scholarly journals Baron Münchhausen Redeems Himself: Bounds for a Coin-Weighing Puzzle

10.37236/524 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Tanya Khovanova ◽  
Joel Brewster Lewis
Keyword(s):  
Upper Bound ◽  
Moscow Math ◽  
Better Than

We investigate a coin-weighing puzzle that appeared in the 1991 Moscow Math Olympiad. We generalize the puzzle by varying the number of participating coins, and deduce an upper bound on the number of weighings needed to solve the puzzle that is noticeably better than the trivial upper bound. In particular, we show that logarithmically-many weighings on a balance suffice.

scholarly journals On a new converse of Jensen's inequality

2009 ◽  
Vol 85 (99) ◽  
pp. 107-110 ◽  
Author(s):  
Slavko Simic
Keyword(s):  
Upper Bound ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Discrete Inequality ◽  
Better Than

We give another global upper bound for Jensen's discrete inequality which is better than already existing ones. For instance, we determine a new converses for generalized A-G and G-H inequalities.

scholarly journals Defect-Tolerant Architectures for Nanoelectronic Crossbar Memories

2007 ◽  
Vol 7 (1) ◽  
pp. 151-167 ◽  
Author(s):  
Dmitri B. Strukov ◽  
Konstantin K. Likharev
Keyword(s):  
Upper Bound ◽  
Memory Cell ◽  
Error Correcting Codes ◽  
Cell Fraction ◽  
Access Time ◽  
Initial Stage ◽  
Order Of Magnitude ◽  
Pitch Ratio ◽  
Better Than

We have calculated the maximum useful bit density that may be achieved by the synergy of bad bit exclusion and advanced (BCH) error correcting codes in prospective crossbar nanoelectronic memories, as a function of defective memory cell fraction. While our calculations are based on a particular ("CMOL") memory topology, with naturally segmented nanowires and an area-distributed nano/CMOS interface, for realistic parameters our results are also applicable to "global" crossbar memories with peripheral interfaces. The results indicate that the crossbar memories with a nano/CMOS pitch ratio close to 1/3 (which is typical for the current, initial stage of the nanoelectronics development) may overcome purely semiconductor memories in useful bit density if the fraction of nanodevice defects (stuck-on-faults) is below ∼15%, even under rather tough, 30 ns upper bound on the total access time. Moreover, as the technology matures, and the pitch ratio approaches an order of magnitude, the crossbar memories may be far superior to the densest semiconductor memories by providing, e.g., a 1 Tbit/cm2 density even for a plausible defect fraction of 2%. These highly encouraging results are much better than those reported in literature earlier, including our own early work, mostly due to more advanced error correcting codes.

Investigating the Upper-Bound Performance of Sparse-Coding-Based Spectral Reconstruction from RGB Images

2021 ◽  
Vol 2021 (29) ◽  
pp. 19-24
Author(s):  
Yi-Tun Lin ◽  
Graham D. Finlayson
Keyword(s):  
Sparse Coding ◽  
Upper Bound ◽  
Linear Mapping ◽  
Spectral Space ◽  
Spectral Reconstruction ◽  
Image Patches ◽  
Coding Method ◽  
Rgb Images ◽  
Spectral Neighborhood ◽  
Better Than

In Spectral Reconstruction (SR), we recover hyperspectral images from their RGB counterparts. Most of the recent approaches are based on Deep Neural Networks (DNN), where millions of parameters are trained mainly to extract and utilize the contextual features in large image patches as part of the SR process. On the other hand, the leading Sparse Coding method ‘A+’—which is among the strongest point-based baselines against the DNNs—seeks to divide the RGB space into neighborhoods, where locally a simple linear regression (comprised by roughly 102 parameters) suffices for SR. In this paper, we explore how the performance of Sparse Coding can be further advanced. We point out that in the original A+, the sparse dictionary used for neighborhood separations are optimized for the spectral data but used in the projected RGB space. In turn, we demonstrate that if the local linear mapping is trained for each spectral neighborhood instead of RGB neighborhood (and theoretically if we could recover each spectrum based on where it locates in the spectral space), the Sparse Coding algorithm can actually perform much better than the leading DNN method. In effect, our result defines one potential (and very appealing) upper-bound performance of point-based SR.

