arXiv subjects
Publications and source records attributed to Dhairya Shah.
This study develops a complex-potential framework for the electric field near the Triple Contact Point in electrowetting. A global slit model provides the electrostatic potential, surface-charge structure and endpoint expansion. The resulting solution also gives an analytical approximation to the droplet shape and exhibits the characteristic edge singularity of the zero-contact-angle slit model.
Sensing the motion of physical objects in an environment enables numerous applications, from tracking occupancy in buildings and monitoring vital signs to diagnosing faults in machines. Typically, these application scenarios involve attaching a sensor, such as an accelerometer, to the object of interest, like a wearable device that tracks our steps. However, many of these scenarios require tracking motion in a noncontact manner where the sensor is not in touch with the object. A sensor in such a scenario observes variations in radio, light, acoustic, and infrared fields disturbed by the object's motion. Current noncontact sensing mechanisms often require substantial energy and involve complex processing on sophisticated hardware. We present TunnelSense, a novel mechanism that rethinks noncontact sensing using tunnel diode oscillators. They are highly sensitive to changes in their electromagnetic environments. The motion of an object near a tunnel diode oscillator induces corresponding changes in its resonant frequency and thus in the generated radio waves. Additionally, the low-power characteristics of the tunnel diode allow tags designed using them to operate on less than 100microwatt of power consumption and with a biasing voltage starting at 70 millivolt. This enables prolonged tag operation on a small battery or energy harvested from the environment. Among numerous applications enabled by the TunnelSense system, this work demonstrates its ability to detect breathing at distances up to 30 centimeter between the subject and the TunnelSense tag.
Embedded camera systems are ubiquitous, representing the most widely deployed example of a wireless embedded system. They capture a representation of the world - the surroundings illuminated by visible or infrared light. Despite their widespread usage, the architecture of embedded camera systems has remained unchanged, which leads to limitations. They visualize only a tiny portion of the world. Additionally, they are energy-intensive, leading to limited battery lifespan. We present PixelGen, which re-imagines embedded camera systems. Specifically, PixelGen combines sensors, transceivers, and low-resolution image and infrared vision sensors to capture a broader world representation. They are deliberately chosen for their simplicity, low bitrate, and power consumption, culminating in an energy-efficient platform. We show that despite the simplicity, the captured data can be processed using transformer-based image and language models to generate novel representations of the environment. For example, we demonstrate that it can allow the generation of high-definition images, while the camera utilises low-power, low-resolution monochrome cameras. Furthermore, the capabilities of PixelGen extend beyond traditional photography, enabling visualization of phenomena invisible to conventional cameras, such as sound waves. PixelGen can enable numerous novel applications, and we demonstrate that it enables unique visualization of the surroundings that are then projected on extended reality headsets. We believe, PixelGen goes beyond conventional cameras and opens new avenues for research and photography.
Regarding the rising number of people suffering from mental health illnesses in today's society, the importance of mental health cannot be overstated. Wearable sensors, which are increasingly widely available, provide a potential way to track and comprehend mental health issues. These gadgets not only monitor everyday activities but also continuously record vital signs like heart rate, perhaps providing information on a person's mental state. Recent research has used these sensors in conjunction with machine learning methods to identify patterns relating to different mental health conditions, highlighting the immense potential of this data beyond simple activity monitoring. In this research, we present a novel algorithm called the Hybrid Random forest - Neural network that has been tailored to evaluate sensor data from depressed patients. Our method has a noteworthy accuracy of 80\% when evaluated on a special dataset that included both unipolar and bipolar depressive patients as well as healthy controls. The findings highlight the algorithm's potential for reliably determining a person's depression condition using sensor data, making a substantial contribution to the area of mental health diagnostics.
In the following work, we first propose two (partial summation) formulas involving the floor and ceiling functions. We use principle of mathematical induction to prove the propositions. Another formula relating to the difference of floor and ceiling functions is deduced using aforementioned pair. Finally, in the same section, we propose generalisation of Faulhaber's formula without proof and deduce certain new results using the generalised results. Thereafter, we introduce F-Hurwitz and C-Hurwitz Zeta functions (infinite series involving floor and ceiling functions respectively) which can be considered as the generalizations of Hurwitz Zeta function. For both infinite series, there exist equivalent series and two distinct methods are used to prove the same. Certain new relations are deduced using new Zeta functions. Thereafter, it is shown that even if new deductions have poles at s=q, their differences at the same are convergent. Further some special cases are given for particular values of the Zeta functions. Lastly, certain open problems are provided which might be helpful for further advancements in the field.