Multiple Verification Research Articles

A Novel Versatile Decoupling Structure and Expedited Inverse-Model-Based Re-Design Procedure for Compact Single-and Dual-Band MIMO Antennas

Multiple-input multiple-output (MIMO) antennas are considered to be the key components of fifth generation (5G) mobile communications. One of the challenges pertinent to the design of highly integrated MIMO structures is to minimize the mutual coupling among the antenna elements. The latter arises from two sources, the coupling in the free space and the coupling currents propagating on a ground plane. In this paper, an array of H-shaped parasitic patches is proposed as a decoupling structure for compact MIMO antennas to reduce propagation of the coupling currents on a shared ground plane. The proposed decoupling structure is generic, and it can be applied to different antenna configurations as demonstrated in the work. Furthermore, it is employed to develop a new high-performance compact dual-band MIMO structure featuring acceptable level of element coupling at both operating frequencies. The design is validated both numerically and experimentally. The mutual coupling levels are less than -17 dB and -20 dB, with the total efficiency of 89% and 90%, and the realized gain of 6.6 dB and 7 dB at the two resonant frequencies of 5 GHz and 6 GHz, respectively. Topological complexity of the compact MIMO systems featuring elaborated decoupling structures, a large number of geometry parameters, as well as the necessity of handling multiple performance figures, constitute the major challenges of antenna design, in particular, its re-design for various specifications. To alleviate these difficulties, the paper also provides a procedure for rapid geometry scaling of the dual-band MIMO antennas. Our approach is based on inverse surrogate modeling methods, and results in numerically-derived expressions that enable a precise control over the operating antenna bands within broad ranges thereof (from 4 GHz to 8 GHz for the lower band, and from 1.1 to 1.3 ratio of the upper to lower operating frequency). The aforementioned procedure is accompanied by an optimization-based design refinement scheme. A practical utility of the procedure is corroborated using multiple verification case studies as well as physical measurements of the antenna designed for the exemplary set of performance specifications.

(028) Recommendation for prohibiting unauthorized division of a type specimen

According to Rec. 7A.1 of the Code (Turland & al. in Regnum Veg. 159. 2018), it is strongly recommended that the material on which the name of a taxon is based, especially the holotype, be scrupulously conserved. For nomenclatural stability, the hope is that the holotype will last forever. For some kinds of plants, however, a type is under severe threat of destruction, especially in the study of bryophytes, where taking without permission portions of the type specimen for making duplicates has occasionally occurred in the past through ignorance or arrogance. Bryophyte specimens usually consist of many individual plants, which are small and kept in a paper packet (or often, historically, glued to a mounting sheet), and thus it may be easier to make duplicates than for vascular plants. Such unauthorized divisions of a type specimen, which contain a much smaller volume than that of the original type, have usually been kept by investigators for their own herbarium, and thus these specimens remain hidden until he/she has passed away. Such specimens are occasionally called “kleptotypes”, an unofficial term meaning “(stolen) fragment of type” (Beentje & Williamson, The Kew Plant Glossary. 2010) or “a type or fragment of a type that should not be in its current location (because it was deliberately stolen, borrowed and not returned, etc.)” (Turland, The Code Decoded, ed. 2. 2019). However, according to the current Code (Art. 8 Ex. 8), they are merely treated as duplicates, i.e. isotypes, without any mention of the prohibited practice by which these specimens were derived. We believe that unauthorized division of a type specimen should be prohibited explicitly in the Code. Pfister & Rossman (in Taxon 33: 295–296. 1984) already pointed out a problem with the creation of kleptotypes and mentioned that the unauthorized division of a type specimen should be immediately discontinued as it is destructive, wasteful, and unethical. Because the unauthorized division of a type results in a loss from the original type specimen, such action most likely complicates the work of future generations and may lead to confusion regarding the original concept of the species and to ambiguity and may therefore require multiple verifications in future revisions because researchers usually leave few tracks of their investigations. Pfister & Rossman (l.c.: 295) also noted “Most of us could dredge up a story about a collection of kleptotypes being destroyed—accidently or on purpose—because the contents were obtained through theft.” Most herbaria now ask that all parts of dissections should be returned and that the unauthorized division of a type specimen should no longer occur. As researchers and curators, however, we also believe that when such specimens are found, they should not be destroyed but kept in herbaria as a formal duplicate, e.g. an isotype. We believe that sharing the hidden or emerging information regarding existing kleptotypes is more useful than destroying them on purpose, even if they may contain only a small volume of material. We therefore propose a new Recommendation to prevent unauthorized division of a type specimen. “8A.n. The unauthorized division of a type specimen should be prevented to avoid a loss of the type specimen. Such action most likely complicates the work of future generations and the resulting reduced collections may give a misleading concept of the species. When found, such “kleptotype” specimens should not be destroyed but preserved as duplicates. Formal notification of the existence and location of these specimens should also be published.” We thank Prof. Rod Seppelt for his constructive comments and for checking the English text.

