A Non-terrestrial Network (NTN) comprising Low Earth Orbit (LEO) satellites can enable connectivity to underserved areas, thus complementing existing telecom networks. The high-speed satellite motion poses several challenges at the physical layer such as large Doppler frequency shifts. In this paper, an analytical framework is developed for statistical characterization of Doppler shift in an NTN where LEO satellites provide communication services to terrestrial users. Using tools from stochastic geometry, the users within a cell are grouped into disjoint clusters to limit the differential Doppler across users. Under some simplifying assumptions, the cumulative distribution function (CDF) and the probability density function are derived for the Doppler shift magnitude at a random user within a cluster. The CDFs are also provided for the minimum and the maximum Doppler shift magnitude within a cluster. Leveraging the analytical results, the interplay between key system parameters such as the cluster size and satellite altitude is examined. Numerical results validate the insights obtained from the analysis.

We consider the problem of protecting and manipulating elections by recounting and changing ballots, respectively. Our setting involves a plurality-based election held across multiple districts, and the problem formulations are based on the model proposed recently by~[Elkind et al, IJCAI 2019]. It turns out that both of the manipulation and protection problems are NP-complete even in fairly simple settings. We study these problems from a parameterized perspective with the goal of establishing a more detailed complexity landscape. The parameters we consider include the number of voters, and the budgets of the attacker and the defender. While we observe fixed-parameter tractability when parameterizing by number of voters, our main contribution is a demonstration of parameterized hardness when working with the budgets of the attacker and the defender.

Several nonlinear model reduction techniques are compared for the three cases of the non-parallel version of the Kuramoto-Sivashinsky equation, the transient regime of flow past a cylinder at $Re=100$ and fully developed flow past a cylinder at the same Reynolds number. The linear terms of the governing equations are reduced by Galerkin projection onto a POD basis of the flow state, while the reduced nonlinear convection terms are obtained either by a Galerkin projection onto the same state basis, by a Galerkin projection onto a POD basis representing the nonlinearities or by applying the Discrete Empirical Interpolation Method (DEIM) to a POD basis of the nonlinearities. The quality of the reduced order models is assessed as to their stability, accuracy and robustness, and appropriate quantitative measures are introduced and compared. In particular, the properties of the reduced linear terms are compared to those of the full-scale terms, and the structure of the nonlinear quadratic terms is analyzed as to the conservation of kinetic energy. It is shown that all three reduction techniques provide excellent and similar results for the cases of the Kuramoto-Sivashinsky equation and the limit-cycle cylinder flow. For the case of the transient regime of flow past a cylinder, only the pure Galerkin techniques are successful, while the DEIM technique produces reduced-order models that diverge in finite time.

This paper reviews the Challenge on Image Demoireing that was part of the New Trends in Image Restoration and Enhancement (NTIRE) workshop, held in conjunction with CVPR 2020. Demoireing is a difficult task of removing moire patterns from an image to reveal an underlying clean image. The challenge was divided into two tracks. Track 1 targeted the single image demoireing problem, which seeks to remove moire patterns from a single image. Track 2 focused on the burst demoireing problem, where a set of degraded moire images of the same scene were provided as input, with the goal of producing a single demoired image as output. The methods were ranked in terms of their fidelity, measured using the peak signal-to-noise ratio (PSNR) between the ground truth clean images and the restored images produced by the participants' methods. The tracks had 142 and 99 registered participants, respectively, with a total of 14 and 6 submissions in the final testing stage. The entries span the current state-of-the-art in image and burst image demoireing problems.

We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure solution has a low regularity, which manifests in sub-optimal convergence rates for well-known inf-sup stable mixed finite element methods in numerical simulations, see [10]. We show that eliminating this gradient part from the noise in the numerical scheme leads to optimally convergent mixed finite element methods, and that this conceptual idea may be used to retool numerical methods that are well-known in the deterministic setting, including pressure stabilization methods, so that their optimal convergence properties can still be maintained in the stochastic setting. Computational experiments are also provided to validate the theoretical results and to illustrate the conceptional usefulness of the proposed numerical approach.

