Miracle-dz/UniFAR-FTUs huggingface dataset:
Beyond Perfection: On Relaxations and Superclasses

H a b i l i t a t i o n s s c h r i f t zur Erlangung des akademischen Grades doctor rerum naturalium habilitatus Färbungszahl χ(G) eines Graphen ist jedoch i.a. NP-schwer. Die Cliquen-zahl ω(G) ist eine natürliche untere Schranke für χ(G); für perfekte Graphen G gilt stets Gleichheit (für alle induzierten Untergraphen), im Allgemeinen können die beiden Parameter jedoch beliebig weit auseinander liegen [70]. Eine natürliche Frage ist also, für welche Graphenklassen die Differenz zwi-schen Cliquenzahl ω(G) und Färbungszahl χ(G) unter Kontrolle ist. Wir be-schäftigen uns mit zwei Konzepten, um diese Frage zu beantworten: oberen Schranken für χ(G) als Funktion von ω(G) und dem Imperfektheitsgrad eines Graphen. iii iv Eine Graphenklasse G ist χ-bound mit Bindingfunktion b, falls χ(G ′) ≤ b(ω(G ′)) für alle induzierten Untergraphen G ′ von Graphen G ∈ G gilt [51]. Perfekte Graphen sind genau die Graphen mit Bindingfunktion b(x) = x und Klassen mit linearer Bindingfunktion b(x) = bx + c habenähnlich gute Färbungseigenschaften. Wir untersuchen in Kapitel 2 verschiedene Klassen mit Bindingfunktion b(x) = x + 1. Gerke und McDiarmid führten in [45] alsähnliches Konzept den Imper-fektheitsgrad eines Graphen G ein als imp(G) = max χ f (G, c) ω(G, c) | c : V (G) → N \ {0} wobei χ f (G, c) die fraktionale gewichtete Färbungszahl und ω(G, c) die ge-wichtete Cliquenzahl ist. Jeder perfekte Graph G hat imp(G) = 1 und alle Graphen mit einem kleinen Imperfektheitsgrad können als 'fast per-fekt' angesehen werden. Wir geben für einige Klassen obere Schranken für den Imperfektheitsgrad an, siehe Sektion 5.2. Weiter leiten wir für Klassen mit unbeschränktem Imperfektheitsgrad eine hinreichende Bedingung für die Nichtexistenz von Bindingfunktionen her, siehe Sektion 2.3.
Asymptotic Unbiasedness and Consistency of Cross-Correlogram Estimators of Response Functions in Linear Continuous Systems

У роботі розглядається задача оцінювання невідомої дійснозначної перехідної функції лінійної однорідної системи. Припускається, що на вхід системи подається сім’я цент­рованих стаціонарних гауссівських процесів, близьких до білого шуму. Як оцінка для перехідної функції береться інтегральна сумісна корелограма між процесами на вході та виході системи. Належність перехідної функції до простору \begin{equation}L_{2}\left(\mathbb{R}\right)\end{equation} є основним припущенням роботи. Відповідна корелограмна оцінка залежить від двох параметрів – параметра схеми серій і довжини інтервалу усереднення – та є зсуненою. Метою роботи є дослідження властивостей асимптотичної незсуненості та конзистентності оцінки. Для вивчення цих властивостей додатково вводились умова рівномірної ліпшицевості перехідної функції та балансні умови між кореляційними функціями вхідних процесів і параметром схеми серій. Зокрема, при встановленні фактів використовувались властивості перетворення Фур’є, деякі властивості ядер Фейєра та нерівність Юнга для згортки функцій. У результаті, для корелограмної оцінки було отримано достатні умови асимптотичної незсуненості та кон­зистентності у середньому квадратичному.
Orthogonal polynomials, lattice paths, and skew Young tableaux

