1

Can anybody explain me the meaning of the below mathematical expression in simple English? Here $\text{index}, l, i, j$ are positive integers. $m$'s and $x$'s are decimal numbers.

$$\text{index}=\underset{l}\arg\left[\underset{l=1}{\overset{N}{\wedge}}\underset{j=1}{\overset{n}{\vee}}|m_{ij}-x_j|\right]$$

Meaning of the $\wedge, \vee$ signs are not clear to me as the expression is absolutely not related to propositional logic.

I have come across the expression while studying the paper "A Low-Cost EMG-Controlled Anthropomorphic Robotic Hand for Power and Precision Grasp" (ScienceDirect link). This is equation (11) in section 2.2.1 ("Bio-signal classification subsystem").

Here's a screenshot of the surrounding text:

enter image description here

YuiTo Cheng
  • 4,705
Debbie
  • 155
  • 3
    We'd need a LOT more context.... – Randall Mar 20 '20 at 13:15
  • 2
    As said above, we can't answer unless you give us some more context, for example a link to where you saw this equation and what other text was surrounding it. Usually odd notations are explained elsewhere in a paper – lioness99a Mar 20 '20 at 13:20
  • 1
    Let me guess $\vee$ means $\max$ and $\wedge$ means $\min$, and the overall expression means that value of $l$ that maximizes the minimum... – kimchi lover Mar 20 '20 at 13:23
  • I came across this expression while going through a paper. Unfortunately nothing to tell u. Those are just some decimals or integers (I've mentioned). Even I didn't get any extra information from the paper.

    I think, as @kimchilover said the l which minimizes the value of the absolute difference, is the resultant index.

     – Debbie Mar 20 '20 at 13:29
  • Conceivably, this concerns meets and joins over a partially-ordered set. Could you provide the name of the paper (and a link to it)? Perhaps a screenshot of the page on which the expression is displayed? (Should the index variable under the "$\wedge$" be an $i$ instead of an $l$?) – Blue Mar 20 '20 at 13:30
  • @Blue : This is the link to the paper:

    https://www.sciencedirect.com/science/article/pii/S0208521619304693

     – Debbie Mar 20 '20 at 13:33

1 Answers1

1

Reference [25] of your paper is H. Sossa, R. Barron and R. A. Vazquez, "Real-valued pattern classification based on extended associative memory," Proceedings of the Fifth Mexican International Conference in Computer Science, 2004. ENC 2004., Colima, Mexico, 2004, pp. 213-219.

The notation is explained towards in section 3 of that paper, just after equation (10):

In the first case, operators $\vee\equiv\max$ and $\wedge\equiv\min$ execute morphological operations on the difference of the absolute values of the elements $m_{ij}$ of $\mathbf M$ and the components $x_j$ of the pattern $\mathbf X$ to be classified. Thus $\vee_{j=1}^n |m_{lj}−x_j|$ is the metric of the max between row $l$ of $M$ and pattern $\mathbf X$, it can thus be written as $d(\mathbf x,m_l)≡\vee_{j=1}^n |m_{lj}−x_j|$, $m_l$ row of $\mathbf M$.

It's not my field, but it seems to me that anyone interested in low cost EMG should read up on EAM as expounded by Sousa, et al.

kimchi lover
  • 24,277