Neural networks have opened up many new opportunities to utilize remotely sensed images in meteorology. Common applications include image classification, e.g., to determine whether an image contains a tropical cyclone, and image translation, e.g., to emulate radar imagery for satellites that only have passive channels. However, there are yet many open questions regarding the use of neural networks in meteorology, such as best practices for evaluation, tuning and interpretation. This article highlights several strategies and practical considerations for neural network development that have not yet received much attention in the meteorological community, such as the concept of effective receptive fields, underutilized meteorological performance measures, and methods for NN interpretation, such as synthetic experiments and layer-wise relevance propagation. We also consider the process of neural network interpretation as a whole, recognizing it as an iterative scientist-driven discovery process, and breaking it down into individual steps that researchers can take. Finally, while most work on neural network interpretation in meteorology has so far focused on networks for image classification tasks, we expand the focus to also include networks for image translation.

We consider generic optimal Bayesian inference, namely, models of signal reconstruction where the posterior distribution and all hyperparameters are known. Under a standard assumption on the concentration of the free energy, we show how replica symmetry in the strong sense of concentration of all multioverlaps can be established as a consequence of the Franz-de Sanctis identities; the identities themselves in the current setting are obtained via a novel perturbation of the prior distribution of the signal. Concentration of multioverlaps means that asymptotically the posterior distribution has a particularly simple structure encoded by a random probability measure (or, in the case of binary signal, a non-random probability measure). We believe that such strong control of the model should be key in the study of inference problems with underlying sparse graphical structure (error correcting codes, block models, etc) and, in particular, in the derivation of replica symmetric formulas for the free energy and mutual information in this context.

Smart meters enable remote and automatic electricity, water and gas consumption reading and are being widely deployed in developed countries. Nonetheless, there is still a huge number of non-smart meters in operation. Image-based Automatic Meter Reading (AMR) focuses on dealing with this type of meter readings. We estimate that the Energy Company of Paran'a (Copel), in Brazil, performs more than 850,000 readings of dial meters per month. Those meters are the focus of this work. Our main contributions are: (i) a public real-world dial meter dataset (shared upon request) called UFPR-ADMR; (ii) a deep learning-based recognition baseline on the proposed dataset; and (iii) a detailed error analysis of the main issues present in AMR for dial meters. To the best of our knowledge, this is the first work to introduce deep learning approaches to multi-dial meter reading, and perform experiments on unconstrained images. We achieved a 100.0% F1-score on the dial detection stage with both Faster R-CNN and YOLO, while the recognition rates reached 93.6% for dials and 75.25% for meters using Faster R-CNN (ResNext-101).

An approach is given for solving large linear systems that combines Krylov methods with use of two different grid levels. Eigenvectors are computed on the coarse grid and used to deflate eigenvalues on the fine grid. GMRES-type methods are first used on both the coarse and fine grids. Then another approach is given that has a restarted BiCGStab (or IDR) method on the fine grid. While BiCGStab is generally considered to be a non-restarted method, it works well in this context with deflating and restarting. Tests show this new approach can be very efficient for difficult linear equations problems.

Despite the improvements in helmet technology, helmets may prevent skull fractures, but they do not prevent concussions.

The present invention relates to a compound of formula A, wherein R is alkyl. Compound A may be used as an intermediate in the preparation of O-desmethyl venlafaxine or a salt thereof, and the present invention provides such a preparation, as well as a process for preparing the compound of formula A.

Disclosed herein is a method for producing an alcohol and an amine from an amide under an atmosphere of hydrogen with the use of, as a catalyst, a ruthenium complex that is easily prepared, easy to handle, and relatively cheaply obtained. Specifically, the method is a method for producing an alcohol and/or an amine from an amide compound under an atmosphere of hydrogen with the use of as a catalyst, a ruthenium carbonyl complex represented by the following general formula (1): RuXY(CO)(L) (1) wherein X and Y may be the same or different from each other and each represents an anionic ligand and L represents a tridentate aminodiphosphine ligand containing two phosphino groups and a —NH— group.

The invention relates to a method for producing nitrobenzene, in which crude nitrobenzene is first produced by nitrating benzene and said crude nitrobenzene is then washed in succession in at least one acid wash, in at least one alkaline wash and in at least one neutral wash, at least one additional wash with an aqueous solution of a potassium salt being interposed between the last alkaline wash and the first neutral wash.

A nonmetallic compound having an ionic bond with a halide ion is used as a catalyst for living radical polymerization. Even if a radical initiator is not used, a monomer can be subjected to a radical polymerization to obtain a polymer having narrow molecular weight distribution. The cost of the living radical polymerization can be remarkably reduced, and it is made possible to prevent adverse effects of using a radical initiator (such as side reactions). The present invention is significantly more environmentally friendly and economically excellent than conventional living radical polymerization methods, due to advantages such as low toxicity of the catalyst, low amount of the catalyst necessary, high solubility of the catalyst, mild reaction conditions, and no coloration/no odor, etc. The catalyst can be applied to various monomers and enables synthesis of high molecular weight polymers.