Orthogonal polynomials, lattice paths, and skew Young tableaux A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University, Waltham, Massachusetts by Jordan Olliver Tirrell We give two applications of the combinatorial theory of orthogonal polynomials developed by Viennot and Flajolet. First we discuss the classic Chung-Feller theorem for flawed Dyck paths, and an analog for flawed Motzkin paths found by Eu, Liu, and Yeh in 2002. Their result states that the number of flawed Motzkin paths of length n with a fixed number of flaws can be expressed as a linear combination of Motzkin numbers. We will give a generalization that unifies the classic Chung-Feller theorem and the Motzkin path analog. Using orthogonal polynomials, we will give a combinatorial interpretation for the coefficients in these linear combinations of Motzkin numbers. Next, we extend the bijection between Motzkin paths and Young tableaux with at most three rows to the skew case. Amitai Regev conjectured in 2009, and Doron Zeilberger proved, that for fixed skew part (2,1), the number of skew Young tableaux of fixed size is a difference of two Motzkin numbers. Sen-Peng Eu showed in 2010 that for any fixed skew part and total size, the number can be written as a linear combination of Motzkin numbers. Jong Hyun Kim found an explicit formula for this general case which had an unexpected connection with the Chebyshev polynomials. Again, we use insights from the combinatorial theory of orthogonal polynomials to give a combinatorial proof. We first work with “skew-reduced” Young tableaux, and then the regular skew Young tableaux case follows, and we obtain a refinement of Kim’s formula.
Reasoning and Verification with Data Petri Nets

Data-aware processes represent and integrate structural and behavioural constraints in a single model, and are thus increasingly investigated in business process management and artificial intelligence. In this spectrum, Data Petri nets (DPNs) have gained growing popularity thanks to their ability to balance simplicity with expressiveness. To faithfully model real-world processes, the data perspective often requires arithmetic, which renders basic problems undecidable. Nonetheless, we show here that by appropriately restricting the constraint language or structure, a number of important tasks becomes decidable for practical classes of systems: This includes linear-and branching-time model checking, strategic reasoning, and verification of data-aware soundness.
Addressing Function Approximation Error in Actor-Critic Methods : Supplementary Material A . Proof of Convergence of Clipped Double Q-Learning

In a finite MDP setting, Double Q-learning is often used to deal with noise induced by random rewards or state transitions, and so either Q or Q is updated randomly. However, in a function approximation setting, the interest may be more towards the approximation error and thus we can update both Q and Q at each iteration. The proof extends naturally to updating either randomly. The proof borrows heavily from the proof of convergence of SARSA (Singh et al., 2000) as well as Double Q-learning (Van Hasselt, 2010). The proof of lemma 1 can be found in Singh et al. (2000), building on a proposition from Bertsekas (1995). Lemma 1. Consider a stochastic process (ζt,∆t, Ft), t ≥ 0 where ζt,∆t, Ft : X → R satisfy the equation: ∆t+1(xt) = (1− ζt(xt))∆t(xt) + ζt(xt)Ft(xt), (3)
Improving the Performance of Backward Chained Behavior Trees using Reinforcement Learning

—In this letter we show how to improve the performance of backward chained behavior trees (BTs) using re-inforcement learning (RL). BTs represent a hierarchical and modular way of combining control policies into higher level control policies. Backward chaining is a design principle that leads to BTs that combine reactivity with goal directed actions in a structured way. The backward chained structure has also enabled convergence proofs for BTs, identifying a set of local conditions that lead to the convergence of all trajectories to a set of desired goal states. The key idea of this letter is to improve performance of backward chained BTs by using the conditions identiﬁed in the theoretical convergence proof to setup RL problems for individual controllers. In particular, the analysis identiﬁed important sub-goals, so-called active constraint conditions (ACCs), that should be preserved in order to avoid having to go back and address them again. We propose to setup the RL problems to not only achieve each immediate subgoal, but also avoid violating the identiﬁed ACCs. The resulting performance improvement can be seen to depend on how often ACC violations occured before the update, and how much effort was needed to re-achieve them. The proposed approach is illustrated in a dynamic simulation environment.
Is Chinese cosmology metaphysics

