dataesr/scientific-paragraphs-categorization huggingface dataset:
Grating Coupler 2 A similar experiment was conducted on data obtained from another vertical grating coupler design, as depicted in Figure  5  (Bottom). Compared to the previous example, here a section based on a subwavelength metamaterial is introduced in the device structure, as described in  [1, 24]. While the number of variables defining the structure is also five -(L 1 , • • • , L 4 , n swg ), the variable n swg represents a different physical quantity -the effective material index of the subwavelength metamaterial section -which has a different interpretation as well as a different order of magnitude  [21]. The other four variables, as previously, represent silicon segment widths. The complete dataset consists of 1502 optimized designs (coupling efficiency > 74%) of which half were used as the test set.
The complete dataset consists of 645 designs that achieve at least 97% coupling efficiency, defined as the amount of power coupled into the output ports (since the device is symmetric the power is guaranteed to be split equally). The optimized structures are obtained from hundreds of gradient based optimizations with random initial conditions. Figure  8  represents the performance results on this dataset for two different choices of the reduced dimension. Similar to previous experiments, PCA-Robust method outperforms its competitors except for PCA at the smallest dataset regime, where their performance is comparable. An interesting outcome revealed by these two experiments is the observation that with 100 samples, the average projection error for PCA reduced to 5 dimensions (108 ± 0. 7) is marginally better than that of PCA-Robust reduced to 4 (114 ± 1.
Breast Cancer Wisconsin Dataset The Breast Cancer Wisconsin Dataset  [27] , included in sci-kit learn package  [28] , consists of 569 total samples labeled "benign" and "malignant". These labels are irrevelant for our purposes since we're interested in comparing the average projection error in the dimensionality reduction of PCA and PCA-Robust. Each sample contains 30 real-valued features describing charecteristics of the cell nuclei depicted in an image of a fine-needle aspirate of a breast mass. Since the feature size is 30 we expanded the width of our vase as compared to our earlier experiments. The new width had 100 nodes and a bottleneck of 15 nodes (to obtain 15 reduced dimensions), resulting in 30-100-30-15-30-100-30 size architecture. Figure  9b  shows that, the PCA-Robust autoencoder outperforms other methods on all except for the smallest data set size, where its performance is comparable to that of PCA.
Conclusion and Future Work We demonstrated that autoencoders, with proper initialization, offer a viable solution for dimensionality reduction even in a limited data regime for problems where number of data points is larger than the number of features. Accordingly, a choice does not have to be made between linear and nonlinear model fitting on small datasets. Instead, stable PCA initialization provides the best of both worlds, allowing the AE training to proceed smoothly and introducing nonlinearity only to the extent allowed by the data. These results are encouraging in domains where, due to data scarcity, only PCA has been used for dimensionality reduction. Furthermore, the explicit encoding-decoding nature of autoencoders allow sampling the low-dimensional space for applications such as nanophotonic component design.
When End(E 0 ) is unknown, we prove that there is a subexponential attack. The attack is further supported by a SageMath  [36]  proof-of-concept implementation available at: https://github. com/Breaking-SIDH/direct-attack In the case where End(E 0 ) is unknown, Robert  [32]  proved, following the first version of this work, that there also is a polynomial-time attack. This is asymptotically the fastest known attack in this setting. However, it involves the computation of a special 8-dimensional endomorphism of E 4 0 ×E 4 A (or 4-dimensional, under plausible heuristics), which may limit its practicality. Finally, note that as in  [8]  and  [32] , our attack makes full use of the public torsion points, and as such, it has no effect on isogeny-based cryptosystems that do not publish images of points under a secret isogeny, such as CSIDH  [9] , CSI-FiSh  [3] , and SQISign  [14].
