We prove that the modulus function MODm of n variables can be computed by a threshold circuit C of energy e and size s = O(e(n/m)1/(e−1)) for any integer e ≥ 2, where the energy e is defined to be the maximum number of gates outputting “1” over all inputs to C, and the size s to be the number of gates in C. Our upper bound on the size s almost matches the known lower bound s = Ω(e(n/m)1/e). We ...

VMODEX is an interactive visualization tool to support system-level Design Space Exploration (DSE) of MPSoC architectures. It provides insight into the search process of Multi-Objective Evolutionary Algorithms (MOEAs) that are typically used in the DSE process, and it facilitates the analysis of the DSE results. In this paper we extend VMODEX to enable designers to evaluate and compare the prop...

This paper presents a Taylor series approach for solving linear fractional decentralized bi-level multi-objective decision-making (LFDBL-MODM) problems with a single decision maker at the upper level and multiple decision makers at the lower level. In the proposed approach, the membership functions associated with each objective(s) of the level(s) of LFDBL-MODM are transformed to a linear form ...

We give a new proof of recent results of Grolmusz and Tardos on the computing power of constant-depth circuits consisting of a single layer of MODm gates followed by a fixed number of layers of MODpk -gates, where p is prime.

This paper presents a Taylor series approach for solving linear fractional de-centralized bi-level multi-objective decision-making (LFDBL-MODM) problems with asingle decision maker at the upper level and multiple decision makers at the lower level.In the proposed approach, the membership functions associated with each objective(s) ofthe level(s) of LFDBL-MODM are transformed by using a Taylor s...

In this note, we derive an explicit formula for the equitable chromatic number of a complete n-partite graph Kp1 ;p2 ;:::;pn . Namely, if M is the largest integer such that pi (modM)¡ ⌈pi M ⌉ (i = 1; 2; : : : ; n) then e(Kp1 ;p2 ;:::;pn) = n ∑

A graph G is a Zm-well-covered graph if |I1| ≡ |I2| (modm) for all maximal independent sets I1 and I2 in V (G) [3]. The recognition problem of Zm-well-covered graphs is a Co-NP-Complete problem. We give a characterization of Zm-well-covered graphs for chordal, simplicial and circular arc graphs. c © 2001 Elsevier Science B.V. All rights reserved.

It is proved in this paper that for m ≡ 0; 2; 6; 10 (mod 12) there exists a resolvable group divisible design of order v, block size 4 and group size m if and only v ≡ 0 (mod 4), v ≡ 0 (modm), v − m ≡ 0 (mod 3), except when (3; 12) and except possibly when (3; 264); (3; 372); (8; 80); (8; 104), (9; 396) (40; 400) or (40; 520). c © 2002 Elsevier Science B.V. All rights reserved.

this paper will investigate the optimum portfolio for an investor, taking into account 5 criteria. the mean variance model of portfolio optimization that was introduced by markowitz includes two objective functions; these two criteria, risk and return do not encompass all of the information about investment; information like annual dividends, s&p star ranking and return in later years which...

We investigate the modular communication complexity of the graph accessibility problem GAP and its modular counting versions MODk{GAP, k 2. Due to arguments concerning variation ranks and certain projection reductions, we prove that, for any partition of the input variables and for any moduls k and m, GAP and MODk{GAP have MODm{communication complexity (n), where n denotes the number of nodes o...