In literature about Chinese philosophy, there are two prevailing views: (1) Chinese philosophy lacks interest in metaphysical pursuit and is preoccupied with practical affairs; and (2) There is a rich cosmology in Chinese thought. However, when we put these two views together, we get a disturbing and puzzling result: (3) Chinese cosmology is not metaphysics. This paper seeks to address the question “is Chinese cosmology metaphysics? ” by asking questions about the following three topics. (a) Is there a shared Chinese cosmology that is unique to Chinese tradition but is sharply different from Greek cosmology? (b) Precisely what is the nature of the elation between Chinese ethics and Chinese cosmology? (c) Chinese cosmology and the issue of being. Although a full discussion of the issue is beyond the scope of one paper, I will try to identify some major problems in outline. My approach is through a comparison between Chinese cosmology and Greek cosmology/metaphysics. Introduction: Problem and Approach IN LITERATURE about Chinese philosophy, there are two prevailing views: (1) Chinese philosophy lacks interest in metaphysical pursuit and is preoccupied with practical affairs; and (2) There is a rich cosmology in Chinese thought. Let me call (1) the ―lack of metaphysics‘ view, and (2) the ―rich cosmology‖ view. The position (2), the ―rich cosmology‖ view, cannot be mistaken. Developed in the classical texts such as Mencius, Xunzi, Laozi, Zhuangzi, Guanzi, The Book of Changes, Huainanzi etc, Chinese cosmology has contributed many influential theories, such as that of tian (Heaven), Dao, Ying/yang, five phases, qi, the cyclical changes, tian-ren ho-yi (―the unity of tian and man‖), and so on. The view (1), the ―lack of metaphysics‖ view, is also strongly justified. It is shared by those who defend the philosophical nature of Chinese philosophy (Fung, 1952, vol.1, 1-6), as well as those who reject the philosophical nature of Chinese thought (Zeller, 1997, 2). 1 There are also prominent comparativists who believe that the lack of theoretical interest in metaphysical pursuits is indeed one of the major differences between Chinese thought and Western philosophy (e.g. G. E. R. Lloyd, 1990, 124) . However, when we put these two views together, the result appears to be: (3) Chinese cosmology is not metaphysics. *JIYUAN YU, Professor, Department of Philosophy, State University of New York at Buffalo, Buffalo, NY 14260, U.S.A. and Changjiang Chair Professor, Department of Philosophy, Shandong University, Jinan, China. Email: jyyu@buffalo.edu 1 Indeed, for those who accuse Chinese thought of not being a real philosophy, what they actually mean is that Chinese philosophy does not study metaphysical
Remapping in a recurrent neural network model of navigation and context inference

Neurons in navigational brain regions provide information about position, orientation, and speed relative to environmental landmarks. These cells also change their firing patterns (“remap”) in response to changing contextual factors such as environmental cues, task conditions, and behavioral state, which influence neural activity throughout the brain. How can navigational circuits preserve their local computations while responding to global context changes? To investigate this question, we trained recurrent neural network models to track position in simple environments while at the same time reporting transiently-cued context changes. We show that these combined task constraints (navigation and context inference) produce activity patterns that are qualitatively similar to population-wide remapping in the entorhinal cortex, a navigational brain region. Furthermore, the models identify a solution that generalizes to more complex navigation and inference tasks. We thus provide a simple, general, and experimentally-grounded model of remapping as one neural circuit performing both navigation and context inference.
Predicting Blood Pressure with Deep Bidirectional LSTM Network

