First-order Representation Research Articles

Abstraction of Situation Calculus Concurrent Game Structures

We present a general framework for abstracting agent behavior in multi-agent synchronous games in the situation calculus, which provides a first-order representation of the state and allows us to model how plays depend on the data and objects involved. We represent such games as action theories of a special form called situation calculus synchronous game structures (SCSGSs), in which we have a single action "tick" whose effects depend on the combination of moves selected by the players. In our framework, one specifies both an abstract SCSGS and a concrete SCSGS, as well as a refinement mapping that specifies how each abstract move is implemented by a Golog program defined over the concrete SCSGS. We define notions of sound and complete abstraction with respect to a mapping over such SCSGS. To express strategic properties on the abstract and concrete games we adopt a first-order variant of alternating-time mu-calculus mu-ATL-FO. We show that we can exploit abstraction in verifying mu-ATL-FO properties of SCSGSs under the assumption that agents can always execute abstract moves to completion even if not fully controlling their outcomes.

Hierarchical relationship modeling in multi-agent reinforcement learning for mixed cooperative–competitive environments

In multi-agent reinforcement learning (MARL), information fusion through relationship modeling can effectively learn behavior strategies. However, the high dynamics among heterogeneous interactive agents in mixed cooperative–competitive environments pose difficulties for relational modeling. Traditional MARL solutions concatenate all agents’ states based on the global relationship, which is unrealistic and unscalable under large-scale conditions. Other methods fuse local information by modeling neighbor relationships, but local features lead to suboptimal strategies. From this perspective, we propose a novel relational information fusion approach for mixed tasks to fuse local and global features by modeling heterogeneous relationships through a hierarchical graph. During training, remote agents’ global features are fused through second-order graph representation to help strategy optimization. During decision making, the practicality and scalability of strategy are improved by fusing neighbor agents’ local features through first-order graph representation. Our approach consistently outperforms the state-of-the-art MARL methods in several multi-agent tasks, such as the Predator–Prey and Soccer Games. In particular, it achieves an 83.7% win rate, which is 11.5% higher than baselines in the 4 vs. 4 Soccer Game, and can scale from 4 vs. 4 to 13 vs. 13 in the Predator–Prey Game while maintaining good performance.

The Iconic-Symbolic Spectrum

It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule have divergent forms, occupying opposite poles on a spectrum of naturalness. Symbolic rules are composed entirely of primitive juxtapositions of sign types with contents, while iconic rules determine contents entirely by uniform natural relations with sign types. This distinction is marked explicitly in the formal semantics of familiar sign systems, both for atomic first-order representations, like words, pixel colors, and dials, and for complex second-order representations, like sentences, diagrams, and pictures.

Combining the Inner Self with the Map of the Body: Evidence for White Matter Contribution to the Relation Between Interoceptive Sensibility and Nonaction-oriented Body Representation

Very recent studies on healthy individuals suggest that changes in the sensibility toward internal bodily sensations across the lifespan affect the ability to mentally represent one’s body, in terms of action-oriented and nonaction-oriented body representation (BR). Little is known about the neural correlates of this relation. Here we fill this gap using the neuropsychological model provided by focal brain damage. Sixty-five patients with unilateral stroke (20 with left and 45 with right brain damage, LBD and RBD, respectively) participated in this study. Both action-oriented BR and nonaction-oriented BR were tested; interoceptive sensibility was assessed as well. First, we tested whether interoceptive sensibility predicted action-oriented BR and nonaction-oriented BR, in RBD and LBD separately. Then, a track-wise hodological lesion-deficit analysis was performed in a subsample of twenty-four patients to test the brain network supporting this relation. We found that interoceptive sensibility predicted the performances in the task tapping nonaction-oriented BR. The higher interoceptive sensibility was, the worse patients performed. This relation was associated with the disconnection probability of the corticospinal tract, the fronto-insular tract, and the pons. We expand over the previous findings on healthy individuals, supporting the idea that high levels of interoceptive sensibility negatively affect BR. Specific frontal projections and frontal u-shaped tracts may play a pivotal role in such an effect, likely affecting the development of a first-order representation of the self within the brainstem autoregulatory centers and posterior insula and of a second-order representation of the self within the anterior insula and higher-order prefrontal areas.

