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The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current result about the well-studied switch Markov chain is that it is rapidly mixing on P-stable degree sequences (see DOI:10.1016/j.ejc.2021.103421). The switch Markov chain does not change any degree sequence. However, there are cases where degree intervals are specified rather than a single degree sequence. (A natural scenario where this problem arises is in hypothesis testing on social networks that are only partially observed.) Rechner, Strowick, and M\"uller-Hannemann introduced in 2018 the notion of degree interval Markov chain which uses three (separately well-studied) local operations (switch, hinge-flip and toggle), and employing on degree sequence realizations where any two sequences under scrutiny have very small coordinate-wise distance. Recently Amanatidis and Kleer published a beautiful paper (arXiv:2110.09068), showing that the degree interval Markov chain is rapidly mixing if the sequences are coming from a system of very thin intervals which are centered not far from a regular degree sequence. In this paper we extend substantially their result, showing that the degree interval Markov chain is rapidly mixing if the intervals are centred at P-stable degree sequences.

In Statistical Relational Artificial Intelligence, a branch of AI and machine learning which combines the logical and statistical schools of AI, one uses the concept {\em para\-metrized probabilistic graphical model (PPGM)} to model (conditional) dependencies between random variables and to make probabilistic inferences about events on a space of "possible worlds". The set of possible worlds with underlying domain $D$ (a set of objects) can be represented by the set $\mathbf{W}_D$ of all first-order structures (for a suitable signature) with domain $D$. Using a formal logic we can describe events on $\mathbf{W}_D$. By combining a logic and a PPGM we can also define a probability distribution $\mathbb{P}_D$ on $\mathbf{W}_D$ and use it to compute the probability of an event. We consider a logic, denoted $PLA$, with truth values in the unit interval, which uses aggregation functions, such as arithmetic mean, geometric mean, maximum and minimum instead of quantifiers. However we face the problem of computational efficiency and this problem is an obstacle to the wider use of methods from Statistical Relational AI in practical applications. We address this problem by proving that the described probability will, under certain assumptions on the PPGM and the sentence $\varphi$, converge as the size of $D$ tends to infinity. The convergence result is obtained by showing that every formula $\varphi(x_1, \ldots, x_k)$ which contains only "admissible" aggregation functions (e.g. arithmetic and geometric mean, max and min) is asymptotically equivalent to a formula $\psi(x_1, \ldots, x_k)$ without aggregation functions.

We introduce a new distortion measure for point processes called functional-covering distortion. It is inspired by intensity theory and is related to both the covering of point processes and logarithmic loss distortion. We obtain the distortion-rate function with feedforward under this distortion measure for a large class of point processes. For Poisson processes, the rate-distortion function is obtained under a general condition called constrained functional-covering distortion, of which both covering and functional-covering are special cases. Also for Poisson processes, we characterize the rate-distortion region for a two-encoder CEO problem and show that feedforward does not enlarge this region.

This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and difficulties in system parameterization. Existing methods to design the control objective on a Lie group and then derive the gradient for controller design are non-trivial and can result in slow convergence in tracking control. We show that with a proper left-invariant metric, setting the gradient of the cost function as the tracking error in the Lie algebra leads to a quadratic Lyapunov function that enables globally exponential convergence. In the PD control case, we show that our controller can maintain an exponential convergence rate even when the initial error is approaching $\pi$ in SO(3). We also show the merit of this proposed framework in trajectory optimization. The proposed cost function enables the iterative Linear Quadratic Regulator (iLQR) to converge much faster than the Differential Dynamic Programming (DDP) with a well-adopted cost function when the initial trajectory is poorly initialized on SO(3).

Computer vision systems today are primarily N-purpose systems, designed and trained for a predefined set of tasks. Adapting such systems to new tasks is challenging and often requires non-trivial modifications to the network architecture (e.g. adding new output heads) or training process (e.g. adding new losses). To reduce the time and expertise required to develop new applications, we would like to create general purpose vision systems that can learn and perform a range of tasks without any modification to the architecture or learning process. In this paper, we propose GPV-1, a task-agnostic vision-language architecture that can learn and perform tasks that involve receiving an image and producing text and/or bounding boxes, including classification, localization, visual question answering, captioning, and more. We also propose evaluations of generality of architecture, skill-concept transfer, and learning efficiency that may inform future work on general purpose vision. Our experiments indicate GPV-1 is effective at multiple tasks, reuses some concept knowledge across tasks, can perform the Referring Expressions task zero-shot, and further improves upon the zero-shot performance using a few training samples.

