arXiv subjects

Monika Yadav

Publications and source records attributed to Monika Yadav.

11 recordsLinked to original sources

arXiv2026

Maximal achievable service rates of some classes of linear codes

In this paper, we investigate lower bounds on the maximum achievable service rates for data symbols in certain classes of linear codes, including cyclic codes and low-density parity-check (LDPC) codes, that are derived from combinatorial structures such as $t$-designs, difference sets, and balanced incomplete block designs (BIBDs). We first establish a lower bound on the maximum achievable service rate for each data symbol in the following two cases: (i) systematic linear codes $C$ under the assumption that the supports of codewords of a fixed weight in $C^\perp$ form a BIBD, and (ii) non-systematic binary codes under the assumption that the supports of codewords of a fixed weight in $C^\perp$ form a $t$-design. We then investigate the linear codes obtained from the incidence matrices of BIBDs, particularly certain classes of BIBD-LDPC codes, and show how the parameters of the underlying designs can be exploited to determine lower bounds on the maximum achievable service rates for the data symbols of the corresponding linear code. In addition, we analyze the maximum achievable service rates of systematic extended linear codes. We show that the existence of a symmetric BIBD (SBIBD) corresponding to a dual codeword can be used to derive a lower bound on the maximum achievable service rate of the associated systematic cyclic code. We also present some families of cyclic codes constructed from difference sets and obtain explicit lower bounds on the maximum achievable service rates for their data symbols. In particular, we determine the exact values of the maximum achievable service rates for each data symbol of cyclic codes arising from Singer difference sets.

cs.IT↗

arXiv2026

Contact Surgery Numbers of the 3-torus

We study contact surgery numbers for contact structures on the 3-torus. We show that all contact structures obtained via contact surgery along a Legendrian Borromean ring are overtwisted, and that this construction yields infinitely many pairwise non-contactomorphic contact structures on $\mathbb{T}^3$. We prove an obstruction on the maximal Thurston-Bennequin invariant of 3-component links to produce $\mathbb{T}^3$ by Dehn surgery. On a side note, using Legendrian surgery and the ruling invariant, we show that the total symplectic homology of Stein fillings of $(\mathbb{T}^3, \xi_1)$ is non-zero.

math.SG↗

arXiv2025

Contact surgery distance

In this article, we define the contact surgery distance of two contact 3-manifolds $(M,\xi)$ and $(M',\xi')$ as the minimal number of contact surgeries needed to obtain $(M,\xi)$ from $(M',\xi')$. Our main result states that the contact surgery distance between two contact $3$-manifolds is at most $5$ larger than the topological surgery distance between the underlying smooth manifolds. As a byproduct of our proof, we classify the rational homology $3$-spheres on which the $d_3$-invariant of a $2$-plane field already determines its $\Gamma$-invariant and Euler class.

math.GT↗

arXiv2025

A recursive approach to the construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic

Let $\mathcal{R}_{e,m}$ be a finite commutative chain ring of even characteristic with maximal ideal $\langle u \rangle$ of nilpotency index $e \geq 2,$ Teichm$\ddot{u}$ller set $\mathcal{T}_{m},$ and residue field $\mathcal{R}_{e,m}/\langle u \rangle$ of order $2^m.$ Suppose that $2 \in \langle u^{\kappa}\rangle \setminus \langle u^{\kappa+1}\rangle$ for some even positive integer $ \kappa \leq e.$ In this paper, we provide a recursive method to construct a self-orthogonal code $\mathcal{C}_e$ of type $\{\lambda_1, \lambda_2, \ldots, \lambda_e\}$ and length $n$ over $\mathcal{R}_{e,m}$ from a chain $\mathcal{D}^{(1)}\subseteq \mathcal{D}^{(2)} \subseteq \cdots \subseteq \mathcal{D}^{(\lceil \frac{e}{2} \rceil)}$ of self-orthogonal codes of length $n$ over $\mathcal{T}_{m},$ and vice versa, where $\dim \mathcal{D}^{(i)}=\lambda_1+\lambda_2+\cdots+\lambda_i$ for $1 \leq i \leq \lceil \frac{e}{2} \rceil,$ the codes $\mathcal{D}^{(\lfloor \frac{e+1}{2} \rfloor-\kappa)},\mathcal{D}^{(\lfloor \frac{e+1}{2} \rfloor -\kappa+1)},\ldots,\mathcal{D}^{(\lfloor \frac{e}{2}\rfloor-\lfloor \frac{\kappa}{2} \rfloor)}$ satisfy certain additional conditions, and $\lambda_1,\lambda_2,\ldots,\lambda_e$ are non-negative integers satisfying $2\lambda_1+2\lambda_2+\cdots+2\lambda_{e-i+1}+\lambda_{e-i+2}+\lambda_{e-i+3}+\cdots+\lambda_i \leq n$ for $\lceil \frac{e+1}{2} \rceil \leq i\leq e.$ This construction guarantees that $Tor_i(\mathcal{C}_e)=\mathcal{D}^{(i)}$ for $1 \leq i \leq \lceil \frac{e}{2} \rceil.$ By employing this recursive construction method, together with the results from group theory and finite geometry, we derive explicit enumeration formulae for all self-orthogonal and self-dual codes of an arbitrary length over $\mathcal{R}_{e,m}.$ We also demonstrate these results through examples.

