We construct semiglobal singular spacetimes for the Einstein equations coupled to a massless scalar field. Consistent with the heuristic analysis of Belinskii, Khalatnikov, Lifshitz or BKL for this system, there are no oscillations due to the scalar field. (This is much simpler than the oscillatory BKL heuristics for the Einstein vacuum equations.) Prior results are due to Andersson and Rendall in the real analytic case, and Rodnianski and Speck in the smooth near-spatially-flat-FLRW case. Similar to Andersson and Rendall we give asymptotic data at the singularity, which we refer to as final data, but our construction is not limited to real analytic solutions. This paper is a test application of tools (a graded Lie algebra formulation of the Einstein equations and a filtration) intended for the more subtle vacuum case. We use homological algebra tools to construct a formal series solution, then symmetric hyperbolic energy estimates to construct a true solution well-approximated by truncations of the formal one. We conjecture that the image of the map from final data to initial data is an open set of anisotropic initial data.

We construct a 2-equivalence $mathfrak{CohTheory}^ ext{op} simeq mathfrak{TypeSpaceFunc}$. Here $mathfrak{CohTheory}$ is the 2-category of positive theories and $mathfrak{TypeSpaceFunc}$ is the 2-category of type space functors. We give a precise definition of interpretations for positive logic, which will be the 1-cells in $mathfrak{CohTheory}$. The 2-cells are definable homomorphisms. The 2-equivalence restricts to a duality of categories, making precise the philosophy that a theory is `the same' as the collection of its type spaces (i.e. its type space functor).

In characterising those functors that arise as type space functors, we find that they are specific instances of (coherent) hyperdoctrines. This connects two different schools of thought on the logical structure of a theory.

The key ingredient, the Deligne completeness theorem, arises from topos theory, where positive theories have been studied under the name of coherent theories.

In this paper we construct an equivariant embedding of the affine space $mathbb{A}^n$ with the translation group action into a complete non-projective algebraic variety $X$ for all $n geq 3$. The theory of toric varieties is used as the main tool for this construction. In the case of $n = 3$ we describe the orbit structure on the variety $X$.

Recent studies of optimization methods and GNC of spacecraft near small bodies focusing on descent, landing, rendezvous, etc., with key safety constraints such as line-of-sight conic zones and soft landings have shown promising results; this paper considers descent missions to an asteroid surface with a constraint that consists of an onboard camera and asteroid surface markers while using a stochastic convex MPC law. An undermodeled asteroid gravity and spacecraft technology inspired measurement model is established to develop the constraint. Then a computationally light stochastic Linear Quadratic MPC strategy is presented to keep the spacecraft in satisfactory field of view of the surface markers while trajectory tracking, employing chance based constraints and up-to-date estimation uncertainty from navigation. The estimation uncertainty giving rise to the tightened constraints is particularly addressed. Results suggest robust tracking performance across a variety of trajectories.

In this paper, we characterize a mixed graph $F$ which contains $k$ edge and arc disjoint spanning mixed arborescences $F_{1}, ldots, F_{k}$, such that for each $v in V(F)$, the cardinality of ${i in [k]: v ext{ is the root of } F_{i}}$ lies in some prescribed interval. This generalizes both Nash-Williams and Tutte's theorem on spanning tree packing for undirected graphs and the previous characterization on digraphs which was given by Cai [in: Arc-disjoint arborescences of digraphs, J. Graph Theory 7(2) (1983), 235-240] and Frank [in: On disjoint trees and arborescences, Algebraic Methods in Graph Theory, Colloquia Mathematica Soc. J. Bolyai, Vol. 25 (North-Holland, Amsterdam) (1978), 159-169].

We study the non-relativity for two real analytic K"ahler manifolds and complex space forms of three types. The first one is a K"ahler manifold whose polarization of local K"ahler potential is a Nash function in a local coordinate. The second one is the Hartogs domain equpped with two canonical metrics whose polarizations of the K"ahler potentials are the diastatic functions.

