We present the correspondence between Lax integrable systems with spectral parameter on a Riemann surface, and Conformal Field Theories, in quite general set-up suggested earlier by the author. This correspondence turns out to give a prequantization of the integrable systems in question.

Several problems of artificial intelligence, such as predictive learning, formal concept analysis or inductive logic programming, can be viewed as a special case of half-space separation in abstract closure systems over finite ground sets. For the typical scenario that the closure system is given via a closure operator, we show that the half-space separation problem is NP-complete. As a first approach to overcome this negative result, we relax the problem to maximal closed set separation, give a greedy algorithm solving this problem with a linear number of closure operator calls, and show that this bound is sharp. For a second direction, we consider Kakutani closure systems and prove that they are algorithmically characterized by the greedy algorithm. As a first special case of the general problem setting, we consider Kakutani closure systems over graphs, generalize a fundamental characterization result based on the Pasch axiom to graph structured partitioning of finite sets, and give a sufficient condition for this kind of closures systems in terms of graph minors. For a second case, we then focus on closure systems over finite lattices, give an improved adaptation of the greedy algorithm for this special case, and present two applications concerning formal concept and subsumption lattices. We also report some experimental results to demonstrate the practical usefulness of our algorithm.

For future Internet of Things (IoT)-based Big Data applications (e.g., smart cities/transportation), wireless data collection from ubiquitous massive smart sensors with limited spectrum bandwidth is very challenging. On the other hand, to interpret the meaning behind the collected data, it is also challenging for edge fusion centers running computing tasks over large data sets with limited computation capacity. To tackle these challenges, by exploiting the superposition property of a multiple-access channel and the functional decomposition properties, the recently proposed technique, over-the-air computation (AirComp), enables an effective joint data collection and computation from concurrent sensor transmissions. In this paper, we focus on a single-antenna AirComp system consisting of $K$ sensors and one receiver (i.e., the fusion center). We consider an optimization problem to minimize the computation mean-squared error (MSE) of the $K$ sensors' signals at the receiver by optimizing the transmitting-receiving (Tx-Rx) policy, under the peak power constraint of each sensor. Although the problem is not convex, we derive the computation-optimal policy in closed form. Also, we comprehensively investigate the ergodic performance of AirComp systems in terms of the average computation MSE and the average power consumption under Rayleigh fading channels with different Tx-Rx policies. For the computation-optimal policy, we prove that its average computation MSE has a decay rate of $O(1/sqrt{K})$, and our numerical results illustrate that the policy also has a vanishing average power consumption with the increasing $K$, which jointly show the computation effectiveness and the energy efficiency of the policy with a large number of sensors.

Restless multi-armed bandits are a class of discrete-time stochastic control problems which involve sequential decision making with a finite set of actions (set of arms). This paper studies a class of constrained restless multi-armed bandits (CRMAB). The constraints are in the form of time varying set of actions (set of available arms). This variation can be either stochastic or semi-deterministic. Given a set of arms, a fixed number of them can be chosen to be played in each decision interval. The play of each arm yields a state dependent reward. The current states of arms are partially observable through binary feedback signals from arms that are played. The current availability of arms is fully observable. The objective is to maximize long term cumulative reward. The uncertainty about future availability of arms along with partial state information makes this objective challenging. Applications for CRMAB abound in the domain of cyber-physical systems. This optimization problem is analyzed using Whittle's index policy. To this end, a constrained restless single-armed bandit is studied. It is shown to admit a threshold-type optimal policy, and is also indexable. An algorithm to compute Whittle's index is presented. Further, upper bounds on the value function are derived in order to estimate the degree of sub-optimality of various solutions. The simulation study compares the performance of Whittle's index, modified Whittle's index and myopic policies.

We present a sound and complete method for the verification of qualitative liveness properties of replicated systems under stochastic scheduling. These are systems consisting of a finite-state program, executed by an unknown number of indistinguishable agents, where the next agent to make a move is determined by the result of a random experiment. We show that if a property of such a system holds, then there is always a witness in the shape of a Presburger stage graph: a finite graph whose nodes are Presburger-definable sets of configurations. Due to the high complexity of the verification problem (non-elementary), we introduce an incomplete procedure for the construction of Presburger stage graphs, and implement it on top of an SMT solver. The procedure makes extensive use of the theory of well-quasi-orders, and of the structural theory of Petri nets and vector addition systems. We apply our results to a set of benchmarks, in particular to a large collection of population protocols, a model of distributed computation extensively studied by the distributed computing community.

