A study of 3D cover glass design that improves handheld device drop reliability

Cover glass in commercial handheld devices is now evolving from flat (2D) to curved (3D) shapes. For example, some commercial devices have utilized sled‐shape cover glass, 1 which partially covers long edges of the device. According to the patents published by key handheld manufacturers, 2 , 3 we can expect more variety of 3D shaped cover glass for handheld devices in the market. In this study, we have focused on the reliability of 3D cover glass when it is dropped to a rigid surface. The key parameters under study are the corner/edge bend radius and angle of the cover glass, which determines the 3D shape of the cover glass. To achieve this goal, we developed a finite element model to simulate the drop 4 - 13 of a handheld device with 3D‐shaped glass. The model uses explicit algorithm to simulate the high speed impact on the device during the drop test. The glass performance was evaluated based on contact force between the glass and the ground and maximum principal stress in the glass. We showed that to avoid severe damage because of first impact between the glass and the ground, the bend angle of 3D glass has to be in the range between 0 and 45°. For drop angles of 45° and higher, with the proposed glass bend angle, the impact can be taken over by the edge of the back cover of the device. In addition, we showed that optimum glass bend radius is in the range of 3.8 mm and larger. This is required to reduce stress in glass because of impact. The approach and conclusions from the current study can serve as a general guideline to improve the 3D cover glass reliability of a handheld device.     

Path partitions of hypercubes

A path partition of a graph G is a set of vertex-disjoint paths that cover all vertices of G. Given a set of pairs of distinct vertices of the n-dimensional hypercube Qn, is there a path partition of Qn such that ai and bi are endvertices of Pi? Caha and Koubek showed that for 6m?n, such a path partition exists if and only if the set P is balanced in the sense that it contains the same number of vertices from both classes of bipartition of Qn.In this paper we show that this result holds even for 2m−e<n, where e is the number of pairs of P that form edges of Qn. Moreover, our bound is optimal in the sense that for every n?3, there is a balanced set P in Qn such that 2m−e=n, but no path partition with endvertices prescribed by P exists.     

Disjoint essential sets of implicates of a CQ Horn function

In this paper we study a class of CQ Horn functions introduced in Boros et al. (Ann Math Artif Intell 57(3–4):249–291, 2010). We prove that given a CQ Horn function f, the maximal number of pairwise disjoint essential sets of implicates of f equals the minimum number of clauses in a CNF representing f. In other words, we prove that the maximum number of pairwise disjoint essential sets of implicates of f constitutes a tight lower bound on the size (the number of clauses) of any CNF representation of f.     

Convex combinations of strict t-norms

Alsina, Frank, and Schweizer posed a question whether a non-trivial convex combination of triangular norms can ever be a triangular norm. In this paper we deal with the class of strict t-norms with well-defined first partial derivatives along their zero borders. We show that the answer to the question is negative for certain couples of such t-norms and we state out possible further research.     

Estimation of time-dependent input from neuronal membrane potential

The set of firing rates of the presynaptic excitatory and inhibitory neurons constitutes the input signal to the postsynaptic neuron. Estimation of the time-varying input rates from intracellularly recorded membrane potential is investigated here. For that purpose, the membrane potential dynamics must be specified. We consider the Ornstein-Uhlenbeck stochastic process, one of the most common single-neuron models, with time-dependent mean and variance. Assuming the slow variation of these two moments, it is possible to formulate the estimation problem by using a state-space model. We develop an algorithm that estimates the paths of the mean and variance of the input current by using the empirical Bayes approach. Then the input firing rates are directly available from the moments. The proposed method is applied to three simulated data examples: constant signal, sinusoidally modulated signal, and constant signal with a jump. For the constant signal, the estimation performance of the method is comparable to that of the traditionally applied maximum likelihood method. Further, the proposed method accurately estimates both continuous and discontinuous time-variable signals. In the case of the signal with a jump, which does not satisfy the assumption of slow variability, the robustness of the method is verified. It can be concluded that the method provides reliable estimates of the total input firing rates, which are not experimentally measurable.     

The joint movement of pebbles in solving the ($$N^2-1$$)-puzzle suboptimally and its applications in rule-based cooperative path-finding

The present paper deals with the problem of solving the (\(n^2 - 1\))-puzzle and cooperative path-finding (CPF) problems sub-optimally by rule-based algorithms. To solve the puzzle, we need to rearrange \(n^2 - 1\) pebbles in the \(n \times n\)-sized square grid using one vacant position to achieve the goal configuration. An improvement to the existing polynomial-time algorithm is proposed and experimentally analyzed. The improved algorithm represents an attempt to move pebbles in a more efficient way compared to the original algorithm by grouping them into so-called snakes and moving them together as part of a snake formation. An experimental evaluation has shown that the snakeenhanced algorithm produces solutions which are 8–9 % shorter than the solutions generated by the original algorithm. Snake-like movement has also been integrated into the rule-based algorithms used in solving CPF problems sub-optimally, which is a closely related task. The task in CPF consists in moving a group of abstract robots on an undirected graph to specific vertices. The robots can move to unoccupied neighboring vertices; no more than one robot can be placed in each vertex. The (\(n^2 - 1\))-puzzle is a special case of CPF where the underlying graph is a 4-connected grid and only one vertex is vacant. Two major rule-based algorithms for solving CPF problems were included in our study—BIBOX and PUSH-and-SWAP (PUSH-and-ROTATE). The use of snakes in the BIBOX algorithm led to consistent efficiency gains of around 30 % for the (\(n^2 - 1\))-puzzle and up to 50 % in for CPF problems on biconnected graphs with various ear decompositions and multiple vacant vertices. For the PUSH-and-SWAP algorithm, the efficiency gain achieved from the use of snakes was around 5–8 %. However, the efficiency gain was unstable and hardly predictable for PUSH-and-SWAP.     

Using meta‐modeling in design and implementation of component‐based systems: the SOFA case study

To allow efficient and user‐friendly development of a component‐based application, component systems have to provide a rather complex development infrastructure, including a tool for component composition, component repository, and a run‐time infrastructure. In this paper, we present and evaluate benefits of using meta‐modeling during the process of defining a component system and also during creation of the development and run‐time infrastructures. Most of the presented arguments are based on a broad practical experience with designing the component systems SOFA and SOFA 2; the former designed in a classical ad hoc ‘manual’ way, whereas the latter with the help of meta‐modeling. Copyright © 2010 John Wiley & Sons, Ltd.