Dual role of MdSND1 in the biosynthesis of lignin and in signal transduction in response to salt and osmotic stress in apple

Clarifying the stress signal transduction pathway would be helpful for understanding the abiotic stress resistance mechanism in apple (Malus × domestica Borkh.) and could assist in the development of new varieties with high stress tolerance by genetic engineering. The key NAC transcription factor SND1, which is involved in the lignin biosynthesis process in apple, was functionally analyzed. The results of the stress treatments indicated that MdSND1 could be induced by salt, mannitol and ABA. Compared with wild-type GL-3 plants, MdSND1-overexpressing apple plants with greater antioxidant capacity and lignin were more resistant to salt and simulated osmotic stress, while RNAi plants were more vulnerable. Additionally, molecular experiments confirmed that MdSND1 could regulate the biosynthesis of lignin by activating the transcription of MdMYB46/83. Moreover, genes known to be involved in the stress signal transduction pathway (MdAREB1A, MdAREB1B, MdDREB2A, MdRD29A, and MdRD22) were screened for their close correlations with the expression of MdSND1 and the response to salt and osmotic stress. Multiple verification tests further demonstrated that MdSND1 could directly bind to these gene promoters and activate their transcription. The above results revealed that MdSND1 is directly involved in the regulation of lignin biosynthesis and the signal transduction pathway involved in the response to both salt and osmotic stress in apple.

Efficient verification of parallel matrix multiplication in public cloud: the MapReduce case

With the advent of cloud-based parallel processing techniques, services such as MapReduce have been considered by many businesses and researchers for different applications of big data computation including matrix multiplication, which has drawn much attention in recent years. However, securing the computation result integrity in such systems is an important challenge, since public clouds can be vulnerable against the misbehavior of their owners (especially for economic purposes) and external attackers. In this paper, we propose an efficient approach using Merkle tree structure to verify the computation results of matrix multiplication in MapReduce systems while enduring an acceptable overhead, which makes it suitable in terms of scalability. Using the Merkle tree structure, we record fine-grained computation results in the tree nodes to make strong commitments for workers; they submit a commitment value to the verifier which is then used to challenge their computation results’ integrity using elected input data as verification samples. Evaluation outcomes show significant improvements comparing with the state-of-the-art technique; in case of 300*300 matrices, 73% reduction in generated proof size, 61% reduction in the proof construction time, and 95% reduction in the verification time.

An Improved Fuzzy Vector Signature with Reusability

Fuzzy vector signature (FVS) is a new primitive where a fuzzy (biometric) data w is used to generate a verification key (VKw), and, later, a distinct fuzzy (biometric) data w′ (as well as a message) is used to generate a signature (σw′). The primary feature of FVS is that the signature (σw′) can be verified under the verification key (VKw) only if w is close to w′ in a certain predefined distance. Recently, Seo et al. proposed an FVS scheme that was constructed (loosely) using a subset-based sampling method to reduce the size of helper data. However, their construction fails to provide the reusability property that requires that no adversary gains the information on fuzzy (biometric) data even if multiple verification keys and relevant signatures of a single user, which are all generated with correlated fuzzy (biometric) data, are exposed to the adversary. In this paper, we propose an improved FVS scheme which is proven to be reusable with respect to arbitrary correlated fuzzy (biometric) inputs. Our efficiency improvement is achieved by strictly applying the subset-based sampling method used before to build a fuzzy extractor by Canetti et al. and by slightly modifying the structure of the verification key. Our FVS scheme can still tolerate sub-linear error rates of input sources and also reduce the signing cost of a user by about half of the original FVS scheme. Finally, we present authentication protocols based on fuzzy extractor and FVS scheme and give performance comparison between them in terms of computation and transmission costs.

