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Manpreet Singh

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Published work

12 published item(s)

preprint2026arXiv

CodeEvolve: LLM-Driven Evolutionary Optimization with Runtime-Enriched Target Selection for Multi-Language Code Enhancement

We present CodeEvolve, an evolutionary framework for improving program performance and code quality with Large Language Models (LLMs). CodeEvolve extends OpenEvolve with runtime-guided target selection, Monte Carlo Tree Search (MCTS), automated code refinement, and language-specific evaluation pipelines for Java and Salesforce Apex. The system uses Java Flight Recorder (JFR) profiles to build weighted component graphs and select optimization targets that account for most execution cost, reducing reliance on manual bottleneck identification. For each target, CodeEvolve generates candidate edits, evaluates them through build validation, unit tests, performance checks, static analysis, and LLM-based review, and retains only variants that preserve functional correctness. Across real-world optimization tasks, CodeEvolve improves performance and code metrics while maintaining correctness. On a large enterprise Java codebase, it achieves an average speedup of 15.22$\times$ across seven hotspot functions and outperforms single-pass LLM optimization on five of them. An ablation study on Apex optimization shows that the full MCTS-augmented configuration produces 19.5 valid programs out of 20 on average, indicating that search, filtering, and refinement each contribute to more reliable optimization.

preprint2025arXiv

Effects of Coronal Mass Ejection on PSR J1022+1001 and Possible Mode Change of PSR J2145-0750 in the InPTA DR2

The Indian Pulsar Timing Array (InPTA) has recently published its second data release (DR2), comprising the timing analysis of seven years of data on 27 millisecond pulsars (MSPs), observed simultaneously in the 300-500 MHz (band 3) and 1260-1460 MHz (band 5), using the upgraded Giant Metrewave Radio Telescope (uGMRT). The low-frequency data, particularly in band 3, is highly sensitive to propagation effects such as dispersion measure (DM) fluctuations, which can be imprints of some astrophysical phenomena (scientific outliers). Here, we analyze the two outliers of possible astrophysical origin coming from the band 3 DM time series of two pulsars: PSR J1022+1001, with an ecliptic latitude of -0.06 degree, and PSR J2145-0750, one of the brightest MSPs, with multi-component profile morphology. Our study reveals compelling evidence for a coronal mass ejection (CME) event traced in the data of PSR J1022+1001, and reports evidence for a potential mode-changing event in PSR J2145-0750. By contrasting these two cases, we show that DM fluctuations due to CME interacions and intrinsic mode-changing events produce distinct observational signatures, enabling a physically informed classification of scientific outliers in PTA datasets. Extending the analyses presented here to the full sample of InPTA-DR2 pulsars is expected to reveal additional CME events, and possible mode-changing events. Such detections will not only improve our understanding of solar and pulsar magnetospheric plasma interactions but will also enable more accurate modelling of DM variations, leading to improved pulsar timing solutions, which are crucial for high-precision Pulsar Timing Array (PTA) science.

preprint2022arXiv

Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice

We investigate pairing and superconductivity in the attractive Fermi Hubbard model on the one-dimensional sawtooth lattice, which exhibits a flat band by fine-tuning the hopping rates. We first solve the two-body problem, both analytically and numerically, to extract the binding energy and the effective mass of the pairs. Based on the DMRG method, we address the ground-state properties of the many-body system, assuming equal spin populations. We compare our results with those available for a linear chain, where the model is integrable by Bethe ansatz, and show that the multiband nature of the system substantially modifies the physics of the BCS-BEC crossover. Near a flat band, the chemical potential remains always close to its zero-density limit predicted by the two-body physics. In contrast, the pairing gap exhibits a remarkably strong density dependence and, differently from the pair binding energy, it is no longer peaked at the flat-band point. We show that these results can be interpreted in terms of polarization screening effects, due to an anomalous attraction between pairs in the medium and single fermions. Importantly, we unveil that three-body bound states (trimers) exist in the sawtooth lattice, in sharp contrast with the linear chain geometry, and we compute their binding energy. The nature of these states is investigated via a strong coupling variational approach, revealing that they originate from tunneling-induced exchange processes.

preprint2020arXiv

Derivations of quandles

The aim of this paper is to propose a theory of derivations for quandles. Given a quandle $A$ admitting an action by a quandle $Q$, derivations from $Q$ to $A$ are introduced as twisted analogues of quandle homomorphisms. It is shown that for each quandle $Q$ there exists a unique $Q$-quandle $\mathcal{A}_Q$ (the derived quandle of $Q$) such that derivations from $Q$ to any $Q$-quandle $A$ are in bijective correspondence with $Q$-quandle homomorphisms from $\mathcal{A}_Q$ to $A$. Further, it is proved that the set of all derivations to an abelian $Q$-quandle $A$ has the structure of an abelian quandle, and inherits many other properties from $A$. In the end, the ideas are extended to the setting of virtual quandles.

preprint2020arXiv

Enhanced visibility of the Fulde-Ferrell-Larkin-Ovchinnikov state in one dimensional Bose-Fermi mixtures near the immiscibility point

