arXiv subjects

Ranveer Singh

Publications and source records attributed to Ranveer Singh.

At least 19 recordsLinked to original sources

arXiv2026

Exponential Lower Bounds for the Pfaffian Number of Graphs

Galluccio--Loebl and Tesler showed that the perfect-matching polynomial of a graph embedded in an orientable surface of genus $g$ can be written as a linear combination of at most $4^g$ Pfaffians. We show that, in general, exponentially many Pfaffians are necessary. More precisely, for every $g\ge1$, there exists a graph of orientable genus at most $g$ whose perfect-matching polynomial requires at least $(8/3)^g$ Pfaffians in any such linear representation. In particular, for every even integer $n\ge6$, there is a graph on $n$ vertices with Pfaffian number at least $(8/3)^{\lfloor n/6\rfloor}$. Moreover, the lower bound is witnessed even by cubic bipartite matching-covered graphs. We prove this by showing that expressing the permanent of an $n\times n$ matrix of distinct variables as a linear combination of determinants obtained by changing signs of its entries requires exponentially many determinants. As a consequence, we improve a recent linear lower bound on the Pfaffian number due to Junchaya, Miranda, and Lucchesi to an exponential lower bound.

math.CO↗

arXiv2026

Revealing the origin of ionic conduction in silver-iodide-doped silver phosphate glass

Fast ionic transport is a defining feature of many solid electrolytes, yet its microscopic origin is not fully understood. In the absence of microscopic insights, the development of next-generation solid-state batteries remains largely empirical. Most existing measurements access either the low-frequency transport response or the high-frequency bound polarization, yet the intermediate mesoscopic frequency regime is where ionic transport emerges. By varying the $\mathrm{AgI}$ concentration ($x$) and performing time-domain terahertz spectroscopy (TDTS) in a prototypical glassy electrolyte $\left(\mathrm{AgI}\right)_{x}\left(\mathrm{AgPO_3}\right)_{(1-x)}$, we reveal this intermediate frequency regime and identify a crossover from bound-current-dominated conduction to conductivity arising from short-range dispersive ionic transport. We find that bound polarization associated with the bond-bending motion of the $\mathrm{P{-}O^- -Ag^+}$ motif is present across compositions but is insufficient to produce ionic transport on its own. Transport emerges only when this polarization is embedded in a sufficiently soft $\mathrm{AgPO_3}$ glassy matrix and accompanied by a high carrier density. These ingredients together take the system from a vibrationally bound response to short-range dispersive motion.

cond-mat.mtrl-sci↗

arXiv2026

Online Convex Optimization with Dueling Feedback

We study online convex optimization with dueling (pairwise comparison) feedback, where the learner observes only a binary preference between two queried points. While dueling feedback is well understood in discrete or stochastic settings, the adversarial convex setting has remained unexplored. We propose a simple reduction that converts dueling feedback into approximate gradients, enabling the use of standard first-order methods. We show that regret guarantees transfer under this reduction, yielding the first results for this setting, including $\mathcal{O}(T^{3/4})$ static, adaptive, and dynamic regret. Under additional structure, we obtain improved rates of $\mathcal{O}(T^{2/3})$ for smooth objectives and $\mathcal{O}(\sqrt{T \log T})$ for strongly convex functions.

cs.LG↗

arXiv2026

A Neurosymbolic Approach for Constructing Planning Domain Models from Clinical Narratives

Surgical procedures such as laparoscopic appendectomy are complex, high-stakes processes, yet formalizing their workflows for decision support remains a significant challenge. Inducing probabilistic planning domain models in this setting is particularly difficult due to the lack of structured event data and the prevalence of implicit actions in clinical narratives, which neither empirical symbolic methods nor Large Language Models (LLMs) can adequately address on their own. We introduce NSPIN, a neurosymbolic framework for inducing probabilistic planning domain models from unstructured clinical narratives. Our method extracts and imputes structured event sequences from raw text using a pretrained LLM, then induces a PPDDL model and refines its preconditions with LLM-proposed revisions, guided by empirical validation. We evaluate the approach on 2,660 laparoscopic appendectomy notes written by 9 surgeons. NSPIN yields models that generalize to unseen notes, and expert clinical review indicates its induced knowledge is largely consistent with surgical practice.

