On stable exponential solutions in Einstein–Gauss–Bonnet cosmology with zero variation of <Emphasis Type="Italic">G</Emphasis>

A D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological constant Λ is considered. Assuming diagonal cosmological metrics, we find, for certain Λ > 0, new examples of solutions with an exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h < 0, corresponding to submanifolds of dimensions m and l, respectively, with (m, l) = (4, 2), (5, 2), (5, 3), (6, 7), (7, 5), (7, 6) and D = 1 + m + l. Any of these solutions describes an exponential expansion of our 3-dimensional factor space with the Hubble parameter H and zero variation of the effective gravitational constant G. We also prove the stability of these solutions in the class of cosmological solutions with diagonal metrics.     

Nonparametric estimation of signal amplitude in white Gaussian noise

We assume that a transmitted signal is of the form S(t)f(t), where f(t) is a known function vanishing at some points of the observation interval and S(t) is a function of a known smoothness class. The signal is transmitted over a communication channel with additive white Gaussian noise of small intensity ?. For this model, we construct an estimator for S(t) which is optimal with respect to the rate of convergence of the risk to zero as ? → 0.     

Exact and approximate flexible aggregate similarity search

Aggregate similarity search, also known as aggregate nearest-neighbor (Ann) query, finds many useful applications in spatial and multimedia databases. Given a group Q of M query objects, it retrieves from a database the objects most similar to Q, where the similarity is an aggregation (e.g., \({{\mathrm{sum}}}\), \(\max \)) of the distances between each retrieved object p and all the objects in Q. In this paper, we propose an added flexibility to the query definition, where the similarity is an aggregation over the distances between p and any subset of \(\phi M\) objects in Q for some support \(0< \phi \le 1\). We call this new definition flexible aggregate similarity search and accordingly refer to a query as a flexible aggregate nearest-neighbor ( Fann ) query. We present algorithms for answering Fann queries exactly and approximately. Our approximation algorithms are especially appealing, which are simple, highly efficient, and work well in both low and high dimensions. They also return near-optimal answers with guaranteed constant-factor approximations in any dimensions. Extensive experiments on large real and synthetic datasets from 2 to 74 dimensions have demonstrated their superior efficiency and high quality.     

Simple and efficient local codes for distributed stable network construction

In this work, we study protocols so that populations of distributed processes can construct networks. In order to highlight the basic principles of distributed network construction, we keep the model minimal in all respects. In particular, we assume finite-state processes that all begin from the same initial state and all execute the same protocol. Moreover, we assume pairwise interactions between the processes that are scheduled by a fair adversary. In order to allow processes to construct networks, we let them activate and deactivate their pairwise connections. When two processes interact, the protocol takes as input the states of the processes and the state of their connection and updates all of them. Initially all connections are inactive and the goal is for the processes, after interacting and activating/deactivating connections for a while, to end up with a desired stable network. We give protocols (optimal in some cases) and lower bounds for several basic network construction problems such as spanning line, spanning ring, spanning star, and regular network. The expected time to convergence of our protocols is analyzed under a uniform random scheduler. Finally, we prove several universality results by presenting generic protocols that are capable of simulating a Turing Machine (TM) and exploiting it in order to construct a large class of networks. We additionally show how to partition the population into k supernodes, each being a line of \(\log k\) nodes, for the largest such k. This amount of local memory is sufficient for the supernodes to obtain unique names and exploit their names and their memory to realize nontrivial constructions.     

Spatial dependence of entanglement renormalization in <Emphasis Type="Italic">XY</Emphasis> model

In this article, a comparative study of the renormalization of entanglement in one-, two- and three-dimensional space and its relation with quantum phase transition (QPT) near the critical point is presented by implementing the quantum renormalization group (QRG) method using numerical techniques. Adopting the Kadanoff’s block approach, numerical results for the concurrence are obtained for the spin \({-}\)1/2 XY model in all the spatial dimensions. The results show similar qualitative behavior as we move from the lower to the higher dimensions in space, but the number of iterations reduces for achieving the QPT in the thermodynamic limit. We find that in the two-dimensional and three-dimensional spin \({-}\)1/2 XY model, maximum value of the concurrence reduce by the factor of 1 / n \((n=2,3)\) with reference to the maximum value of one-dimensional case. Moreover, we study the scaling behavior and the entanglement exponent. We compare the results for one-, two- and three-dimensional cases and illustrate how the system evolves near the critical point.     

