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 $n$-vertex graphs with treewidth $k = O(n^{1/2-epsilon})$ and an arbitrary $epsilon>0$, we present a word-RAM algorithm to compute vertex separators using only $O(n)$ bits of working memory. As an application of our algorithm, we give an $O(1)$-approximation algorithm for tree decomposition. Our algorithm computes a tree decomposition in $c^k n (log log n) log^* n$ time using $O(n)$ bits for some constant $c > 0$.

We finally use the tree decomposition obtained by our algorithm to solve Vertex Cover, Independent Set, Dominating Set, MaxCut and $3$-Coloring by using $O(n)$ bits as long as the treewidth of the graph is smaller than $c' log n$ for some problem dependent constant $0 < c' < 1$.

Stockhusen and Tantau (IPEC 2013) defined the operators paraW and paraBeta for parameterised space complexity classes by allowing bounded nondeterminism with multiple read and read-once access, respectively. Using these operators, they obtained characterisations for the complexity of many parameterisations of natural problems on graphs.

In this article, we study the counting versions of such operators and introduce variants based on tail-nondeterminism, paraW[1] and paraBetaTail, in the setting of parameterised logarithmic space. We examine closure properties of the new classes under the central reductions and arithmetic operations. We also identify a wide range of natural complete problems for our classes in the areas of walk counting in digraphs, first-order model-checking and graph-homomorphisms. In doing so, we also see that the closure of #paraBetaTail-L under parameterised logspace parsimonious reductions coincides with #paraBeta-L. We show that the complexity of a parameterised variant of the determinant function is #paraBetaTail-L-hard and can be written as the difference of two functions in #paraBetaTail-L for (0,1)-matrices. Finally, we characterise the new complexity classes in terms of branching programs.

We develop a supervised machine learning algorithm that is able to learn topological phases for finite condensed matter systems from bulk data in real lattice space. The algorithm employs diagonalization in real space together with any supervised learning algorithm to learn topological phases through an eigenvector ensembling procedure. We combine our algorithm with decision trees and random forests to successfully recover topological phase diagrams of Su-Schrieffer-Heeger (SSH) models from bulk lattice data in real space and show how the Shannon information entropy of ensembles of lattice eigenvectors can be used to retrieve a signal detailing how topological information is distributed in the bulk. The discovery of Shannon information entropy signals associated with topological phase transitions from the analysis of data from several thousand SSH systems illustrates how model explainability in machine learning can advance the research of exotic quantum materials with properties that may power future technological applications such as qubit engineering for quantum computing.

There exist two notions of equivalence of behavior between states of a Labelled Markov Process (LMP): state bisimilarity and event bisimilarity. The first one can be considered as an appropriate generalization to continuous spaces of Larsen and Skou's probabilistic bisimilarity, while the second one is characterized by a natural logic. C. Zhou expressed state bisimilarity as the greatest fixed point of an operator $mathcal{O}$, and thus introduced an ordinal measure of the discrepancy between it and event bisimilarity. We call this ordinal the "Zhou ordinal" of $mathbb{S}$, $mathfrak{Z}(mathbb{S})$. When $mathfrak{Z}(mathbb{S})=0$, $mathbb{S}$ satisfies the Hennessy-Milner property. The second author proved the existence of an LMP $mathbb{S}$ with $mathfrak{Z}(mathbb{S}) geq 1$ and Zhou showed that there are LMPs having an infinite Zhou ordinal. In this paper we show that there are LMPs $mathbb{S}$ over separable metrizable spaces having arbitrary large countable $mathfrak{Z}(mathbb{S})$ and that it is consistent with the axioms of $mathit{ZFC}$ that there is such a process with an uncountable Zhou ordinal.