The largest field extension involved in computing φ f is F p 176 , for the 353-isogeny. As e = 1, no extension is required to perform point division. This runs in less than 1 minute on a single core on a standard laptop. Our code for attacking both of the above parameter sets is available at: https://github. com/Breaking-SIDH/direct-attack Challenge parameters: We consider one of the sets of challenge parameters put forward by Microsoft  [12] : A = 3 67 , B = 2 110 , i = 7, e = 1, j = 2, f = 5 • 7 • 13 3 • 43 2 • 73 • 151 • 241 • 269 • 577 • 613 • 28111 • 321193. The largest field extension we would need for the computation of φ 321193 using √ élu is of degree 642384; in this case it might be faster to use a variant of Kohel's algorithm to avoid the extension field arithmetic (see Section 3.
Acknowledgements We would like to thank  Christophe Petit  for useful comments regarding methods to compute isogenies with irrational kernel points and  Eda Kirimli , for useful discussions. We are also extremely grateful to  Luca De Feo , who shared with us a better method to find attack parameters during ANTS-XV, which in particular led to the argument in this paper that our algorithm has subexponential complexity. We would also like to thank  COSIC  and  KU Leuven , especially  Wouter Castryck  and  Thomas Decru , for hosting  Luciano Maino  as an intern, sparking his collaboration that led to this paper.
The implementation and algorithmic details of the implementation were contributed by  Panny  and Pope. This research was funded in part by the  UK Engineering and Physical Sciences Research Council (EPSRC) Centre for Doctoral Training  (CDT) in Trust,  Identity ,  Privacy and Security in Large-scale Infrastructures  ( TIPS-at-Scale ) at the  Universities of Bristol and Bath , the  Academia Sinica  Investigator Award  AS-IA-109-M01 , the  Agence Nationale de la Recherche  under grant  ANR   MELODIA  ( ANR-20-CE40-0013 ), and the  France 2030 program  under grant agreement No. ANR-22-PETQ-0008 PQ-TLS. Date of this document:  2023-03-10.
Finally, we recall the notion of asymptotic cones and prove the main result in Section 5. Acknowledgements. This work was supported by Polish Narodowe Centrum Nauki UMO-2017/25/B/ST1/01335 as well as by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund. The collaboration that led to this article was initiated at the 2019 Simons Semester in Geometric and Analytic Group Theory in Warsaw. The first named author was supported by the ERC grant GroIsRan. The second named author was supported by CEFIPRA grant number 5801-1, "Interactions between dynamical systems, geometry and number theory. ".
A well-crafted packaging message serves as a source of information and establishes an emotional connection with consumers  (Silayoi & Speece, 2007). Conveying the information, benefits, and identity of a product helps shape consumers' expectations and perceptions  (Rebollar et al. , 2017). Additionally, such messages can present a coherent and persuasive narrative about the product, resulting in a favorable image in consumers' minds  (Gómez-Chova et al. , 2015; Solja et al. , 2018). Furthermore, emphasizing a product's unique characteristics, claims, or benefits in a packaging message helps differentiate a product from other products in the line and creates competitive products  (Hidalgo-Baz et al. , 2017). Thus, packaging messages can create a distinct identity and value proposition for a product.
| Method The study employs a 2 (packaging message: absent vs. unconventional) × 2 (product type: impulsive vs. planned) betweensubjects design. Following pretest 1, potato chips and prepackaged meals serve as the impulsive and planned product purchases, respectively. Based on the results of pretest 2, we add the unconventional packaging message "Yummy Snappy Treats" to the potato chips packaging in the unconventional condition; however, the absent condition includes no packaging message. Similarly, for prepackaged meals, we exclude a packaging message in the absent condition but include "Artisanal Nourishment" in the unconventional condition (see Supporting Information: Web Appendix B for the stimuli). We use Adobe Photoshop to create the study stimuli. We use an online questionnaire hosted on Qualtrics to gather data from participants on the Prolific Academic online marketplace.
| Method We recruited a total of 275 participants to take part in the study from Prolific Academic. The sample size is adequate, providing a power of 0. 95. The sample consists of 49. 5% females; 33. 5% are between 25 and 34 years old. The data collection process is similar to study 1b, except for three changes. First, following pretest 1, we use cookies as the impulsive product. Second, we employ "Irresistibly Soft Chocobites" as the unconventional packaging message condition and "Soft Choco Cookies" as the conventional packaging message condition. The absent condition does not include a packaging message (see Supporting Information: Web Appendix E for the stimuli). Third, participants answer questions about curiosity (i. e. , four items adapted from  Menon & Soman, 2002 ; α = 0. 97), along with purchase intentions (α = 0.
