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Ranjana Mehta

Publications and source records attributed to Ranjana Mehta.

12 recordsLinked to original sources
arXiv2026

Generalized binomial edge ideals of whisker graphs via an extension of generalized corona products

In this paper, we initiate a systematic study of generalized binomial edge ideals of whisker graphs by working within a substantially broader class of graphs. We extend the notion of generalized corona products, and through this enlarged framework, investigate fundamental algebraic invariants such as depth, (Castelnuovo-Mumford) regularity, and the Cohen-Macaulay property. In particular, we establish a sharp lower bound on the depth of generalized binomial edge ideals for our extended class, and further obtain explicit depth formula for a broad subclass of this family, which in turn recovers the depth formula for whisker graphs. We also establish sharp upper bounds for the regularity, and in the case of binomial edge ideals of whisker graphs over gap-free graphs, determine the exact value of the regularity. Finally, for our extended class, we provide a combinatorial classification of all Cohen-Macaulay binomial edge ideals, which in turn yields a new construction of Cohen-Macaulay binomial edge ideals.

math.AC↗
arXiv2025

On a regularity-conjecture of generalized binomial edge ideals

In this paper, we prove the upper bound conjecture proposed by Saeedi Madani \& Kiani on the Castelnuovo-Mumford regularity of generalized binomial edge ideals. We give a combinatorial upper bound of regularity for generalized binomial edge ideals, which is better than the bound claimed in that conjecture. Also, we show that the bound is tight by providing an infinite class of graphs.

math.AC↗
arXiv2025

Tangent Cones of Concatenated Numerical Semigroups

We study the tangent cone at the origin and the Hilbert series for a family of numerical semigroups generated by concatenation of arithmetic sequences. We prove that all the concatenation classes have Cohen-Macaulay tangent cones except the symmetric class, however, the symmetric class does satisfy Rossi's conjecture.

math.AC↗
arXiv2025

Tangent Cones of Bresinsky and Arslan Curves

In this paper, we study the Apery tables for the numerical semigroups given by Bresinsky and Arslan. Using the Apery tables we write the tangent cones of the Bresinsky and Arsalan curves at the origin. Further, we calculate Hilbert series of the tangent cone of the Bresinsky and Arslan curves. We prove that both classes of the curve have Cohen- Macaulay tangent cone.

math.AC↗
arXiv2024

Neural, Muscular, and Perceptual responses with shoulder exoskeleton use over Days

Passive shoulder exoskeletons have been widely introduced in the industry to aid upper extremity movements during repetitive overhead work. As an ergonomic intervention, it is important to understand how users adapt to these devices over time and if these induce external stress while working. The study evaluated the use of an exoskeleton over a period of 3 days by assessing the neural, physiological, and perceptual responses of twenty-four participants by comparing a physical task against the same task with an additional cognitive workload. Over days adaptation to task irrespective of task and group were identified. Electromyography (EMG) analysis of shoulder and back muscles reveals lower muscle activity in the exoskeleton group irrespective of task. Functional connectivity analysis using functional near infrared spectroscopy (fNIRS) reveals that exoskeletons benefit users by reducing task demands in the motor planning and execution regions. Sex-based differences were also identified in these neuromuscular assessments.

q-bio.QM↗
arXiv2024

On the Depth of Generalized Binomial Edge Ideals

This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of $d$-compatible map for the pairs of a complete graph and an arbitrary graph, and using it, we give a combinatorial lower bound for the depth of generalized binomial edge ideals. Subsequently, we determine an upper bound for the depth of generalized binomial edge ideals in terms of the vertex-connectivity of graphs. We demonstrate that the difference between the upper and lower bounds can be arbitrarily large, even in cases when one of the bounds is sharp. In addition, we calculate the depth of generalized binomial edge ideals of certain classes of graphs, including cyclic graphs and graphs with Cohen-Macaulay binomial edge ideals.

math.AC↗
arXiv2023

Evaluating Mental Stress Among College Students Using Heart Rate and Hand Acceleration Data Collected from Wearable Sensors

Stress is various mental health disorders including depression and anxiety among college students. Early stress diagnosis and intervention may lower the risk of developing mental illnesses. We examined a machine learning-based method for identification of stress using data collected in a naturalistic study utilizing self-reported stress as ground truth as well as physiological data such as heart rate and hand acceleration. The study involved 54 college students from a large campus who used wearable wrist-worn sensors and a mobile health (mHealth) application continuously for 40 days. The app gathered physiological data including heart rate and hand acceleration at one hertz frequency. The application also enabled users to self-report stress by tapping on the watch face, resulting in a time-stamped record of the self-reported stress. We created, evaluated, and analyzed machine learning algorithms for identifying stress episodes among college students using heart rate and accelerometer data. The XGBoost method was the most reliable model with an AUC of 0.64 and an accuracy of 84.5%. The standard deviation of hand acceleration, standard deviation of heart rate, and the minimum heart rate were the most important features for stress detection. This evidence may support the efficacy of identifying patterns in physiological reaction to stress using smartwatch sensors and may inform the design of future tools for real-time detection of stress.

cs.HC↗
arXiv2019

Betti numbers of Bresinsky's curves in $\mathbb{A}^{4}$

Bresinsky defined a class of monomial curves in $\mathbb{A}^{4}$ with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behaviour of unboundedness is true for all the Betti numbers and construct an explicit minimal free resolution for this class.

math.AC↗