With the continued digitalization of societal processes, we are seeing an explosion in available data. This is referred to as big data. In a research setting, three aspects of the data are often viewed as the main sources of challenges when attempting to enable value creation from big data: volume, velocity and variety. Many studies address volume or velocity, while much fewer studies concern the variety. Metric space is ideal for addressing variety because it can accommodate any type of data as long as its associated distance notion satisfies the triangle inequality. To accelerate search in metric space, a collection of indexing techniques for metric data have been proposed. However, existing surveys each offers only a narrow coverage, and no comprehensive empirical study of those techniques exists. We offer a survey of all the existing metric indexes that can support exact similarity search, by i) summarizing all the existing partitioning, pruning and validation techniques used for metric indexes, ii) providing the time and storage complexity analysis on the index construction, and iii) report on a comprehensive empirical comparison of their similarity query processing performance. Here, empirical comparisons are used to evaluate the index performance during search as it is hard to see the complexity analysis differences on the similarity query processing and the query performance depends on the pruning and validation abilities related to the data distribution. This article aims at revealing different strengths and weaknesses of different indexing techniques in order to offer guidance on selecting an appropriate indexing technique for a given setting, and directing the future research for metric indexes.

We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality !L*, which has a limited edition of the contraction and permutation rules. The categorical part of the semantics is a monoidal biclosed category with a coalgebra modality, very similar to the structure of a Differential Category. We instantiate this category to finite dimensional vector spaces and linear maps via "quantisation" functors and work with three concrete interpretations of the coalgebra modality. We apply the model to construct categorical and concrete semantic interpretations for the motivating example of !L*: the derivation of a phrase with a parasitic gap. The effectiveness of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrase one, using BERT, Word2Vec, and FastText vectors and Relational tensors.

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Designology Interiors' Deanna Goguen has three bathrooms in her South Hill-area home, each with its own personality.…

Warm summer nights are on the way.…

Erin Haskell Gourde isn't afraid to mix it up a little.…

Various embodiments provide lossless compression of an enumeration space for genetic founder lines. In one embodiment, an input comprising a set of genetic founder lines and a maximum number of generations G is obtained. A set of genetic crossing templates of a height h is generated. A determination is made if at least a first genetic crossing template in the set of genetic crossing templates is redundant with respect to a second genetic crossing template in the set of genetic crossing templates. Based on the at least first genetic crossing template being redundant is redundant with respect to the second genetic crossing template, the at least first genetic crossing template is removed from the set of genetic crossing templates. This process of removing the at least first genetic crossing template from the set of genetic crossing templates the redundant creates an updated set of genetic crossing templates.

A computer implemented method for automatic chemical assay classification, the method comprising steps the computer is programmed to perform, the steps comprising: receiving a plurality of sets of parameters, each one of the received sets of parameters characterizing a respective assay of a chemical reaction, calculating a space enhancing proximity among points representative of assays of qualitatively identical chemical reactions, and representing each one of at least two of the received sets of parameters as a respective point in the calculated space, and dividing the points in the calculated space into a number of groups, according to proximity among the points in the calculated space, each group pertaining to a respective chemical reaction, thereby classifying the assays.

An electronic data tablet has a controller and transition manager. The controller is to store in a memory of the tablet virtual configuration space information for a peripheral device of a computer, and the transition manager is to control the controller to operate in a first mode and a second mode. The virtual configuration space information is stored in the tablet memory when the first mode is to be switched to the second mode. When the second mode is switched to the first mode, the virtual configuration space information is accessed to control recognition of the peripheral device of the computer without performing a re-scanning operation.

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for computing numeric representations of words. One of the methods includes obtaining a set of training data, wherein the set of training data comprises sequences of words; training a classifier and an embedding function on the set of training data, wherein training the embedding function comprises obtained trained values of the embedding function parameters; processing each word in the vocabulary using the embedding function in accordance with the trained values of the embedding function parameters to generate a respective numerical representation of each word in the vocabulary in the high-dimensional space; and associating each word in the vocabulary with the respective numeric representation of the word in the high-dimensional space.

Techniques for sorting and filtering a list in a space-constrained viewing area are described. A filter widget and a list of items are displayed in a view of an electronic display screen. In response to user input selecting the filter widget, and without changing to a different view, a filter category overlay is displayed in the view to provide various selectable filter categories. In response to selection of a filter category, a visual depiction of the selected filter category is displayed in the view. The list of items is filtered according to the selected filter category and displayed in the view without changing to any other view. Subsequently added visual depictions are linearly stacked in the view. Further, a filter modification overlay, which provides selectable filtering attributes, is displayed upon selection of a visual depiction.