A multi-flow information flow tracking approach for proving quantitative hardware security properties

Information Flow Tracking (IFT) is an established formal method for proving security properties related to confidentiality, integrity, and isolation. It has seen promise in identifying security vulnerabilities resulting from design flaws, timing channels, and hardware Trojans for secure hardware design. However, existing IFT methods tend to take a qualitative approach and only enforce binary security properties, requiring strict non-interference for the properties to hold while real systems usually allow a small amount of information flows to enable desirable interactions. Consequently, existing methods are inadequate for reasoning about quantitative security properties or measuring the security of a design in order to assess the severity of a security vulnerability. In this work, we propose two multi-flow solutions - multiple verifications for replicating existing IFT model and multi-flow IFT method. The proposed multi-flow IFT method provides more insight into simultaneous information flow behaviors and allows for proof of quantitative information flow security properties, such as diffusion, randomization, and boundaries on the amount of simultaneous information flows. Experimental results show that our method can be used to prove a new type of information flow security property with verification performance benefits.

Trustworthiness and a Zero Leakage OTMP-P2L Scheme Based on NP Problems for Edge Security Access.

Resource constraints have prevented comprehensive cryptography and multifactor authentication in numerous Internet of Things (IoT) connectivity scenarios. Existing IoT systems generally adopt lightweight security protocols that lead to compromise and privacy leakage. Edge computing enables better access control and privacy protection, furthermore, blockchain architecture has achieved a trusted store of value by open-source and distributed consensus mechanisms. To embrace these new paradigms, we propose a scheme that employs one-time association multitasking proofs for peer to local authentication (OTMP-P2L). The scheme chooses relevant nondeterministic polynomial (NP) problem tasks, and manages localized trust and anonymity by using smart devices such as phones and pads, thereby enabling IoT devices to autonomously perform consensus validation with an enhanced message authentication code. This nested code is a one-time zero-knowledge proof that comprises multiple logic verification arguments. To increase diversity and reduce the workload of each one, these arguments are chained by a method that establishes some of the inputs of the following task from the output of previous tasks. We implemented a smart lock system and confirmed that the scheme outperforms IoT authentication methods. The result demonstrates superior flexibility through dynamic difficulty strategies and succinct non-interactive peer-to-peer (P2P) verification.

Representing Model Uncertainty by Multi-Stochastic Physics Approaches in the GRAPES Ensemble

To represent model uncertainties more comprehensively, a stochastically perturbed parameterization (SPP) scheme consisting of temporally and spatially varying perturbations of 18 parameters in the microphysics, convection, boundary layer, and surface layer parameterization schemes, as well as the stochastically perturbed parameterization tendencies (SPPT) scheme, and the stochastic kinetic energy backscatter (SKEB) scheme, is applied in the Global and Regional Assimilation and Prediction Enhanced System—Regional Ensemble Prediction System (GRAPES-REPS) to evaluate and compare the general performance of various combinations of multiple stochastic physics schemes. Six experiments are performed for a summer month (1–30 June 2015) over China and multiple verification metrics are used. The results show that: (1) All stochastic experiments outperform the control (CTL) experiment, and all combinations of stochastic parameterization schemes perform better than the single SPP scheme, indicating that stochastic methods can effectively improve the forecast skill, and combinations of multiple stochastic parameterization schemes can better represent model uncertainties; (2) The combination of all three stochastic physics schemes (SPP, SPPT, and SKEB) outperforms any other combination of two schemes in precipitation forecasting and surface and upper-air verification to better represent the model uncertainties and improve the forecast skill; (3) Combining SKEB with SPP and/or SPPT results in a notable increase in the spread and reduction in outliers for the upper-air wind speed. SKEB directly perturbs the wind field and therefore its addition will greatly impact the upper-air wind-speed fields, and it contributes most to the improvement in spread and outliers for wind; (4) The introduction of SPP has a positive added value, and does not lead to large changes in the evolution of the kinetic energy (KE) spectrum at any wavelength; (5) The introduction of SPPT and SKEB would cause a 5%–10% and 30%–80% change in the KE of mesoscale systems, and all three stochastic schemes (SPP, SPPT, and SKEB) mainly affect the KE of mesoscale systems. This study indicates the potential of combining multiple stochastic physics schemes and lays a foundation for the future development and design of regional and global ensembles.

