arXiv subjects

Priyanshu Tiwari

Publications and source records attributed to Priyanshu Tiwari.

6 recordsLinked to original sources

arXiv2026

From One Solution to Many: An Oracle-Based FPT Framework for Diverse Solutions under Generalized Diversity Measures

The problem of computing \emph{diverse} solutions has recently emerged as an important area of study, motivated by applications in fairness, robustness, and security. Instead of returning a single feasible or optimal solution, the goal is to output a \emph{collection} of meaningfully different solutions, often measured by symmetric differences. Diverse variants have been studied using sparsification, network-flow reductions, and algebraic techniques. We investigate the fixed-parameter tractability of diverse variants of an implicit set-system problem. Given parameters $k$ and $r$ and a threshold $b$, the task is to compute $r$ feasible solutions, each of size at most $k$, whose diversity under a specified objective is at least $b$. Our main contribution is an oracle-based meta-theorem. We identify a broad class of objectives, called \emph{consistently diverse}, that includes several standard measures. Assuming an \emph{exact empty-extension oracle} given a forbidden set ${\sf Forb}$, which returns a feasible solution of a prescribed size avoiding ${\sf Forb}$ or reports that none exists, we obtain a fixed-parameter tractable algorithm parameterized by $k+r$. The algorithm makes at most $(2kr)^{kr} \cdot r$ oracle calls, and in each call the oracle parameter satisfies $s+|{\sf Forb}| \leq k+2kr$. Our framework unifies and strengthens previous oracle-based approaches. Compared with Kumabe's framework (ESA 2025), which gives a doubly exponential bound on the number of oracle calls, our approach achieves the single exponential bound $2^{O(kr\log(kr))}$ and directly constructs the desired tuple of solutions. We recover fixed-parameter tractable algorithms for all problems covered by that framework, with improved oracle complexity, and obtain strong bounds for diverse variants of classical graph and matroid problems.

cs.DS↗

arXiv2026

Loss-aware pulse sequence optimization for generating photonic Fock states

We investigate the preparation of frequency-tunable photonic Fock states in a hybrid cavity system consisting of a nonlinear medium and a two-level system. Employing a gradient-based optimization approach, we construct multipulse driving protocols that control the system dynamics through pulse amplitudes, phases, and inter-pulse delays. Assuming unitary dynamics, the optimized sequences enable near-deterministic preparation of low-photon-number Fock states. We extend the optimization framework to open-system dynamics by modeling atomic decay and photon loss within the Lindblad master equation. This allows us to identify pulse sequences that exhibit enhanced robustness against dissipation compared to those optimized under idealized assumptions. Furthermore, we find that optimal pulse sequences obey strict constraints on relative phases, which are limited to values of 0 or $π$. These phase restrictions are supported by an analytical study that investigates a simple two-pulse sequence treating the second pulse perturbatively.

quant-ph↗

arXiv2026

dirichletprocess: An R Package for Fitting Complex Bayesian Nonparametric Models

The dirichletprocess package provides software for creating flexible Dirichlet process objects. Users can perform nonparametric Bayesian analysis using Dirichlet processes without the need to program their own inference algorithms. Instead, the user can utilise our pre-built models or specify their own models whilst allowing the dirichletprocess package to handle the Markov chain Monte Carlo sampling. Our Dirichlet process objects can act as building blocks for a variety of statistical models including: density estimation, clustering and prior distributions in hierarchical models.

stat.CO↗

arXiv2026

Digital Twin-assisted belief-state reinforcement learning for latency-robust ISAC in 6G networks

Integrated Sensing and Communication (ISAC) enables joint data transmission and environmental perception for sixth-generation (6G) networks, but centralized and virtualized RAN control loops introduce telemetry latency that yields stale observations and unstable control. This paper proposes a Digital Twin-assisted belief-state reinforcement learning framework for latency-robust ISAC. A Digital Twin (DT) reconstructs a synchronized belief state from delayed telemetry using an Extended Kalman Filter, and a Proximal Policy Optimization agent performs joint beamforming and power allocation for communication and sensing. Closed-loop simulations with telemetry delays up to 100 ms demonstrate consistent performance gains over latency-unaware deep reinforcement learning (DRL) and heuristic baselines. At 50 ms latency, the proposed method improves median throughput by 12% and reduces sensing error by 7% relative to a DT-only controller, while achieving an order-of-magnitude reduction in reliability violations. Even at 100 ms latency, the proposed approach retains approximately 88% of its zero-latency throughput. These results show that Digital Twin-assisted belief-state control enables stable and efficient ISAC operation under realistic telemetry delays in 6G networks.

cs.NI↗

arXiv2026

Asian option valuation under price impact

We develop a tractable framework for valuing Asian options when trading the underlying generates market impact and execution costs. Starting from a discrete-time, quote-level model, we construct a reference midpoint suitable for Asian payoffs and separate market impact into a transient component and a permanent drift distortion driven by signed trading. This specification admits continuous-time limits where the midpoint and impact state converge to a coupled system in which the midpoint drift depends on the transient impact state and in the endogenous regime on the hedger's trading rate, with correlated price and order-flow shocks. We study valuation in two complementary regimes. In an exogenous benchmark, the impact state evolves independently of the hedger. When the order-flow volatility is deterministic, we obtain a closed-form expression for the geometric Asian call. In an endogenous regime, trading volumes feed back into prices and costs, leading to a stochastic control problem and Hamilton-Jacobi-Bellman equations. We define reservation bid and ask prices via cost-based indifference which produces an impact-driven bid-ask spread. For computations, we propose a CRR-style tree-based Bellman algorithm. Numerical experiments show that exogenous impact effects are modest relative to frictionless benchmarks, while endogenous indifference prices generate nontrivial bid-ask spreads that grow super-linearly in impact parameters, widen when execution costs are lower, and shrink with faster mean reversion, highlighting the interaction between averaging in Asian options, price impact effects, and strategic trading.

q-fin.MF↗

arXiv2024

A hybrid source of quantum light for generation of frequency tunable Fock states

We propose a scheme for quantum-light generation in a nonlinear cavity hybridized with a 2-level system and theoretically show that, when excited by a series of controlled pump pulses, the hybrid source generates Fock states with high probabilities. E.g., 1- and 2-photon states can be generated near-on-demand, and Fock states with up to $7$ photons with a probability above $50\%$. The tailorable nature of the nonlinear cavity allows for generating Fock states with arbitrary frequencies, even with a fixed 2-level system, creating fundamentally new opportunities in all areas of quantum technologies.

quant-ph↗