteed state estimators for linear time-invariant systems

Guaranteed state estimation computes the set of possible states of dynamical systems given the bounds of model uncertainties, disturbances, and noises. For the first time, we evaluate and compare a broad class of guaranteed state estimators for linear time-invariant systems regarding scalability, accuracy, and real-time applicability. In particular, we consider strip-based observers, set-propagation observers, and interval observers. The performance of most guaranteed state estimators is significantly affected by the chosen set representation. Zonotopes have emerged as a popular set representation since important operations such as linear maps and Minkowski sum can be computed exactly and efficiently. Furthermore, we provide comparisons with ellipsoids and constrained zonotopes as set representations. The comparison is conducted on various models for state estimation of autonomous vehicles.

Piecewise deterministic Markov process for condition-based maintenance models — Application to critical infrastructures with discrete-state deterioration

In recent decades, the technology and techniques for condition monitoring have experienced a rapid development. However, there is still a need for reducing unnecessary inspections and/or preventive maintenance actions and their associated cost, through optimal design of condition-based maintenance (CBM) strategies. Accordingly, mathematical modelling and optimization of CBM has become of interest for industry managers and researchers. This work explores on the application of a piecewise deterministic Markov process (PDMP) to encompass different modelling assumptions as non-negligible maintenance delays and inspection-based condition monitoring. These assumptions are relevant for many critical infrastructures in civil engineering or in oil & gas industry whose deterioration states are classified at a very high level of abstraction among a finite and small set of possible states. A formalism to model this type of problems is proposed in which the deterministic motion of the PDMP is reduced to a trivial differential equation to track the time elapsed between events. A numerical scheme for quantification, as an approximation of the Chapman–Kolmogorov equation, is presented. Later, an illustration case dealing with CBM of road bridges by the NPRA (Norwegian Public Roads Administration) is presented, guiding through the modelling and quantification approach.

An effective similarity measurement under epistemic uncertainty

The epistemic uncertainty stems from the lack of knowledge and it can be reduced when the knowledge increases. Such interpretation works well with data represented as a set of possible states and therefore, multivalued similarity measures. Unfortunately, set-valued extensions of similarity measures are not computationally feasible even when the data is finite. Measures with properties that allow efficient calculation of their extensions, need to be found. Analysis of various similarity measures indicated logic-based (additive) measures as an excellent candidate. Their unique properties are discussed and efficient algorithms for computing set-valued extensions are given. The work presents results related to various classes of fuzzy set families: general ones, intervals of fuzzy sets, and their finite sums. The first case is related to the concept of the Fuzzy Membership Function Family, the second corresponds to the Interval-Valued Fuzzy Sets, while the third class is equivalent to the concept of Typical Interval-Valued Hesitant Fuzzy Sets.

