Write a $3-4$ page research paper on the topic "Introduction to Mobile Computing: Overview of Mobile Devices, their unique characteristics, and the challenges associated with designing architectures for battery$-$powered devices." Your paper should cover the following aspects:

$1.$ Introduction to mobile computing and its significance in today's technology landscape.

$2.$ Overview of mobile devices and their unique characteristics in terms of size, mobility, and connectivity.

$3.$ Challenges faced in designing architectures for battery$-$powered mobile devices, including power constraints and energy efficiency considerations.

$4.$ Discussion on the impact of power constraints on mobile device architecture design decisions.

$5.$ Analysis of techniques used to optimize power consumption in mobile computing, such as dynamic power management and low$-$power modes.

$6.$ Examination of trade$-$offs involved in balancing performance and power efficiency in mobile architectures.

$7.$ Overview and relevance of heterogeneous multi$-$core systems in mobile computing.

$8.$ Importance of memory hierarchy in mobile device architectures and its relationship with power consumption.

$9.$ Role and significance of energy$-$aware instruction set architectures $($ISAs$)$ in mobile computing.

$10.$ Discussion on system$-$level power management techniques and their contribution to extending battery life on mobile devices.

Ensure that your research paper includes proper citations and references to support your arguments and findings. All papers should use proper APA formatting.