ON THE QUASI-STATIONARY DISTRIBUTION OF SIS MODELS

2016 ◽  
Vol 30 (4) ◽  
pp. 622-639 ◽  
Author(s):  
Gaofeng Da ◽  
Maochao Xu ◽  
Shouhuai Xu
Keyword(s):  
Stationary Distribution ◽  
Upper Bound ◽  
Hazard Rate ◽  
State Of The Art ◽  
Upper Bounds ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Novel Method ◽  
Better Than ◽  
Quasi Stationary Distribution

In this paper, we propose a novel method for constructing upper bounds of the quasi-stationary distribution of SIS processes. Using this method, we obtain an upper bound that is better than the state-of-the-art upper bound. Moreover, we prove that the fixed point map Φ [7] actually preserves the equilibrium reversed hazard rate order under a certain condition. This allows us to further improve the upper bound. Some numerical results are presented to illustrate the results.

scholarly journals Upper Bound on the Bit Error Probability of Systematic Binary Linear Codes via Their Weight Spectra

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jia Liu ◽  
Mingyu Zhang ◽  
Chaoyong Wang ◽  
Rongjun Chen ◽  
Xiaofeng An ◽  
...  
Keyword(s):  
Upper Bound ◽  
Error Probability ◽  
Linear Codes ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
High Signal ◽  
Binary Linear Codes ◽  
Enumerating Function ◽  
Bit Error Probability ◽  
Better Than

In this paper, upper bound on the probability of maximum a posteriori (MAP) decoding error for systematic binary linear codes over additive white Gaussian noise (AWGN) channels is proposed. The proposed bound on the bit error probability is derived with the framework of Gallager’s first bounding technique (GFBT), where the Gallager region is defined to be an irregular high-dimensional geometry by using a list decoding algorithm. The proposed bound on the bit error probability requires only the knowledge of weight spectra, which is helpful when the input-output weight enumerating function (IOWEF) is not available. Numerical results show that the proposed bound on the bit error probability matches well with the maximum-likelihood (ML) decoding simulation approach especially in the high signal-to-noise ratio (SNR) region, which is better than the recently proposed Ma bound.

scholarly journals An Efficient Algorithm for Delay and Delay- Variation Bounded Core Based Tree Generation

2010 ◽  
pp. 202-207
Author(s):  
Manoj Kumar Patel ◽  
MANAS RANJAN KABAT ◽  
Chita Ranjan Tripathy
Keyword(s):  
Upper Bound ◽  
Heuristic Algorithms ◽  
Multicast Tree ◽  
End To End Delay ◽  
Tree Generation ◽  
Core Selection ◽  
End To End ◽  
Better Than ◽  
Delay Variation

Many multimedia group applications require the construction of multicast tree satisfying the quality of service (QoS) requirements. To support real time communication, computer networks need to optimize the Delay and Delay-Variation Bounded Multicast Tree (DVBMT). The problem is to satisfy the end-to-end delay and delay-variation within an upper bound. The DVBMT problem is known to be NP complete. In this paper, we propose an efficient core selection algorithm for satisfying the end-to-end delay and delay-variation within an upper bound. The efficiency of the proposed algorithm is validated through the simulation. The simulation results reveal that our algorithm performs better than the existing heuristic algorithms.

scholarly journals Lower bounds to eigenvalues of the Schrödinger equation by solution of a 90-y challenge

2020 ◽  
Vol 117 (28) ◽  
pp. 16181-16186
Author(s):  
Rocco Martinazzo ◽  
Eli Pollak
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Spectral Features ◽  
Numerical Examples ◽  
Tunneling Splittings ◽  
Order Of Magnitude ◽  
Bound Theorem ◽  
Math Phys ◽  
Better Than