39, p < 0. 01, partial η 2 = 0. 083). Specifically, an unconventional packaging message (M = 4. 47, SD = 1. 64) results in a higher level of curiosity toward the product compared to when a conventional packaging message (M = 3. 89, SD = 1. 64, p < 0. 05) or no packaging message (M = 3. 24, SD = 1. 74, p < 0. 01) is used. The results indicate a similar pattern in the relationship when control variables are included. We test the mediating role of curiosity with PROCESS Model 4 using the SPSS macro with 5000 bootstrapping samples  (Hayes, 2018). Purchase intentions are included as the dependent variable, curiosity as the mediator, and packaging message (i. e. , 0 for unconventional, 1 for conventional, and 2 for absent) as the fixed factor in the analysis. Because the independent variable is multicategorial, we create dummy variables, and mediation is tested by comparing the unconventional packaging message condition with the conventional packaging message condition and the unconventional packaging message condition with the absent condition.
Given that the experiment was designed to allow asserting the null hypothesis (i. e. , eye movements and hand movements induce the same amount of RHI), non-significant interactions between spatial-congruency and effector-type were further tested through Bayesian t-tests on the difference between spatially congruent/incongruent conditions in each type of movement. This allowed us to determine whether the datasupported the null hypothesis or if, alternatively, the null result could reflect insufficient statistical power. 26 All the ANOVAs were conducted using IBM SPSS Statistics for Windows, version 23 (IBM Corp. ,USA). Bayesian analyses were run on JASP v. 0. 12. 1 (JASP Team 2016, University of Amsterdam).
ACKNOWLEDGMENTS This study was supported by a  Sponsored Research Agreement from Oculus VR, LLC  to the  University of London. O. D was supported by a  Co-Sense  grant from the  Volkswagen Foundation  and by an  EIC PATHFINDER EMERGE  (n. 101070918). We thank  Alessandro Farne  `,  Luke Miller ,  Malika Auvray ,  Alessandro Moscatelli ,  Merle Fairhurst ,  Harriet Allen , and Elisabeth Pares-Pujolras for advice and assistance.
g. in documents and databases that have been designed to allow such an importation). These KR bases can be either privately developed or, preferably, collaboratively developed. In this article, these KR bases are simply called KBs and, before going further, need to be more introduced now. Such KBs do not store texts or other data; they store KRs (or simply, "knowledge"), i. e. logic-based representations of semantic relations between pieces of informationsemantic relations being relations that can be represented in a logic-based way. The boxes and figures in Sections 2. 1 and 3 include many examples. In this article, the notions referred to by the words "knowledge" (KRs) and "data" are mutually exclusive. "Data" refers to information not explicitly organized -or poorly organized -by semantic relations, e.
g. as in databases or XML documents: they are mainly organized by predefined structural relations (i. e. partOf ones) and few semantic relations of very few predefined types (mostly typeOf relations and sometimes subtype relations). In KBs, unlike in relational databases, all the types (i. e. relation types and concept types) and their definitions are userprovided (not predefined by the database designer); most of the knowledge in many KBs are expressed via such definitions; large KBs such as CYC  [1, 2] , Freebase  [3]  and DBpedia  [4]  have hundreds of thousands of subtype relations. Document-based technologies and database systems generally only handle data, although deductive databases may be seen as steps towards KBs. A KB is composed of an ontology and, generally, a base of facts. An ontology is (i) a formal terminology, i.
e. a set of terms (alias, object identifiers) used in the representations stored in the KB, along with (ii) representations of term definitions, and thereby direct or indirect semantic relations between these terms. Databases and natural-language-based documents cannot automatically be converted into KBs that are well-organized via generalization and implication relations, if only because these documents and bases most often lack the necessary information to derive such relations (these relations are rarely made explicit by document authors and even human readers often cannot infer such relations with certainty). These relations -and thus, manually or semi-automatically built KBs -are necessary for the support of (i) semantic-based searches, via queries or navigation, and (ii) any scalable way of integrating or organizing information.
