Equivalence Rule Research Articles

PolyJuice: Detecting Mis-compilation Bugs in Tensor Compilers with Equality Saturation Based Rewriting

Tensor compilers are essential for deploying deep learning applications across various hardware platforms. While powerful, they are inherently complex and present significant challenges in ensuring correctness. This paper introduces PolyJuice, an automatic detection tool for identifying mis-compilation bugs in tensor compilers. Its basic idea is to construct semantically-equivalent computation graphs to validate the correctness of tensor compilers. The main challenge is to construct equivalent graphs capable of efficiently exploring the diverse optimization logic during compilation. We approach it from two dimensions. First, we propose arithmetic and structural equivalent rewrite rules to modify the dataflow of a tensor program. Second, we design an efficient equality saturation based rewriting framework to identify the most simplified and the most complex equivalent computation graphs for an input graph. After that, the outcome computation graphs have different dataflow and will likely experience different optimization processes during compilation. We applied it to five well-tested industrial tensor compilers, namely PyTorch Inductor, OnnxRuntime, TVM, TensorRT, and XLA, as well as two well-maintained academic tensor compilers, EinNet and Hidet. In total, PolyJuice detected 84 non-crash mis-compilation bugs, out of which 49 were confirmed with 20 fixed.

Prefrontal and lateral entorhinal neurons co-dependently learn item-outcome rules.

The ability to learn novel items depends on brain functions that store information about items classified by their associated meanings and outcomes1-4, but the underlying neural circuit mechanisms of this process remain poorly understood. Here we show that deep layers of the lateral entorhinal cortex (LEC) contain two groups of 'item-outcome neurons': one developing activity for rewarded items during learning, and another for punished items. As mice learned an olfactory item-outcome association, we found that the neuronal population of LEC layers 5/6 (LECL5/6) formed an internal map of pre-learned and novel items, classified into dichotomic rewarded versus punished groups. Neurons in the medial prefrontal cortex (mPFC), which form a bidirectional loop circuit with LECL5/6, developed an equivalent item-outcome rule map during learning. When LECL5/6 neurons were optogenetically inhibited, tangled mPFC representations of novel items failed to split into rewarded versus punished groups, impairing new learning by mice. Conversely, when mPFC neurons were inhibited, LECL5/6 representations of individual items were held completely separate, disrupting both learning and retrieval of associations. These results suggest that LECL5/6 neurons and mPFC neurons co-dependently encode item memory as a map of associated outcome rules.

Identification of ECA rules forming MACA in periodic boundary condition

Cellular automaton (CA) is a computing model which is emerging rapidly. It is largely used in different types of scientific applications and simulations due to its ability to solve complex problems using simple rule(s). Cellular automata (CAs) are used in different types of applications like cryptography, VLSI systems, fault detection, etc. Typically, most of these applications utilize one-dimensional, 2-state, 3-neighborhood CAs. This paper explores the concept of Next State RMT Transition Diagram (NSRTD) for characterization of all the Elementary Cellular Automata (ECA) rules in periodic boundary condition leading to the identification of all ECA rules forming more than two fixed points (referred to as Single Length Cycle Multi-Attractor CA (MACA)) for an arbitrary CA length (n). For this, the 88 Wolfram classification rules and their equivalent rules have been utilized to reduce the search complexity by avoiding exhaustive searching on all the 256 ECA rules.

Spotted Hyena skull size variation across geography favors the energetic equivalence rule over Bergmann's Rule.

Much historic work has focused on establishing geographical and ecological rules that broadly explain patterns in size variation. We examined geographic variation in Spotted Hyena skull size using geometric morphometrics and spatial statistics. We quantified size variation and sexual size dimorphism of the skull, and evaluated the influence of temperature, precipitation, land cover type, and population density on skull size. We found that female spotted hyenas are slightly larger on average than males. Our analysis of regional differences did not indicate geographic variation in sexual size dimorphism. Skull size of Spotted Hyenas varies with geography but does not adhere to Bergmann's Rule. The smallest individuals of both sexes occur between -5.00° and 10.00° latitude and east of 28.50° longitude, with larger individuals being found elsewhere. Although Spotted Hyena skull size co-varies in some views with such variables as habitat type and climate indicators, skull size in this species most strongly co-varies with population density. The highest population densities are associated with the smallest skull size, possibly reflecting a relationship between high population density and access to resources. These results suggest that geographic variation in Spotted Hyena skull size is better explained by the energetic equivalence rule than Bergmann's Rule.

