Bashスクリプトがcrontabで機能しない

私はダウンロードしたものを確認し、ダウンロードした場合はスキャンする必要があるBashスクリプトを作成しようとしています。起動時に起動するにはcrontabを使用しましたが、その部分は機能しません。

これは私のコードです。

#!/bin/bash

inotifywait ~/Downloads -m -r -e modify -e moved_to --format '%w%f' | while read file
do
    $(clamscan --bell --recursive --max-filesize=99999 --log log/myLogs.txt $file)
    CLAMSCAN="$?"

    if [ $CLAMSCAN -eq 1 ]; then
        $(xmessage -buttons Ok:0,"Remove":1,"View Logs":2 -default Ok -center "Infected file: $file is found...")
        CHOICE="$?"

        if [ $CHOICE -eq 1 ]; then
            $(rm -r $file)
        elif [ $CHOICE -eq 2 ]; then
            $(xmessage -buttons Ok:0 -default Ok -center -file log/myLogs.txt)
        fi      
    fi
done

私のスケジュール：

# Edit this file to introduce tasks to be run by cron.
# 
# Each task to run has to be defined through a single line
# indicating with different fields when the task will be run
# and what command to run for the task
# 
# To define the time you can provide concrete values for
# minute (m), hour (h), day of month (dom), month (mon),
# and day of week (dow) or use '*' in these fields (for 'any').# 
# Notice that tasks will be started based on the cron's system
# daemon's notion of time and timezones.
# 
# Output of the crontab jobs (including errors) is sent through
# email to the user the crontab file belongs to (unless redirected).
# 
# For example, you can run a backup of all your user accounts
# at 5 a.m every week with:
# 0 5 * * 1 tar -zcf /var/backups/home.tgz /home/
# 
# For more information see the manual pages of crontab(5) and cron(8)
# 
# m h  dom mon dow   command
SHELL=/bin/sh
@reboot sh $HOME/.custom_security/Downloads_sec.sh

ディレクトリを「/」に変更して実行すると、sh $HOME/.custom_security/Downloads_sec.sh次のエラーが発生します。

    Setting up watches.  Beware: since -r was given, this may take a while!
Watches established.
ERROR: Can't open log/myLogs.txt in append mode (check permissions!).
ERROR: Problem with internal logger.

このスクリプトはスタンドアロンスクリプトとしてうまく機能します！