Structural controllability challenges arise from imprecise system modeling and system interconnections in large scale systems. In this paper, we study structural control of bilinear systems on the special Euclidean group. We employ graph theoretic methods to analyze the structural controllability problem for driftless bilinear systems and structural accessibility for bilinear systems with drift. This facilitates the identification of a sparsest pattern necessary for achieving structural controllability and discerning redundant connections. To obtain a graph theoretic characterization of structural controllability and accessibility on the special Euclidean group, we introduce a novel idea of solid and broken edges on graphs; subsequently, we use the notion of transitive closure of graphs.
Multimodal generative AI systems like Stable Diffusion, DALL-E, and MidJourney have fundamentally changed how synthetic images are created. These tools drive innovation but also enable the spread of misleading content, false information, and manipulated media. As generated images become harder to distinguish from photographs, detecting them has become an urgent priority. To combat this challenge, we release MS COCOAI, a novel dataset for AI generated image detection consisting of 96000 real and synthetic datapoints, built using the MS COCO dataset. To generate synthetic images, we use five generators: Stable Diffusion 3, Stable Diffusion 2.1, SDXL, DALL-E 3, and MidJourney v6. Based on the dataset, we propose two tasks: (1) classifying images as real or generated, and (2) identifying which model produced a given synthetic image. The dataset is available at https://huggingface.co/datasets/Rajarshi-Roy-research/Defactify_Image_Dataset.
This article examines the fractional prey-predator model through the use of fractional physics-informed neural networks (fPINNs). The methodology focuses on the implementation of fPINN algorithms to approximate solutions to systems governed by fractional-order differential equations. Furthermore, key parameters of the models, based on Holling's-type functional responses I, II, and II, were estimated with fPINNs. A detailed study is conducted on the impact of data noise, various data sets, and if only one population is available (prey), then how to predict the other population (predator). Our computational experiments indicate that JPINNs are extremely effective, both in parameter estimation and in accurately forecasting prey-predator populations.
Deterministic inference is a comforting ideal in classical software: the same program on the same input should always produce the same output. As large language models move into real-world deployment, this ideal has been imported wholesale into inference stacks. Recent work from the Thinking Machines Lab has presented a detailed analysis of nondeterminism in LLM inference, showing how batch-invariant kernels and deterministic attention can enforce bitwise-identical outputs, positioning deterministic inference as a prerequisite for reproducibility and enterprise reliability. In this paper, we take the opposite stance. We argue that, for LLMs, deterministic inference kills. It kills the ability to model uncertainty, suppresses emergent abilities, collapses reasoning into a single brittle path, and weakens safety alignment by hiding tail risks. LLMs implement conditional distributions over outputs, not fixed functions. Collapsing these distributions to a single canonical completion may appear reassuring, but it systematically conceals properties central to artificial cognition. We instead advocate Stochastic CHAOS, treating distributional variability as a signal to be measured and controlled. Empirically, we show that deterministic inference is systematically misleading. Single-sample deterministic evaluation underestimates both capability and fragility, masking failure probability under paraphrases and noise. Phase-like transitions associated with emergent abilities disappear under greedy decoding. Multi-path reasoning degrades when forced onto deterministic backbones, reducing accuracy and diagnostic insight. Finally, deterministic evaluation underestimates safety risk by hiding rare but dangerous behaviors that appear only under multi-sample evaluation.
Alignment in large language models (LLMs) is still largely static: after training, the policy is frozen. DPO, GRPO methods typically imprint one behavior into the weights, leaving little runtime control beyond prompt hacks or expensive re-alignment. We introduce ECLIPTICA, which treats alignment as instruction-driven and runtime-controllable: natural-language alignment instructions act as an explicit behavioral contract (stance, refusal boundary, verbosity) that modulates behavior on the fly under evolving safety requirements, user roles, and governance constraints. We introduce CITA (Contrastive Instruction-Tuned Alignment), combining SFT with contrastive preference optimization under an explicit geometric anchor to a reference model. This yields a stable Riemannian chart and keeps instruction updates within a shared neighborhood, so regimes stay nearby and traversable for reliable switching. To isolate policy switching from ordinary instruction following, we release the ECLIPTICA benchmark: 3000 controlled cases (300 prompts x 10 instruction types) where the user request is fixed and only the alignment instruction changes. On Llama-3.1-8B across five suites (ECLIPTICA, TruthfulQA, Conditional Safety, Length Control, LITMUS), CITA reaches 86.7