Labeling-Based Recipient Identification with Low-Order Modulation

Labeling-Based Recipient Identification (LABRID) brings the possibility of representing the destination station address in a Bit-Interleaved Coded Modulation with Iterative Decoding (BICM-ID) system by a signal labeling rule. Low-order modulations, such as BPSK or QPSK, pose a general problem for BICM-ID due to a limited convergence of iterative decoding. In the context of LABRID, they have one more drawback—a small number of different labeling rules in general; the number of the optimal ones, which exhibit the maximal asymptotic coding gain, is reduced even further. Meanwhile, LABRID needs a sizable collection of different optimal labeling rules to serve many users in large wireless networks. In this paper, the author suggests the use of hypercube BPSK or QPSK labeling to overcome all these challenges. By means of the Reactive Tabu Search (RTS) algorithm, more than 1500 equivalent optimal hypercube labeling rules are found. Analytical error bounds of the system are developed and supported by simulation experiments. Then, the focus is moved to the criterion to determine the frame destination at the LABRID receiver; a simple threshold-based method is proposed to keep the incorrect decision probability below 10−5. Finally, it is shown that LABRID outperforms a reference BICM-ID system in terms of computational complexity.

Life history scaling in a tropical forest

Abstract Both tree size and life history variation drive forest structure and dynamics, but little is known about how life history frequency changes with size. We used a scaling framework to quantify ontogenetic size variation and assessed patterns of abundance, richness, productivity and light interception across life history strategies from >114,000 trees in a primary, neotropical forest. We classified trees along two life history axes: a fast–slow axis characterized by a growth–survival trade‐off, and a stature–recruitment axis with tall, long‐lived pioneers at one end and short, short‐lived recruiters at the other. Relative abundance, richness, productivity and light interception follow an approximate power law, systematically shifting over an order of magnitude with tree size. Slow saplings dominate the understorey, but slow trees decline to parity with rapidly growing fast and long‐lived pioneer species in the canopy. Like the community as a whole, slow species are the closest to obeying the energy equivalence rule (EER)—with equal productivity per size class—but other life histories strongly increase productivity with tree size. Productivity is fuelled by resources, and the scaling of light interception corresponds to the scaling of productivity across life history strategies, with slow and all species near solar energy equivalence. This points towards a resource‐use corollary to the EER: the resource equivalence rule. Fitness trade‐offs associated with tree size and life history may promote coexistence in tropical forests by limiting niche overlap and reducing fitness differences. Synthesis. Tree life history strategies describe the different ways trees grow, survive and recruit in the understorey. We show that the proportion of trees with a pioneer life history strategy increases steadily with tree size, as pioneers become relatively more abundant, productive, diverse and capture more resources towards the canopy. Fitness trade‐offs associated with size and life history strategy offer a mechanism for coexistence in tropical forests.

Research on the Temperature and Thermal Stress of the Roll Quenching Process of Thin Plates

The roll quenching process can be approximated as a high-pressure jet impinging on a high-temperature moving steel plate. The process can greatly improve the strength and overall mechanical properties of the steel plate. However, the cooling uniformity and other factors lead to the problem of poor plate shape after quenching. It is found that in the roll quenching process, the roller conveyor speed has a large influence on the temperature field and stress field. This paper establishes a roll quenching mechanism model, iterates the convective heat transfer coefficient on the steel plate surface through the inverse heat transfer method, and performs a numerical simulation. Through the numerical simulation of the roll quenching process in the high-pressure zone of the steel plate, the temperature and equivalent force change rule of the transient of each position of the steel plate in the thick direction are obtained. It is found that the plate does not reach its maximum value when it is in the quenching zone, but there is some hysteresis that becomes more pronounced as it gets closer to the core. These findings are valuable for regulating the roll-hardening process and maintaining optimal strip surface quality in industrial production environments.

Exploring the effects of different BCI-based attention training games on the brain: A functional near-infrared spectroscopy study

BCI games have been widely employed as non-invasive therapeutic interventions for conditions, but their efficacy remains a subject of debate. This study explores the efficacy of two prevalent forms of Brain-Computer Interface (BCI)-based attention training games: video games (VG) and physical games (PG). The effectiveness of these games has been examined through the lens of neuroscience, using functional Near-Infrared Spectroscopy (fNIRS) to monitor cortical activation. After the fNIRS test, subjects completed an Intrinsic Motivation Inventory (IMI) questionnaire. PG tasks activated six channels (L-PFC, R-PFC and R-TL), while VG tasks activated only one (R-PFC). Furthermore, females exhibited stronger activation during PG tasks, while males had none in either. Our findings suggest that under equivalent game rules and themes, PG may prove more effective for cognitive rehabilitation than VG, with stronger intrinsic motivation. We also found this result may exhibit gender differences. Finally, this research offers valuable insights for the future design of BCI-based games from a neuroscience perspective.