cs.LG↗

arXiv2026

A Neurosymbolic Approach for Explainable Early Diagnosis of Alzheimer's Disease

Identifying reliable Alzheimer's disease (AD) markers typically requires manual, labor-intensive transcription and expert analysis, limiting its scale. We introduce an automated pipeline that extracts qualitative knowledge about potential AD progression indicators directly from audio recordings of verbal fluency tests. Our method uses pretrained foundation models to process raw audio and extract clinically relevant variables to construct a Bayesian Network (BN); this BN is used to reason about the AD progression markers and infer their qualitative relationships. Our system successfully recovers known clinical knowledge and identifies novel relationships between linguistic markers.

cs.LG↗

arXiv2026

Dynamic Structural Causal Modeling for Sleep

The causal dynamics of sleep-disordered breathing are complex and vary across patient populations, hindering the development of targeted interventions. We learn dynamic causal graphs of sleep-disordered breathing from Home Sleep Apnea Test (HSAT) recordings, revealing systematic differences in causal structure across sex and age subcohorts. We do so using the PCMCI+ algorithm on windowed fractional variables derived from 105 HSAT recordings, exploiting domain knowledge via edge blacklisting and employing bootstrap aggregation to address small subcohort sizes. The learned graphs show that temporal self-dependencies and the apnea-desaturation relationship persist across all cohorts, while other relationships vary substantially.

cs.LG↗

arXiv2026

Upper-Linearizability of Online Non-Monotone DR-Submodular Maximization over Down-Closed Convex Sets

We study online maximization of non-monotone Diminishing-Return(DR)-submodular functions over down-closed convex sets, a regime where existing projection-free online methods suffer from suboptimal regret and limited feedback guarantees. Our main contribution is a new structural result showing that this class is $1/e$-linearizable under carefully designed exponential reparametrization, scaling parameter, and surrogate potential, enabling a reduction to online linear optimization. As a result, we obtain $O(T^{1/2})$ static regret with a single gradient query per round and unlock adaptive and dynamic regret guarantees, together with improved rates under semi-bandit, bandit, and zeroth-order feedback. Across all feedback models, our bounds strictly improve the state of the art.

cs.LG↗

arXiv2026

Permanental Energy of Graphs

For a simple graph $G$ with adjacency matrix $A(G)$, let $π(G,x):=\mathrm{per}(xI-A(G))$ be its permanental polynomial with roots $μ_1,\ldots,μ_n \in \mathbb{C}$, and define the permanental energy $E_{\mathrm{per}}(G):=\sum_{i=1}^n |μ_i|$. We prove a sharp universal lower bound: for every $m$-edge graph $G$, $E_{\mathrm{per}}(G) \ge 2\sqrt{m}$, with equality if and only if $G$ is a star together with isolated vertices. We also prove the general upper bound $E_{\mathrm{per}}(G) \le nρ(G)$, where $ρ(G)$ is the spectral radius, and we study $E_{\mathrm{per}}(G)$ on several graph families.

math.CO↗

arXiv2026

On Chollet's Permanent Conjecture for Graph Laplacians

In 1982, Chollet conjectured that $\mathrm{per}(A\circ B)\le \mathrm{per}(A)\mathrm{per}(B)$ for Hermitian positive semidefinite matrices $A,B$, where $\circ$ denotes the Hadamard product, and observed that in the real symmetric case it suffices to prove $\mathrm{per}(A\circ A)\le \mathrm{per}(A)^2$. We prove $\mathrm{per}(A\circ A)\le \mathrm{per}(A)^2$ for symmetric $Z$-matrices with nonnegative diagonal whose support graph is bipartite. Motivated by this, we study the Laplacian inequality $\mathrm{per}(L_G\circ L_G)\le \mathrm{per}(L_G)^2$ for the graph Laplacian $L_G$. We introduce a compositional framework for permanental inequalities on graph Laplacians, showing that Chollet's inequality is preserved under vertex coalescence. This enables the extension of the inequality from basic graph classes to large structured families, revealing new tractable regimes for a fundamentally $\#P$-hard quantity.

math.CO↗

arXiv2026

Stronger Approximation Guarantees for Non-Monotone γ-Weakly DR-Submodular Maximization