Systems and methods of a 3D mobile user interface with configurable workspace management are disclosed. In one aspect, embodiments of the present disclosure include a method, which may be implemented on a system, of a three-dimensional, multi-layer user interface of a mobile device in a mobile network. User environment may include one or more layers or levels of applications, services, or accounts that are all easily accessible to and navigable by the user. For example, an indicator can be used to access a workspace in 3D representing a category or grouping of services or applications for the user. The user can customize or create a unique, non-mutually exclusive grouping, aggregation, or category of applications, services, accounts, or items. The grouping of indicators can be used to swiftly and efficiently navigate to a desired application, service, account or item, in a 3D-enabled user environment.

Disclosed herein is a method for determining a trajectory for a transfer of a spacecraft from a starting space body to a target space body with respect to a given central space body, wherein the determined trajectory is optimal with respect to a given space mission requirement to be met by the transfer of the spacecraft. The method comprises providing, according to the Pontryagin maximum principle, a physical-mathematical model relating model quantities and physical quantities representing the transfer of the spacecraft with respect to the given central space body.

Methods for creating and using space-time surrogate models of subsurface regions, such as subsurface regions containing at least one hydrocarbon formation. The created surrogate models are explicit models that may be created from implicit models, such as computationally intensive full-physics models. The space-time surrogate models are parametric with respect to preselected variables, such as space, state, and/or design variables, while also indicating responsiveness of the preselected variables with respect to time. In some embodiments, the space-time surrogate model may be parametric with respect to preselected variables as well as to time. Methods for updating and evolving models of subsurface regions are also disclosed.

A laser relay module for free space optical communications including an optical telescope for receiving and transmitting optical beams; an optical diplexer for separating transmitting and received optical beams; an optical amplifier; a modulated beacon laser for line of sight control of a plurality of communicating remote network nodes; a beacon beam detector for detecting an incoming beacon optical beam for line of sight control of the optical telescope and receiving data from other network nodes; and means for inserting an output of the modulated beacon laser into the optical telescope for transmission to another network node, and for transporting the incoming beacon optical beam to the beacon detector.

A modular, adjustable, prosthetic hip/shoulder spacer adapted to being implanted in the hip or shoulder joint; the spacer comprises a frame that supports a rotatable cylinder from which a neck extends with the ball element of the joint attached to its end, and rotating the cylinder reposition the ball in the socket; the stem is connected to the base of the frame and is implanted in the long bone (femur or humerus); the stem may be modified to include a system for delivering medication to the implantation site following surgery. The stem leg and stem base may be modified to form a modular unit to adjust the relation between a center line of the stem leg and a center line of the frame and position of the neck and ball.

Disclosed is an assembly and method for implant installation between adjacent vertebral bodies of a patient. The implant has a support body and a rotatable insert therein and the support body is curved for installation between adjacent vertebral bodies transforaminally. An installation instrument is also disclosed for removable attachment to implant and engagement with the rotatable insert to selectively permit rotation between the insert and the support body. The installation instrument extends along a longitudinal tool axis and when the installation instrument is in a first position the insert is rotationally fixed with respect to the support body and when the installation instrument is in a second position the support body may rotate with respect to the insert.

A low profile, wrappable spacer and method for maintaining a pair of elongate members in fixed, spaced relation to one another is provided. The wrappable spacer includes a flexible elongate body having oppositely facing inner and outer faces extending along laterally spaced, lengthwise extending edges between opposite ends. The inner face has an adhesive surface. At least one member extends between the edges transversely to the lengthwise extending edges. The member extends outwardly from the adhesive surface, wherein the adhesive surface is configured for adhesion to at least one of the member, the elongate members or the outer face.