A Framework for Certified Boolean Branch-and-Bound Optimization

We consider optimization problems of the form (S, cost), where S is a clause set over Boolean variables x ₁?...?x _n , with an arbitrary cost function \(\mathit{cost}\colon \mathbb{B}^n \rightarrow \mathbb{R}\), and the aim is to find a model A of S such that cost(A) is minimized. Here we study the generation of proofs of optimality in the context of branch-and-bound procedures for such problems. For this purpose we introduce \(\mathtt{DPLL_{BB}}\), an abstract DPLL-based branch-and-bound algorithm that can model optimization concepts such as cost-based propagation and cost-based backjumping. Most, if not all, SAT-related optimization problems are in the scope of \(\mathtt{DPLL_{BB}}\). Since many of the existing approaches for solving these problems can be seen as instances, \(\mathtt{DPLL_{BB}}\) allows one to formally reason about them in a simple way and exploit the enhancements of \(\mathtt{DPLL_{BB}}\) given here, in particular its uniform method for generating independently verifiable optimality proofs.     

On Cosmology in Nonlinear Multidimensional Gravity with Multiple Factor Spaces

Within the scope of multidimensional Kaluza–Klein gravity with nonlinear curvature terms and two spherical extra spaces of dimensions m and n, we study the properties of an effective action for the scale factors of extra dimensions. Dimensional reduction leads to an effective 4D multiscalar-tensor theory. Based on qualitative estimates of the Casimir energy contribution at a physically reasonable length scale, we demonstrate the existence of such sets of the initial parameters of the theory in the case m = n that provide a minimum of the effective potential at this scale which yields a fine-tuned value of the effective 4D cosmological constant The corresponding size of extra dimensions depends of which conformal frame is interpreted as the observational one: it is about three orders of magnitude larger than the standard Planck length if we adhere to the Einstein frame, but it is n-dependent in the Jordan frame, and its invisibility requirement restricts the total dimension to values D = 4 + 2n ≤ 20.     

Efficient hierarchical identity based encryption scheme in the standard model over lattices

Using lattice basis delegation in a fixed dimension, we propose an efficient lattice-based hierarchical identity based encryption (HIBE) scheme in the standard model whose public key size is only (dm² + mn) log q bits and whose message-ciphertext expansion factor is only log q, where d is the maximum hierarchical depth and (n, m, q) are public parameters. In our construction, a novel public key assignment rule is used to averagely assign one random and public matrix to two identity bits, which implies that d random public matrices are enough to build the proposed HIBE scheme in the standard model, compared with the case in which 2d such public matrices are needed in the scheme proposed at Crypto 2010 whose public key size is (2dm² + mn +m) log q. To reduce the message-ciphertext expansion factor of the proposed scheme to log q, the encryption algorithm of this scheme is built based on Gentry’s encryption scheme, by which m² bits of plaintext are encrypted into m² log q bits of ciphertext by a one time encryption operation. Hence, the presented scheme has some advantages with respect to not only the public key size but also the message-ciphertext expansion factor. Based on the hardness of the learning with errors problem, we demonstrate that the scheme is secure under selective identity and chosen plaintext attacks.     

Cache-Oblivious R-Trees

We develop a cache-oblivious data structure for storing a set S of N axis-aligned rectangles in the plane, such that all rectangles in S intersecting a query rectangle or point can be found efficiently. Our structure is an axis-aligned bounding-box hierarchy and as such it is the first cache-oblivious R-tree with provable performance guarantees. If no point in the plane is contained in more than a constant number of rectangles in S, we can construct, for any constant ε, a structure that answers a rectangle query using \(O(\sqrt{N/B}+T/B)\) memory transfers and a point query using O((N/B) ^ε ) memory transfers, where T is the number of reported rectangles and B is the block size of memory transfers between any two levels of a multilevel memory hierarchy. We also develop a variant of our structure that achieves the same performance on input sets with arbitrary overlap among the rectangles. The rectangle query bound matches the bound of the best known linear-space cache-aware structure.     

Making Doubling Metrics Geodesic

The starting point of our research is the following problem: given a doubling metric ?=(V,d), can one (efficiently) find an unweighted graph G′=(V′,E′) with V?V′ whose shortest-path metric d′ is still doubling, and which agrees with d on V×V? While it is simple to show that the answer to the above question is negative if distances must be preserved exactly. However, allowing a (1+ε) distortion between d and d′ enables us bypass this hurdle, and obtain an unweighted graph G′ with doubling dimension at most a factor O(log?ε ^?1) times the doubling dimension of G.More generally, this paper gives algorithms that construct graphs G′ whose convex (or geodesic) closure has doubling dimension close to that of ?, and the shortest-path distances in G′ closely approximate those of ? when restricted to V×V. Similar results are shown when the metric ? is an additive (tree) metric and the graph G′ is restricted to be a tree.     