There currently exist some large projects, such as the Norwegian INSITU (Sharing Incident and Threat Information for Common Situational Understanding) project (2019-2022)  [10] , which focus on harmonizing terminologies or on tools for the collaborative synthesis of information in classic media (databases, textual documents, maps,. ), not via KBs. The use of classic media make the harmonization of terminologies useful for supporting lexical searches (i. e. those proposed by current Web search engines and document editors; these are not semantic search tools). However, such an harmonization is a complex task which requires committees (hence an hierarchy-based decision-making organization) and it is useful only when its guidelines are followed (something that is not easy to do). Via KBs, harmonizing terminologies is not necessary since relations of equivalence or generalization between terms within KBs or across KBs can be added in a decentralized and incremental way by each provider of terms or knowledge.
Examples of early landmark works related to general KS were Ontolingua (server, ontologies and vision)  [11]  and the still on-going above-cited CYC project. These two meanings are unfortunately very rarely distinguished, even indirectly, e. g. by the World Wide Web Consortium (W3C). With respect to KS, the W3C has a "Semantic Web vision"  [12]  of a "Web of Linked data"  [13]. As the use of the word "data" may suggest, and as explained in Section 2, the techniques and vision proposed for these Linked Data are mainly focused on restricted KS. Indeed, the W3C had to focus on the basics and convince industries of the interests of KBs over databases. However, after 1997 -the beginning of the popularization of the W3C visions and languages -KS was mainly learned about and operationalized via the W3C documents and languages, and thus almost all research works in KS were implicitly in restricted KS.
Among research articles related to risk or emergency management and that advocate using KBs, most rely on the W3C techniques or approach -e. g. the articles of  [14]  (about ontology-supported rule-based reasoning), of  [15]  (about ontology-supported access to particular databases) and of  [16]  (about a small ontology mainly including 38 concept types and 21 subtype relations, about some crisis management procedures). Previous studies into risk/emergency management have not addressed general KS in these domains and are insufficient to address the distributed and large number of potentially useful sources of information for such a management. This insufficiency is also one reason for the above-cited lack of large publicly accessible content ontologies or KBs related to disaster management.
These constraints are not satisfied by networked KBs based on distributed or federated database systems. Indeed, in these systems, the protocols that distribute or exchange information and forward queries exploit the fact that each individual KB or database has a fixed database schema or ontology, i. e. one that is not modified by its end-users (e. g. data providers). On the other hand, in general KS, the ontologies of the individual KBs are often updated by their contributors. Many networked KB architectures exploit such database systems, including the architectures advocated in risk/emergency management related articles, e. g. those of  [15]. Similarly, these constraints are not satisfied by networked KBs based on peer-to-peer (P2P) protocols or multi-agent system (MAS) protocols. Indeed, for exploiting the KRs within these KB -e.
e. those only based on classic structures such as object-oriented classes. Therefore, such maps should remain abstract data structures but should be represented or implemented in much richer structures than those in binary formats for the 2D/3D abstract maps: raster image formats (pixel-based formats) and vector formats (graphics/geometry + texture based format, e. g. SVG and OBJ). More information can be described via the Geography Markup Language (GML) which uses a very restricted kind of KRL -GML is used by the Web Feature Service (WFS), an interface model created by the Open Geospatial Consortium (OGC) to support requests for geographical features across the web using platform-independent calls. However, GML is not for storage purposes. In any case, ideally, for each physical object, such a map would store a reference (e.