A method for reading a track of data may include positioning a read head at an initial position relative to the track of data and obtaining initial track signals, filtering the initial track signals, positioning the read head at an initial subsequent position relative to the track of data and obtaining initial subsequent track signals, and filtering the initial subsequent track signals. In an initial equalization, the filtered initial track signals and the filtered initial subsequent track signals are equalized to obtain equalized track signals. The read head is positioned at a further subsequent position relative to the track of data and further subsequent track signals are obtained The further subsequent track signals are filtered. In a subsequent equalization, previously obtained equalized track signals and the filtered further subsequent track signals are equalized. A storage device operating according to the method may have an equalizer in hardware or firmware.

The spacer is adapted for a rolling bearing comprising an inner ring, an outer ring and at least one row of contact rollers disposed between raceways provided on the rings. The spacer comprises opposite inner and outer portions, facing one another and a lateral portion extending transversally between the inner and outer portions and connected to said portions. The inner and outer portions delimit together with the lateral portion a pocket configured to receive a contact roller. The pocket is laterally open on the side opposite to the lateral portion.

A perforated collapsible spacer controllably takes up space between two bearings on an automotive pinion. The perforated collapsible spacer is formed from a steel sheet having longitudinal edges that are joined together in a form of a tube having longitudinal perforated sections formed in its central portion. As a pinion nut is tightened, an axial clamping force is applied to the collapsible spacer that is located between tail and head bearing cones, where the central portion of the collapsible spacer is caused to buckle, so as to adjust the final space between the bearing cones while a spring force is maintained on the bearings. Yield points of the central portion with the perforated sections that buckle, are controllable depending on the steel sheet material thickness, and the size, shape and quantity of perforations in the steel sheet.

An intervertebral fusion cage that is adapted to contain an inserter within its inner volume during insertion of the cage.

An exemplary center housing rotating assembly includes a turbine wheel (260); a compressor wheel (240); a center housing (210) that includes a through bore (215), extending from a compressor end to a turbine end along a bore axis, and a recess (217), adjacent the bore, in a plane orthogonal to the bore axis; a bearing assembly (230) positioned in the bore that includes a keyway (233); and an anti-rotation component (280) seated in the recess and at least partially in the keyway to restrict rotation of the bearing assembly in the bore. Various other exemplary devices, systems, methods, etc., are also disclosed.

A display apparatus includes a lower substrate, an upper substrate, a spacer and an image display layer. The spacer includes a main spacer, a first sub-spacer and a second sub-spacer. The main spacer has a height greater than that of the first and second sub-spacers. The second sub-spacer has an area wider than that of the main spacer and the first sub-spacer.

An improved grid for a nuclear reactor fuel assembly that has an egg-crate base grid as the primary support structure with each support cell of the base grid that supports a fuel rod having a lock-support sleeve that is rotatable within the support cell between a first and second orientation. In the first orientation the lock-support sleeve fits loosely within the support cell of the base grid and respectively, loosely receives the fuel rods that are loaded therein. The lock-support sleeves are then rotated to a second orientation that locks the fuel rods axially within the support cells.

A method of fabricating a nuclear fuel comprising a fissile material, one or more hollow microballoons, a phenolic resin, and metal matrix. The fissile material, phenolic resin and the one or more hollow microballoons are combined. The combined fissile material, phenolic resin and the hollow microballoons are heated sufficiently to form at least some fissile material carbides creating a nuclear fuel particle. The resulting nuclear fuel particle comprises one or more fission product collection spaces. In a preferred embodiment, the fissile material, phenolic resin and the one or more hollow microballoons are combined by forming the fissile material into microspheres. The fissile material microspheres are then overcoated with the phenolic resin and microballoon. In another preferred embodiment, the fissile material, phenolic resin and the one or more hollow microballoons are combined by overcoating the microballoon with the fissile material, and phenolic resin.

Embodiments of the present disclosure can include devices for storing and exchanging color space encoded images. The encoded images can store input data into high capacity multi-colored composite two-dimensional pictures having different symbols organized in specific order using sets in a color space. The encoding can include performing two-level error correction and generating frames based on the color space for formatting and calibrating the encoded images during decoding. The decoding can use the frames to perform color restoration and distortion correction. The decoding can be based on a pseudo-Euclidean distance between a distorted color and a color in a color calibration cells. In some embodiments, an encoded image can be further divided into sub-images during encoding for simplified distortion correction.

