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Two CNF formulas are called ucp-equivalent, if they behave in the same way with respect to the unit clause propagation (UCP). A formula is called ucp-irredundant, if removing any clause leads to a formula which is not ucp-equivalent to the original one. As a consequence of known results, the ratio of the size of a ucp-irredundant formula and the size of a smallest ucp-equivalent formula is at most $n^2$, where $n$ is the number of the variables. We demonstrate an example of a ucp-irredundant formula for a symmetric definite Horn function which is larger than a smallest ucp-equivalent formula by a factor $\Omega(n/\ln n)$ and, hence, a general upper bound on the above ratio cannot be smaller than this.

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Designing cable harnesses can be time-consuming and complex due to many design and manufacturing aspects and rules. Automating the design process can help to fulfil these rules, speed up the process, and optimize the design. To accommodate this, we formulate a harness routing optimization problem to minimize cable lengths, maximize bundling by rewarding shared paths, and optimize the cables' spatial location with respect to case-specific information of the routing environment, e.g., zones to avoid. A deterministic and computationally effective cable harness routing algorithm has been developed to solve the routing problem and is used to generate a set of cable harness topology candidates and approximate the Pareto front. Our approach was tested against a stochastic and an exact solver and our routing algorithm generated objective function values better than the stochastic approach and close to the exact solver. Our algorithm was able to find solutions, some of them being proven to be near-optimal, for three industrial-sized 3D cases within reasonable time (in magnitude of seconds to minutes) and the computation times were comparable to those of the stochastic approach.

Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed marginals, in a way that minimizes expected cost. We formulate a novel variant of this problem in which the cost functions are unknown, but can be learned through noisy observations; however, only one function can be sampled at a time. We develop a semi-myopic algorithm that couples online learning with stochastic approximation, and prove that it achieves optimal convergence rates, despite the non-smoothness of the stochastic gradient and the lack of strong concavity in the objective function.

We provide the first useful, rigorous analysis of ensemble sampling for the stochastic linear bandit setting. In particular, we show that, under standard assumptions, for a $d$-dimensional stochastic linear bandit with an interaction horizon $T$, ensemble sampling with an ensemble of size $m$ on the order of $d \log T$ incurs regret bounded by order $(d \log T)^{5/2} \sqrt{T}$. Ours is the first result in any structured setting not to require the size of the ensemble to scale linearly with $T$ -- which defeats the purpose of ensemble sampling -- while obtaining near $\sqrt{T}$ order regret. Ours is also the first result that allows infinite action sets.

We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how actuators affect an end effector in parallel robots, and make it explicit in the two cases case of Stewart Platforms, and cable-driven parallel robots. We also show how to use Lie derivatives with the Newton-Raphson Method to solve the forward kinematic problem for over constrained parallel actuators. Finally, we derive the equations of motion of the end effector in dual quaternion form, which include the effect of inertia from the actuators.

We propose an individual claims reserving model based on the conditional Aalen--Johansen estimator, as developed in Bladt and Furrer (2023b). In our approach, we formulate a multi-state problem, where the underlying variable is the individual claim size, rather than time. The states in this model represent development periods, and we estimate the cumulative density function of individual claim costs using the conditional Aalen--Johansen method as transition probabilities to an absorbing state. Our methodology reinterprets the concept of multi-state models and offers a strategy for modeling the complete curve of individual claim costs. To illustrate our approach, we apply our model to both simulated and real datasets. Having access to the entire dataset enables us to support the use of our approach by comparing the predicted total final cost with the actual amount, as well as evaluating it in terms of the continuously ranked probability score, as discussed in Gneiting and A. E. Raftery (2007)

Named Entity Recognition (NER) frequently suffers from the problem of insufficient labeled data, particularly in fine-grained NER scenarios. Although $K$-shot learning techniques can be applied, their performance tends to saturate when the number of annotations exceeds several tens of labels. To overcome this problem, we utilize existing coarse-grained datasets that offer a large number of annotations. A straightforward approach to address this problem is pre-finetuning, which employs coarse-grained data for representation learning. However, it cannot directly utilize the relationships between fine-grained and coarse-grained entities, although a fine-grained entity type is likely to be a subcategory of a coarse-grained entity type. We propose a fine-grained NER model with a Fine-to-Coarse(F2C) mapping matrix to leverage the hierarchical structure explicitly. In addition, we present an inconsistency filtering method to eliminate coarse-grained entities that are inconsistent with fine-grained entity types to avoid performance degradation. Our experimental results show that our method outperforms both $K$-shot learning and supervised learning methods when dealing with a small number of fine-grained annotations.

Self-testing is a method to certify quantum states and measurements in a device-independent way. The device-independent certification of quantum properties is purely based on input-output measurement statistics of the involved devices with minimal knowledge about their internal workings. Bipartite pure entangled states can be self-tested, but, in the case of multipartite pure entangled states, the answer is not so straightforward. Nevertheless, \v{S}upi\'{c} et al. recently introduced a novel self-testing method for any pure entangled quantum state, which leverages network assistance and relies on bipartite entangled measurements. Hence, their scheme loses the true device-independent flavor of self-testing. In this regard, we provide a self-testing scheme for genuine multipartite pure entangle states in the true sense by employing a generalized Hardy-type non-local argument. It is important to note that our approach involves only local operations and classical communications and it does not depend on bipartite entangled measurements and is free from any network assistance. In addition, we provide the device-independent bound of the maximum probability of success of the generalized Hardy-type nonlocality test.

Electrodermal activity (EDA) is considered a standard marker of sympathetic activity. However, traditional EDA measurement requires electrodes in steady contact with the skin. Can sympathetic arousal be measured using only an optical sensor, such as an RGB camera? This paper presents a novel approach to infer sympathetic arousal by measuring the peripheral blood flow on the face or hand optically. We contribute a self-recorded dataset of 21 participants, comprising synchronized videos of participants' faces and palms and gold-standard EDA and photoplethysmography (PPG) signals. Our results show that we can measure peripheral sympathetic responses that closely correlate with the ground truth EDA. We obtain median correlations of 0.57 to 0.63 between our inferred signals and the ground truth EDA using only videos of the participants' palms or foreheads or PPG signals from the foreheads or fingers. We also show that sympathetic arousal is best inferred from the forehead, finger, or palm.

The Business Process Modeling Notation (BPMN) is a widely used standard notation for defining intra- and inter-organizational workflows. However, the informal description of the BPMN execution semantics leads to different interpretations of BPMN elements and difficulties in checking behavioral properties. In this article, we propose a formalization of the execution semantics of BPMN that, compared to existing approaches, covers more BPMN elements while also facilitating property checking. Our approach is based on a higher-order transformation from BPMN models to graph transformation systems. To show the capabilities of our approach, we implemented it as an open-source web-based tool.

We unify Ryser's and Glynn's formulas for computing the permanent into a single framework. We then show via an orbital bound argument that the product rank of the permanent is asymptotically upper bounded by $ \frac{\exp\left(\pi\sqrt{\frac{2n}{3}}\right)}{4\sqrt{3}n} $.

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