Hierarchical sliding mode-based adaptive fuzzy control for uncertain switched under-actuated nonlinear systems with input saturation and dead-zone

PurposeThis paper aims to study the issues of adaptive fuzzy control for a category of switched under-actuated systems with input nonlinearities and external disturbances.Design/methodology/approachA control scheme based on sliding mode surface with a hierarchical structure is introduced to enhance the responsiveness and robustness of the studied systems. An equivalent control and switching control rules are co-designed in a hierarchical sliding mode control (HSMC) framework to ensure that the system state reaches a given sliding surface and remains sliding on the surface, finally stabilizing at the equilibrium point. Besides, the input nonlinearities consist of non-symmetric saturation and dead-zone, which are estimated by an unknown bounded function and a known affine function.FindingsBased on fuzzy logic systems and the hierarchical sliding mode control method, an adaptive fuzzy control method for uncertain switched under-actuated systems is put forward.Originality/valueThe “cause and effect” problems often existing in conventional backstepping designs can be prevented. Furthermore, the presented adaptive laws can eliminate the influence of external disturbances and approximation errors. Besides, in contrast to arbitrary switching strategies, the authors consider a switching rule with average dwell time, which resolves control problems that cannot be resolved with arbitrary switching signals and reduces conservatism.

Ricoeur, Gift and Poetics

Abstract In Ricoeur’s last works, we can find what he calls a poetics of love. Choosing the “dialectic” path of a comparison between love and justice, Ricoeur claims that justice lies in the rule of equivalence (give to each his own); the disorientation of love, instead, suspends the return, the equivalence, the exchange. Love does not say: “do ut des”, but rather (if we can transform the expression) it says “do ut dem”, to offer without expecting anything in return: this is what Ricoeur calls a “first gift”. However, it is an expectation that is always open to the possibility of a “surprise”: the surprise of a “second first gift” able to fulfill the gratuity of the original act of donation. This essay questions this possibility of “mutual gift”.

Equivalent Transformations of Complex Circuits in Calculations of Power Supply Systems of Agrocomplex

he tasks at the stage of planning and operation of power supply systems are related to the calculation of the parameters of their operation modes. With the massive nature of such complex calculations, their execution is possible only with the help of appropriate software and computing tools, that is, using an electronic computer. (Research purpose) The research purpose is to substantiate the algorithm of equivalence of power supply systems or their individual sections as an integral part of the algorithms complex for calculating electrical systems. (Materials and methods) It has been shown that at present there are many agricultural consumers, interruptions in the power supply of which lead to significant damage, in this regard, closed power supply systems are becoming increasingly used, as the requirements for reliability, uninterrupted power supply and the quality of electricity supplied to the consumer are increasing. It was determined that the calculation of closed systems is more complicated than open ones. It was revealed that when solving a wide range of tasks related to the creation and modernization of power supply systems, there is a need to simplify the systems or their individual sections. (Results and discussion) The equivalence rule was formed and methods for calculating equivalent resistances and electromotive force of the converted sections of the replacement circuits were given, which simplifies the circuit and accelerates the process of calculating and analyzing the modes of power supply systems. (Conclusions) It was established that the proposed equivalence algorithm is based on universal formulas for calculating intrinsic and mutual resistances, which were previously obtained by the authors for use in problems of calculating steady-state modes of power supply systems. It was stated that the calculation algorithm is also applicable for the equivalence of forward and reverse sequence circuits in the calculation of currents of asymmetric short circuits and in the analysis of the dynamic stability of electric power systems

A decoupled T-stub component model for the cyclic modelling of steel joints

The reliable estimation of the cyclic behaviour of steel beam-to-column joints is essential for the safe design of steel structures under seismic loading. The T-stub is an essential component in steel beam-to-column joints. This paper presents the framework and implementation of a decoupled component model for the T-stub under cyclic loading. This decoupled model splits the single hysteretic spring representation of the T-stub into two separate hysteretic springs, one representing the quadrant where tensile forces are present and the other the quadrant with compressive forces. The results indicate that because of the degradation of the response of the T-stub with multiple loading cycles, the equivalence between the single spring model, and the decoupled double spring model is not trivial. Exact equivalence rules are proposed for the definition of the properties of the decoupled model. The accuracy of the model is validated by comparison with experimental test results. The decoupled model overcomes the problem of using a single spring to represent the T-stub in a steel joint that is not able to lead to correct results because it is unable to mobilize compressive forces in the T-stub as it occurs.