A method for preparation of an aryl poly(oxalkyl) quaternary ammonium compound is provided, said method comprising steps of: 1) reacting a phenol with a dihalopolyalkylene ether under the action of a phase transfer catalyst, to obtain an arylpoly(oxalkyl) halide; 2) reacting said arylpoly(oxalkyl) halide with an amination reagent under the action of a phase transfer catalyst, to obtain an arylpoly(oxalkyl) amine; 3) reacting said arylpoly(oxalkyl) amine with an alkylation reagent, to obtain an aryl poly(oxalkyl) quaternary ammonium compound; wherein R1 is H or a C1 to C16 alkyl group, located in the ortho, meta or para position; n is an integer of 2 to 6; R2 is H or a C1 to C16 alkyl group; R3 is H or a C1 to C16 alkyl group; R4 is a C1 to C16 alkyl group; X1 is Br or Cl; X is Cl, Br, or I. The preparation method according to the present invention requires low temperature and low pressure, the reaction time is short, and an overall yield can reach 75%. The operation is simple, the cost is low, and the product can be separated easily and have a purity of pharmaceutical grade, thereby facilitating the large-scale production.

Provided is a method for stably and economically producing xylylenediamine with a high yield and long catalyst service life by hydrogenating dicyanobenzene that is obtained by ammoxidating xylene. By bringing an aqueous basic solution into contact with a dicyanobenzene-absorbed liquid, which is obtained by bringing an ammoxidation reaction gas into contact with an organic solvent, under specified temperature conditions, and subjecting a base and a carboxylic acid in the dicyanobenzene-absorbed liquid to a neutralization reaction so as to form an aqueous phase that contains a water-soluble salt, and then subjecting an organic phase and the aqueous phase to liquid-liquid separation so as to remove the aqueous phase, it is possible to remove the carboxylic acid contained in the dicyanobenzene-absorbed liquid with high selectivity while inhibiting loss of the dicyanobenzene. By subjecting the raw material dicyanobenzene, which is obtained by separating low boiling point compounds from the post liquid-liquid separation organic phase by distillation under reduced pressure, to hydrogenation, xylylenediamine is produced with a high yield and the service life of the hydrogenation catalyst is extended.

Provided are an anti-static and anti-microbial surface treatment agent including a quaternary ammonium salt compound as an active ingredient and a method of preventing a polymer fiber from developing static electricity by using the surface treatment agent. The quaternary ammonium salt compound has excellent anti-static and anti-microbial effects for the prevention or improvement of static electricity in a polymer fiber. Accordingly, the quaternary ammonium salt compound is suitable for use as a fabric softener, or an anti-static agent, and also, provides anti-microbial effects to a polymer fiber.

The invention relates to a method for preparing ring-halogenated N,N-dialkylbenzylamines and intermediates obtainable therefrom for preparing agrochemicals and pharmaceutically active ingredients.

A system and method assesses and manages risk of an operation of a user. A rules engine of computer executable instructions stored in the storage device determines at least one of a safety risk measurement based on key performance indicators, an operational safety risk measurement for the operation as a function of the operational safety risk measurement information stored in a storage device and/or a conditional safety risk measurement for the operation as a function of the conditional safety risk measurement information stored in the storage device. A processor connected to the storage device executes the rules engine. An output interface connected to the processor indicates the determined safety risk for the operation.

Processing metadata includes storing, in a data storage system, a specification for each of multiple sources, each specification including information identifying one or more data elements of the corresponding source; and processing, in a data processing system coupled to the data storage system, data elements from the sources, including generating a set of rules for each source based on a corresponding one of the stored specifications, and matching data elements of different sources and determining a quality metric characterizing a given match between a first data element of a first source and a second data element of a second source according to the set of rules generated for the first source and the set of rules generated for the second source.

The current application is directed to monitoring subsystems, and monitoring methods incorporated within the monitoring subsystems, that monitor operation of devices and systems in order to identify normal states and to quickly determine when a device or system transitions from a normal state to an abnormal state. The methods and monitoring components to which the current application is directed employ self-organizing maps and moving-average self-organizing maps to both characterize normal system behavior and to identify transitions to abnormal system behaviors.

