Descriptive complexity provides intrinsic, that is,machine-independent, characterizations of the major complexity classes. On the other hand, logic can be useful for designing programs in a natural ...declarative way. This is particularly important for parallel computation models such as cellular automata, because designing parallel programs is considered a difficult task.This paper establishes three logical characterizations of the three classical complexity classes modeling minimal time, called real-time, of one-dimensional cellular automata according to their canonical variants: unidirectional or bidirectional communication, input word given in a parallel or sequential way.Our three logics are natural restrictions of existential second-order Horn logic with built-in successor and predecessor functions. These logics correspond exactly to the three ways of deciding a language on a square grid circuit of side n according to one of the three canonical locations of an input word of length n: along a side of the grid, on the diagonal that contains the output cell, or on the diagonal opposite to the output cell.The key ingredient of our results is a normalization method that transforms a formula from one of our three logics into an equivalent normalized formula that faithfully mimics a grid circuit.Then, we extend our logics by allowing a limited use of negation on hypotheses like in Stratified Datalog. By revisiting in detail a number of representative classical problems - recognition of the set of primes by Fisher’s algorithm, Dyck language recognition, Firing Squad Synchronization problem,etc. - we show that this extension makes easier programming and we prove that it does not change the complexity of our logics in real-time.Finally, starting from our experience in expressing those representative problems in logic, we argue that our logics are high-level programming languages: they allow to express in a natural,precise and synthetic way the algorithms of literature, based on signals, and to translate them automatically into cellular automata of the same complexity.
During the last four decades, digital technologies have disrupted many industries. Car control systems have gone from mechanical to digital. Telephones have changed from sound boxes to portable ...computers. But have the firms that digitized their products and services become more valuable than firms that didn't? Here we introduce the construct of digital proximity, which considers the interdependent activities of firms linked in an economic network. We then explore how the digitization of products and services affects a company's Tobin's q-the ratio of market value over assets-a measure of the intangible value of a firm. Our panel regression methods and robustness tests suggest the positive influence of a firm's digital proximity on its Tobin's q. This implies that firms able to come closer to the digital sector have increased their intangible value compared to those that have failed to do so. These findings contribute a new way of measuring digitization and its impact on firm performance that is complementary to traditional measures of information technology (IT) intensity.
In this paper, we consider secure downlink transmission in a multicell massive multiple-input multiple-output (MIMO) system where the numbers of base station (BS) antennas, mobile terminals, and ...eavesdropper antennas are asymptotically large. The channel state information of the eavesdropper is assumed to be unavailable at the BS and hence, linear precoding of data and artificial noise (AN) are employed for secrecy enhancement. Four different data precoders (i.e., selfish zero-forcing (ZF)/regularized channel inversion (RCI) and collaborative ZF/RCI precoders) and three different AN precoders (i.e., random, selfish/collaborative null-space-based precoders) are investigated and the corresponding achievable ergodic secrecy rates are analyzed. Our analysis includes the effects of uplink channel estimation, pilot contamination, multicell interference, and path-loss. Furthermore, to strike a balance between complexity and performance, linear precoders that are based on matrix polynomials are proposed for both data and AN precoding. The polynomial coefficients of the data and AN precoders are optimized, respectively, for minimization of the sum-mean-squared-error of and the AN leakage to the mobile terminals in the cell of interest using tools from free probability and random matrix theory. Our analytical and simulation results provide interesting insights for the design of secure multicell massive MIMO systems and reveal that the proposed polynomial data and AN precoders closely approach the performance of selfish RCI data and null-space-based AN precoders, respectively.
Instance segmentation is one of the fundamental vision tasks. Recently, fully convolutional instance segmentation methods have drawn much attention as they are often simpler and more efficient than ...two-stage approaches like Mask R-CNN. To date, almost all such approaches fall behind the two-stage Mask R-CNN method in mask precision when models have similar computation complexity, leaving great room for improvement. In this work, we achieve improved mask prediction by effectively combining instance-level information with semantic information with lower-level fine-granularity. Our main contribution is a blender module which draws inspiration from both top-down and bottom-up instance segmentation approaches. The proposed BlendMask can effectively predict dense per-pixel position-sensitive instance features with very few channels, and learn attention maps for each instance with merely one convolution layer, thus being fast in inference. BlendMask can be easily incorporate with the state-of-the-art one-stage detection frameworks and outperforms Mask R-CNN under the same training schedule while being faster. A light-weight version of BlendMask achieves 36.0 mAP at 27 FPS evaluated on a single 1080Ti. Because of its simplicity and efficacy, we hope that our BlendMask could serve as a simple yet strong baseline for a wide range of instance-wise prediction tasks.
PDF