Maximizing submodular objectives under constraints is a fundamental problem in machine learning and optimization. We study the maximization of a nonnegative, non-monotone $γ$-weakly DR-submodular function over a down-closed convex body. Our main result is an approximation algorithm whose guarantee depends smoothly on $γ$; in particular, when $γ=1$ (the DR-submodular case) our bound recovers the $0.401$ approximation factor, while for $γ<1$ the guarantee degrades gracefully and, it improves upon previously reported bounds for $γ$-weakly DR-submodular maximization under the same constraints. Our approach combines a Frank-Wolfe-guided continuous-greedy framework with a $γ$-aware double-greedy step, yielding a simple yet effective procedure for handling non-monotonicity. This results in state-of-the-art guarantees for non-monotone $γ$-weakly DR-submodular maximization over down-closed convex bodies.

cs.LG↗

arXiv2025

Permanental Analog of the Rank-Nullity Theorem for Symmetric Matrices

The rank of an n x n matrix A is equal to the size of its largest square submatrix with a nonzero determinant, and it can be computed in O(n^2.37) time. Analogously, the size of the largest square submatrix with nonzero permanent is defined as the permanental rank. Computing the permanent or the coefficients of the permanental polynomial is #P-complete. The permanental nullity is defined as the multiplicity of zero as a root of the permanental polynomial. We establish a permanental analog of the rank-nullity theorem, showing that the sum of the permanental rank and the permanental nullity equals n for symmetric nonnegative matrices, positive semidefinite matrices, and adjacency matrices of balanced signed graphs. Using this theorem, we can compute the permanental nullity for symmetric nonnegative matrices and adjacency matrices of balanced signed graphs in polynomial time. For symmetric matrices with entries in {0, plus or minus 1}, we also provide a complete characterization of when the permanental rank-nullity identity holds.

math.CO↗

arXiv2025

Cartesian Prime Graphs and Cospectral Families

We introduce a method for constructing larger families of connected cospectral graphs from two given cospectral families of sizes $p$ and $q$. The resulting family size depends on the Cartesian primality of the input graphs and can be one of $pq$, $p + q - 1$, or $\max(p, q)$, based on the strictness of the applied conditions. Under the strictest condition, our method generates $O(p^3q^3)$ new cospectral triplets, while the more relaxed conditions yield $\varOmega(pq^3 + qp^3)$ such triplets. We also use the existence of specific cospectral families to establish that of larger ones.

cs.DM↗

arXiv2025

Permanent of bipartite graphs in terms of determinants

Computing the permanent of a $(0,1)$-matrix is a well-known $\#P$-complete problem. In this paper, we present an expression for the permanent of a bipartite graph in terms of the determinant of the graph and its subgraphs, obtained by successively removing rows and columns corresponding to vertices involved in vertex-disjoint $4k$-cycles. Our formula establishes a general relationship between the permanent and the determinant for any bipartite graph. Since computing the permanent of a biadjacency matrix is equivalent to counting the number of its perfect matchings, this approach also provides a more efficient method for counting perfect matchings in certain types of bipartite graphs.

cs.DM↗

arXiv2025

Strengthening Wilf's lower bound on clique number

Given an integer $k$, deciding whether a graph has a clique of size $k$ is an NP-complete problem. Wilf's inequality provides a spectral bound for the clique number of simple graphs. Wilf's inequality is stated as follows: $\frac{n}{n - λ_{1}} \leq ω$, where $λ_1$ is the largest eigenvalue of the adjacency matrix $A(G)$, $n$ is the number of vertices in $G$, and $ω$ is the clique number of $G$. Strengthening this bound, Elphick and Wocjan proposed a conjecture in 2018, which is stated as follows: $\frac{n}{n - \sqrt{s^{+}}} \leq ω$, where $s^+ = \sum_{λ_{i} > 0} λ_{i}^2$ and $λ_i$ are the eigenvalues of $A(G)$. In this paper, we have settled this conjecture for some classes of graphs, such as conference graphs, strongly regular graphs with $λ= μ$ (i.e., $srg(n, d, μ, μ)$) and $n\geq 2d$, the line graph of $K_{n}$, the Cartesian product of strongly regular graphs, and Ramanujan graph with $n\geq 11d$.

cs.DM↗

arXiv2025

A Hybrid Similarity-Aware Graph Neural Network with Transformer for Node Classification

