Finite-region boundedness and stabilization for 2D continuous-discrete systems in Roesser model

This paper investigates the finite-region boundedness (FRB) and stabilization problems for two-dimensional continuous-discrete linear Roesser models subject to two kinds of disturbances. For two-dimensional continuous-discrete system, we first put forward the concepts of finite-region stability and FRB. Then, by establishing special recursive formulas, sufficient conditions of FRB for two-dimensional continuous-discrete systems with two kinds of disturbances are formulated. Furthermore, we analyze the finite-region stabilization issues for the corresponding two-dimensional continuous-discrete systems and give generic sufficient conditions and sufficient conditions that can be verified by linear matrix inequalities for designing the state feedback controllers which ensure the closed-loop systems FRB. Finally, viable experimental results are demonstrated by illustrative examples

Characterization of Group-Strategyproof Mechanisms for Facility Location in Strictly Convex Space

We characterize the class of group-strategyproof mechanisms for the single facility location game in any unconstrained strictly convex space. A mechanism is \emph{group-strategyproof}, if no group of agents can misreport so that all its members are \emph{strictly} better off. A strictly convex space is a normed vector space where $\|x+y\|<2$ holds for any pair of different unit vectors $x \neq y$, e.g., any $L_p$ space with $p\in (1,\infty)$. We show that any deterministic, unanimous, group-strategyproof mechanism must be dictatorial, and that any randomized, unanimous, translation-invariant, group-strategyproof mechanism must be \emph{2-dictatorial}. Here a randomized mechanism is 2-dictatorial if the lottery output of the mechanism must be distributed on the line segment between two dictators' inputs. A mechanism is translation-invariant if the output of the mechanism follows the same translation of the input. Our characterization directly implies that any (randomized) translation-invariant approximation algorithm satisfying the group-strategyproofness property has a lower bound of $2$-approximation for maximum cost (whenever $n \geq 3$), and $n/2 - 1$ for social cost. We also find an algorithm that $2$-approximates the maximum cost and $n/2$-approximates the social cost, proving the bounds to be (almost) tight.Comment: Accepted to ACM Conference on Economics and Computation (EC) 202

On the Coherency of Completed Group Algebra

We investigate coherency properties of certain completed integral group rings, precisely for compact $p$-adic Lie groups.Comment: 16 pages. Submitte

New Definitions and Evaluations for Saliency Methods: Staying Intrinsic, Complete and Sound

Saliency methods compute heat maps that highlight portions of an input that were most {\em important} for the label assigned to it by a deep net. Evaluations of saliency methods convert this heat map into a new {\em masked input} by retaining the $k$ highest-ranked pixels of the original input and replacing the rest with \textquotedblleft uninformative\textquotedblright\ pixels, and checking if the net's output is mostly unchanged. This is usually seen as an {\em explanation} of the output, but the current paper highlights reasons why this inference of causality may be suspect. Inspired by logic concepts of {\em completeness \& soundness}, it observes that the above type of evaluation focuses on completeness of the explanation, but ignores soundness. New evaluation metrics are introduced to capture both notions, while staying in an {\em intrinsic} framework -- i.e., using the dataset and the net, but no separately trained nets, human evaluations, etc. A simple saliency method is described that matches or outperforms prior methods in the evaluations. Experiments also suggest new intrinsic justifications, based on soundness, for popular heuristic tricks such as TV regularization and upsampling.Comment: NeurIPS 2022 (Oral

Skill-Mix: a Flexible and Expandable Family of Evaluations for AI models

With LLMs shifting their role from statistical modeling of language to serving as general-purpose AI agents, how should LLM evaluations change? Arguably, a key ability of an AI agent is to flexibly combine, as needed, the basic skills it has learned. The capability to combine skills plays an important role in (human) pedagogy and also in a paper on emergence phenomena (Arora & Goyal, 2023). This work introduces Skill-Mix, a new evaluation to measure ability to combine skills. Using a list of $N$ skills the evaluator repeatedly picks random subsets of $k$ skills and asks the LLM to produce text combining that subset of skills. Since the number of subsets grows like $N^k$, for even modest $k$ this evaluation will, with high probability, require the LLM to produce text significantly different from any text in the training set. The paper develops a methodology for (a) designing and administering such an evaluation, and (b) automatic grading (plus spot-checking by humans) of the results using GPT-4 as well as the open LLaMA-2 70B model. Administering a version of to popular chatbots gave results that, while generally in line with prior expectations, contained surprises. Sizeable differences exist among model capabilities that are not captured by their ranking on popular LLM leaderboards ("cramming for the leaderboard"). Furthermore, simple probability calculations indicate that GPT-4's reasonable performance on $k=5$ is suggestive of going beyond "stochastic parrot" behavior (Bender et al., 2021), i.e., it combines skills in ways that it had not seen during training. We sketch how the methodology can lead to a Skill-Mix based eco-system of open evaluations for AI capabilities of future models

Heterogeneous N2O5 reactions on atmospheric aerosols at four Chinese sites : improving model representation of uptake parameters

Heterogeneous reactivity of N2O5 on aerosols is a critical parameter in assessing NOx fate, nitrate production, and particulate chloride activation. Accurate measurement of its uptake coefficient (gamma N2O5) and representation in air quality models are challenging, especially in the polluted environment. With an in situ aerosol flow-tube system, the gamma N2O5 was directly measured on ambient aerosols at two rural sites in northern and southern China. The results were analyzed together with the gamma N2O5 derived from previous field studies in China to obtain a holistic picture of gamma N2O5 uptake and the influencing factors under various climatic and chemical conditions. The field-derived or measured gamma N2O5 was generally promoted by the aerosol water content and suppressed by particle nitrate. Significant discrepancies were found between the measured gamma N2O5 and that estimated from laboratory-determined parameterizations. An observation-based empirical parameterization was derived in the present work, which better reproduced the mean value and variability of the observed gamma N2O5. Incorporating this new parameterization into a regional air quality model (WRF-CMAQ) has improved the simulation of N2O5, nitrogen oxides, and secondary nitrate in the polluted regions of China.Peer reviewe