cs.IT↗

arXiv2025

Recursive construction and enumeration of self-orthogonal and self-dual codes over finite commutative chain rings of even characteristic

Let $\mathscr{R}_{e,m}$ denote a finite commutative chain ring of even characteristic with maximal ideal $\langle u \rangle$ of nilpotency index $e \geq 3,$ Teichm$\ddot{u}$ller set $\mathcal{T}_{m},$ and residue field $\mathscr{R}_{e,m}/\langle u \rangle$ of order $2^m.$ Suppose that $2 \in \langle u^{\kappa}\rangle \setminus \langle u^{\kappa+1}\rangle$ for some odd integer $\kappa$ with $3 \leq \kappa \leq e.$ In this paper, we first develop a recursive method to construct a self-orthogonal code $\mathscr{D}_e$ of type $\{\lambda_1, \lambda_2, \ldots, \lambda_e\}$ and length $n$ over $\mathscr{R}_{e,m}$ from a chain $\mathcal{C}^{(1)}\subseteq \mathcal{C}^{(2)} \subseteq \cdots \subseteq \mathcal{C}^{(\lceil \frac{e}{2} \rceil)} $ of self-orthogonal codes of length $n$ over $\mathcal{T}_{m},$ and vice versa, subject to certain conditions, where $\lambda_1,\lambda_2,\ldots,\lambda_e$ are non-negative integers satisfying $2\lambda_1+2\lambda_2+\cdots+2\lambda_{e-i+1}+\lambda_{e-i+2}+\lambda_{e-i+3}+\cdots+\lambda_i \leq n$ for $\lceil \frac{e+1}{2} \rceil \leq i\leq e,$ and $\lfloor \cdot \rfloor$ and $\lceil \cdot \rceil$ denote the floor and ceiling functions, respectively. This construction ensures that $Tor_i(\mathscr{D}_e)=\mathcal{C}^{(i)}$ for $1 \leq i \leq \lceil \frac{e}{2} \rceil.$ With the help of this recursive construction method and by applying results from group theory and finite geometry, we obtain explicit enumeration formulae for all self-orthogonal and self-dual codes of an arbitrary length over $\mathscr{R}_{e,m}.$ We also illustrate these results with some examples.

cs.IT↗

arXiv2025

On The Cost Function Associated With Legendrian Knots

In this article, we introduce a non-negative integer-valued function that measures the obstruction for converting topological isotopy between two Legendrian knots into a Legendrian isotopy. We refer to this function as the Cost function. We show that the Cost function induces a metric on the set of topologically isotopic Legendrian knots. Hence, the set of topologically isotopic Legendrian knots can be seen as a graph with path-metric given by the Cost function. Legendrian simple knot types are shown to be characterized using the Cost function. We also get a quantitative version of Fuchs-Tabachnikov's Theorem that says any two Legendrian knots in $(\mathbb{S}^3,ξ_{std})$ in the same topological knot type become Legendrian isotopic after sufficiently many stabilizations. We compute the Cost function for Legendrian simple knots (for example torus knots) and we note the behavior of Cost function for twist knots and cables of torus knots (some of which are Legendrian non-simple). We also construct examples of Legendrian representatives of 2-bridge knots and compute the Cost between them. Further, we investigate the behavior of the Cost function under the connect sum operation. We conclude with some questions about the Cost function, its relation with the standard contact structure, and the topological knot type.

math.GT↗

arXiv2025

Simulating Unruh Radiation in High-Intensity Laser-Electron Interactions for Near-Term Experimental Tests