The adoption of Unmanned Aerial Vehicles (UAVs) for public safety applications has skyrocketed in the last years. Leveraging on Physical Random Access Channel (PRACH) preambles, in this paper we pioneer a novel localization technique for UAVs equipped with cellular base stations used in emergency scenarios. We exploit the new concept of Orthogonal Time Frequency Space (OTFS) modulation (tolerant to channel Doppler spread caused by UAVs motion) to build a fully standards-compliant OTFS-modulated PRACH transmission and reception scheme able to perform time-of-arrival (ToA) measurements. First, we analyze such novel ToA ranging technique, both analytically and numerically, to accurately and iteratively derive the distance between localized users and the points traversed by the UAV along its trajectory. Then, we determine the optimal UAV speed as a trade-off between the accuracy of the ranging technique and the power needed by the UAV to reach and keep its speed during emergency operations. Finally, we demonstrate that our solution outperforms standard PRACH-based localization techniques in terms of Root Mean Square Error (RMSE) by about 20% in quasi-static conditions and up to 80% in high-mobility conditions.

Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fern\'andez-Duque that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he provided a complete axiomatisation in an extended language. In this paper, we consider dynamic topological logic over scattered spaces, which are topological spaces where every nonempty subspace has an isolated point. Scattered spaces appear in the context of computational logic as they provide semantics for provability and enjoy definable fixed points. We exhibit the first sound and complete dynamic topological logic in the original trimodal language. In particular, we show that the version of $\mathbf{DTL}$ based on the class of scattered spaces is finitely axiomatisable over the original language, and that the natural axiomatisation is sound and complete.

Universal coding of integers~(UCI) is a class of variable-length code, such that the ratio of the expected codeword length to $\max\{1,H(P)\}$ is within a constant factor, where $H(P)$ is the Shannon entropy of the decreasing probability distribution $P$. However, if we consider the ratio of the expected codeword length to $H(P)$, the ratio tends to infinity by using UCI, when $H(P)$ tends to zero. To solve this issue, this paper introduces a class of codes, termed generalized universal coding of integers~(GUCI), such that the ratio of the expected codeword length to $H(P)$ is within a constant factor $K$. First, the definition of GUCI is proposed and the coding structure of GUCI is introduced. Next, we propose a class of GUCI $\mathcal{C}$ to achieve the expansion factor $K_{\mathcal{C}}=2$ and show that the optimal GUCI is in the range $1\leq K_{\mathcal{C}}^{*}\leq 2$. Then, by comparing UCI and GUCI, we show that when the entropy is very large or $P(0)$ is not large, there are also cases where the average codeword length of GUCI is shorter. Finally, the asymptotically optimal GUCI is presented.

This paper reports on a follow-up study of the work reported in Sakai, which explored suitable evaluation measures for ordinal quantification tasks. More specifically, the present study defines and evaluates, in addition to the quantification measures considered earlier, a few variants of an ordinal quantification measure called Root Normalised Order-aware Divergence (RNOD), as well as a measure which we call Divergence based on Kendall's $\tau$ (DNKT). The RNOD variants represent alternative design choices based on the idea of Sakai's Distance-Weighted sum of squares (DW), while DNKT is designed to ensure that the system's estimated distribution over classes is faithful to the target priorities over classes. As this Priority Preserving Property (PPP) of DNKT may be useful in some applications, we also consider combining some of the existing quantification measures with DNKT. Our experiments with eight ordinal quantification data sets suggest that the variants of RNOD do not offer any benefit over the original RNOD at least in terms of system ranking consistency, i.e., robustness of the system ranking to the choice of test data. Of all ordinal quantification measures considered in this study (including Normalised Match Distance, a.k.a. Earth Mover's Distance), RNOD is the most robust measure overall. Hence the design choice of RNOD is a good one from this viewpoint. Also, DNKT is the worst performer in terms of system ranking consistency. Hence, if DNKT seems appropriate for a task, sample size design should take its statistical instability into account.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.