A Brief Roadmap into Uncertain Knowledge Representation via Probabilistic Description Logics

Logic-based knowledge representation is one of the main building blocks of (logic-based) artificial intelligence. While most successful knowledge representation languages are based on classical logic, realistic intelligent applications need to handle uncertainty in an adequate manner. Over the years, many different languages for representing uncertain knowledge—often extensions of classical knowledge representation languages—have been proposed. We briefly present some of the defining properties of these languages as they pertain to the family of probabilistic description logics. This limited view is intended to help pave the way for the interested researcher to find the most adequate language for their needs, and potentially identify the remaining gaps.

Bell-Inequality and Two Slit Experiments: Comparing Misapplication of Classical Probability by Feynman and Bell

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit experiment is treatment of conditional probabilities corresponding to different experimental contexts as unconditional ones. Then we move to the Bell type inequalities. Bell applied classical probability theory in the same manner as Feynman and, as can be expected, he also obtained the impossibility statement. In contrast to Feynman, he formulated his no-go statement not in the probabilistic terms, but by appealing to nonlocality. This note can be considered as a part of the author's attempts for getting rid off nonlocality from quantum physics.

Stochastic Gene Expression Revisited

We investigate the model of gene expression in the form of Iterated Function System (IFS), where the probability of choice of any iterated map depends on the state of the phase space. Random jump times of the process mark activation periods of the gene when pre-mRNA molecules are produced before mRNA and protein processing phases occur. The main idea is inspired by the continuous-time piecewise deterministic Markov process describing stochastic gene expression. We show that for our system there exists a unique invariant limit measure. We provide full probabilistic description of the process with a comparison of our results to those obtained for the model with continuous time.

ROBUST MATHEMATICAL FORMULATION AND PROBABILISTIC DESCRIPTION OF AGENT-BASED COMPUTATIONAL ECONOMIC MARKET MODELS

In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic market models: the Levy–Levy–Solomon model and the Franke–Westerhoff model. We derive time-continuous formulations of both models, and in particular, we discuss the impact of the time-scaling on the model behavior for the Levy–Levy–Solomon model. For the Franke–Westerhoff model, we proof that a constraint required in the original model is not necessary for stability of the time-continuous model. It is shown that a semi-implicit discretization of the time-continuous system preserves this unconditional stability. In addition, this semi-implicit discretization can be computed at cost comparable to the original model. Furthermore, we discuss possible probabilistic descriptions of time-continuous agent-based computational economic market models. Especially, we present the potential advantages of kinetic theory in order to derive mesoscopic descriptions of agent-based models. Exemplified, we show two probabilistic descriptions of the Levy–Levy–Solomon and Franke–Westerhoff model.

The inherent uncertainty of temporal networks is a true challenge for control

Recently, it has been suggested that network temporality can be exploited to substantially reduce the energy required to control complex networks. This somewhat counterintuitive finding was explained through an evocative example of the advantage of temporal networks: when navigating a sailboat, we raise the sails when the wind helps us while lowering them when it works against us. Unfortunately, controlling complex networks inherits a further analogy with navigating a sailboat: having to face the inherent uncertainty of future winds. We rarely, if ever, have deterministic knowledge of the evolution of the network we want to control. Here, our challenge is to exploit the potential advantages of temporality when only a probabilistic description of the future is available. We prove that, in this more realistic setting, exploiting temporality is no more a panacea for network control, but rather an asset of a wider toolbox made available by the scientific community. One that can indeed turn out useful, provided that the temporality of the network structure matches the intrinsic time scales of the nodes we want to control.

Probabilistic Characterization of the Vegetated Hydrodynamic System Using Non-Parametric Bayesian Networks

The increasing risk of flooding requires obtaining generalized knowledge for the implementation of distinct and innovative intervention strategies, such as nature-based solutions. Inclusion of ecosystems in flood risk management has proven to be an adaptive strategy that achieves multiple benefits. However, obtaining generalizable quantitative information to increase the reliability of such interventions through experiments or numerical models can be expensive, laborious, or computationally demanding. This paper presents a probabilistic model that represents interconnected elements of vegetated hydrodynamic systems using a nonparametric Bayesian network (NPBN) for seagrasses, salt marshes, and mangroves. NPBNs allow for a system-level probabilistic description of vegetated hydrodynamic systems, generate physically realistic varied boundary conditions for physical or numerical modeling, provide missing information in data-scarce environments, and reduce the amount of numerical simulations required to obtain generalized results—all of which are critically useful to pave the way for successful implementation of nature-based solutions.

The Broadcast Approach in Communication Networks

In this paper we review the theoretical and practical principles of the broadcast approach to communication over state-dependent channels and networks in which the transmitters have access to only the probabilistic description of the time-varying states while remaining oblivious to their instantaneous realizations. When the temporal variations are frequent enough, an effective long-term strategy is adapting the transmission strategies to the system’s ergodic behavior. However, when the variations are infrequent, their temporal average can deviate significantly from the channel’s ergodic mode, rendering a lack of instantaneous performance guarantees. To circumvent a lack of short-term guarantees, the broadcast approach provides principles for designing transmission schemes that benefit from both short- and long-term performance guarantees. This paper provides an overview of how to apply the broadcast approach to various channels and network models under various operational constraints.

Synergetic approach to macroeconomic studies

This paper confirms the principal possibility of using synergetics in macroeconomic studies. It noted that the presence in economic systems of all science typologies requires using subjects of natural and engineering sciences for the study of economic objects as well. Ignoring this fact hinders the development of fundamental economic knowledge and, as consequence, conditions the use of metaphysical concepts in developed models. Since the above interdisciplinarity is inherent in synergetics, its applicability in macroeconomics is considered. On the example of modeling economic systems, it is demonstrated that their essence (nonlinear space-time structure) corresponds to the basic provisions of synergetics. Therefore, its tools are eligible in the tasks of macroeconomic analysis. As an example, this paper proposes the stochastic model of economic cycles explaining their phenomenon as well as providing the quantitative (parametric) description of cycles. Novelty of the model describing the cycles as random oscillations is tied to the probabilistic description of the investment function and the perception of the economic system as a material object with certain inherent properties. According to a proposed model, the income oscillations are induced by both exogenous (investment fluctuations) and endogenous (economic system elasticity) causes. The values of fluctuations of the income function around its longterm trend relate to the value of intensity of investment fluctuations as well as the gain (efficiency) of the economic system. The duration of the cycle is related to the inclusive wealth of the system and its dynamic factor, which characterizes the system’s ability to withstand investment fluctuations as well as to eliminate their consequences. Prospects of practical applications of the considered model were demonstrated on the example of cycle management.