One of the main open problems in the qualitative theory of real planar differential systems is the study of limit cycles. In this article, we present an algorithmic approach for detecting how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems via the averaging method. We propose four symbolic algorithms to implement the averaging method. The first algorithm is based on the change of polar coordinates that allows one to transform a considered differential system to the normal form of averaging. The second algorithm is used to derive the solutions of certain differential systems associated to the unperturbed term of the normal of averaging. The third algorithm exploits the partial Bell polynomials and allows one to compute the integral formula of the averaged functions at any order. The last algorithm is based on the aforementioned algorithms and determines the exact expressions of the averaged functions for the considered differential systems. The implementation of our algorithms is discussed and evaluated using several examples. The experimental results have extended the existing relevant results for certain classes of differential systems.

Rescue vessels are the main actors in maritime safety and rescue operations. At the same time, aerial drones bring a significant advantage into this scenario. This paper presents the research directions of the AutoSOS project, where we work in the development of an autonomous multi-robot search and rescue assistance platform capable of sensor fusion and object detection in embedded devices using novel lightweight AI models. The platform is meant to perform reconnaissance missions for initial assessment of the environment using novel adaptive deep learning algorithms that efficiently use the available sensors and computational resources on drones and rescue vessel. When drones find potential objects, they will send their sensor data to the vessel to verity the findings with increased accuracy. The actual rescue and treatment operation are left as the responsibility of the rescue personnel. The drones will autonomously reconfigure their spatial distribution to enable multi-hop communication, when a direct connection between a drone transmitting information and the vessel is unavailable.

We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of hybrid dynamical systems. The hybrid version of (i) asserts that a globally-defined "hybrid complete Lyapunov function" exists for every hybrid system in this class. Motivated by mechanics and control settings where physical or engineered events cause abrupt changes in a system's governing dynamics, our results apply to a large class of Lagrangian hybrid systems (with impacts) studied extensively in the robotics literature. Viewed formally, these results generalize those of Conley and Franks for continuous-time and discrete-time dynamical systems, respectively, on metric spaces. However, we furnish specific examples illustrating how our statement of sufficient conditions represents merely an early step in the longer project of establishing what formal assumptions can and cannot endow hybrid systems models with the topologically well characterized partitions of limit behavior that make Conley's theory so valuable in those classical settings.

By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $Sigma$ and a stochastic memoryless map $Psi$. After that, we extend the result to the class of large scale systems in which: $Sigma$ consists of many sub-systems; and $Psi$ consists of many "stochastic actuators" and "probability controllers" that control the actuator's output events. We will demonstrate the proposed approach by showing the design procedures to globally stabilize the manufacturing systems while locally balance the stock levels in any production process.

By Evan H. DeLucia Courtesy of EOS Critics of biofuels like ethanol argue they are an unsustainable use of land. But with careful management, next-generation grass-based biofuels can net climate savings and improve their ecosystems. As the world seeks strategies … Continue reading →

Biocidal compositions and their use in aqueous media, such as metalworking fluids, the compositions comprising a biocidal agent; and a non-biocidal primary amino alcohol compound of the formula (I); wherein R1, R2, R3, R4, and R5 are as defined herein.

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.

Methods and arrangements for conducting a search using query logs. A query log is consulted and query rewrite rules are learned automatically based on data in the query log. The learning includes obtaining click-through data present in the query log.

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.

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.

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.

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 radiation curable coating systems on the basis of aqueous polyurethane dispersions, to a method for the production thereof, to the use of the coating systems as paints and/or adhesives, and to objects and substrates provided with said paints and/or adhesives.

A coating/sealant system that includes a coating and a sealant deposited over at least a portion of the coating, in which the coating includes a reaction product formed from reactants comprising a phosphated epoxy resin and a curing agent, and the sealant includes a sulfur-containing polymer.

The invention in particular has as an object detecting incompatibility between equipment items of a on-board system. A logic interface associated with one equipment item comprises at least one input while a logic interface associated with another equipment item comprises at least one output. The input and the output are connected. After a minimal data definition level associated with the input and a data definition level associated with the output have been obtained (505), the said minimal data definition level associated with the input is compared (515) with the said data definition level associated with the output. Following this comparison, if the said minimal data definition level associated with the input is lower than the said data definition level associated with the output, an alarm indicating an incompatibility of these two equipment items is generated (545).

The present inventions are related to systems and methods for data processing, and more particularly to systems and methods for variable rate coding in a data processing system.