The Ritz upper bound to eigenvalues of Hermitian operators is essential for many applications in science. It is a staple of quantum chemistry and physics computations. The lower bound devised by Temple in 1928 [G. Temple,Proc. R. Soc. A Math. Phys. Eng. Sci.119, 276–293 (1928)] is not, since it converges too slowly. The need for a good lower-bound theorem and algorithm cannot be overstated, since an upper bound alone is not sufficient for determining differences between eigenvalues such as tunneling splittings and spectral features. In this paper, after 90 y, we derive a generalization and improvement of Temple’s lower bound. Numerical examples based on implementation of the Lanczos tridiagonalization are provided for nontrivial lattice model Hamiltonians, exemplifying convergence over a range of 13 orders of magnitude. This lower bound is typically at least one order of magnitude better than Temple’s result. Its rate of convergence is comparable to that of the Ritz upper bound. It is not limited to ground states. These results complement Ritz’s upper bound and may turn the computation of lower bounds into a staple of eigenvalue and spectral problems in physics and chemistry.

Combined Lower and Upper Bound Plastic Analysis: Better than the Sum of its Parts

2009 ◽  
Vol 96 (12) ◽  
pp. 65-74
Author(s):  
Andrew Jackson ◽  
Campbell Middleton
Keyword(s):  
Upper Bound ◽  
Plastic Analysis ◽  
Better Than

scholarly journals Acyclic Coloring of Graphs of Maximum Degree $\Delta$

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Guillaume Fertin ◽  
André Raspaud
Keyword(s):  
Chromatic Number ◽  
Upper Bound ◽  
Maximum Degree ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Acyclic Coloring ◽  
International Audience ◽  
Better Than

International audience An acyclic coloring of a graph $G$ is a coloring of its vertices such that: (i) no two neighbors in $G$ are assigned the same color and (ii) no bicolored cycle can exist in $G$. The acyclic chromatic number of $G$ is the least number of colors necessary to acyclically color $G$, and is denoted by $a(G)$. We show that any graph of maximum degree $\Delta$ has acyclic chromatic number at most $\frac{\Delta (\Delta -1) }{ 2}$ for any $\Delta \geq 5$, and we give an $O(n \Delta^2)$ algorithm to acyclically color any graph of maximum degree $\Delta$ with the above mentioned number of colors. This result is roughly two times better than the best general upper bound known so far, yielding $a(G) \leq \Delta (\Delta -1) +2$. By a deeper study of the case $\Delta =5$, we also show that any graph of maximum degree $5$ can be acyclically colored with at most $9$ colors, and give a linear time algorithm to achieve this bound.

scholarly journals Thresholding Bandits with Augmented UCB

2017 ◽  
Author(s):  
Subhojyoti Mukherjee ◽  
Naveen Kolar Purushothama ◽  
Nandan Sudarsanam ◽  
Balaraman Ravindran
Keyword(s):  
Upper Bound ◽  
State Of The Art ◽  
Loss Probability ◽  
Problem Complexity ◽  
Bandit Problem ◽  
Simulation Experiments ◽  
Extensive Simulation ◽  
Mean And Variance ◽  
Variance Estimates ◽  
Better Than

In this paper we propose the Augmented-UCB (AugUCB) algorithm for a fixed-budget version of the thresholding bandit problem (TBP), where the objective is to identify a set of arms whose quality is above a threshold. A key feature of AugUCB is that it uses both mean and variance estimates to eliminate arms that have been sufficiently explored; to the best of our knowledge this is the first algorithm to employ such an approach for the considered TBP. Theoretically, we obtain an upper bound on the loss (probability of mis-classification) incurred by AugUCB. Although UCBEV in literature provides a better guarantee, it is important to emphasize that UCBEV has access to problem complexity (whose computation requires arms' mean and variances), and hence is not realistic in practice; this is in contrast to AugUCB whose implementation does not require any such complexity inputs. We conduct extensive simulation experiments to validate the performance of AugUCB. Through our simulation work, we establish that AugUCB, owing to its utilization of variance estimates, performs significantly better than the state-of-the-art APT, CSAR and other non variance-based algorithms.

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