Blood pressure (BP) has been a difficult vascular risk factor to measure continuously and precisely with a small cuffless electronic gadget. In the meantime, it is the key biomarker for control of cardiovascular diseases (CVD), the leading cause of death worldwide. In this work, we addressed the current limitation of BP prediction models by formulating BP extraction as a temporal sequence prediction problem in which both the input and target are sequential data. By incorporating both a bidirectional layer structure and a deep architecture in a standard long short term-memory (LSTM), we established a deep bidirectional LSTM (DB-LSTM) network that can adaptively discover the latent structures of different timescales in BP sequences and automatically learn such multiscale dependencies. We evaluated our proposed model on a one-day and four-day continuous BP dataset, and the results show that DB-LSTM network can effectively learn different timescale dependencies in the BP sequences and advances the state-of-the-art by achieving superior accuracy performance than other leading methods on both datasets. To the best of our knowledge, this is the first study to validate the ability of recurrent neural networks to learn the different timescale dependencies of long-term continuous BP sequence.
Predicting and estimating probability density functions of chaotic systems

In the present work, for the first time, we employ Ulam's method to estimate and to predict the existence of the probability density functions of single species populations with chaotic dynamics. In particular, given a chaotic map, we show that Ulam's method generates a sequence of density functions in L 1 -space that may converge weakly to a function in L 1 -space. In such a case we show that the limiting function generates an absolutely continuous (w.r.t. the Lebesgue measure) invariant measure (w.r.t. the given chaotic map) and therefore the limiting function is the probability density function of the chaotic map. This fact can be used to determine the existence and estimate the probability density functions of chaotic biological systems.
The Micromorphic Approach to Generalized Heat Equations

Abstract In this paper, the micromorphic approach, previously developed in the mechanical context is applied to heat transfer and shown to deliver new generalized heat equations as well as the nonlocal effects. The latter are compared to existing formulations: the classical Fourier heat conduction, the hyperbolic type with relaxation time, the gradient of temperature or entropy theories, the double temperature model, the micro-temperature model or micro-entropy models. A new pair of thermodynamically-consistent micromorphic heat equations are derived from appropriate Helmholtz-free energy potentials depending on an additional micromorphic temperature and its first gradient. The additional micromorphic temperature associated with the classical local temperature is introduced as an independent degree of freedom, based on the generalized principle of virtual power. This leads to a new thermal balance equation taking into account the nonlocal thermal effects and involving an internal length scale which represents the characteristic size of the system. Several existing extended generalized heat equations could be retrieved from constrained micromorphic heat equations with suitable selections of the Helmholtz-free energy and heat flux expressions. As an example the propagation of plane thermal waves is investigated according to the various generalized heat equations. Possible applications to fast surface processes, nanostructured media and nanosystems are also discussed.
Offline Reinforcement Learning for Road Traffic Control

Traffic signal control is an important problem in urban mobility with a significant potential of economic and environmental impact. While there is a growing interest in Reinforcement Learning (RL) for traffic control, the work so far has focussed on learning through interactions which, in practice, is costly. Instead, real experience data on traffic is available and could be exploited at minimal costs. Recent progress in offline or batch RL has enabled just that. Model-based offline RL methods, in particular, have been shown to generalize to the experience data much better than others. We build a model-based learning framework, A-DAC, which infers a Markov Decision Process (MDP) from dataset with pes-simistic costs built in to deal with data uncertainties. The costs are modeled through an adaptive shaping of rewards in the MDP which provides better regularization of data compared to the prior related work. A-DAC is evaluated on a complex signalized roundabout us-ing multiple datasets varying in size and in batch collection policy. The evaluation results show that it is possible to build high performance control policies in a data efficient manner using simplistic batch collection policies.
Do Neural Network Cross-Modal Mappings Really Bridge Modalities?