The present disclosure relates to a one piece multi-rib fastener including at least two groups of ribs, each rib with one or more hooks, wherein the groups are separated by a space less than the width of the maximum number of ribs within one of the groups.

A method of providing a user with an extra-terrestrial somatosensory experience includes equipping the user with an underwater breathing apparatus, having the user occupy an underwater environment, such environment providing buoyancy to the user, and while the user occupies the underwater environment, using a computer-implemented virtual reality system to present to the user a virtual reality environment modeling an extra-terrestrial setting. The virtual reality system inhibits visual perception by the user of items outside of the virtual reality environment so that the user experiences the virtual reality environment under a buoyancy condition provided by the underwater environment. The buoyancy condition enhances the experience of the virtual reality environment.

A fire pit includes a circular bottom plate and a circular, centrally-apertured log-supporting plate. A plurality of legs secured about the periphery of the log-supporting plate maintain the bottom and log-supporting plates in vertically spaced, parallel relation to one another. Each leg has a hollow uppermost end. A plurality of arcuate grates is mounted about the periphery of the log-supporting plate and a vertically-oriented post is secured to each of the grates, mid-length thereof. Each of the posts has a lowermost end slideably received within the hollow uppermost end of its associated leg to releasably connect each grate to the log-supporting plate. Arcuate openings positioned radially outwardly of the central opening enhance the flow of oxygen into the areas where combustion occurs. The log-supporting plate is inverted and the grates are stacked atop it when the fire pit is in its storage configuration.

A spacer fluid comprises a fluid and a viscosity agent. The viscosity agent is a mixture of at least two polyvinylalcohol compositions. A first polyvinylalcohol composition comprises polyvinylalcohols having a first degree of hydrolysis and a second polyvinylalcohol composition comprises polyvinylalcohols having a second degree of hydrolysis. The first and second degrees of hydrolysis are substantially different such that the rheology of the spacer fluid is stable during temperatures changes.

Sheets are bound to form a bound document by fastening together the sheets and a binding strip. A spacer is applied to a back sheet adjacent to the feet of the fasteners. A wraparound portion of the binding strip is folded around the spine edges of the sheets so that adhesive on the strip contacts the spacer or the back sheet farther from the spine than the feet of the fasteners. The adhesive is affixed to the back sheet. The binding strip includes a spacer adjacent to the heads of the fasteners, protruding above the face-attachment portion at least as far as the heads of the fasteners do.

A binding strip includes a substrate having an interior surface and an exterior surface, a spine-alignment edge, a free edge opposite the spine-alignment edge and substantially non-perpendicular thereto, a face-attachment portion of the exterior surface adjacent to the spine-alignment edge, and a wraparound portion of the interior surface adjacent to the free edge. A border is defined laterally between the face-attachment portion and the wraparound portion and substantially parallel to the spine-alignment edge. An adhesive layer is arranged over the wraparound portion. A first spacer is affixed to the interior surface opposite the face-attachment portion so that a fastener area is defined. The spacer has a selected thickness.

A bound document has front, back, and interior sheets with spine edges. The document has a binding strip and fasteners binding the sheets and the binding strip together. The strip has a flexible substrate with a face-attachment portion through which the fasteners are driven, and a wraparound portion that is bent so adhesive on the wraparound portion contacts the back sheet farther from the spine edge of the book than the feet of the fasteners. The strip also has a first spacer affixed to the interior surface opposite the face-attachment portion so that a fastener area is defined, the spacer at least as thick as the protrusion of the heads of the fasteners above the face-attachment portion.

White-pigmented and unpigmented base paints and stains are custom-tinted using an automated colorant dispenser having a minimum fluid dispensing quantity less than 0.01 fluid ounce (

A spacecraft carrier is disclosed. The carrier has a large internal volume for housing at least one spacecraft. The carrier can be used as a repair and maintenance facility in space for spacecraft. Manned and unmanned devices can be stored, repaired and resupplied. The carrier can also transport a number of spacecraft to other locations allowing for an efficient coordinated movement of many spacecraft.