A Sequence Labeling Method for First-order Logic Representation

Extracting logic knowledge is an important part of natural language understanding. This study introduces a new dataset for the purpose of measuring the model's ability to transfer natural language to logic form. Since logic represents how various concepts infer and reason from/to each other, it is essential to learn logical structure in any form of language while trying to comprehend its meaning of it. There have recently been many interests in deploying machine learning and deep learning methods for extracting logical knowledge and representing logic from natural language. The promising generative model that applied to recent sequence labeling work is used in the task of representing logic. Experiments have shown that generative methods can extract logic form from natural language texts. To be more specific, a sequence-to-sequence model is quite a convenient option when it deals with extraction tasks. The model provided in this study would be inspiring for future studies to work out more efficient solutions.

Hybrid-Order Representation Learning for Electricity Theft Detection

Electricity theft is the primary cause of electrical losses in power systems, which severely harms the economic benefits of electricity providers and threatens the safety of the power supply. However, due to the inherent complex correlation and periodicity of electricity consumption and the low efficiency of large-scale data processing, detecting anomalies in electricity consumption data accurately and efficiently remains challenging. Existing methods usually focus on first-order information and ignore the second-order representation learning that can efficiently model global temporal dependency and facilitate discriminative representation learning of electricity consumption data. In this article, we propose a novel electricity theft detection framework named hybrid-order representation learning network (HORLN). Specifically, the sequential electricity consumption data is transformed into the matrix format containing weekly consumption records. Then, an inter-and-intra week convolution block is designed to capture multiscale features in a local-to-global manner. Meanwhile, a self-dependency modeling module is proposed to learn the second-order representations from self-correlation matrices, which are finally combined with the first-order representations to predict the anomaly scores of electricity consumers. Extensive experiments on a real-world benchmark demonstrate the advantages of our HORLN over state-of-the-art methods.

Multi-head second-order pooling for graph transformer networks

Graph transformer networks (GTNs) have great potential in graph-related tasks, particularly graph classification. GTNs use self-attention mechanism to extract both semantic and structural information, after which a class token is used as the global representation for graph classification.However, the class token completely abandons all information held by nodes, which leads to a huge loss of information and neglects the dependencies among different feature dimensions. Therefore, we propose a Multi-head Global Second-Order Pooling (MGSOP) to utilize the rich second-order statistics of all nodes. To this end, a second-order pooling module incorporated with multi-head structure generates multiple covariance representations for GTNs. Then, the first-order representation and concatenation of all covariance matrices are combined by an adaptive fusion module for better performance on different types of data. Furthermore, we introduce an efficient dropout-based normalization to utilize the geometry of covariance representation. Experiments conducted on six real-world graph benchmarks show our MGSOP outperforms its counterparts and achieves competitive results against state-of-the-arts.

Generating functions for reciprocal Catalan-type sums: approach to linear differentiation equation and ($p$-adic) integral equations

This article is inspired by the reciprocal Catalan sums associated with problem 11765, proposed by David Beckwith and Sag Harbor. For this reason, partial derivative equations, the first-order linear differentiation equation and integral representations for series and generating functions for reciprocal Catalan-type sums containing the Catalan-type numbers are constructed. Some special values of these series and generating functions, which are given solutions of problem 11765, are found. Partial derivative equations of the generating function for the Catalan-type numbers are given. By using these equations, recurrence relations and derivative formulas involving these numbers are found. Finally, applying the $p$-adic Volkenborn integral to the Catalan-type polynomials, some combinatorial sums and identities involving the Bernoulli numbers, the Stirling numbers and the Catalan-type numbers are derived.