An error control encoding system produces a codeword from a data word, where the resulting codeword includes the data word and three or more parity segments produced using the data word. The system includes a first encoder to encode the data word in two or more first data segments in order to produce two or more first parity segments, where each of the two or more first data segments includes a respective sequential portion of the data word. The system includes a second encoder to encode the data word in one or more second data segments in order to produce a corresponding one or more second parity segments, where each of the one or more second data segments includes a respective sequential portion of the data word, and each of the one or more second data segments also includes a sequential portion of the data included in a plurality of the two or more first data segments. Further, the system includes a controller configured to provide the two or more first data segments of the data word to the first encoder for encoding and to provide the one or more second data segments of the data word to the second encoder for encoding.

Certain exemplary embodiments can provide a system, machine, device, manufacture, circuit, composition, and/or user interface adapted for and/or resulting from, and/or a method and/or machine-readable medium comprising machine-implementable instructions for, activities that can comprise and/or relate to, in a treatment zone, reacting an oxygen-comprising gas, one or more selected ferric/ferrous chelates, one or more selected nitrates and/or nitrites, and/or anaerobic wastewater.

Apparatus and a method for decomposing a body of a deceased person, as an alternative to traditional cremation. The apparatus includes a primary vessel where the body is treated with a highly basic solvent to render the body into skeletal remains and liquid remains. A clamp is applied to the skull during processing for solvent access to the skull. A secondary vessel is used to receive the liquid remains from the primary vessel and further treat them. During this further treatment, the skeletal remains left in the primary vessel after the liquefied portion has been transferred to the secondary vessel, can be treated to be decolorized and deodorized, and then returned to the decedent's next of kin as ash-like material.

Various embodiments of the present invention provide systems and methods for data processing. As an example, a data processing circuit is disclosed that includes a data detector circuit. The data detector circuit includes an anti-causal noise predictive filter circuit and a data detection circuit. In some cases, the anti-causal noise predictive filter circuit is operable to apply noise predictive filtering to a detector input to yield a filtered output, and the data detection circuit is operable to apply a data detection algorithm to the filtered output derived from the anti-causal noise predictive filter circuit.

Solving computational problems may include generating a logic circuit representation of the computational problem, encoding the logic circuit representation as a discrete optimization problem, and solving the discrete optimization problem using a quantum processor. Output(s) of the logic circuit representation may be clamped such that the solving involves effectively executing the logic circuit representation in reverse to determine input(s) that corresponds to the clamped output(s). The representation may be of a multiplication circuit. The discrete optimization problem may be composed of a set of miniature optimization problems, where each miniature optimization problem encodes a respective logic gate from the logic circuit representation. A multiplication circuit may employ binary representations of factors, and these binary representations may be decomposed to reduce the total number of variables required to represent the multiplication circuit.

Apparatus and method for processing linear systems of equations and finding a n×1 vector x satisfying Ax=b where A is a symmetric, positive-definite n×n matrix corresponding to n×n predefined high-precision elements and b is an n1 vector corresponding to n predefined high-precision elements. A first iterative process generates n low-precision elements corresponding to an n×1 vector xl satisfying Alxl=bl where Al, bl are elements in low precision. The elements are converted to high-precision data elements to obtain a current solution vector x. A second iterative process generates n low-precision data elements corresponding to an n×1 correction vector dependent on the difference between the vector b and the vector product Ax. Then there is produced from the n low-precision data elements of the correction vector respective high-precision data elements of an n×1 update vector u. The data elements of the current solution vector x are updated such that x=x+u.

Techniques for medium access control. Some techniques include receiving, at a first computing device, a solicitation for at least a first medium access request that specifies at least one time period for transmitting the first medium access request to the second computing device; encoding the first medium access request at least in part by using a compressive sensing encoding technique to obtain a first encoded medium access request; and transmitting the first encoded medium access request to the second computing device during the at least one time period specified in the received solicitation.

A variety of biomedical devices are provided which include thiol-ene or thiol-yne shape memory polymers. The biomedical devices of the invention are capable of exhibiting shape memory behavior at physiological temperatures and may be used in surgical procedures. Methods of making the devices of the invention are also provided.

A memory system includes a CPU that communicates commands and addresses to a main-memory module. The module includes a buffer circuit that relays commands and data between the CPU and the main memory. The memory module additionally includes an embedded processor that shares access to main memory in support of peripheral functionality, such as graphics processing, for improved overall system performance. The buffer circuit facilitates the communication of instructions and data between CPU and the peripheral processor in a manner that minimizes or eliminates the need to modify CPU, and consequently reduces practical barriers to the adoption of main-memory modules with integrated processing power.