Leaderless consensus is advantageous in applications exhibiting swarm behaviour, such as opinions coagulation in social networks, symbiotic relationship in biological systems, search and rescue, scientific reconnaissance, security, rendezvous or even attitude synchronisation of unmanned aerial vehicles, to name a few. By opting for leaderless configuration, the collected behaviour is not influenced by a single member and each agent can act independently to any adverse circumstance  (Rao and Ghose, 2013). In a directed network, this concept translates into confluence of behaviour of all the agents This work was supported by the CEFIPRA under the grant number 6001-A E. Panteley and A. Loría's work is also supported by the ANR (project HANDY, contract number ANR-18-CE40-0010). that can transmit information to all the other agents in the communication topology to form the collective consensus behaviour.
They use back-propagation algorithm to fit the dataset  [4]. These approaches discard all other possible parametrizations of the network that might also fit the input dataset well, they also lack explainability, and fail to give the uncertainty of a prediction. Furthermore, pointestimate NNs generally tend to be overconfident about their predictions even though NN receive out-of distribution data to infer. Alternatively, Bayesian Neural Networks (BayNNs)  [5]  offer a principled approach to train uncertainty-aware neural networks. Recent work shows that Dropout, which is typically used in neural networks to reduce overfitting, can be used as an approximation for Gaussian processes  [6]. Therefore, to evaluate the quality of NN results, the model uncertainty can be obtained with a very low cost, from common Dropout models.
Where, ⊙ is the Hadamard product. 3) Out-of Distribution Data and Uncertainty in NNs: Ideally, a neural network model should generalize well to inference data that were not used during the training. For example, in the simple case of MNIST dataset, the distribution of training and inference data are the same, e. g. , both training and inference data contain handwritten digits 0 • • • 9. A data that the NN model is not trained for, i. e. , has a different distribution, is referred to as out-of distribution data. Preferably, when a NN receives an out-of distribution data, it should either not predict at all or treat it as uncertain input, i. e. , return a result with high uncertainty. Otherwise, this situation can be utilized to completely crash the NN by adding specially calculated noise to the data  [13].
In contrast, aleatoric uncertainty refers to the uncertainty brought about by the noise in the observations. More data are not associated with a decline in aleatory uncertainty. 4) Bayesian neural networks: BayNNs are stochastic NNs trained using a Bayesian approach. BayNNs can be seen as a probabilistic deep learning model. It assigns prior distributions over the models' parameters to find parameters that could have generated the given dataset. Typically, a standard Gaussian distribution is set over the model parameters, P (θ) = N (0, I). BayNNs make predictions over an ensemble of an infinite number of NNs, i. e. , NNs with various configurations of the weights and biases, which is computationally intractable. Variational inference  [14]  provides a solution by approximating the distribution of NN parameters with a simpler known distribution, the approximate variational distribution, and minimizing the Kullback-Leibler (KL) divergence between those distributions.
KL divergence encourages the approximate variational distribution to become similar to the prior distribution, and minimization of that term is similar to minimizing negative evidence lower bound (ELBO). However, it requires integrating over all parameters space and is intractable. It can be estimated with Monte-Carlo (MC) sampling over θ of the NN. As a result, BayNNs can estimate uncertainty, reduces over-fitting, and makes it easier for the NN to learn from small datasets. 5) Dropout as Bayesian Approximation: Gal et al. [6]  provided mathematical groundwork showing in the case of variational distribution, that columns which are randomly set to zero with a probability p can also act as an approximation of the intractable posterior distribution. Also, minimizing the L 2 regularization is similar to minimizing the KL divergence.
For this purpose, the two modes of operation of the MTJ are explored, respectively, the stochastic feature implemented in the SpinDrop module and the deterministic behavior for the synapse storing in the crossbar array. This approach has the benefit of not requiring changes in the bit-cell of the crossbar architecture compared to  [20] , all design changes occur in the peripheral circuits. Moreover, compared to the RRAM based stochastic engine presented in  [21] , the STT-MRAM operates at lower voltages (around 1V), thus resulting in less power consumption.