Node classification has gained significant importance in graph deep learning with real-world applications such as recommendation systems, drug discovery, and citation networks. Graph Convolutional Networks and Graph Transformers have achieved superior performance in node classification tasks. However, the key concern with Graph Convolutional Networks is over-squashing, which limits their ability to capture long-range dependencies in the network. Additionally, Graph Transformers face scalability challenges, making it difficult to process large graphs efficiently. To address this, we propose a novel framework, A Hybrid SImilarity-Aware Graph Neural Network with Transformer for Node Classification (SIGNNet), which capitalizes on local and global structural information, enhances the model's capability to effectively capture fine-grained relationships and broader contextual patterns within the graph structure. The proposed method leverages Graph Convolutional Networks alongside a score-based mechanism to effectively capture local and global node interactions while addressing the limitations of over-squashing. Our proposed method employs a novel Personalized PageRank-based node sampling method to address scalability issues by generating subgraphs of nodes. Additionally, SIGNNet incorporates a novel attention mechanism, Structure-Aware Multi-Head Attention (SA-MHA), which integrates node structural information for informed attention weighting, enabling the model to prioritize nodes based on topological significance. Extensive experiments demonstrate the significant improvements achieved by the proposed method over existing state-of-the-art methods, with average accuracy gains of 6.03%, 5.47%, 4.78%, 19.10%, 19.61%, 7.22%, 19.54%, and 14.94% on Cora, Citeseer, CS, Wisconsin, Texas, Actor, Cornell and Chameleon datasets, respectively.

cs.SI↗

arXiv2025

Combining Planning and Reinforcement Learning for Solving Relational Multiagent Domains

Multiagent Reinforcement Learning (MARL) poses significant challenges due to the exponential growth of state and action spaces and the non-stationary nature of multiagent environments. This results in notable sample inefficiency and hinders generalization across diverse tasks. The complexity is further pronounced in relational settings, where domain knowledge is crucial but often underutilized by existing MARL algorithms. To overcome these hurdles, we propose integrating relational planners as centralized controllers with efficient state abstractions and reinforcement learning. This approach proves to be sample-efficient and facilitates effective task transfer and generalization.

cs.MA↗

arXiv2024

Computing the permanental polynomial of $4k$-intercyclic bipartite graphs

Let $G$ be a bipartite graph with adjacency matrix $A(G)$. The characteristic polynomial $ϕ(G,x)=\det(xI-A(G))$ and the permanental polynomial $π(G,x) = \text{per}(xI-A(G))$ are both graph invariants used to distinguish graphs. For bipartite graphs, we define the modified characteristic polynomial, which is obtained by changing the signs of some of the coefficients of $ϕ(G,x)$. For $4k$-intercyclic bipartite graphs, i.e., those for which the removal of any $4k$-cycle results in a $C_{4k}$-free graph, we provide an expression for $π(G,x)$ in terms of the modified characteristic polynomial of the graph and its subgraphs. Our approach is purely combinatorial in contrast to the Pfaffian orientation method found in the literature to compute the permanental polynomial.

math.CO↗

arXiv2024

Si/AlN p-n heterojunction interfaced with ultrathin SiO2

Ultra-wide bandgap (UWBG) materials hold immense potential for high-power RF electronics and deep ultraviolet photonics. Among these, AlGaN emerges as a promising candidate, offering a tunable bandgap from 3.4 eV (GaN) to 6.1 eV (AlN) and remarkable material characteristics. However, achieving efficient p-type doping in high aluminum composition AlGaN remains a formidable challenge. This study presents an alternative approach to address this issue by fabricating a p+ Si/n-AlN/n+ AlGaN heterojunction structure by following the semiconductor grafting technique. Atomic force microscopy (AFM) analysis revealed that the AlN and the nanomembrane surface exhibited a smooth topography with a roughness of 1.96 nm and 0.545 nm, respectively. High-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) confirmed a sharp and well-defined Si/AlN interface, with minimal defects and strong chemical bonding, crucial for efficient carrier transport. X-ray photoelectron spectroscopy (XPS) measurements demonstrated a type-I heterojunction with a valence band offset of 2.73 eV-2.84 eV and a conduction band offset of 2.22 eV -2.11 eV. The pn diode devices exhibited a linear current-voltage (I-V) characteristic, an ideality factor of 1.92, and a rectification ratio of 3.3E4, with a turn-on voltage of indicating effective p-n heterojunction. Temperature-dependent I-V measurements showed stable operation up to 90 C. The heterojunction's high-quality interface and electrical performance showcase its potential for advanced AlGaN-based optoelectronic and electronic devices.

physics.app-ph↗