The Unruh effect predicts that a uniformly accelerating observer perceives the vacuum as a thermal bath, yet direct observation remains elusive [1]. We simulate Unruh radiation in realistic high-intensity laser-electron collisions relevant to FACET-II and LUXE using fully three-dimensional Monte Carlo methods. In our model, Unruh emission is treated as scattering from a rest-frame thermal spectrum with Klein-Nishina cross sections, while nonlinear Compton radiation is computed across many harmonic orders with photon recoil. We map the laboratory-frame spectral-angular distributions and identify phase-space regions where the Unruh-to-Compton ratio is maximized. For current FACET-II-like parameters (a0 = 5), favorable windows for observing Unruh radiation occur at 200-400 microrad and 2-3 GeV, although the absolute signal is small. For future LUXE Phase-1 (a0 = 23.6), the ratio increases by more than two orders of magnitude, with optimal angles around 800 microrad and photon energies 2-6 GeV. Our results suggest that targeted off-axis, mid-energy selections can enhance sensitivity to Unruh-like signatures, motivating dedicated measurements and further theoretical scrutiny of the emission model at high field strengths.

hep-ex↗

arXiv2025

Contact surgery numbers of projective spaces

We classify all contact projective spaces with contact surgery number one. In particular, this implies that there exist infinitely many non-isotopic contact structures on the real projective 3-space which cannot be obtained by a single rational contact surgery from the standard tight contact 3-sphere. Large parts of our proofs deal with a detailed analysis of Gompf's $\Gamma$-invariant of tangential 2-plane fields on 3-manifolds. From our main result we also deduce that the $\Gamma$-invariant of a tangential 2-plane field on the real projective 3-space only depends on its $d_3$-invariant.

math.GT↗

arXiv2024

DiffSTOCK: Probabilistic relational Stock Market Predictions using Diffusion Models

In this work, we propose an approach to generalize denoising diffusion probabilistic models for stock market predictions and portfolio management. Present works have demonstrated the efficacy of modeling interstock relations for market time-series forecasting and utilized Graph-based learning models for value prediction and portfolio management. Though convincing, these deterministic approaches still fall short of handling uncertainties i.e., due to the low signal-to-noise ratio of the financial data, it is quite challenging to learn effective deterministic models. Since the probabilistic methods have shown to effectively emulate higher uncertainties for time-series predictions. To this end, we showcase effective utilisation of Denoising Diffusion Probabilistic Models (DDPM), to develop an architecture for providing better market predictions conditioned on the historical financial indicators and inter-stock relations. Additionally, we also provide a novel deterministic architecture MaTCHS which uses Masked Relational Transformer(MRT) to exploit inter-stock relations along with historical stock features. We demonstrate that our model achieves SOTA performance for movement predication and Portfolio management.

cs.LG↗

arXiv2022

On a generalization of Jones polynomial and its categorification for Legendrian Knots

In this article, we explore a polynomial invariant for Legendrian knots which is a natural extension of Jones polynomial for (topological) knots. To this end, a new type of skein relation is introduced for the front projections of Legendrian knots. Further, we give a categorification of the polynomial invariant for Legendrian knots which is a natural extension of Khovanov homology for knots. The Thurston-Bennequin invariant of Legendrian knot appears naturally in the construction of the homology as the grade-shift. The constructions of the polynomial invariant and its categorification are natural in the sense that if we treat Legendrian knots as only knots (that is, we forget the geometry on the knots), then we recover the Jones polynomial and Khovanov homology respectively. In the end, we discuss strengths and limitations of these invariants.

math.GT↗

arXiv2021

An Innovative Transverse Emittance Cooling Technique using a Laser-Plasma Wiggler

We propose an innovative beam cooling scheme based on laser driven plasma wakefields to address the challenge of high luminosity generation for a future linear collider. For linear colliders, beam cooling is realised by means of damping rings equipped with wiggler magnets and accelerating cavities. This scheme ensures systematic reduction of phase space volume through synchrotron radiation emission whilst compensating for longitudinal momentum loss via an accelerating cavity. In this paper, the concept of a plasma wiggler and its effective model analogous to a magnetic wiggler are introduced; relation of plasma wiggler characteristics with damping properties are demonstrated; underpinning particle-in-cell simulations for laser propagation optimisation are presented. The oscillation of transverse wakefields and resulting sinusoidal probe beam trajectory are numerically demonstrated. The formation of an order of magnitude larger effective wiggler field compared to conventional wigglers is successfully illustrated. Potential damping ring designs on the basis of this novel plasma-based technology are presented and performance in terms of damping times and footprint was compared to an existing conventional damping ring design.

physics.acc-ph↗