arXiv subjects

Vaibhav Pandey

Publications and source records attributed to Vaibhav Pandey.

30 records · Page 2Linked to original sources

arXiv2020

N=1 Modelling of Lifestyle Impact on SleepPerformance

Sleep is critical to leading a healthy lifestyle. Each day, most people go to sleep without any idea about how their night's rest is going to be. For an activity that humans spend around a third of their life doing, there is a surprising amount of mystery around it. Despite current research, creating personalized sleep models in real-world settings has been challenging. Existing literature provides several connections between daily activities and sleep quality. Unfortunately, these insights do not generalize well in many individuals. For these reasons, it is important to create a personalized sleep model. This research proposes a sleep model that can identify causal relationships between daily activities and sleep quality and present the user with specific feedback about how their lifestyle affects their sleep. Our method uses N-of-1 experiments on longitudinal user data and event mining to generate understanding between lifestyle choices (exercise, eating, circadian rhythm) and their impact on sleep quality. Our experimental results identified and quantified relationships while extracting confounding variables through a causal framework. These insights can be used by the user or a personal health navigator to provide guidance in improving sleep.

cs.CY↗

arXiv2020

Cohomological dimension of ideals defining Veronese subrings

Given a standard graded polynomial ring over a commutative Noetherian ring $A$, we prove that the cohomological dimension and the height of the ideals defining any of its Veronese subrings are equal. This result is due to Ogus when $A$ is a field of characteristic zero, and follows from a result of Peskine and Szpiro when $A$ is a field of positive characteristic; our result applies, for example, when $A$ is the ring of integers.

math.AC↗

arXiv2020

Continuous Health Interface Event Retrieval

Knowing the state of our health at every moment in time is critical for advances in health science. Using data obtained outside an episodic clinical setting is the first step towards building a continuous health estimation system. In this paper, we explore a system that allows users to combine events and data streams from different sources to retrieve complex biological events, such as cardiovascular volume overload. These complex events, which have been explored in biomedical literature and which we call interface events, have a direct causal impact on relevant biological systems. They are the interface through which the lifestyle events influence our health. We retrieve the interface events from existing events and data streams by encoding domain knowledge using an event operator language.

cs.HC↗

arXiv2019

Synchronizing Geospatial Information for Personalized Health Monitoring

The health effects of air pollution have been subject to intense study in recent decades. Exposure to pollutants such as airborne particulate matter and ozone has been associated with increases in morbidity and mortality, especially with regards to respiratory and cardiovascular diseases. Unfortunately, individuals do not have readily accessible methods by which to track their exposure to pollution. This paper proposes how pollution parameters like CO, NO2, O3, PM2.5, PM10 and SO2 can be monitored for respiratory and cardiovascular personalized health during outdoor exercise events. Using location tracked activities, we synchronize them to public data sets of pollution sensors. For improved accuracy in estimation, we use heart rate data to understand breathing volume mapped with the local air quality sensors via constant GPS tracking.

cs.HC↗

arXiv2018

Surface Type Estimation from GPS Tracked Bicycle Activities

Road conditions affect both machine and human powered modes of transportation. In the case of human powered transportation, poor road conditions increase the work for the individual to travel. Previous estimates for these parameters have used computationally expensive analysis of satellite images. In this work, we use a computationally inexpensive and simple method by using only GPS data from a human powered cyclist. By estimating if the road taken by the user has high or low variations in their directional vector, we classify if the user is on a paved road or on an unpaved trail. In order to do this, three methods were adopted, changes in frequency of the direction of slope in a given path segment, fitting segments of the path, and finding the first derivative and the number of points of zero crossings of each segment. Machine learning models such as support vector machines, K-nearest neighbors, and decision trees were used for the classification of the path. We show in our methods, the decision trees performed the best with an accuracy of 86\%. Estimation of the type of surface can be used for many applications such as understanding rolling resistance for power estimation estimation or building exercise recommendation systems by user profiling as described in detail in the paper.

cs.LG↗

arXiv2018

Ubiquitous Event Mining to Enhance Personal Health

Advances in user interfaces, pattern recognition, and ubiquitous computing continue to pave the way for better navigation towards our health goals. Quantitative methods which can guide us towards our personal health goals will help us optimize our daily life actions, and environmental exposures. Ubiquitous computing is essential for monitoring these factors and actuating timely interventions in all relevant circumstances. We need to combine the events recognized by different ubiquitous systems and derive actionable causal relationships from an event ledger. Understanding of user habits and health should be teleported between applications rather than these systems working in silos, allowing systems to find the optimal guidance medium for required interventions. We propose a method through which applications and devices can enhance the user experience by leveraging event relationships, leading the way to more relevant, useful, and, most importantly, pleasurable health guidance experience.

cs.HC↗

arXiv2018

Cross-Modal Health State Estimation

Individuals create and consume more diverse data about themselves today than any time in history. Sources of this data include wearable devices, images, social media, geospatial information and more. A tremendous opportunity rests within cross-modal data analysis that leverages existing domain knowledge methods to understand and guide human health. Especially in chronic diseases, current medical practice uses a combination of sparse hospital based biological metrics (blood tests, expensive imaging, etc.) to understand the evolving health status of an individual. Future health systems must integrate data created at the individual level to better understand health status perpetually, especially in a cybernetic framework. In this work we fuse multiple user created and open source data streams along with established biomedical domain knowledge to give two types of quantitative state estimates of cardiovascular health. First, we use wearable devices to calculate cardiorespiratory fitness (CRF), a known quantitative leading predictor of heart disease which is not routinely collected in clinical settings. Second, we estimate inherent genetic traits, living environmental risks, circadian rhythm, and biological metrics from a diverse dataset. Our experimental results on 24 subjects demonstrate how multi-modal data can provide personalized health insight. Understanding the dynamic nature of health status will pave the way for better health based recommendation engines, better clinical decision making and positive lifestyle changes.