Risk-informed reliability improvement optimization for verification and validation planning based on set covering modeling

Verification and validation plays a crucial role in the new product development process since it is able to assure product performance and eventually determine customer satisfaction. The verification and validation planning assigns a set of verification and validation activities such as computational simulations and physical tests, which are proposed to mitigate the design risks of specific failure modes, to verify and validate that the product conforms to the design objectives. This article formulates the optimal verification and validation planning using set covering, set partition, and set packing concepts. An extended optimization model based on set covering is also formulated, which can well accommodate the requirements including minimizing the overall risk of the product design, meeting pre-specified risk thresholds of specific failure modes, and covering identified critical failure modes. Additional constraints such as the implementation sequences, time gaps of various types of verification and validation activities, and the distinct effectiveness of each verification and validation activity in reducing design risks are considered in the verification and validation planning optimization models. The decay of the improvement effectiveness of a failure mode with multiple verification and validation activities over time is also considered. The application of the proposed mathematical optimization models for product verification and validation planning is illustrated through the product development of a power generation system within a diesel engine.

A novel fault tolerant multiplier using single digit conversion based self checking scheme

Digital multipliers are key component of all digital signal processing applications. Numerous algorithms and architectures have been proposed to design high-speed and self repairable multipliers for critical applications like space craft and medical applications. This work proposes a self checking scheme for fixed-width array multipliers. The proposed scheme verifies multiply operation by single digit conversion based verification, mainly relying on the use of addition called (MVA) multiplication verification algorithm. To tolerate the fault that occurs in the multiplier circuit, redundancy replicas of multiplier modules are used to replace faulty one. Our proposed multiplier has been implemented using synopsis complier tool, which achieve a low-cost fault-tolerant design when compare with conventional redundancy based error tolerant techniques.

Prediction of ionic liquids heat capacity at variable temperatures based on the norm indexes

The heat capacity of ILs is essential in the chemical engineering and design applications. In this study, the dataset consisting of 5964 heat capacity data points within a wide temperature range (191.13–550.00 K) of 185 ILs was collated. Based on the concept of norm index, a serial of norm indexes were derived and adopted to develop the QSPR model. Here, the temperature parameters were adjusted on the basis of the molecular structure information. The linear model is precise for estimating heat capacity of ILs at variable temperatures with square of correlation coefficient R2 = 0.996, average absolute relative deviation AARD = 2.49% and the root mean square error RMSE = 19.43. Besides, the good results of multiple verification methods further illustrate the stability and reliability of this work. Consequently, this norm-index based work could provide a correlation method to describe the heat capacity of different structures ILs at variable temperatures.

Evaluation of TIGGE Daily Accumulated Precipitation Forecasts over the Qu River Basin, China

Quantitative precipitation forecasts (QPFs) provided by three operational global ensemble prediction systems (EPSs) from the THORPEX (The Observing System Research and Predictability Experiment) Interactive Grand Global Ensemble (TIGGE) archive were evaluated over the Qu River basin, China during the plum rain and typhoon seasons of 2009–13. Two post-processing methods, the ensemble model output statistics based on censored shifted gamma distribution (CSGD-EMOS) and quantile mapping (QM), were used to reduce bias and to improve the QPFs. The results were evaluated by using three incremental precipitation thresholds and multiple verification metrics. It is demonstrated that QPFs from NCEP and ECMWF presented similarly skillful forecasts, although the ECMWF QPFs performed more satisfactorily in the typhoon season and the NCEP QPFs were better in the plum rain season. Most of the verification metrics showed evident seasonal discriminations, with more satisfactory behavior in the plum rain season. Lighter precipitation tended to be overestimated, but heavier precipitation was always underestimated. The post-processed QPFs showed a significant improvement from the raw forecasts and the effects of post-processing varied with the lead time, precipitation threshold, and EPS. Precipitation was better corrected at longer lead times and higher thresholds. CSGD-EMOS was more effective for probabilistic metrics and the root-mean-square error. QM had a greater effect on removing bias according to bias and categorical metrics, but was unable to warrant reliabilities. In general, raw forecasts can provide acceptable QPFs eight days in advance. After post-processing, the useful forecasts can be significantly extended beyond 10 days, showing promising prospects for flood forecasting.