Broadband absorber with dispersive metamaterials

Abstract A broadband absorber that utilizes a dispersive metamaterial and covers the entire microwave X-band (8–12 GHz) is proposed in the present study. An ideal absorber attached to the surface of a perfect electric conductor requires the permittivity of the absorbing layer to be anomalously dispersive in the targeted broad frequency band. We show that anomalous dispersion of the permittivity for the X-band can be fitted to a two-pole Lorentz oscillator model and realized with the use of a double-layered, square-loop metamaterial. We explain the connection between the two-pole oscillator model and the double-layered, square-loop metamaterial using an equivalent circuit model and present explicit design rules for the metamaterial. We fabricate a 4-mm-thick metamaterial absorber with flexible silicon rubber, a resistor element, and conductive wire using carbon and silver conductive ink. Our metamaterial absorber achieves a reflectance of less than −20 dB over the entire X-band region.

Free-damped vibration tangential wave responses of FG-sandwich merged hemispherical-cylindrical shells under effects of artificial springs at merging and boundary conditions

This article is formed to extract the frequencies with free-damped vibration characteristics of the tangential waves related to the Functionally Graded (FG) sandwich Merged Hemispherical-Cylindrical Shells (MHCS) under elastic springs. The wall of the MHCS contains three layers of embodied Functionally Graded Material (FGM). The material characteristics of the structure change functionally along the thickness of each layer. Equivalent Single Layer (ESL) and Rule of Mixture (RM) are applied to determine the mechanical features of the materials. In addition, eight sandwich types are examined here. Moreover, both merging and support conditions are assumed to be flexible. Artificial transitional and rotational springs are modeled to apply the effect of a semi-rigid merging between hemispherical and cylindrical parts and the support’s flexibility. Further, Donnell's hypothesis and Hamilton's scheme are utilized to acquire the kinetic differential equations related to the MCHS. A recognized semi-analytical method, labeled the Generalized Differential Quadrature Method (GDQM), is being implemented to discretize the kinetic equations. In addition, the tangential wave frequencies are determined by solving the eigenvalue problem. The available results in the submitted framework are compared with the outputs of the FE-based software to validate the proposed procedure. Several innovative parametric studies will be implemented to illustrate the impacts of different general boundary conditions, semi-rigid connections, and material features on the vibrational behavior of MHCS.

Multi-Query Optimization Revisited: A Full-Query Algebraic Method.

Sharing data and computation among concurrent queries has been an active research topic in database systems. While work in this area developed algorithms and systems that are shown to be effective, there is a lack of logical foundation for query processing and optimization. In this paper, we present PsiDB, a system model for processing a large number of database queries in a batch. The key idea is to generate a single query expression that returns a global relation containing all the data needed for individual queries. For that, we propose the use of a type of relational operators called -operators in combining the individual queries into the global expression. We tackle the algebraic optimization problem in PsiDB by developing equivalence rules to transform concurrent queries with the purpose of revealing query optimization opportunities. Centering around the -operator, our rules not only cover many optimization techniques adopted in existing batch processing systems, but also revealed new optimization opportunities. Experiments conducted on an early prototype of PsiDB show a performance improvement of up to 36X over a mainstream commercial DBMS.

Article 12 of the Protocol on the Rights of Persons with Disabilities in Africa: A critical analysis

AbstractThis contribution analyses Article 12 of the Protocol to the African Charter on Human and Peoples’ Rights on the Rights of Persons with Disabilities in Africa (the Protocol). It examines the purpose, scope and contribution of this Article to the legal protection of persons with disabilities in armed conflict and its implementation. The analysis is divided into four parts. The first part will start by identifying and analysing the background to this provision, which provides specific protection to persons with disabilities in armed conflict. The second part will examine Article 12 in the light of other similar regional instruments and of the protection challenges that persons with disabilities face during conflict. This will highlight the specific nature of the Article's provisions, together with its shortcomings and its progressive aspects. Part three will look at the interaction between Article 12 and equivalent rules of international humanitarian law, and how Article 12 contributes to the development of legal protection for persons with disabilities in armed conflict. Finally, the fourth part will examine the challenges to the implementation of Article 12. It will also propose ways of overcoming those challenges and hence of enabling Article 12 to have its intended effect.

