Akanksha Tiwari

Indar Kumar, Akanksha Tiwari

Effective ride-hailing dispatch requires anticipating demand patterns that vary substantially across time-of-day, day-of-week, season, and special events. We propose a regime-calibrated approach that (i) segments historical trip data into demand regimes, (ii) matches the current operating period to the most similar historical analogues via a similarity ensemble combining Kolmogorov-Smirnov distance, Wasserstein-1 distance, feature distance, variance ratio, event pattern similarity, and temporal proximity, and (iii) uses the resulting calibrated demand prior to drive both an LP-based fleet repositioning policy and batch dispatch with Hungarian matching. In ablation, a distributional-only metric subset achieves the strongest mean-wait reduction, while the full ensemble is retained as a robustness-oriented default that preserves calendar and event context. Evaluated on 5.2 million NYC TLC trips across 8 diverse scenarios (winter/summer, weekday/weekend/holiday, morning/evening/night) with 5 random seeds each, our method reduces mean rider wait times by 31.1% (bootstrap 95% CI: [26.5, 36.6]; Friedman chi-squared = 80.0, p = 4.25e-18; Cohen's d = 7.5-29.9). P95 wait drops 37.6% and the Gini coefficient of wait times improves from 0.441 to 0.409. The two contributions compose multiplicatively: calibration provides 16.9% reduction relative to the replay baseline; LP repositioning adds a further 15.5%. The approach requires no training, is deterministic and explainable, generalizes to Chicago (23.3% wait reduction using the NYC-built regime library without retraining), and is robust across fleet sizes (32-47% improvement for 0.5x-2.0x fleet scaling). Code is available at https://github.com/IndarKarhana/regime-calibrated-dispatch.

Akanksha Tiwari, Ritumoni Sarma

Let $R^t$ denote the finite chain ring $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle},$ where $p$ is a prime and $t$ is a positive integer. In this article, for a prime $p$ and an automorphism $θ$ of $\mathbb{F}_{p^m}$, we give the structure of the left ideals of the ring $\frac{R^t[x,Θ]}{\langle f(x) \rangle},$ where $f(x)$ is in the center of the skew polynomial ring $R^t[x,Θ]$ and $Θ$ is an automorphism of $R^t$ that extends $θ$ with $Θ(u)=u$. These left ideals are also referred to as skew polycyclic codes associated to $f(x).$ In particular, when the central element \( f(x)\) is \(x^{np^s}-λ\), where $λ=λ_0+uλ_1+\cdots +u^{t-1}λ_{t-1}$ with $λ_0\ne0,$ and \( n=1,2 \), we give a more refined form of the left ideals (which are also called skew constacyclic codes). Moreover, the case $λ_1 \neq 0$ is analyzed in detail, yielding a simpler form of generators that reveals a more refined structural characterization of the left ideals. As an application, for $n=1,t=3$ and $n=2,t=2$ we give a full description of the left ideals by including certain necessary conditions that were omitted in available literature, preventing the different classes of left ideals from being mutually disjoint and in certain cases, we also compute $i$-th torsion codes.

Akanksha Tiwari, Pramod Kanwar, Ritumoni Sarma

The purpose of this article is to study constacyclic codes of length $np^s$ over $R^t:=\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle },$ where $t$ is a natural number and $\gcd(n,p)=1$. We give generators of all the ideals of $R^{t,n}_δ:=\frac{R^t[x]}{\langle x^{np^s}-δ\rangle},$ where $δ= δ_0+uδ_1+\dots+u^{t-1}δ_{t-1}$ is a unit in $R^t$. For $n=1,\ 2, \ 3$ and $t=3$, we provide all types of ideals (constacyclic codes) and also give the torsional degrees as well as cardinalities of these codes.

Indar Kumar, Akanksha Tiwari, Sai Krishna Jasti et al.