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English

Determining protein denaturation of sardine (Sardina pilchardus) marinates before and after the maturation

In this study, sardine fish (Sardina pilchardus) was subjected to marination at different degrees of acidity (2.5%–5%). On the basis of the duration of maturation (22 days) and postmaturation period (three months after maturation), protein denaturation and quality changes of marinades were determined. Quality parameters, such as pH, acidity, salinity, and lipid oxidation, were examined for both periods. As a result of the study carried out for 22 days at different acidity levels, the change in the amount of TVB-N was found to be insignificant (p > 0.05), but the differences in pH, TBARS, acidity, and salinity levels were found to be significant (p < 0.05). In the postmaturation period, the change in the TBARS amount was insignificant (p > 0.05), and the other parameters were found to be significant (p < 0.05). SDS-PAGE analysis showed that fish muscle and brine proteins showed different profiles and a decrease in densities of MHC, actin, and TM bands during the maturation period was observed. Practical applications Protein denaturation is important in fisheries products, so multiple verification tests should be performed to monitor this process. It was suggested that DSC and SDS-PAGE techniques are easier and quicker analyses for determining protein denaturation in seafood products compared with traditional techniques.

Uso del móvil y las redes sociales como canales de verificación de fake news. El caso de Maldita.es

The viral diffusion of information in social networks, mobile devices and messaging services favors the sharing of false and unverified news. Spain is one of the European countries that leads the reception of this type of content. This article analyzes the case of Maldita.es, a platform that identifies fake news and combats misinformation. The analysis is focused on four points: mobiles as working devices, social networks as a channel for the viralization of hoaxes and denials, the organization of verification, and the organizational model. The results show that mobile devices and social networks are the two pillars of the project: they allow to organize the information input and output, as well as the tasks of the team, and help to carry out a multiple verification work.

Proficient Justification of Data Accuracy for Cloud Storage Using Dual Protection

The cloud security is one of the essential roles in cloud, here we can preserve our data into cloud storage. More and more clients would like to keep their data to PCS (public cloud servers) along with the rapid development of cloud computing. Cloud storage services allow users to outsource their data to cloud servers to save local data storage costs. Multiple verification tasks from different users can be performed efficiently by the auditor and the cloud-stored data can be updated dynamically. It makes the clients check whether their outsourced data is kept intact without downloading the whole data. In our system we are using the own auditing based on the token generation. Using this key generation technique compare the key values from original keys we can find out the changes about the file. A novel public verification scheme for cloud storage using in distinguishability obfuscation, which requires a lightweight computation on the auditor and delegate most computation to the cloud. Not only stored also the content will be encrypted in the cloud server. If anyone try to hack at the cloud end is not possible to break the two different blocks. The security of our scheme under the strongest security model. They need first decrypt the files and also combine the splitted files from three different locations. This is not possible by anyone. Anyone can download the files from the server with file holder permission. At the time of download key generated (code based key generation) and it will send to the file owner. We can download the file need to use the key for authentication and some other users want to download file owner permission is necessary.

Accuracy of digital and conventional dental implant impressions for fixed partial dentures: A comparative clinical study.

PURPOSEThe newest technologies for digital implant impression (DII) taking are developing rapidly and showing acceptable clinical results. However, scientific literature is lacking data from clinical studies about the accuracy of DII. The aim of this study was to compare digital and conventional dental implant impressions (CII) in a clinical environment.MATERIALS AND METHODSTwenty-four fixed zirconia restorations supported by 2 implants were fabricated using conventional open-tray impression technique with splinted transfers (CII group) and scan with Trios 3 IOS (3Shape) (DII group). After multiple verification procedures, master models were scanned using laboratory scanner D800 (3Shape). 3D models from conventional and digital workflow were imported to reverse engineering software and superimposed with high resolution 3D CAD models of scan bodies. Distance between center points, angulation, rotation, vertical shift, and surface mismatch of the scan bodies were measured and compared between conventional and digital impressions.RESULTSStatistically significant differences were found for: a) inter-implant distance, b) rotation, c) vertical shift, and d) surface mismatch differences, comparing DII and CII groups for mesial and dist al implant scan bodies (P≤.05).CONCLUSIONRecorded linear differences between digital and conventional impressions were of limited clinical significance with two implant-supported restorations.

