Search results for " Complexity"
showing 10 items of 623 documents
New separation between $s(f)$ and $bs(f)$
2011
In this note we give a new separation between sensitivity and block sensitivity of Boolean functions: $bs(f)=(2/3)s(f)^2-(1/3)s(f)$.
A Tight Lower Bound on Certificate Complexity in Terms of Block Sensitivity and Sensitivity
2014
Sensitivity, certificate complexity and block sensitivity are widely used Boolean function complexity measures. A longstanding open problem, proposed by Nisan and Szegedy, is whether sensitivity and block sensitivity are polynomially related. Motivated by the constructions of functions which achieve the largest known separations, we study the relation between 1-certificate complexity and 0-sensitivity and 0-block sensitivity. Previously the best known lower bound was $C_1(f)\geq \frac{bs_0(f)}{2 s_0(f)}$, achieved by Kenyon and Kutin. We improve this to $C_1(f)\geq \frac{3 bs_0(f)}{2 s_0(f)}$. While this improvement is only by a constant factor, this is quite important, as it precludes achi…
Computational Complexity and Communication: Coordination in Two-Player Games
2002
The main contribution of this paper is the development and application of cryptographic techniques to the design of strategic communication mechanisms. One of the main assumptions in cryptography is the limitation of the computational power available to agents. We introduce the concept of limited computational complexity, and by borrowing results from cryptography, we construct a communication protocol to establish that every correlated equilibrium of a two-person game with rational payoffs can be achieved by means of computationally restricted unmediated communication. This result provides an example in game theory where limitations of computational abilities of players are helpful in solv…
The absolute center of a unicyclic network
1989
Abstract A unicyclic network is one generalization of a tree network. In this paper we examine the problem of finding an absolute center of a unicyclic network. We show that this problem can be solved in linear time with respect to the number of vertices in the network.
Using FOCAP tool for teaching microarchitecture simulation and optimization
2013
This paper presents our new developed FOCAP tool (Framework for optimizing the Computer Architecture Performance) in order to gain a better understanding and familiarity of the students with new advanced learning methods and tools in the Microarchitecture Simulation and Optimization. At this stage, FOCAP allows a mono-objective automatic design space exploration (DSE) of a superscalar processor by varying several architectural parameters. Such DSE tools are very useful, since it is impossible to simulate all the configurations of a highly parameterized microarchitecture. Therefore, heuristic methods, local search algorithms and advanced machine learning methods are good candidates to find n…
Predicting perceived visual complexity of abstract patterns using computational measures: The influence of mirror symmetry on complexity perception
2017
Visual complexity is relevant for many areas ranging from improving usability of technical displays or websites up to understanding aesthetic experiences. Therefore, many attempts have been made to relate objective properties of images to perceived complexity in artworks and other images. It has been argued that visual complexity is a multidimensional construct mainly consisting of two dimensions: A quantitative dimension that increases complexity through number of elements, and a structural dimension representing order negatively related to complexity. The objective of this work is to study human perception of visual complexity utilizing two large independent sets of abstract patterns. A w…
Application of Statistical Process Control to Continuous Processes
2002
Control charts represent an efficient and easy tool to assure the state of statistical quality control in a manufacturing process. These tools are also implemented in continuous processes, where the critical parameters are often monitored by on line sensors measuring data with short time intervals. In this paper a continuous process is monitored by using control charts and its dynamic is modeled through linear time series that allow the effects of the autocorrelation to be eliminated. In this way, the control charts can operate on residuals that result identically and independently distributed. A statistical analysis on EWMA, CUSUM and control charts for individual measurements has been car…
Systems chemical analytics: introduction to the challenges of chemical complexity analysis
2019
Understanding complex (bio/geo)systems is a pivotal challenge in modern sciences that fuels a constant development of modern analytical technology, finding innovative solutions to resolve and analyse. In this introductory paper to the Faraday Discussion "Challenges in the analysis of complex natural systems", we aim to present concepts of complexity, and complex chemistry in systems subjected to biotic and abiotic transformations, and introduce the analytical possibilities to disentangle chemical complexity into its elementary parts (i.e. compositional and structural resolution) as a global integrated approach termed systems chemical analytics.
Numerical experiments with a parallel fast direct elliptic solver on Cray T3E
1997
A parallel fast direct O(N log N) solver is shortly described for linear systems with separable block tridiagonal matrices. A good parallel scalability of the proposed method is demonstrated on a Cray T3E parallel computer using MPI in communication. Also, the sequential performance is compared with the well-known BLKTRI-implementation of the generalized. cyclic reduction method using a single processor of Cray T3E.
Dynamics and topological mass of skyrmionic spin structures (presentation video)
2014
Skyrmions are topologically protected particle-like configurations, with a topological complexity described by their Skyrmion number. In magnetic systems, they have been numerically predicted to exhibit rich dynamics, such as the gyrotropic and breathing modes, dominated by their topology. Recent experimental advances brought their static manipulation well under control. However, their dynamical behaviour is largely unexplored experimentally. In this work, we provide with the first direct observation of eigenmode skyrmion dynamics. In particular, we present dynamical imaging data with high temporal and spatial resolution to demonstrate the GHz gyrotropic mode of a single skyrmion bubble, as…