A system and method for providing more than two levels of classification distinction of a user state are provided. The first and second general states of a user are sensed. The first general state is classified as either a first state or a second state, and the second general state is classified as either a third state or a fourth state. The user state of the user is then classified as one of at least three different classification states.

An apparatus for selecting a motion signifying artificial feeling is provided. The apparatus includes: an feeling expression setting unit configured to set probabilities of each feeling expression behavior performed for each expression element of a robot for each predetermined feeling; a behavior combination generation unit configured to generate at least one behavior combination combined by randomly extracting the feeling expression behaviors in each expression element one by one; and a behavior combination selection unit configured to calculate an average for the probabilities of the feeling expression behaviors included in each behavior combination for each feeling of a robot and select behavior combinations in which the average of the probabilities of the feeling expression behaviors most approximates the predetermined feeling value of a robot from each behavior combination.

A method for performing relational analysis of parsed input is employed to create a visual map of knowledge information. A title, header or subject line for an input item of information is parsed into syntactical components of at least a subject component and any predicate component(s) relationally linked as topic and subtopics. A search of topics and subtopics is carried out for each parsed component. If a match is found, then the parsed component is taken as a chosen topic/subtopic label. If no match is found, then the parsed component is formatted as a new entry in the knowledge map. A translation function for translating topics and subtopics from an original language into one or more target languages is enabled by user request or indicated user preference for display on a generated visual map of knowledge information.

A computer-implemented method for classifying documents for data loss prevention may include 1) identifying training documents for a machine learning classifier configured for data loss prevention, 2) performing a semantic analysis on training documents to identify topics within the set training documents, 3) applying a similarity metric to the topics to identify at least one unrelated topic with a similarity to the other topics within the plurality of topics, as determined by the similarity metric, that falls below a similarity threshold, 4) identifying, based on the semantic analysis, at least one irrelevant training document within the set of training documents in which a predominance of the unrelated topic is above a predominance threshold, and 5) excluding the irrelevant training document from the set of training documents based on the predominance of the unrelated topic within the irrelevant training document. Various other methods, systems, and computer-readable media are also disclosed.

An apparatus for recognizing a representative user behavior includes a unit-data extracting unit configured to extract at least one unit data from sensor data, a feature-information extracting unit configured to extract feature information from each of the at least one unit data, a unit-behavior recognizing unit configured to recognize a respective unit behavior for each of the at least one unit data based on the feature information, and a representative-behavior recognizing unit configured to recognize at least one representative behavior based on the respective unit behavior recognized for each of the at least one unit data.

Systems and methods are disclosed that may be implemented for network management system (NMS) configuration management support for network devices using a learning and natural language processing application to capture the usage and behavior of the Command Line Interface (CLI) of a network device with the aid of a CLI knowledge model, which in one example may be ontology-based.

Systems and methods for recommending media content items are provided. In some implementations, a method includes, identifying a first set of media items selected by a first plurality of users; causing a second set of media items to be displayed to a second user not included in the first plurality of users in accordance with the first set of media items. The first set of media items and the second set of media items are associated with a same media item category. In some implementations, the method optionally includes, identifying the second set of media items without regard to media content item selection history associated with the second user. In some implementations, the first and second sets of media items are news items.

An approach is provided for contextual content suggestion. A recommendation platform processes and/or facilitates a processing of contextual information associated with at least one device to determine one or more locations, one or more contextual parameter values, or a combination thereof. The recommendation platform also determines popularity data associated with one or more content items with respect to the one or more locations, the one or more contextual parameter values, or a combination. The popularity data is determined from one or more other devices sharing at least substantially the one or more locations, the one or more contextual parameter values, or a combination thereof. The recommendation platform then causes, at least in part, a recommendation of the one or more content items to the at least one device based, at least in part, on the popularity information.

To provide a latent variable model estimation apparatus capable of implementing the model selection at high speed even if the number of model candidates increases exponentially as the latent state number and the kind of the observation probability increase. A variational probability calculating unit 71 calculates a variational probability by maximizing a reference value that is defined as a lower bound of an approximation amount, in which Laplace approximation of a marginalized log likelihood function is performed with respect to an estimator for a complete variable. A model estimation unit 72 estimates an optimum latent variable model by estimating the kind and a parameter of the observation probability with respect to each latent state. A convergence determination unit 73 determines whether a reference value, which is used by the variational probability calculating unit 71 to calculate the variational probability, converges.

