Dhagash Mehta

BlackRock (United States)

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Reliable mixture critical point computation using polynomial homotopy continuation

AIChE Journal (2016)

Hythem Sidky Jonathan K. Whitmer Dhagash Mehta

The numerical computation of multicomponent mixture critical points has been the subject of much study due to their theoretical and practical importance. Both deterministic and stochastic methods have been applied with varying degrees of reliability and robustness. In this work, we utilize numerical polynomial homotopy continuation (NPHC) to reliably identify all mixture critical points. This method is unique due to its robustness, initialization‐free nature and ease of parallelization. For a given system of equations, all complex solutions are found. Computational times are also found to be invariant to mixture composition. We validate this technique against previous work and extend the method to mixtures of up to eight components. NPHC is shown to be a modern and powerful technique which offers mathematical reliability at a moderate computational cost. © 2016 American Institute of Chemical Engineers AIChE J , 62: 4497–4507, 2016

Initialization

Robustness

Continuation

Homotopy Analysis Method

Critical point (mathematics)

10.1002/aic.15319

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Citations (9)

Dimitrios Vamvourellis Máté Tóth Snigdha Bhagat Dhruv Desai Dhagash Mehta

Similarity (geometry)

10.1109/cifer62890.2024.10772990

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Citations (2)

’t Hooft-Polyakov monopoles in latticeSU(N)+adjoint Higgstheory

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology (2009)

S. R. Edwards Dhagash Mehta Arttu Rajantie Lorenz von Smekal

We investigate twisted $C$-periodic boundary conditions in $\mathrm{SU}(N)$ gauge field theory with an adjoint Higgs field. We show that with a suitable twist for even $N$ one can impose a nonzero magnetic charge relative to residual U(1) gauge groups in the broken phase, thereby creating a 't Hooft-Polyakov magnetic monopole. This makes it possible to use lattice Monte Carlo simulations to study the properties of these monopoles in the quantum theory.

Lattice (music)

Lattice gauge theory

10.1103/physrevd.80.065030

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Citations (8)

A Comparative Study of DSPy Teleprompter Algorithms for Aligning Large Language Models Evaluation Metrics to Human Evaluation

arXiv (Cornell University) (2024)

Bhaskarjit Sarmah Krishna Dutta Anna Grigoryan Sachin Tiwari Stefano Pasquali

We argue that the Declarative Self-improving Python (DSPy) optimizers are a way to align the large language model (LLM) prompts and their evaluations to the human annotations. We present a comparative analysis of five teleprompter algorithms, namely, Cooperative Prompt Optimization (COPRO), Multi-Stage Instruction Prompt Optimization (MIPRO), BootstrapFewShot, BootstrapFewShot with Optuna, and K-Nearest Neighbor Few Shot, within the DSPy framework with respect to their ability to align with human evaluations. As a concrete example, we focus on optimizing the prompt to align hallucination detection (using LLM as a judge) to human annotated ground truth labels for a publicly available benchmark dataset. Our experiments demonstrate that optimized prompts can outperform various benchmark methods to detect hallucination, and certain telemprompters outperform the others in at least these experiments.

10.48550/arxiv.2412.15298

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Three Formulations of the Kuramoto Model as a System of Polynomial Equations

arXiv (Cornell University) (2016)

Tianran Chen Jakub Mareček Dhagash Mehta Matthew Niemerg

We compare three formulations of stationary equations of the Kuramoto model as systems of polynomial equations. In the comparison, we present bounds on the numbers of real equilibria based on the work of Bernstein, Kushnirenko, and Khovanskii, and performance of methods for the optimisation over the set of equilibria based on the work of Lasserre, both of which could be of independent interest.