Test-time adaptation (TTA) enables neural forecasters to adapt to distribution shifts in streaming time series, but existing methods apply the same adaptation intensity regardless of the nature of the shift. We propose Regime-Guided Test-Time Adaptation (RG-TTA), a meta-controller that continuously modulates adaptation intensity based on distributional similarity to previously-seen regimes. Using an ensemble of Kolmogorov-Smirnov, Wasserstein-1, feature-distance, and variance-ratio metrics, RG-TTA computes a similarity score for each incoming batch and uses it to (i) smoothly scale the learning rate -- more aggressive for novel distributions, conservative for familiar ones -- and (ii) control gradient effort via loss-driven early stopping rather than fixed budgets, allowing the system to allocate exactly the effort each batch requires. As a supplementary mechanism, RG-TTA gates checkpoint reuse from a regime memory, loading stored specialist models only when they demonstrably outperform the current model (loss improvement >= 30%). RG-TTA is model-agnostic and strategy-composable: it wraps any forecaster exposing train/predict/save/load interfaces and enhances any gradient-based TTA method. We demonstrate three compositions -- RG-TTA, RG-EWC, and RG-DynaTTA -- and evaluate 6 update policies (3 baselines + 3 regime-guided variants) across 4 compact architectures (GRU, iTransformer, PatchTST, DLinear), 14 datasets (6 real-world multivariate benchmarks + 8 synthetic regime scenarios), and 4 forecast horizons (96, 192, 336, 720) under a streaming evaluation protocol with 3 random seeds (672 experiments total). Regime-guided policies achieve the lowest MSE in 156 of 224 seed-averaged experiments (69.6%), with RG-EWC winning 30.4% and RG-TTA winning 29.0%. Overall, RG-TTA reduces MSE by 5.7% vs TTA while running 5.5% faster; RG-EWC reduces MSE by 14.1% vs standalone EWC.

Ankit Hemant Lade, Sai Krishna Jasti, Nikhil Sinha et al.

Multi-channel sensor networks in industrial IoT often exceed available bandwidth. We propose PCA-Triage, a streaming algorithm that converts incremental PCA loadings into proportional per-channel sampling rates under a bandwidth budget. PCA-Triage runs in O(wdk) time with zero trainable parameters (0.67 ms per decision). We evaluate on 7 benchmarks (8--82 channels) against 9 baselines. PCA-Triage is the best unsupervised method on 3 of 6 datasets at 50% bandwidth, winning 5 of 6 against every baseline with large effect sizes (r = 0.71--0.91). On TEP, it achieves F1 = 0.961 +/- 0.001 -- within 0.1% of full-data performance -- while maintaining F1 > 0.90 at 30% budget. Targeted extensions push F1 to 0.970. The algorithm is robust to packet loss and sensor noise (3.7--4.8% degradation under combined worst-case).

Akanksha Tiwari, Pramod Kanwar, Ritumoni Sarma

The purpose of this article is to study polycyclic codes over the ring $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle}, \,t \geq 1$, and their associated torsion codes. It is shown that if $ϕ$ is a surjective ring homomorphism from a commutative ring $A$ to a Noetherian ring $B$ with $ ker(ϕ)=\langle π\rangle$ then for every ideal $I$ of $A$, there exists $a_1,a_2,\dots,a_n$ in $I$ such that $I=\langle a_1,a_2,\dots,a_n\rangle+π(I:π)$. Using this, we obtain generators of all ideals of the ring $\frac{\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle}[x]}{\langle ω(x)\rangle},$ where $ω(x)\in \frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle}[x] $. For the case when $ω(x)=f(x)^{p^s}$, where $f(x)$ is an irreducible polynomial in $\mathbb{F}_{p^m}[x]$ and $s$ is a non-negative integer, we obtain several other results including computation of torsion ideals and their torsional degrees when $t=4$. We use the torsional degree to compute the cardinality of polycyclic codes over the ring $\frac{\mathbb{F}_{p^m}[u]}{\langle u^4 \rangle}$.