Validation of the Spanish version of the Neal, Griffin and Hart safety behavior scale

ABSTRACT Objectives. The safety behavior scale (SBS), developed by Neal, Griffin and Hart, is one of the most widely used conceptualizations in the field of occupational safety. Previous studies have evaluated the psychometric properties of this scale in different populations. However, few validation studies have been conducted in the Latin American context. To fill these gaps in the literature, this study aimed to assess the validity, reliability and measurement invariance of this instrument in the context of the Latin American mining industry. Methods. Data were collected from 398 workers from Ecuadorian mining companies. The questionnaire was translated into Spanish following a back-translation process. The latent factorial structure of the SBS was explored by estimating a series of confirmatory factor analysis (CFA) and exploratory equation modeling (ESEM) models. Results. The analyses showed that the two correlated first-order factor CFA representation was the most appropriate model for the data. Measurement invariance by age, type of contract and firm size was also confirmed. Conclusions. The SBS is a valid and reliable measure of safety behavior. In addition, this study determined the applicability of this instrument in the Latin American context, which enhances opportunities for future research in the region.

Analyzing binding extent in 3CPS

To date, the most effective approach to compiling strict, higher-order functional languages (such as OCaml, Scheme, and SML) has been to use whole-program techniques to convert the program to a first-order monomorphic representation that can be optimized using traditional compilation techniques. This approach, popularized by MLton, has limitations, however. We are interested in exploring a different approach to compiling such languages, one that preserves the higher-order and polymorphic character of the program throughout optimization. To enable such an approach, we must have effective analyses that both provide precise information about higher-order programs and that scale to larger units of compilation. This paper describes one such analysis for determining the extent of variable bindings. We classify the extent of variables as either register (only one binding instance can be live at any time), stack (the lifetimes of binding instances obey a LIFO order), or heap (binding lifetimes are arbitrary). These extents naturally connect variables to the machine resources required to represent them. We believe that precise information about binding extents will enable efficient management of environments, which is a key problem in the efficient compilation of higher-order programs. At the core of the paper is the 3CPS intermediate representation, which is a factored CPS-based intermediate representation (IR) that statically marks variables to indicate their binding extent. We formally specify the management of this binding structure by means of a small-step operational semantics and define a static analysis that determines the extents of the variables in a program. We evaluate our analysis using a standard suite of SML benchmark programs. Our implementation gets surprisingly high yield and exhibits scalable performance. While this paper uses a CPS-based IR, the algorithm and results are easily transferable to other λ-calculus IRs, such as ANF.

Distinguishability in quantum interference with multimode squeezed states

Distinguishability theory is developed for quantum interference of the squeezed vacuum states on unitary linear interferometers. It is found that the entanglement of photon pairs over the Schmidt modes is one of the sources of distinguishability. The distinguishability is quantified by the symmetric part of the internal state of $n$ pairs of photons, whose normalization $q_{2n}$ is the probability that $2n$ photons interfere as indistinguishable. For two pairs of photons $q_{4}=(1+ 2\mathbb{P} )/3$, where $\mathbb{P} $ is the purity of the squeezed states ($K=1/\mathbb{P} $ is the Schmidt number). For a fixed purity $\mathbb{P}$, the probability $q_{2n}$ decreases exponentially fast in $n$. For example, in the experimental Gaussian boson sampling of H.-S.~Zhong \textit{et al} [Science \textbf{370}, 1460 (2020)], the achieved purity $\mathbb{P}\approx 0.938$ for the average number of photons $2n\ge 43$ gives $q_{2n}\lesssim 0.5$, i.e., close to the middle line between $n$ indistinguishable and $n$ distinguishable pairs of photons. In derivation of all the results the first-order quantization representation based on the particle decomposition of the Hilbert space of identical bosons serves as an indispensable tool. The approach can be applied also to the generalized (non-Gaussian) squeezed states, such as those recently generated in the three-photon parametric down-conversion.