The aim of this paper is to obtain a generalized CK-extension theorem in superspace for the bi-axial Dirac operator. In the classical commuting case, this result can be written as a power series of Bessel type of certain differential operators acting on a single initial function. In the superspace setting, novel structures appear in the cases of negative even superdimensions. In these cases, the CK-extension depends on two initial functions on which two power series of differential operators act. These series are not only of Bessel type but they give rise to an additional structure in terms of Appell polynomials. This pattern also is present in the structure of the Pizzetti formula, which describes integration over the supersphere in terms of differential operators. We make this relation explicit by studying the decomposition of the generalized CK-extension into plane waves integrated over the supersphere. Moreover, these results are applied to obtain a decomposition of the Cauchy kernel in superspace into monogenic plane waves, which shall be useful for inverting the super Radon transform.

We prove that all non-degenerate relative equilibria of the planar Newtonian $n$--body problem can be continued to spaces of constant curvature $kappa$, positive or negative, for small enough values of this parameter. We also compute the extension of some classical relative equilibria to curved spaces using numerical continuation. In particular, we extend Lagrange's triangle configuration with different masses to both positive and negative curvature spaces.

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing rescaling of the distance functions. In this paper, we analyse some of the possible complete and incomplete invariants for weak isometry and we introduce a dissimilarity measure that asses how far two spaces are from being weakly isometric. Furthermore, we compare these ideas with the theory of persistent homology, to study how the two are related.

In this paper we study manifolds $M_{Sigma}$ with fibered singularities, more specifically, a relevant space $Riem^{psc}(X_{Sigma})$ of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space $Riem^{psc}(X_{Sigma})$ is homotopy invariant under certain surgeries on $M_{Sigma}$.

The global health threat from COVID-19 has been controlled in a number of instances by large-scale testing and contact tracing efforts. We created this document to suggest three functionalities on how we might best harness computing technologies to supporting the goals of public health organizations in minimizing morbidity and mortality associated with the spread of COVID-19, while protecting the civil liberties of individuals. In particular, this work advocates for a third-party free approach to assisted mobile contact tracing, because such an approach mitigates the security and privacy risks of requiring a trusted third party. We also explicitly consider the inferential risks involved in any contract tracing system, where any alert to a user could itself give rise to de-anonymizing information.

More generally, we hope to participate in bringing together colleagues in industry, academia, and civil society to discuss and converge on ideas around a critical issue rising with attempts to mitigate the COVID-19 pandemic.

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.

Retired Soccer Star Briana Scurry describes how the computerized baseline test works and how it is used for athletes who have sustained a concussion.

When you bookmark pages on the web, it’s challenging to remember the name of the page. As you dive back into your bookmarks to find it, you see a small icon next to the page. You recognize the icon and realize it’s the website you viewed prior. This icon, known as a favicon, is small, […]

The post What is a Favicon? [+4 Tips for Creating an Impactful Favicon] appeared first on WebFX Blog.

There are no legal skirmishes in Ford v Ferrari.…

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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.…

The Inlander is a community newspaper covering news, politics, events, happy hour, everything that's happening today, things to do on the weekend, in Spokane, Coeur d'Alene, the greater Inland Northwest and beyond.

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.

A self-priming spackling compound includes between about 35% by weight and about 65% by weight acrylic latex resin, between about 20% by weight and about 50% by weight filler material, and between about 1% by weight and about 20% by weight water. In certain aspects, the latex resin may have an average latex particle size of less than about 0.18 microns, a minimum film formation temperature of less than about 15 degrees Celsius, and/or a glass transition temperature (Tg) of less than about 25 degrees Celsius. To further enhance the self-priming performance of the spackling compound, the formulation may further comprise a colorant such as titanium dioxide.

A dielectric ceramic material comprises a primary component of barium titanate (BaTiO3) and at least one additive component. The additive component has a mole percentage from 1% to 50% and is selected from the group consisting of lithium tantalite (LiTaO3), barium cerate (BaCeO3), sodium metaniobate (NaNbO3) and the combinations thereof.