Survey and Review

The use of probabilistic ideas by applied mathematicians has seen a continued increase in recent decades. Probability now appears frequently at the modeling stage. There is widespread interest in investigating the effects of noise and uncertainty. Probabilistic algorithms are routinely applied with much success to the solution of deterministic problems (think of Monte Carlo quadrature or stochastic gradient descent). Markov chains give a simple, widely used tool to describe systems that evolve randomly. They are also a very popular topic in applied mathematics courses. At times \(0\), \(1\), \(2\), łdots, a Markov chain jumps from its current state \(x\) to a randomly chosen new state \(y\); the set of possible states is discrete. The requirement that the jumping times be uniformly spaced is a clear limitation in many situations, and this shortcoming is avoided by considering continuous-time Markov chains. In the continuous-time setting, if the chain has reached state \(x\) at time \(t_i\), it will jump to the randomly chosen \(y\) at time \(t_i+1=t_i+\tau_i\), where the waiting time \(\tau_i>0\) is itself random. Markov chains in continuous time are featured in many applications, including chemistry, ecology, and epidemiology. In a chemical system containing \(n\) species \(S_1\), łdots, \(S_n\), each state corresponds to vector \((c_1\), łdots, \( c_n)\) where \(c_j\) is the number of molecules of species \(S_j\). The species may take part in a number of chemical reactions, let us say \(S_1+2S_2 \rightarrow S_3\), \(2S_1+3S_3 \rightarrow S_4+2S_6\), and so on. At random times, one or another of the \(m\) possible reactions will take place and the state will change. Such a stochastic, molecular approach typically provides a more accurate description of the system than deterministic treatments where the concentrations of the different species are regarded as continuous variables that evolve according to a set of differential equations. This is particularly true in systems where, for some species, the number \(c_j\) is low, as is the case in many biological reactions. The following Survey and Review paper, “Stationary Distributions of Continuous-Time Markov Chains: A Review of Theory and Truncation-Based Approximations,” has been written by Juan Kuntz, Philipp Thomas, Guy-Bart Stan, and Mauricio Barahona. Section 2 provides a reader-friendly introduction to continuous-time Markov chains and their stationary distributions; these are important because they determine the long-time behavior of the chain. A salient future is that the authors present, in an accessible way, results that do not assume the chain to be irreducible (roughly speaking, irreducibility means that the chain is not the juxtaposition of two or more smaller chains that do not talk to each other; irreducibility simplifies the math, but is not a reasonable hypothesis in some applications). After that, the authors concentrate on how to compute invariant distributions. The paper contains numerical results, an extensive bibliography, and a detailed discussion of open problems.

Information space of the economic management system in the business management system

The process of possible automation of developing control actions is considered and presented in the article as the mathematical model that shows the economic mechanism of one or more business processes along with the formalized description of management accounting and controlling procedures. As a result, the information space model of the economic management system is obtained which is filled with a set of possible states created.

Ground states for a nonlocal mixed order cubic-quartic Gross-Pitaevskii equation

We prove existence and qualitative properties of ground state solutions to a generalized nonlocal 3rd-4th order Gross-Pitaevskii equation. Using a mountain pass argument on spheres and constructing appropriately localized Palais-Smale sequences we are able to prove existence of real positive ground states as saddle points. The analysis is deployed in the set of possible states, thus overcoming the problem that the energy is unbounded below. We also prove a corresponding nonlocal Pohozaev identity with no rest term, a crucial part of the analysis.

Do I Know Ω? An Axiomatic Model of Awareness and Knowledge

Abstract In modeling game and decision theory situations, it has been usual to start by considering Ω, the set of conceivable states of the world. I wish to propose a more fundamental view. I do not assume that the agent knows Ω. Instead the agent is assumed to derive for herself a representation of the universe. Given her knowledge and her ability to reason about it the agent deduces a set of conceivable states of the world and a set of possible states of the world. The epistemic model considered in this paper uses a propositional framework. The model distinguishes between the knowledge of the existence of a proposition, which I call awareness, and the knowledge of the truth or the falsity of the proposition. Depending upon whether one assumes that the agent is aware or not of all the propositions, she will or will not have a “complete model” of the world. When the agent is not aware of all the propositions, the states of the world and the possibility correspondence imaginable by her are coarser than the modeler's. The agent has an incomplete knowledge of both the states of the world and the information structure. In addition, I extend the model with “incompleteness” to a dynamic setting. Under the assumption that the agent's knowledge is non-decreasing over time, I show that the set of states of the world conceivable by the agent and her possibility correspondence get finer over time.

Verification of Detectability for Unambiguous Weighted Automata

In this article, we deal with the detectability problem for unambiguous weighted automata (UWAs). The problem is to determine if, after a finite number of observations, the set of possible states is reduced to a singleton. Four types of detectabilities, namely, strong detectability, detectability, strong periodic detectability, and periodic detectability are defined in terms of different requirements for current state estimation. We first construct a deterministic finite state automaton (called observer) over a weighted alphabet and prove that it can be used as the current-state estimator of the studied UWA. Finally, necessary and sufficient conditions based on the observer are proposed to verify detectabilities of a UWA.