10.48550/arxiv.1603.05905

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Citations (4)

Fund2Vec

Vipul Satone Dhruv Desai Dhagash Mehta

Identifying similar mutual funds with respect to the underlying portfolios has found many applications in financial services ranging from fund recommender systems, competitors analysis, portfolio analytics, marketing and sales, etc. The traditional methods are either qualitative, and hence prone to biases and often not reproducible, or, are known not to capture all the nuances (non-linearities) among the portfolios from the raw data. We propose a radically new approach to identify similar funds based on the weighted bipartite network representation of funds and their underlying assets data using a sophisticated machine learning method called Node2Vec which learns an embedded low-dimensional representation of the network. We call the embedding Fund2Vec. Ours is the first ever study of the weighted bipartite network representation of the funds-assets network in its original form that identifies structural similarity among portfolios as opposed to merely portfolio overlaps.

Competitor analysis

Representation

Similarity (geometry)

10.1145/3490354.3494381

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Citations (5)

Minimizing Higgs Potentials via Numerical Polynomial Homotopy Continuation

arXiv (Cornell University) (2012)

M. Maniatis Dhagash Mehta

The study of models with extended Higgs sectors requires to minimize the corresponding Higgs potentials, which is in general very difficult. Here, we apply a recently developed method, called numerical polynomial homotopy continuation (NPHC), which guarantees to find all the stationary points of the Higgs potentials with polynomial-like nonlinearity. The detection of all stationary points reveals the structure of the potential with maxima, metastable minima, saddle points besides the global minimum. We apply the NPHC method to the most general Higgs potential having two complex Higgs-boson doublets and up to five real Higgs-boson singlets. Moreover the method is applicable to even more involved potentials. Hence the NPHC method allows to go far beyond the limits of the Gr\"obner basis approach.

Maxima and minima

Saddle point

Continuation

Numerical continuation

10.48550/arxiv.1203.0409

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Citations (0)

Numerical results regarding the sign problem in 2 dimensional Supersymmetric Yang-Mills theories with 4 and 16 supercharges

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011) (2012)

Richard Galvez Simon Catterall Dhagash Mehta Anosh Joseph

Recently there has been some controversy in the literature concerning the existence of a fermion sign problem in the N = (2, 2) supersymmetric Yang-Mills (SYM) theories on the lattice.In this work, we address this issue by conducting Monte Carlo simulations not only for N = (2, 2) but also for N = (8, 8) SYM in two dimensions for the U(N) theories with N = 2, using the new ideas derived from topological twisting followed by geometric discretization.Our results from simulations provide the evidence that these theories do not suffer from a sign problem as the continuum limit is approached.These results thus boost confidence that these new lattice formulations can be used successfully to explore the nonperturbative aspects of the four-dimensional N = 4 SYM theory.

Lattice (music)

Yang–Mills theory

10.22323/1.139.0064

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Citations (3)

Decomposing the parameter space of biological networks via a numerical discriminant approach

arXiv (Cornell University) (2016)

Heather A. Harrington Dhagash Mehta Helen M. Byrne Jonathan D. Hauenstein

Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and characterize the steady-state solutions as the model parameters vary, a technically challenging problem in a high-dimensional parameter landscape. Rather than simply determining the number and stability of steady-states at distinct points in parameter space, we decompose the parameter space into finitely many regions, the steady-state solutions being consistent within each distinct region. From a computational algebraic viewpoint, the boundary of these regions is contained in the discriminant locus. We develop global and local numerical algorithms for constructing the discriminant locus and classifying the parameter landscape. We showcase our numerical approaches by applying them to molecular and cell-network models.

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Citations (5)

Introduction to numerical polynomial homotopy continuation methods for the power systems practitioners

2022 American Control Conference (ACC) (2016)

Dhagash Mehta

Summary form only given. The polynomial numerical homotopy continuation method has gained quite some attention from the power systems community due to its ability of finding all power flow solutions. The method is able to adapt to power systems on different networks. Hence, the method has a potential to scale fairly better compared to other computational methods that find all power flow solutions. In this talk, I will spell out the basics of the method, with an emphasis on its parallelizablity, and will demonstrate how the method can be used to solve different subproblems, in order to directly solve power flow equations, such as finding stability boundaries of power flow equations.

Continuation

Homotopy Analysis Method

10.1109/acc.2016.7525173

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Citations (0)