The various implementations described herein include systems, methods and/or devices used to enable multipass programming in buffers implemented in non-volatile data storage systems (e.g., using one or more flash memory devices). In one aspect, a portion of memory (e.g., a page in a block of a flash memory device) may be programmed many (e.g., 1000) times before an erase is required. Some embodiments include systems, methods and/or devices to integrate Bloom filter functionality in a non-volatile data storage system, where a portion of memory storing one or more bits of a Bloom filter array may be programmed many (e.g., 1000) times before the contents of the portion of memory need to be moved to an unused location in the memory.

A method for sharing peripheral devices in dual operating systems for an electronic device having at least one peripheral device is provided. The method includes: receiving a setting value for the peripheral device under the first operating system from a user; activating a second operating system; transmitting the setting value to the second operating system; and switching from the first operating system to the second operating system, wherein the second operating system sets the peripheral device with the setting value and enables the electronic device to operate under the second operating system.

A method for efficient dispatch/completion of a work element within a multi-node data processing system. The method comprises: selecting specific processing units from among the processing nodes to complete execution of a work element that has multiple individual work items that may be independently executed by different ones of the processing units; generating an allocated processor unit (APU) bit mask that identifies at least one of the processing units that has been selected; placing the work element in a first entry of a global command queue (GCQ); associating the APU mask with the work element in the GCQ; and responsive to receipt at the GCQ of work requests from each of the multiple processing nodes or the processing units, enabling only the selected specific ones of the processing nodes or the processing units to be able to retrieve work from the work element in the GCQ.

Emulsions, and processes for making the emulsions, useful for imparting water resistance to gypsum products are disclosed. Process for making the emulsion and gypsum products made from the emulsion are also disclosed. The emulsions of the invention include at least one paraffin wax and a hydrophilic metallic salt. The emulsions of the invention may further include a saponifiable wax substitute for montan wax. The emulsions of the invention may further include a biocide.

Emulsions, and processes for making the emulsions, useful for imparting water resistance to gypsum products are disclosed. Process for making the emulsion and gypsum products made from the emulsion are also disclosed. The emulsions of the invention include at least one paraffin wax and a hydrophilic metallic salt. The emulsions of the invention may further include a saponifiable wax substitute for montan wax. The emulsions of the invention may further include a biocide.

A computer-implemented method is provided for evaluating team performance in a product development environment. The method includes receiving a plurality of points of effort made by a team over a plurality of days in a time period, computing a slope associated with a line of best fit through the plurality of points of effort over the plurality of days, computing a deviation of the slope from an ideal slope corresponding to a desired performance rate for the team, and generating a display illustrating at least one of the slope, the ideal slope or the deviation.

Computer-implemented methods for analyzing computer programs written in semi-structured languages are disclosed. The method is based on unification of the two classic forms of program flow analysis, control flow and data flow analysis. As such, it is capable of substantially increased precision, which increases the effectiveness of applications such as automated parallelization and software testing. Certain implementations of the method are based on a process of converting source code to a decision graph and transforming that into one or more alpha graphs which support various applications in software development. The method is designed for a wide variety of digital processing platforms, including highly parallel machines. The method may also be adapted to the analysis of (semi-structured) flows in other contexts including water systems and electrical grids.

Methods and systems to identify and reproduce concurrency bugs in multi-threaded programs are disclosed. An example method disclosed herein includes defining a data type. The data type includes a first predicate associated with a first thread of a multi-threaded program that is associated with a first condition, a second predicate that is associated with a second thread of the multi-threaded program, the second predicate being associated with a second condition, and an expression that defines a relationship between the first predicate and the second predicate. The relationship, when satisfied, causes the concurrency bug to be detected. A concurrency bug detector conforming to the data type is used to detect the concurrency bug in the multi-threaded program.

The present application relates to perfume raw materials, perfume delivery systems and consumer products comprising such perfume raw materials and/or such perfume delivery systems, as well as processes for making and using such perfume raw materials, perfume delivery systems and consumer products. Such perfume raw materials and compositions, including the delivery systems, disclosed herein expand the perfume communities' options as such perfume raw materials can provide variations on character and such compositions can provide desired odor profiles.