Temperatures in microelectronic integrated circuit packages and components may be measured in situ using carbon nanotube networks. An array of carbon nanotubes strung between upstanding structures may be used to measure local temperature. Because of the carbon nanotubes, a highly accurate temperature measurement may be achieved. In some cases, the carbon nanotubes and the upstanding structures may be secured to a substrate that is subsequently attached to a microelectronic package.

The present invention relates to epoxy group-terminated polymers of the formula (I). Said epoxy group-terminated polymers are suited extremely well as impact resistance modifiers, particularly in epoxy resin compositions. They are particularly suited for use in heat-curing epoxy resin adhesives. It has been found that such epoxy resin compositions not only have excellent mechanical properties and high glass transition temperatures, but also above all improved impact resistance properties, both at room temperature and at low temperatures.

Set of compositions for preparing system-in-package type semiconductor device. The composition set consists of underfill composition for preparing underfill part and encapsulation resin composition for preparing resin encapsulation part. 1) A cured product of the underfill composition has a glass transition temperature, Tg, ≧100° C. and is the same with or differs from a Tg of a cured product of the encapsulation resin composition by ≦20° C. 2) Total linear expansion coefficient of the cured product of the underfill composition at a temperature not higher than (Tg−30)° C. and a linear expansion coefficient of the cured product of the encapsulation resin composition at a temperature not higher than (Tg−30)° C. is ≦42 ppm/° C. 3) A ratio of the linear expansion coefficient of the cured product of the encapsulation resin composition to the linear expansion coefficient of the cured product of the underfill composition ranges from 0.3 to 1.0.

A packet transmission/reception apparatus and method is provided. The packet transmission method of the present invention includes acquiring a source payload including partial source symbols from a source block, generating a source packet including the source payload and an identifier (ID) of the source payload, generating a repair packet including a repair payload corresponding to the source payload and an ID of the repair payload, generating a Forward Error Correction (FEC) packet block including the source and repair packets, and transmitting the FEC packet block. The source payload ID includes a source payload sequence number incrementing by 1 per source packet. The packet transmission/reception method of the present invention is advantageous in improving error correction capability and network resource utilization efficiency.

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.

A usage allocation of a hardware resource to each of a number of workloads over time is determined using a demand model. The usage allocation of the resource includes a current and past actual usage allocation of the resource, a future projected usage allocation of the resource, and current and past actual usage of the resource. A capacity allocation of the resource is determined using a capacity model. The capacity allocation of the resource includes a current and past capacity and a future projected capacity of the resource. Whether a gap exists between the usage allocation and the capacity allocation is determined using a mapping model. Where the gap exists between the usage allocation of the resource and the capacity allocation of the resource, a user is presented with options determined using the mapping model and selectable by the user to implement a remediation strategy to close the gap.

Methods and apparatus are provided for evaluating potential resource capacity in a system where there is elasticity and competition between a plurality of containers. A dynamic potential capacity is determined for at least one container in a plurality of containers competing for a total capacity of a larger container. A current utilization by each of the plurality of competing containers is obtained, and an equilibrium capacity is determined for each of the competing containers. The equilibrium capacity indicates a capacity that the corresponding container is entitled to. The dynamic potential capacity is determined based on the total capacity, a comparison of one or more of the current utilizations to one or more of the corresponding equilibrium capacities and a relative resource weight of each of the plurality of competing containers. The dynamic potential capacity is optionally recalculated when the set of plurality of containers is changed or after the assignment of each work element.

A plurality of Field Programmable Gate Arrays (FPGA), high performance transceivers, and memory devices provide a verification module for timing and state debugging of electronic circuit designs. Signal value compression circuits and gigabit transceivers embedded in each FPGA increase the fanout of each FPGA. Ethernet communication ports enable remote software debugging of processor instructions.