Validating gameplay activity inventory (GAIN) for modeling player profiles

In the present study, we validated Gameplay Activity Inventory (GAIN), a short and psychometrically sound instrument for measuring players’ gameplay preferences and modeling player profiles. In Study 1, participants in Finland (\(N=879\)) responded to a 52-item version of GAIN. An exploratory factor analysis was used to identify five latent factors of gameplay activity appreciation: Aggression, Management, Exploration, Coordination, and Caretaking. In Study 2, respondents in Canada (\(N=1322\)) and Japan (\(N=1178\)) responded to GAIN, and the factor structure of a 15-item version was examined using a Confirmatory Factor Analysis. The results showed that the short version of GAIN has good construct validity, convergent validity, and discriminant validity in Japan and in Canada. We demonstrated the usefulness of GAIN by conducting a cluster analysis to identify player types that differ in both demographics and game choice. GAIN can be used in research as a tool for investigating player profiles. Game companies, publishers and analysts can utilize GAIN in player-centric game development and targeted marketing and in generating personalized game recommendations.     

Identification of UX dimensions for incident reporting systems with mobile applications in urban contexts: a longitudinal study

Incident reporting systems enable end-users to report problems that they have experienced in their working activities to authorities. Such applications are sought to sense the quality of the environment, thus enabling authorities to promote safety and well-being among citizens. Many governments are now promoting the use of mobile applications allowing citizens to report incidents in their neighbourhood to the administration. Nonetheless, it is not clear which user experience dimensions affect the adoption of incident reporting systems, and to what extent anticipated use of the system (anticipated UX) is a determinant for predicting the user experience with the final application. In order to understand how citizens perceive incident reporting systems and which factors affect the user experience (UX), we have performed empirical studies including interviews in early phases of the development process and empirical user testing of advanced prototypes. In this paper, we present the results of a longitudinal study on the evolution of the perception of UX dimensions along the development process, from interviews to running prototypes. Hereafter, we describe the method that has been used for coding the findings of these empirical studies according to six UX dimensions (including visual and aesthetic experience, emotions, stimulation, identification, meaning & value and social relatedness/co-experience). Moreover, we describe how the findings have been associated with users’ tasks. The findings from interviews and user testing indicate that whilst the perceived importance of some UX dimensions (such as identification and meaning & value) remains similar over time, other dimensions such as stimulation and emotions do evolve. Beyond the practical implications of this study for the design of incident reporting systems, this work presents an approach that allows comparing the results of UX assessments in different phases of the process.     

Measuring eGovernment success: a public value approach

Measuring the success of eGovernment systems depends on how citizens perceive their value. Our understanding of success has been hampered however by (i) the rapid development and complexity of Internet technologies and (ii) the lack of conceptual bases necessary to represent the ever expanding range of success dimensions. This study proposes Public Value theory to reposition the DeLone and McLean IS Success Model in order to encompass three essential success or value clusters: efficiency, effectiveness and social value. The efficacy of this approach is demonstrated by creating a Public Value-based (Net Benefits) construct to measure IS success from the citizens' perspective within the context of eGovernment 2.0 systems. Survey responses from 347 experienced users of U.S. government Web 2.0 websites confirm that the proposed success measure is reliable and valid and that the nine-factor structure (Cost, Time, Convenience, Personalisation, Communication, Ease of Information Retrieval, Trust, Well-Informedness and Participate in Decision-Making) can explain a major portion of citizens' perceptions of eGovernment success. Additionally, the nine-factor Public Value construct was applied to three identified eGovernment user groups: Passive, Active and Participatory, in order to better understand success in specific usage contexts, including Web 2.0.     

Optimal Path Embedding in the Exchanged Crossed Cube

The (s + t + 1)-dimensional exchanged crossed cube, denoted as ECQ(s, t), combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ(s, t) has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ(s, t). We prove the result in ECQ(s, t): if s ≥ 3, t ≥ 3, for any two different vertices, all paths whose lengths are between \( \max \left\{9,\left\lceil \frac{s+1}{2}\right\rceil +\left\lceil \frac{t+1}{2}\right\rceil +4\right\} \) and 2 ^s+t+1 ? 1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ(s, t) is \( \left\lceil \frac{s+1}{2}\right\rceil +\left\lceil \frac{t+1}{2}\right\rceil +2 \). The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ(s, t) preserves the path embedding capability to a large extent, while it only has about one half edges of CQ _n .     

On transitive partitions of an <Emphasis Type="Italic">n</Emphasis>-cube into codes

We present methods to construct transitive partitions of the set E ⁿ of all binary vectors of length n into codes. In particular, we show that for all n = 2 ^k ? 1, k ≥ 3, there exist transitive partitions of E ⁿ into perfect transitive codes of length n.     