Thermal fatigue load models for fatigue design of steel box girder bridges

Coupling with traffic loads, thermal loads can also contribute to the fatigue damage cumulation of bridges. Referring to traffic and wind fatigue load models, the concepts of two kinds of probabilistic thermal fatigue load models for the first system of steel box girder bridges were proposed. Specifically, the basic forms of the two models are 1) equivalent vertical temperature gradient models based on the damage equivalence rule and 2) the effect ratio curves based on a statistical analysis of thermal actions. Then, two design probabilistic thermal fatigue load models following the given procedures are set up using an extended dataset based on a 350-day long-term in-suit temperature monitoring, and parametric analysis on three damage equivalence factors including geometric features, design life, and degree of indeterminacy was conducted. To validate the proposed models and related approaches, two kinds of fatigue details in a case steel box girder bridge were evaluated. The results show that thermal effects on fatigue damage cumulation are significant and should be taken into consideration, and the proposed thermal fatigue load models are applicable for fatigue design and evaluation.

A Secure and Traceable Vehicles and Parts System Based on Blockchain and Smart Contract.

As society advances, so does the total number of vehicles on the road, creating a massive consumer market for automobiles. According to statistics, a major portion of today’s traffic difficulties are caused by accidents caused by subpar cars and auto parts. As a result, each country has, over time, enacted equivalent rules and regulations to prevent such tragedies. However, in the face of profit, some people are desperate enough to employ illegal parts and illegally modified cars, and auto fraud is rampant. As a result, we employ the blockchain of the symmetrical Blockchain’s digital ledger and smart contract technology to build a decentralized supply chain system that can identify specific parts. In this study, we design and discuss the proposed system framework by user functions and the flow of parts based on blockchain, and we discuss communication protocols that use the symmetry and asymmetry cryptography, algorithms, properties, and security of the mechanism while providing related analysis and comparing the properties and costs of the system with other studies. Overall, the proposed method has the potential to successfully address the issue of automobile fraud.

Novel dynamic equivalent circuit model of integrated energy systems

With the transformation from individual energy systems to integrated energy systems (IES), equivalent circuit IES modeling is developed to represent the heat and electricity consistently for coordinated analysis, control and optimization. However, physical properties of equivalent parameters are a mismatch, and the key operation characteristics, including dynamics and coupling, have not yet been fully described, remaining obstacles for optimal electricity-heat coordination. In this study, a novel IES equivalent circuit modeling methodology is proposed. From the perspective of physical characteristics, the similarity of heat transfer and micro conductivity processes is determined. A novel thermoelectric equivalent rule with matched energy units is proposed, showing the corresponding relations of the basic state, power, and energy quantities between electricity and heat. Then, the equivalent rule is applied in IES equivalent circuit modeling, where the equivalent heat element models are established to characterize the electrothermal coupling and dynamics of heat subsystems. Finally, following the IES system structure, the IES equivalent circuit model is completed. A numerical comparison is performed to verify the effectiveness of the model. The simulation results demonstrate that the proposed model can fully capture the dynamic and coupling characteristics of IES.

Simulation of the Particle Transport Behaviors in Nanoporous Matter

The transport behaviors of proton into nanoporous materials were investigated using different Monte Carlo simulation codes such as GEANT4, Deeper and SRIM. The results indicated that porous structure could enhance the proton scattering effects due to a higher specific surface area and more boundaries. The existence of voids can deepen and widen the proton distribution in the targets due to relatively lower apparent density. Thus, the incident protons would transport deeper and form a wider Bragg peak in the end of the range, as the target materials are in a higher porosity state and/or have a larger pore size. The existence of voids also causes the local inhomogeneity of proton/energy distribution in micro/nano scales. As compared, the commonly used SRIM code can only be used to estimate roughly the incident proton range in nanoporous materials, based on a homogeneous apparent density equivalence rule. Moreover, the estimated errors of the proton range tend to increase with the porosity. The Deeper code (designed for evaluation of radiation effects of nuclear materials) can be used to simulate the transport behaviors of protons or heavy ions in a real porous material with porosity smaller than 52.3% due to its modeling difficulty, while the GEANT4 code has shown advantages in that it is suitable and has been proven to simulate proton transportation in nanoporous materials with porosity in its full range of 0~100%. The GEANT4 simulation results are proved consistent with the experimental data, implying compatibility to deal with ion transportation into homogeneously nanoporous materials.