Riemannian Formulation of Pontryagin’s Maximum Principle for the Optimal Control of Robotic Manipulators

In this work, we consider robotic systems for which the mass tensor is identified to be the metric in a Riemannian manifold. Cost functional invariance is achieved by constructing it with the identified metric. Optimal control evolution is revealed in the form of a covariant second-order ordinary differential equation featuring the Riemann curvature tensor that constrains the control variable. In Pontryagin’s framework of the maximum principle, the cost functional has a direct impact on the system Hamiltonian. It is regarded as the performance index, and optimal control variables are affected by this fundamental choice. In the present context of cost functional invariance, we show that the adjoint variables are the first-order representation of the second-order control variable evolution equation. It is also shown that adding supplementary invariant terms to the cost functional does not modify the basic structure of the optimal control covariant evolution equation. Numerical trials show that the proposed invariant cost functionals, as compared to their non-invariant versions, lead to lower joint power consumption and narrower joint angular amplitudes during motion. With our formulation, the differential equations solver gains stability and operates dramatically faster when compared to examples where cost functional invariance is not considered.

Reply to the comment by Dougherty, A.J. on “Relative sea-level records preserved in Holocene beach-ridge strandplains – An example from tropical northeastern Australia” by Brooke, B.P., Huang, Z., Nicholas, W.A., Oliver, T.S.N., Tamura, T., Woodroffe, C.D., Nichol, S.L.

The approach and results of our 2019 paper (Brooke et al., 2019) have been criticised by Dougherty (2022). We examined the sensitivity of a tropical, coarse sand strandplain to changes in relative sea level as expressed through beach-ridge morphology and the elevation of beach berms preserved in the succession of cyclone-generated beach ridges at Cowley Beach, Queensland, Australia. Rather than presenting a new sea-level curve for this region as suggested by Dougherty, our 2019 study of the Cowley Beach strandplain revealed that when compared with the modelled Holocene relative sea-level record and sea-level indicator data for north-eastern Queensland, the strandplain morphology and stratigraphy provide a first-order representation of sea-level position. Importantly, Dougherty (2022) has overlooked the processes involved in the formation of beach ridges at this site and the spatial coverage of our analysis of the strandplain morphology. Both these factors are fundamental to the approach and conclusions of our 2019 paper. We reiterate here that the Cowley Beach strandplain morphology and succession of beach-berm deposits have elevation patterns that match well the broad trend in the regional relative sea-level model for the past 7 ka. We highlight those key beach-ridge formative processes and data limitations neglected in the Dougherty Comment. Finally, we note the challenges and opportunities for further research into the sedimentary records preserved in this distinctive type of tropical strandplain.

A relational tsetlin machine with applications to natural language understanding

Tsetlin machines (TMs) are a pattern recognition approach that uses finite state machines for learning and propositional logic to represent patterns. In addition to being natively interpretable, they have provided competitive accuracy for various tasks. In this paper, we increase the computing power of TMs by proposing a first-order logic-based framework with Herbrand semantics. The resulting TM is relational and can take advantage of logical structures appearing in natural language, to learn rules that represent how actions and consequences are related in the real world. The outcome is a logic program of Horn clauses, bringing in a structured view of unstructured data. In closed-domain question-answering, the first-order representation produces 10 × more compact KBs, along with an increase in answering accuracy from 94.83% to 99.48%. The approach is further robust towards erroneous, missing, and superfluous information, distilling the aspects of a text that are important for real-world understanding

On the State Approach Representations of Convolutional Codes over Rings of Modular Integers

In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers.

Laguerre-Gramian-based structure-preserving model order reduction for second-order form systems

A new structure-preserving model order reduction technique based on Laguerre-Gramian for second-order form systems is presented in this article. The main task of the proposed approach is to use the Laguerre polynomial expansion of the matrix exponential function to obtain the approximate low-rank decomposition of the Gramians for the equivalent first-order representation of the original second-order form system. The approximate balanced system is generated by a balancing transformation which is directly computed from the expansion coefficients of impulse responses in the space spanned by Laguerre polynomials, without computing the full Gramians for the first-order representation. Then, the reduced second-order model is constructed by truncating the states with small approximate Hankel singular values (HSVs). The above method has a disadvantage that it may unexpectedly result in unstable systems although the original one is stable. Therefore, modified reduction procedure combined with the dominant subspace projection method is presented to alleviate the limitation. Finally, two numerical experiments are provided to demonstrate the effectiveness of the algorithms.