Remark on balanced incomplete block designs,near-resolvable block designs,and <Emphasis Type="Italic">q</Emphasis>-ary constant-weight codes

We prove that any balanced incomplete block design B(v, k, 1) generates a nearresolvable balanced incomplete block design NRB(v, k ? 1, k ? 2). We establish a one-to-one correspondence between near-resolvable block designs NRB(v, k ?1, k ?2) and the subclass of nonbinary (optimal, equidistant) constant-weight codes meeting the generalized Johnson bound.     

On ℤ<Subscript>4</Subscript>-linear codes with the parameters of Reed-Muller codes

For any pair of integers r and m, 0 ≤ r ≤ m, we construct a class of quaternary linear codes whose binary images under the Gray map are codes with the parameters of the classical rth-order Reed-Muller code RM(r, m).     

A logarithmic complexity divide-and-conquer algorithm for multi-flexible-body dynamics including large deformations

A new algorithm is presented for the modeling and simulation of multi-flexible-body systems. This algorithm is built upon a divide-and-conquer-based multibody dynamics framework, and it is capable of handling arbitrary large rotations and deformations in articulated flexible bodies. As such, this work extends the current capabilities of the flexible divide-and-conquer algorithm (Mukherjee and Anderson in Comput. Nonlinear Dyn. 2(1):10–21, 2007), which is limited to the use of assumed modes in a floating frame of reference configuration. The present algorithm utilizes the existing finite element modeling techniques to construct the equations of motion at the element level, as well as at the body level. It is demonstrated that these equations can be assembled and solved using a divide-and-conquer type methodology. In this respect, the new algorithm is applied using the absolute nodal coordinate formulation (ANCF) (Shabana, 1996). The ANCF is selected because of its straightforward implementation and effectiveness in modeling large deformations. It is demonstrated that the present algorithm provides an efficient and robust method for modeling multi-flexible-body systems that employ highly deformable bodies. The new algorithm is tested using three example systems employing deformable bodies in two and three spatial dimensions. The current examples are limited to the ANCF line or cable elements, but the approach may be extended to higher order elements. In its basic form, the divide-and-conquer algorithm is time and processor optimal, yielding logarithmic complexity O(log(N _b )) when implemented using O(N _b ) processors, where N _b is the number of bodies in the system.     

On the Quantum Query Complexity of Local Search in Two and Three Dimensions

The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been determined asymptotically for all fixed d≥5, but the lower dimensional cases present special difficulties, and considerable gaps exist in our knowledge. In the present paper we present near-optimal lower bounds, showing that the quantum query complexity for the 2-dimensional grid [n]² is Ω(n ^1/2?δ ), and that for the 3-dimensional grid [n]³ is Ω(n ^1?δ ), for any fixed δ>0.A general lower bound approach for this problem, initiated by Aaronson (based on Ambainis’ adversary method for quantum lower bounds), uses random walks with low collision probabilities. This approach encounters obstacles in deriving tight lower bounds in low dimensions due to the lack of degrees of freedom in such spaces. We solve this problem by the novel construction and analysis of random walks with non-uniform step lengths. The proof employs in a nontrivial way sophisticated results of Sárközy and Szemerédi, Bose and Chowla, and Halász from combinatorial number theory, as well as less familiar probability tools like Esseen’s Inequality.     

Effects of topological changes in microchannel geometries on the asymmetric breakup of a droplet

Passive asymmetric breakups of a droplet could be done in many microchannels of various geometries. In order to study the effects of different geometries on the asymmetric breakup of a droplet, four types of asymmetric microchannels with the topological equivalence of geometry are designed, which are T-90, Y-120, Y-150, and I-180 microchannels. A three-dimensional volume of fluid multiphase model is employed to investigate the asymmetric rheological behaviors of a droplet numerically. Three regimes of rheological behaviors as a function of the capillary numbers Ca and the asymmetries As defined by As = (b1 ? b2)/(b1 + b2) (where b1 and b2 are the widths of two asymmetric sidearms) have been observed. A power law model based on three major factors (Ca, As and the initial volume ratio r ₀) is employed to describe the volume ratio of two daughter droplets. The analysis of pressure fields shows that the pressure gradient inside the droplet is one of the major factors causing the droplet translation during its asymmetric breakup. Besides the above similarities among various microchannels, the asymmetric breakup in them also have some slight differences as various geometries have different enhancement or constraint effects on the translation of the droplet and the cutting action of flows. It is disclosed that I-180 microchannel has the smallest critical capillary number, the shortest splitting time, and is hardest to generate satellite droplets.