An information providing apparatus for vehicle has a remaining capacity detecting section 110 that detects a remaining capacity of a battery; a power consumption amount detecting section 130 that detects a power consumption amount of the battery; a power consumption amount history generating section 130 that generates a power consumption amount history on the basis of the power consumption amount detected by the power consumption amount detecting section 130; a charge necessity judgment information generating section 130 that generates, on the basis of the power consumption amount history generated by the power consumption amount history generating section 130, charge necessity judgment information which is information for user's judgment about whether or not charging of the battery is necessary; and a providing section 150 that provides information of the remaining capacity of the battery and the charge necessity judgment information with these information correlated with each other to the user. The information providing apparatus can properly provide the information for user's judgment about whether or not charging of the battery to the user.

In one embodiment, a system includes a data collection system configured to collect a data from a control system by using an offline mode of operations. The system further includes a configuration management system configured to manage a hardware configuration and a software configuration for the control system based on the data. The system additionally includes a rule engine configured to use the data as input and to output a health assessment by using a rule database, and a report generator configured to provide a health assessment for the control system.

A computer implemented method of constructing formal definitions in intelligent glossaries for interpreting text, comprising the steps of: providing at least one Distinction having a Boundary, an Indication, a Counter-indication and a Frame; modeling each Distinction as a diagram to provide a Distinction Model; verifying each distinction model as being an instantiation of a generic Distinction Pattern; providing at least one Arrangement made of nonintersecting Marks of Distinction containing Indications from the verified Distinction Model; writing at least one Formulation for each Indication appearing in verified Distinction model and Arrangement, providing well-founded Indications; calculating precise Formulations in Natural Language from well-founded Indications by substituting Variables symbols and/or replacing Constants symbols to transform imprecise Formulations into precise Formulations; selecting a Definition type and embedding at least one precise Formulation and Definition type as a formal Definition in an Intelligent Glossary to provide computerized Semantic Systems of Intelligent Glossaries.

A data warehouse is constructed using the relational mapping of a transactional database without reconstructing the data relationships of the transactional database. First, an application programmer analyzes an object model in order to describe facts and dimensions using the objects, attributes, and paths of the object model. Each of the dimensions has an identifier that correlates an item in the transactional database to a dimension record in the data warehouse. The fact and dimension descriptions are saved to a description file. Second, a Data Warehouse Engine (DWE) then access the description file and uses the object model, fact and dimension descriptions, and object-relational mapping to map transactional data to the data warehouse.

A system and method is described for use with a data grid cluster, which uses cluster quorum to prevent split brain scenario. The data grid cluster includes a plurality of cluster nodes, each of which runs a cluster service. Each cluster service collects and maintains statistics regarding communication flow between its cluster node and the other cluster nodes in the data grid cluster. The statistics are used to determine a status associated with other cluster nodes in the data grid cluster whenever a disconnect event happens. The data grid cluster is associated with a quorum policy, which is defined in a cache configuration file, and which specifies a time period that a cluster node will wait before making a decision on whether or not to evict one or more cluster nodes from the data grid cluster.

Processes for continuous preparation of bioproducts are described herein. The processes include contacting fatty acid glycerides with alcohols in the presence of an acidic heterogeneous catalyst and separating the fatty acid alkyl esters from the reaction products.

Dental compositions are provided comprising a compound of Formula (I) or a pharmaceutically acceptable salt thereof: wherein n is an integer from about 2 to about 5.

A method of forming a product from an oil feedstock, such as a biodiesel product, and a heterogeneous catalyst system used to form said product is disclosed. This catalyst system, which has a high tolerance for the presence of water and free fatty acids (FFA) in the oil feedstock, may simultaneously catalyze both the esterification of FAA and the transesterification of triglycerides present in the oil feedstock. The catalyst system is comprised of a mixture of zinc oxide and a second metal oxide. The zinc oxide includes a mixture of amorphous zinc oxide and zinc oxide nanocrystals, the zinc nanocrystals having a mean grain size between about 20 and 80 nanometers with at least one of the nanocrystals including a mesopore having a diameter of about 5 to 15 nanometers. Preferably, the second metal oxide is a lanthanum oxide, the lanthanum oxide being selected as one from the group of La2CO5, LaOOH, and combinations or mixtures thereof.

The current invention describes processes for obtaining of concentrates of esters of eicosapentaenoic acid and docosahexaenoic acid for their use in massive and regular human consumption either as a pharmaceutical ingredient or as a food ingredient, which are characterized by having neutral and stable organoleptic properties, free of side effects, which are typical from marine oils derivatives, and with low content of Persistent Organic Pollutants (POP).