An optimization method of the multi-group train formation at flat yards

ABSTRACT Formation of multi-group trains is aimed at arranging their cars in a given order and is one of the mass operations performed at railway. In this regard, the reduction of the duration of shunting operations for the formation of multi-group trains is an urgent task for railway transport. In this paper, for a discrete deterministic-controlled system that simulates the operation of the flat yard, a mathematical statement of the problem of choosing the optimal order of multi-group train formation is obtained. The set of possible states of the system under study and the transitions between them are presented in the form of directed graph, which made it possible to reduce the problem of choosing the order of train formation to the problem of searching the shortest paths on the graph. An algorithm of searching the optimal order of train formation is proposed.

Methods for the determination of effective management decisions in insufficient information conditions

The article analyzes the methods of removing uncertainty in conditions of insufficient information for making effective management decisions in complex organizational systems. In such tasks, the choice of an effective solution depends on the state of the external environment of the study and implies the use of a number of methods or mathematical models for solving multi-criteria problems. The main methods used in cases of occurrence of a situation of uncertainty due to insufficient information are the a priori ranking methods and multiple regression analysis. However, methods based on expert judgment have a significant degree of subjectivism, and methods formed on the experimental basis and mathematical planning of research are laborious and generate uncertainty with a large number of objects or elements involved in the situation. An alternative to the above is the method of zoning, which implies dividing the set of possible states of the research environment (nature) into subsets of the dominance of individual actions. The zoning operation is an inverse parametric linear programming problem. Consequently, for solving problems in conditions of insufficient information, one can use vector optimization methods.

Price of dependence: stochastic submodular maximization with dependent items

In this paper, we study the stochastic submodular maximization problem with dependent items subject to packing constraints such as matroid and knapsack constraints. The input of our problem is a finite set of items, and each item is in a particular state from a set of possible states. After picking an item, we are able to observe its state. We assume a monotone and submodular utility function over items and states, and our objective is to select a group of items adaptively so as to maximize the expected utility. Previous studies on stochastic submodular maximization often assume that items' states are independent, however, this assumption may not hold in general. This motivates us to study the stochastic submodular maximization problem with dependent items. We first introduce the concept of \emph{degree of independence} to capture the degree to which one item's state is dependent on others'. Then we propose a non-adaptive policy that approximates the optimal adaptive policy within a factor of $\alpha(1-e^{-\frac{\kappa}{2}+\frac{\kappa}{18m^2}}-\frac{\kappa+2}{3m\kappa})$ where the value of $\alpha$ is depending on the type of constraints, e.g., $\alpha=1$ for matroid constraint, $\kappa$ is the degree of independence, e.g., $\kappa=1$ for independent items, and $m$ is the number of items. We also analyze the adaptivity gap, i.e., the ratio of the values of best adaptive policy and best non-adaptive policy, of our problem with prefix-closed constraints.

Approximate Stream Reasoning with Metric Temporal Logic under Uncertainty

Stream reasoning can be defined as incremental reasoning over incrementally-available information. The formula progression procedure for Metric Temporal Logic (MTL) makes use of syntactic formula rewritings to incrementally evaluate formulas against incrementally-available states. Progression however assumes complete state information, which can be problematic when not all state information is available or can be observed, such as in qualitative spatial reasoning tasks or in robotics applications. In those cases, there may be uncertainty as to which state out of a set of possible states represents the ‘true’ state. The main contribution of this paper is therefore an extension of the progression procedure that efficiently keeps track of all consistent hypotheses. The resulting procedure is flexible, allowing a trade-off between faster but approximate and slower but precise progression under uncertainty. The proposed approach is empirically evaluated by considering the time and space requirements, as well as the impact of permitting varying degrees of uncertainty.