The present application relates to perfume raw materials, perfume delivery systems and consumer products comprising such perfume raw materials and/or such perfume delivery systems, as well as processes for making and using such perfume raw materials, perfume delivery systems and consumer products. Such perfume raw materials and compositions, including the delivery systems, disclosed herein expand the perfume communities' options as such perfume raw materials can provide variations on character and such compositions can provide desired odor profiles.

Navigation systems and associated methods for providing navigation services are provided. Information associated with a desired route for a vehicle, such as a route between a current location and a desired destination, may be determined. Additionally, contextual information associated with the vehicle may be identified. Based upon the desired route and the contextual information, a direction may be generated for presentation to one or more users, and the generated direction may be output for presentation.

An automated process uses a local positioning system to acquire location (i.e., position and orientation) data for one or more movable target objects. In cases where the target objects have the capability to move under computer control, this automated process can use the measured location data to control the position and orientation of such target objects. The system leverages the measurement and image capture capability of the local positioning system, and integrates controllable marker lights, image processing, and coordinate transformation computation to provide tracking information for vehicle location control. The resulting system enables position and orientation tracking of objects in a reference coordinate system.

Vehicle event recorder systems are arranged to be in constant communication with remote servers and administrators via mobile wireless cellular networks. Vehicle event recorders equipped with video cameras capture video and other data records of important events relating to vehicle use. These data are then transmitted over special communications networks having very high coverage space but limited bandwidth. A vehicle may be operated over very large region while maintaining continuous communications connections with a remote fixed server. As such, systems of these inventions may be characterized as including a mobile unit having: a video camera; a microprocessor; memory; an event trigger; and mobile wireless transceivers, and a fixed network portion including: mobile wireless cellular network, a protocol translation gateway, the Internet and an application-specific server.

Disclosed are methods, systems, and articles of manufactures for implementing physical designs by using multiple force models to iteratively morph a layout decomposition. In addition to attractive force model(s) or repulsive force model(s), the physical implementation also uses a containment force model for grouping multiple design blocks or for confining a node of a cell within the boundary of a container. Another aspect is directed at deriving a first force model at the first hierarchical level from a second force model at the second hierarchical level by directly modifying the second model based at least in part on characteristic(s) of the first hierarchical level and of the second hierarchical level. In a design with multiple hierarchies, a cell-based force model is also used to ensure child nodes of a parent cell stay within a close proximity of the parent node of the parent cell.

Quantum annealing may include applying and gradually removing disorder terms to qubits of a quantum processor, for example superconducting flux qubits of a superconducting quantum processor. A problem Hamiltonian may be established by applying control signals to the qubits, an evolution Hamiltonian established by applying disorder terms, and annealing by gradually removing the disorder terms. Change in persistent current in the qubits may be compensated. Multipliers may mediate coupling between various qubits and a global signal line, for example by applying respective scaling factors. Two global signal lines may be arranged in an interdigitated pattern to couple to respective qubits of a communicatively coupled pair of qubits. Pairs of qubits may be communicatively isolated and used to measure a response of one another to defined signals.

Computer-implemented systems and methods are provided for suggesting emoticons for insertion into text based on an analysis of sentiment in the text. An example method includes: determining a first sentiment of text in a text field; selecting first text from the text field in proximity to a current position of an input cursor in the text field; identifying one or more candidate emoticons wherein each candidate emoticon is associated with a respective score indicating relevance to the first text and the first sentiment based on, at least, historical user selections of emoticons for insertion in proximity to respective second text having a respective second sentiment; providing one or more candidate emoticons having respective highest scores for user selection; and receiving user selection of one or more of the provided emoticons and inserting the selected emoticons into the text field at the current position of the input cursor.

A method of signal processing according to one embodiment includes calculating an envelope of a first signal that is based on a low-frequency portion of a speech signal, calculating an envelope of a second signal that is based on a high-frequency portion of the speech signal, and calculating a plurality of gain factor values according to a time-varying relation between the envelopes of the first and second signal. The method includes attenuating, based on a variation over time of a relation between the envelopes of the first and second signals, at least one of the plurality of gain factor values. In one example, the variation over time of a relation between the envelopes is indicated by at least one distance among the plurality of gain factor values.

Methods and systems are described for generating media playlists, or selecting a media asset, according to a “shape” selected by a user. Specifically, a user may “shape” the playlist by designating specific sub-categories of media assets that should be presented at selected times in the playlist. The media application then interpolates the sub-categories for a media asset between the selected times such that adjacent media assets have smooth categorical transitions (e.g., feature incremental changes in the range of sub-categories).