A method for the solvent-free fractionation of jatropha seeds having a phorbol ester content and at least one fraction.

The present invention relates to a method for removing phosphorus-containing compounds from triglyceride-containing compositions.

The invention relates to a continuous method for producing esters, in which at least one polyol ester of formula (I) (R1—COO)mR2 (I), where R1 represents hydrogen or an optionally substituted hydrocarbon group containing 1 to 50 carbon atoms, R2 represents an optionally substituted hydrocarbon group containing 2 to 10 carbon atoms, and m represents a number from 2 to 10 and is smaller than or equal to the number of carbon atoms in R2, is reacted with at least one monohydric alcohol of formula (II) R3—OH (II), where R3 represents an optionally substituted hydrocarbon group containing 1 to 30 C atoms, using microwave radiation in a reaction tube, the longitudinal axis of which extends in the direction of propagation of the microwaves of a single-mode microwave applicator, so as to obtain at least one ester of formula (III) R1—COO—R3 (III), where R1 and R3 have the meanings indicated above.

Methods are provided for refining natural oil feedstocks and producing dibasic esters and/or dibasic acids. The methods comprise reacting a terminal olefin with an internal olefin in the presence of a metathesis catalyst to form a dibasic ester and/or dibasic acid. In certain embodiments, the olefin esters are formed by reacting the feedstock in the presence of a metathesis catalyst under conditions sufficient to form a metathesized product comprising olefins and esters, separating the olefins from the esters in the metathesized product, and transesterifying the esters in the presence of an alcohol to form a transesterified product having olefin esters.

A method for preparing 13C labeled plasmalogens as represented by Formula B: The method involves producing a 13C labeled cyclic plasmalogen precursor of Formula A: and conversion of the precursor to a plasmalogen of Formula B.

Described herein are nitrated lipids and methods of making and using the nitrated lipids.

A method for manufacturing a refined fat or oil, including: carrying out a first steam treatment of bringing a fat or oil into contact with water vapor; and subsequently carrying out a second steam treatment of bringing the fat or oil having a temperature lower by 10° C. or more than a temperature of the fat or oil in the first steam treatment into contact with water vapor in the presence of an organic acid.

Methods and related systems efficiently and effectively recover a significant amount of valuable, useable oil from byproducts formed during a dry milling process used for producing ethanol. The method may include forming a concentrate from the byproduct and recovering oil from the concentrate. The step of forming the concentrate may comprise evaporating the byproduct using a multi-stage evaporator, as well as recovering the oil before the final stage of the evaporator. Further, the step of recovering oil from the concentrate may comprise using a centrifuge and, in particular, a disk stack centrifuge. Other aspects include related methods and subsystems for recovering oil.

The invention relates to ceramide dimers which are constructed from two ceramide molecules which are crosslinked to each other via their lipophilic end. The ceramide molecules thereby have at least one hydrophilic group at their hydrophilic end for increasing the hydration shell of the dimer. The ceramide dimers according to the invention can be used as pharmaceutical preparation or as cosmetic preparation.

Described herein are dicarboxylate-capped estolide compound and methods of making the same. Exemplary dicarboxylate-capped estolide compounds include those of the formula x is, independently for each occurrence, an integer selected from 0 to 20; y is, independently for each occurrence, an integer selected from 0 to 20; W is, independently for each occurrence, selected from —CH2— and —CH═CH—; z is an integer selected from 1 to 40; n is an integer equal to or greater than 0; R5 is selected from hydrogen, optionally substituted alkyl that is saturated or unsaturated, and branched or unbranched, and an estolide residue; and R2 is selected from hydrogen and optionally substituted alkyl that is saturated or unsaturated, and branched or unbranched, wherein each fatty acid chain residue of said at least one compound is independently optionally substituted.

The present invention provides a method for performing regeneration of a decolorization capacity of waste clay that has been used for purification of fats and oils, and production of a thermally recyclable compound as a biofuel from oily ingredients in the waste clay at the same time in a convenient manner. That is, a method for producing purified fats and oils of the invention includes: a method for producing regenerated clay including the steps of mixing waste clay that has been used for purification of fats and oils, lower alcohol, and an acidic catalyst; and performing extraction of oily ingredients from the waste clay, and an esterification reaction between the fats and oils and/or a free fatty acid in the oily ingredients and the lower alcohol at the same time so as to regenerate a decolorization capacity of the waste clay; regenerated clay that is produced by the method for producing the regenerated clay; and a process of decolorizing the fats and oils using the regenerated clay.