A space efficient lavatory module for commercial aircraft includes an aft facing concave wall recess that provides a greater distance from an upper, forward facing portion of a cabin structure, such as an aircraft passenger seat to avoid having a passenger's head impact the aft facing lavatory or enclosure wall in a sudden aircraft deceleration. The aft facing concave wall recess also provides space for mounting of a protective cushion, in order to reduce a passenger's risk of head trauma in a sudden deceleration, as well as other items, such as a video monitor, a bassinet or infant bed, without inhibiting passenger movement.

A system has a plurality of spacecraft in orbit around the earth for collecting energy from the Sun in space, using stimulated emission to configure that energy as well defined states of the optical field and delivering that energy efficiently throughout the region of space surrounding Earth.

Methods and apparatus are presented for spacecraft operation using non-Eigen axis attitude transitions via control momentum gyroscopes (CMGs) to avoid or mitigate singularities by providing a time-varying attitude command vector including a plurality of time-varying attitude command signals or values representing a plurality of spacecraft states and control trajectories as a guidance command input to an attitude controller of the spacecraft without modifying the spacecraft feedback control law.

A space debris remover aiming to remove a space debris object in earth orbits. Angular thrust calculation unit calculates angular thrust. Radial thrust calculation unit calculates radial thrust based on the angular thrust, estimated angular momentum and estimated space debris mass. A foam bonding mechanism connects the space debris remover and the space debris object. A space debris removal controller calculates firing time, and sends a space debris removal control signal comprising the radial thrust, the angular thrust and the firing time. A plurality of first stage thrusters generate the radial thrust and the angular thrust after the firing time. After the stage separator separates a first stage and a second stage of the space debris remover, a plurality of second stage thrusters generate the radial thrust and the angular thrust, and propel the space debris object towards the sun.

An aerial roller spacer apparatus and related methods thereto are provided. The aerial roller spacer apparatus includes a spacer body. At least one saddle is formed on the spacer body. A spacer arm is connected to the spacer body at a first end, wherein the spacer arm extends away from the spacer body. A roller assembly is positioned proximate to a second end of the spacer arm, wherein the roller assembly has two rotatable roller halves that are removably engagable with one another with at least one fastener. A messenger groove is formed between the two rotatable roller halves.

A mold for forming a temporary prosthesis has at least two mold members at least partially separable from each other. The at least two mold members cooperatively define a generally enclosed interior cavity for forming the temporary prosthesis. The mold has a securement structure mounted on the at least two mold members for securing the at least two mold members to each other during the forming of the temporary prosthesis. The securement structure is removable from the at least two mold members by hand and without the use of a tool.

The present teachings provide a modular articulating cement spacer mold for forming a temporary implant comprising a mold first portion, a mold second portion, and a ventilation forming surface feature on an interior surface of at least one of the mold first portion or the mold second portion. The first mold portion and the second mold portion have corresponding interior surfaces that form a cavity therebetween.

A spacer and gasket assembly is shown for receipt between a static structure having an outer and inner surface and fastener holes therethrough and a removable structure having a base with fastener holes and an upper surface and a lower surface. The static structure and removable structure are engaged through a multiplicity of fasteners having a shaft diameter. The fasteners are adapted to apply a compression on the gasket between the static structure and the removable structure. The static structure and the removable structure have opposed, typically flat, facing walls. The spacer and gasket assembly comprising a substantially non-compressible spacer adapted for receipt between the static structure and the removable structure having a spacer thickness. A gasket has a deformable, flowable, elastomeric body and a skeleton having a skeleton thickness, the skeleton substantially integral with the body. The gasket has an uncompressed gasket thickness. The spacer and the gasket are adapted to be placed substantially between the facing walls of the static structure and the removable structure and the removable structure will compress and deform the gasket when the fasteners are torqued down.