Retrieval priming in product verification: Evidence from retrieval-induced forgetting

The conditions under which multiplication verification (3 × 6 = 12, true or false?) involves product retrieval and comparison or familiarity-based recognition judgements has not been clearly established. In two experiments examining verification of single-digit multiplication problems, we used Retrieval-Induced Forgetting (RIF), a signature of retrieval use, as an index of product retrieval in multiplication verification. In Experiment 1, 72 adults practiced multiplication either in a production format or in a verification format and then were tested on corresponding addition and control problems. The results showed RIF (i.e., slower answer production for addition problems whose multiplication counterparts had been practiced) in both the production-practice and the verification-practice groups, but RIF was stronger following true than false verification. Experiment 2 tested verification with related-false and unrelated-false products. Related-false equations produced longer RTs than unrelated false equations. Practice of true, related-false and unrelated-false multiplication equations all produced RIF of the addition counterparts but, overall, related-false multiplication equations produced relatively weak RIF. The results indicated that product retrieval mediates multiplication verification even when false answers are weak associative lures and suggest that a retrieve-and-compare process is the default strategy when false answers are at least plausible. We conclude that the presented answer in verification equations act as retrieval-priming stimuli with true equations priming correct answer retrieval and related-false answers interfering with correct answer retrieval.

Standardizing and optimizing institutional-level documentation in the electronic medical record era.

155 Background: Although electronic medical records (EMR) offer numerous potential benefits, there are significant challenges to balance high quality patient care and clinical efficiency with the rising demands of required documentation. Our objective was to propose and implement a strategy to standardize and optimize EMR documentation. Methods: An EMR taskforce was created within our institution’s radiation oncology (RO) department consisting of representatives of the clinical staff and EMR coders. To optimize clinical documentation, disease-site specific consult templates were created using EMR standard data elements and personalized drop down menus (Smartlists). Meetings were held with the billing department for template review and with the analytics team to begin automated data extraction into research databases. Quality metrics such as the average number of clinic visits billed at levels 4 or 5 (B45) and the average number of hours per visit (AHV) were compared in different clinics within a 6-month pre- and post- template implementation time period. Results: Within 3 months of establishing the taskforce, 32 RO disease-specific templates were created and distributed for usage in clinic. Optimized template features include consistent cancer staging, standardized oncologic history entry, usage of macros for patients’ symptoms for multiple provider verification, imbedded disease-specific protocol list to improve patient screening and enrollment, and multiple Smartlists for common treatment recommendations. In the GI Clinic, B45 increased from 49.3 to 61.4 per month and similar trends were seen in the Thoracic Clinic (B45, 51.4 to 85.2 per month). The AHV decreased in both the GI (21 to 10 hours) and Thoracic (22 to 13 hours) clinics, showing a significant added value to use of standard documentation. Conclusions: EMR systems can be challenging to navigate; however, they also present a unique opportunity to optimize clinical and research efficiency if used properly. The implementation of standard documentation in our department led to significant improvement in clinical efficiency. Further efforts are being made to adopt these changes on an institutional-wide level.

When 2 × 4 is meaningful: the N400 and P300 reveal operand format effects in multiplication verification.

Arithmetic problems share many surface-level features with typical sentences. They assert information about the world, and readers can evaluate this information for sensibility by consulting their memories as the statement unfolds. When people encounter the solution to the problem 3 × 4, the brain elicits a robust ERP effect as a function of answer expectancy (12 being the expected completion; 15 being unexpected). Initially, this was labeled an N400 effect, implying that semantic memory had been accessed. Subsequent work suggested instead that the effect was driven by a target P300 to the correct solutions. The current study manipulates operand format to differentially promote access to language-based semantic representations of arithmetic. Operands were presented either as spoken number words or as sequential Arabic numerals. The critical solution was always an Arabic numeral. In Experiment 1, the correctness of solutions preceded by spoken operands modulated N400 amplitude, whereas solutions preceded by Arabic numerals elicited a P300 for correct problems. In Experiment 2, using only spoken operands, the delay between the second operand and the Arabic numeral solution was manipulated to determine if additional processing time would result in a P300. With a longer delay, an earlier N400 and no distinct P300 were observed. In brief, highly familiar digit operands promoted target detection, whereas spoken numbers promoted semantic level processing-even when solution format itself was held constant. This provides evidence that the brain can process arithmetic fact information at different levels of representational meaningfulness as a function of symbolic format.