arXiv subjects

Suman Saurabh

Publications and source records attributed to Suman Saurabh.

6 recordsLinked to original sources

arXiv2026

Annular Khovanov homology detects three-strand weaving links

For $N\geq1$, let $K_N$ be the annular closure of $(σ_1σ_2^{-1})^N.$ We prove that triply graded annular Khovanov homology over $\mathbb F_2$ detects the underlying unoriented annular link $K_N$. If $3\nmid N$, the only ambiguity is overall orientation reversal. If $3\mid N$, the only ambiguity is independent reversal of components; every such reorientation has the same homology, so this is sharp. The proof combines braid detection from the extremal annular grading with a rigidity theorem: the Jones polynomial and exponent sum determine $(σ_1σ_2^{-1})^N$ up to conjugacy in $B_3$.

math.GT↗

arXiv2026

Equivariant rational sliceness and Klein amphichirality of odd-stranded Turk's head knots

We establish a sharp parity dichotomy for the equivariant $\mathbb Q$-sliceness and Klein amphichirality of odd-stranded Turk's head knots. When the twisting parameter $q$ is odd, we construct a commuting pair of ambient involutions by lifting explicit symmetries of the signed, arrowed Gauss diagram through the associated abstract link diagram and supporting sphere. This proves that the knots are Klein amphichiral and hence equivariantly $\mathbb Q$-slice. When $q$ is even, we prove that the knots are not equivariantly $\mathbb Q$-slice with respect to any strong inversion. The obstruction is the equivariant Fox-Milnor square condition of Di Prisa-Şavk: we show that the Alexander polynomial is not a Laurent square. The even-$q$ argument combines a Burau square factorization arising from Garside conjugacy with a mod-$2$ Seifert-matrix computation.

math.GT↗

arXiv2026

Fox's Trapezoidal Conjecture for Four-Strand Turk's Head Knots and Links

We prove Fox's trapezoidal conjecture for the four-strand Turk's head knots and links $Th(4,q)$, for all $q\geq 1$. Equivalently, we show that the absolute values of the coefficients of the one-variable Alexander polynomial of $Th(4,q)$ form a trapezoidal sequence. The proof begins with a uniform Burau factorization for the closures of $(σ_1σ_2^{-1}σ_3)^q$, which expresses the Alexander polynomial in terms of reciprocal quadratic factors indexed by the $q$-th roots of unity. The odd and even exponent cases then follow from a common log-concavity argument based on a four-block smoothing theorem for reciprocal quartic factors.

math.GT↗

arXiv2026

Spectral Factorization and Hypergeometric Representations of the Alexander Polynomials of $Th(4,2n+1)$

We study the Alexander polynomials of the 4-strand Turk's head knots $Th(4,2n+1)$, defined as the closures of the braid $(σ_1σ_2^{-1}σ_3)^{2n+1}$. Using the reduced Burau representation, we derive an annihilating recurrence of order at most 8 and a rational generating function for the resulting polynomial sequence. By executing a multivariable resultant elimination over the reciprocal constraint, we obtain an exact factorization of the normalized Alexander polynomial in terms of Chebyshev polynomials. This factorization produces a binomial convolution formula for an associated coefficient sequence and a representation by a terminating ${}_4F_3$ hypergeometric series. We evaluate the continuous approximation of this representation using the saddle-point method, demonstrating negative curvature in the asymptotic main term. Finally, we describe analytic obstructions to extracting global discrete error bounds via this method, leaving the formal proof of Fox's Trapezoidal Conjecture for this family open.

math.GT↗

arXiv2023

INA: An Integrative Approach for Enhancing Negotiation Strategies with Reward-Based Dialogue System

In this paper, we propose a novel negotiation dialogue agent designed for the online marketplace. Our agent is integrative in nature i.e, it possesses the capability to negotiate on price as well as other factors, such as the addition or removal of items from a deal bundle, thereby offering a more flexible and comprehensive negotiation experience. We create a new dataset called Integrative Negotiation Dataset (IND) to enable this functionality. For this dataset creation, we introduce a new semi-automated data creation method, which combines defining negotiation intents, actions, and intent-action simulation between users and the agent to generate potential dialogue flows. Finally, the prompting of GPT-J, a state-of-the-art language model, is done to generate dialogues for a given intent, with a human-in-the-loop process for post-editing and refining minor errors to ensure high data quality. We employ a set of novel rewards, specifically tailored for the negotiation task to train our Negotiation Agent, termed as the Integrative Negotiation Agent (INA). These rewards incentivize the chatbot to learn effective negotiation strategies that can adapt to various contextual requirements and price proposals. By leveraging the IND, we train our model and conduct experiments to evaluate the effectiveness of our reward-based dialogue system for negotiation. Our results demonstrate that the proposed approach and reward system significantly enhance the agent's negotiation capabilities. The INA successfully engages in integrative negotiations, displaying the ability to dynamically adjust prices and negotiate the inclusion or exclusion of items in a bundle deal

cs.CL↗

arXiv2019

Mesoscale computational protocols for the design of highly cooperative bivalent macromolecules

The last decade has witnessed a swiftly increasing interest in the design and production of novel multivalent molecules as powerful alternatives for conventional antibodies in the fight against cancer and infectious diseases. However, while it is widely accepted that large-scale flexibility ($10-100$ nm) and free/constrained dynamics (100 ns $- μ$s) control the activity of such novel molecules, computational strategies at the mesoscale still lag behind experiments in optimizing the design of crucial features, such as the binding cooperativity (a.k.a. avidity). In this study, we introduced different coarse-grained models of a polymer-linked, two-nanobody composite molecule, with the aim of laying down the physical bases of a thorough computational drug design protocol at the mesoscale. We show that the calculation of suitable potentials of mean force allows one to apprehend the nature, range and strength of the thermodynamic forces that govern the motion of free and wall-tethered molecules. Furthermore, we develop a simple computational strategy to quantify the encounter/dissociation dynamics between the free end of a wall-tethered molecule and the surface, at the roots of binding cooperativity. This procedure allows one to pinpoint the role of internal flexibility and weak non-specific interactions on the kinetic constants of the NB-wall encounter and dissociation. Finally, we quantify the role and weight of rare events, which are expected to play a major role in real-life situations, such as in the immune synapse, where the binding kinetics is likely dominated by fluctuations.

cond-mat.soft↗