A method of asymmetric asynchronous decoupling of capacitors in an integrated circuit design is provided for faster simulation by circuit simulators, e.g. FastSPICE circuit simulators. This method includes removing a coupling capacitor from a list, which includes coupling capacitors that capacitively couple two nets in the design. The two nets have capacitances C1 and C2, and at least one of capacitances C1 and C2 exceeds a threshold. The coupling capacitor has capacitance Cc. When coupling capacitance Cc is low and only one of capacitances C1 and C2 has a low capacitance, then a forward capacitance can be used at whichever of the two nets has the low capacitance and a lump capacitance can be used at the other net for simulation. When coupling capacitance Cc is low and both of capacitances C1 and C2 have high capacitances, then lump capacitances can be used at the two nets for the simulation.

An integrated circuit includes core logic and a plurality of interface blocks disposed about a periphery of the core logic. A plurality of input or output (I/O) circuits is assigned to one of the plurality of interface blocks. The I/O circuits include external I/O circuits coupled to a device other than the integrated circuit and internal I/O circuits coupled to the integrated circuit. Each interface block includes a first plurality of I/O circuits disposed on a first side of the interface block and a second plurality of I/O circuits disposed on a second side of the interface block. Each interface block also includes interface logic for the interface block between the first plurality of I/O circuits and the second plurality of I/O circuits, and a logic hub that includes a clock distribution of minimal length that drives launch logic and capture logic to form the I/O circuits of the interface block.

The invention relates to a high temperature superconducting tape conductor having a flexible metal substrate that comprises at least one intermediate layer disposed on the flexible metal substrate and comprising terraces on the side opposite the flexible metal substrate, wherein a mean width of the terraces is less than 1 μm and a mean height of the terraces is more than 20 nm, and that comprises at least one high temperature superconducting layer disposed on the intermediate layer, which is disposed on the at least one intermediate layer and comprises a layer thickness of more than 3 μm. The ampacity of the high temperature superconducting tape conductor relative to the conductor width is more than 600 A/cm at 77 K.

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.

Various systems and methods are described for configuring a data storage system. In one embodiment, a plurality of actual capacities of a plurality of storage devices of the data storage system are identified and divided into a plurality of capacity slices. The plurality of capacity slices are combined into a plurality of chunks of capacity slices, each having a combination of characteristics of the underlying physical storage devices. The chunks of capacity slices are then mapped to a plurality of logical storage devices. A group of the plurality of logical storage devices is then organized into a redundant array of logical storage devices.

Described herein is a system and method for detecting underutilized capacity within a storage system environment. The technique comprises collecting performance data of various storage objects within a storage system environment for various performance measures at designated time intervals. The collected performance data may be formatted and stored to a database. One or more parameters may be received specifying at least one performance measure, at least one threshold value, and/or at least one time period. The performance data for target storage objects may be analyzed according to the received parameters to determine any underutilized storage objects. A report may be generated according to the parameters listing the storage objects and address locations of any underutilized storage objects. The report may comprise various information corresponding to the underutilized storage object, such as the business units, tiers, data centers, and levels of service they are associated with.

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.

Devices, systems, and methods for treating a heart of a patient may make use of structures which limit a size of a chamber of the heart, such as by deploying a tensile member to bring a wall of the heart toward (optionally into contact with) a septum of the heart. The implant may include an electrode or other structure for applying pacing signals to one or both ventricles of the heart, for defibrillating the heart, for sensing beating of the heart or the like. A wireless telemetry and control system may allowing the implant to treat congestive heart failure, monitor the results of the treatment, and apply appropriate electrical stimulation.

Cardiac pacing methods for an implantable single chamber pacing system, establish an offset rate for pacing at a predetermined decrement from either a baseline rate (i.e. dictated by a rate response sensor), or an intrinsic rate. Pacing maintains the offset rate until x of y successive events are paced events, at which time the offset rate is switched to the baseline rate for pacing over a predetermined period of time. Following the period, if an intrinsic event is not immediately detected, within the interval of the offset rate, the rate is switched back to baseline for pacing over an increased period of time. Some methods establish a preference rate, between the offset and baseline rates, wherein an additional criterion, for switching from the offset rate to the baseline rate, is established with respect to the preference rate.