Based on the matrix product states method, we investigate numerically the ground state properties of one-dimensional mixtures of repulsive bosons and spin-imbalanced attractive fermions, the latter being in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where Cooper pairs condense at a finite momentum $k=k_{FFLO}$. We find that the visibility of such a state is dramatically enhanced as the repulsive Bose-Fermi mixture is brought close to the phase-separation point. In particular, large amplitude self-induced oscillations with wave-vector $2k_{FFLO}$ appear in both the fermion total density and the boson density profiles, leaving sharp fingerprints in the corresponding static structure factors. We show that these features remain well visible in cold atoms systems trapped longitudinally by a smooth flat-bottom potential. Hence bosons can be used to directly reveal the modulated Fermi superfluid in experiments.

preprint2020arXiv

Mott insulator phases of non-locally coupled bosons in bilayer optical superlattices

We investigate the ground state properties of a non-locally coupled bosonic system in a bilayer optical superlattice by considering bosons in one layer to be of softcore in nature and separately allowing two and three body hardcore constraints on the other layer. We find that the presence of different constraints on bosons in one layer influences the overall phase diagram exhibiting various Mott insulator phases at incommensurate densities due to the presence of the superlattice potential apart from the usual Mott insulators at commensurate densities. Moreover, the presence of two or three-body constraints significantly modifies the Mott insulator-Superfluid phase transition points as a function of the superlattice potential. Due to the various competing interactions, constraints and superlattice potential the phase diagrams exhibit significantly different features. We obtain the complete phase diagrams by using the cluster-mean-field theory approach. We further extend this work to a coupled two-leg ladder superlattice where we obtain similar physics using the density matrix renormalization group method .

preprint2019arXiv

Link quandles are residually finite

Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these results and prove that free products of residually finite quandles are residually finite provided their associated groups are residually finite. As associated groups of link quandles are link groups, which are known to be residually finite, it follows that link quandles are residually finite.

preprint2019arXiv

Topological Dynamics of Enveloping Semigroups

A compact metric space $X$ and a discrete topological acting group $T$ give a flow $(X,T)$. Robert Ellis had initiated the study of dynamical properties of the flow $(X,T)$ via the algebraic properties of its "Enveloping Semigroup" $E(X)$. This concept of \emph{Enveloping Semigroups} that he defined, has turned out to be a very fundamental tool in the abstract theory of `topological dynamics'. The flow $(X,T)$ induces the flow $(2^X,T)$. Such a study was first initiated by Eli Glasner who studied the properties of this induced flow by defining and using the notion of a `circle operator' as an action of $βT$ on $2^X$, where $βT$ is the \emph{Stone-$\check{C}$ech compactification} of $T$ and also a universal enveloping semigroup. We propose that the study of properties for the induced flow $(2^X,T)$ be made using the algebraic properties of $E(2^X)$ on the lines of Ellis' \ theory, instead of looking into the action of $βT$ on $2^X$ via the circle operator as done by Glasner. Such a study requires extending the present theory on the flow $(E(X),T)$. In this article, we take up such a study giving some subtle relations between the semigroups $E(X)$ and $E(2^X)$ and some interesting associated consequences.

preprint2016arXiv

Three-body interacting dipolar bosons and the fate of lattice supersolidity

We investigate a system of dipolar bosons in an optical lattice with local two and three-body interactions. Using the mean-field theory approach, we obtain the ground state phase diagram of the extended Bose-Hubbard (EBH) model with both repulsive and attractive three-body interac- tions. We show that the additional three-body on-site interaction has strong effects on the phase diagram especially on the supersolid phase. Positive values of the three-body interaction lead to the enhancement of the gapped phases at densities larger than unity by reducing the supersolid region. However, a small attractive three-body interaction enhances the supersolid phase.

preprint2014arXiv

Quantum phases of attractive bosons on a Bose-Hubbard ladder with three-body constraint

We obtain the complete quantum phase diagram of bosons on a two-leg ladder in the presence of attractive onsite and repulsive interchain nearest-neighbor interactions by imposing the onsite three-body constraint. We find three distinct phases; namely, the atomic superfluid (ASF), dimer superfluid (DSF), and the dimer rung insulator (DRI). In the absence of the interchain nearest-neighbor repulsion, the system exhibits a transition from the ASF to the DSF phase with increasing onsite attraction. However, the presence of the interchain nearest-neighbor repulsion stabilizes a gapped DRI phase, which is flanked by the DSF phase. We also obtain the phase diagram of the system for different values of the interchain nearest-neighbor interaction. By evaluating different order parameters, we obtain the complete phase diagram and the properties of the phase transitions using the self-consistent cluster mean-field theory.

preprint2012arXiv

Mean field analysis of quantum phase transitions in a periodic optical superlattice

In this paper we analyze the various phases exhibited by a system of ultracold bosons in a periodic optical superlattice using the mean field decoupling approximation. We investigate for a wide range of commensurate and incommensurate densities. We find the gapless superfluid phase, the gapped Mott insulator phase, and gapped insulator phases with distinct density wave orders.

preprint2012arXiv

Three body on-site interactions in ultracold bosonic atoms in optical lattices and superlattices

The Mott insulator-superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also suggest possible experimental signatures to observe the three-body interactions.