cs.CY↗

arXiv2018

Endogenous and Exogenous Multi-Modal Layers in Context Aware Recommendation Systems for Health

People care more about the solutions to their problems rather than data alone. Inherently, this means using data to generate a list of recommendations for a given situation. The rapid growth of multi-modal wearables and sensors have not made this jump effectively in the domain of health. Modern user content consumption and decision making in both cyber (e.g. entertainment, news) and physical (eg. food, shopping) spaces rely heavily on targeted personalized recommender systems. The utility function is the primary ranking method to predict what a given person would explicitly prefer. In this work we describe two unique layers of user and context modeling that can be coupled to traditional recommender system approaches. The exogenous layer incorporates factors outside of the person's body (eg. location, weather, social context), while the endogenous layer integrates data to estimate the physiologic or innate needs of the user. This is accomplished through multi-modal sensor data integration applied to domain-specific utility functions, filters and re-ranking weights. We showcase this concept through a nutrition guidance system focused on controlling sodium intake at a personalized level, dramatically improving upon the fixed recommendations.

cs.CY↗

arXiv2017

A Dedekind Domain with Nontrivial Class Group

Analytic properties of function spaces over the real and the complex fields are different in some ways. This reflects in algebraic properties which are different at times and similar in some other respects. For instance, the ring of real-valued continuous functions on a closed interval like $[0,1]$ behaves similarly to the corresponding ring of complex-valued functions; they depend only on the topology of $[0,1]$. The ring $\mathbf{R}[X,Y]/(X^2+Y^2-1)$ of real-valued polynomial functions on the unit circle is not a unique factorization domain - witness the equation $$\cos^2(t) = (1+ \sin(t))(1- \sin(t)).$$ On the other hand, the ring $\mathbf{C}[X,Y]/(X^2+Y^2-1) \cong \mathbf{C}[X+iY, 1/(X+iY)]$ is a principal ideal domain. Again, the rings of convergent power series (over either of these fields) with radius of convergence larger than some number $ρ$ is a Euclidean domain (and hence, a principal ideal domain) - this can be seen by using for a Euclidean "norm" function, the function which counts zeroes (with multiplicity) in the disc $|z| \leq ρ$. In this note, we consider the rings $C_{an}(S^1;\mathbf{R})$ of real-analytic functions on the unit circle $\mathit{S}^1$ which are real-valued and the corresponding ring $C_{an}(S^1; \mathbf{C})$ of analytic functions that are complex-valued. We will see that the latter is a principal ideal domain while the former is a Dedekind domain which is not a principal ideal domain - the class group having order $2$.

math.RA↗

arXiv2017

Cybernetic Health

Future health ecosystems demand the integration of emerging data technology with an increased focus on preventive medicine. Cybernetics extracts the full potential of data to serve the spectrum of health care, from acute to chronic problems. Building actionable cybernetic navigation tools can greatly empower optimal health decisions, especially by quantifying lifestyle and environmental data. This data to decisions transformation is powered by intuitive event analysis to offer the best semantic abstraction of dynamic living systems. Achieving the goal of preventive health systems in the cybernetic model occurs through the flow of several components. From personalized models we can predict health status using perpetual sensing and data streams. Given these predictions, we give precise recommendations to best suit the prediction for that individual. To enact these recommendations we use persuasive technology in order to deliver and execute targeted interventions.

cs.CY↗

arXiv2016

Ring Of Real Analytic Functions on $[0,1]$

We consider the ring of real analytic functions defined on $[0,1]$, i.e. $$C^ω[0,1] =\lbrace f :[0,1] \longrightarrow \mathbb{R} | f \text{ is analytic on } [0,1]\rbrace$$ In this article, we explore the nature of ideals in this ring. It is well known that the ring $C[0,1]$ of real valued continuous functions on $[0,1]$ has precisely the following maximal ideals: $$\text{For } γ\in [0,1], M_γ := \lbrace f \in C[0,1] | f(γ) =0\rbrace$$ It has been proved that each such $M_γ$ is infinitely generated, in-fact uncountably generated. Observe that $C^ω[0,1]$ is a subring of $C[0,1]$ We prove that for any $γ$ in $[0,1]$, the contraction $M^ω_γ$ of $M_γ$ under the natural inclusion of $C^ω[0,1]$ in $C[0,1]$ is again a maximal ideal (of $C^ω[0,1]$ ), and these are precisely all the maximal ideals of $C^ω[0,1]$. Next we prove that each $M^ω_γ$ is principal (though $M_γ$ is uncountably generated). Surprisingly, this forces all the ideals of the ring $C^ω[0,1]$ to be singly generated, i.e. $C^ω[0,1]$ is a PID.

math.AC↗

arXiv2016

On non-maximal prime ideals of $C[0,1]$

We first show a counter intuitive result that in the ring of real valued continuous functions on $[0,1]$ non maximal prime ideals exist. This is a standard proof and a well known result. Interestingly, a non maximal prime ideal in this ring is actually contained inside a unique maximal ideal. We arrive at this result merely by looking at the zero set of ideals in this ring and by making simple geometrical observations. We end by leaving the reader with an interesting open problem that logically follows from this article.

math.RA↗