Situation calculus for controller synthesis in manufacturing systems with first-order state representation

Manufacturing is transitioning from a mass production model to a service model in which facilities ‘bid’ to produce products. To decide whether to bid for a complex, previously unseen product, a facility must be able to synthesize, on the fly, a process plan controller that delegates abstract manufacturing tasks in a supplied process recipe to the available manufacturing resources. Often manufacturing processes depend on the data and objects (parts) they produce and consume. To formalize this aspect we need to adopt a first-order representation of the state of the processes. First-order representations of the state are commonly considered in reasoning about action in AI, and here we show that we can leverage the wide literature on the Situation Calculus and ConGolog programs to formalize this kind of manufacturing. With such a formalization available, we investigate how to synthesize process plan controllers in this first-order state setting. We also identify two important decidable cases—finite domains and bounded action theories—for which we provide techniques to actually synthesize the controller.

A sophisticated modeling approach for photovoltaic systems in load frequency control

This paper proposes a new model to mimics accurately the real dynamic and steady-state power generation profiles of a photovoltaic (PV) power plant connected to the power system. The model is targeted at load frequency control (LFC) studies, which takes into account the effect of the dynamic behavior of the system frequency on the PV output power. The artificial neural network using the radial bias function (ANN-RBF) is adopted to model the nonlinear behavior of the PV power plant only considering the frequency deviation as one of the inputs at different operating conditions. Also, the ANN prevents going into complex mathematical analysis to get the dynamic behavior of the output power from the PV plant. The input layer of the ANN-RBF receives the temperature, humidity, irradiation level, and frequency deviation, while the output layer represents the output power from the PV power plant. The main idea to include the frequency deviation in the PV modeling is to represent the dynamic behavior of the PV power that is injected by the PV inverter that is synchronized with the power system using the utility grid angle, i.e. system frequency. The ANN-RBF has been trained using actual data collected from a PV power plant in Aswan, Egypt. The ANN dataset contains significant variations of operating parameters to generalize the output modeling of the PV array. Moreover, the shortages in the previous models for the PV system used in the LFC studies, which are the first-order model, second-order model, and noise-based model, are discussed in detail. The simulation results show that the proposed model of the PV system based on the ANN-RBF is more suitable for the LFC studies than the well-known models based on the first-order representation as it takes into account the dynamic behavior of the system frequency during the load disturbance.

Having the Cake and Eating It Too: First-Order, Second-Order and Bifactor Representations of Work Engagement.

Even though work engagement is a popular construct in organizational psychology, the question remains whether it is experienced as a global construct, or as its three components (vigor, dedication, absorption). The present study thus contributes to the ongoing scientific debate about the dimensionality of work engagement systematically compared one-factor, first-order, higher-order, and bifactor confirmatory factor analytic (CFA) representations of work engagement measured by the short version of Utrecht Work Engagement Scale (UWES-9). We also documented the validity evidence of the most optimal representation based on its test-criterion relationship with basic psychological need fulfillment at work, turnover intentions, work addiction, and work satisfaction. Based on responses provided by two distinct samples of employees (N1 = 242, N2 = 505), our results supported the superiority of the bifactor-CFA representation including a global factor of work engagement and three co-existing specific factors of vigor, dedication, and absorption. This representation replicated well across the two samples through tests of measurement invariance. Finally, while global work engagement was substantially related to all correlates, the specific factors also demonstrated meaningful associations over and above the global levels of work engagement.

Erasure decoding of convolutional codes using first-order representations

It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. In this kind of channel, which is important due to its use for data transmission over the Internet, the receiver knows if a received symbol is correct. We study the decoding problem using the state space description of a convolutional code, and this provides in a natural way additional information. With respect to previously known decoding algorithms, our new algorithm has the advantage that it is able to reduce the decoding delay as well as the computational effort in the erasure recovery process. We describe which properties a convolutional code should have in order to obtain a good decoding performance and illustrate it with an example.