Feed-forward networks are widely used in cross-modal applications to bridge modalities by mapping distributed vectors of one modality to the other, or to a shared space. The predicted vectors are then used to perform e.g., retrieval or labeling. Thus, the success of the whole system relies on the ability of the mapping to make the neighborhood structure (i.e., the pairwise similarities) of the predicted vectors akin to that of the target vectors. However, whether this is achieved has not been investigated yet. Here, we propose a new similarity measure and two ad hoc experiments to shed light on this issue. In three cross-modal benchmarks we learn a large number of language-to-vision and vision-to-language neural network mappings (up to five layers) using a rich diversity of image and text features and loss functions. Our results reveal that, surprisingly, the neighborhood structure of the predicted vectors consistently resembles more that of the input vectors than that of the target vectors. In a second experiment, we further show that untrained nets do not significantly disrupt the neighborhood (i.e., semantic) structure of the input vectors.
Acute Postoperative Pain Management

ffective postoperative pain control is an essential compo-nent of the care of the surgical patient. Inadequate paincontrol, apart from being inhumane, may result in in-creased morbidity or mortality (1, 2). Evidence suggests that sur-gery suppresses the immune system and that this suppression isproportionate to the invasiveness of the surgery (3, 4). Goodanalgesia can reduce this deleterious effect. Data available indi-cate that afferent neural blockade with local anesthetics is themost effective analgesic technique. Next in order of effectivenessare high-dose opioids, epidural opioids and clonidine, patient-controlled opioid therapy, and nonsteroidal anti-inflammatoryagents (5). The advantages of effective postoperative pain managementinclude patient comfort and therefore satisfaction, earlier mo-bilization, fewer pulmonary and cardiac complications, a reducedrisk of deep vein thrombosis, faster recovery with less likelihoodof the development of neuropathic pain, and reduced cost of care.The failure to provide good postoperative analgesia is multi-factorial. Insufficient education, fear of complications associatedwith analgesic drugs, poor pain assessment, and inadequate staff-ing are among its causes.
Adenoid cystic carcinoma of the head and neck: predictors of morbidity and mortality.

OBJECTIVES To review 160 patients treated at a single institution for adenoid cystic carcinoma during the 20 years between 1977 and 1996, applying a consistent treatment of surgery and postoperative radiation therapy to 140 patients. To analyze factors governing treatment failure, treatment-related morbidity, and mortality. DESIGN Retrospective review. SETTING Tertiary referral center. PATIENTS Seventy-seven males and 83 females aged 13 to 89 years (average age, 49.5 years). RESULTS AND CONCLUSIONS Combined treatment yielded an 85% locoregional freedom from relapse and disease-specific survival at 5, 10, and 15 years was 89%, 67.4%, and 39.6%, respectively. Thirty-five patients (21.9%) had distant metastases as the only site of failure. Patients treated for paranasal sinus tumor experienced the most treatment-related morbidity vs other sites. Perineural invasion of major nerves, positive margins at surgery, and solid histological features were associated with increased treatment failures. Four or more symptoms present at diagnosis, positive lymph nodes, solid histology, and perineural invasion of major nerves were associated with increased mortality from disease.
Rectangular Young tableaux with local decreases and the density method for uniform random generation

In this article, we consider a generalization of Young tableaux in which we allow some consecutive pairs of cells with decreasing labels. We show that this leads to a rich variety of combinatorial formulas, which suggest that these new objects could be related to deeper structures, similarly to the ubiquitous Young tableaux. Our methods rely on variants of hook-length type formulas, and also on a new efficient generic method (which we call the density method) which allows not only to generate constrained combinatorial objects, but also to enumerate them. We also investigate some repercussions of this method on the D-finiteness of the generating functions of combinatorial objects encoded by linear extension diagrams, and give a limit law result for the average number of local decreases. Copyright c © by the paper’s authors. Copying permitted for private and academic purposes. In: L. Ferrari, M. Vamvakari (eds.): Proceedings of the GASCom 2018 Workshop, Athens, Greece, 18–20 June 2018, published at http://ceur-ws.org
Zero-field superconducting diode effect in twisted trilayer graphene

Jiang-Xiazi Lin1∗, Phum Siriviboon1∗, Harley D. Scammell, Song Liu, Daniel Rhodes, K. Watanabe, T. Taniguchi, James Hone, Mathias S. Scheurer, and J.I. A. Li1∗ Department of Physics, Brown University, Providence, RI 02912, USA School of Physics, the University of New South Wales, Sydney, NSW, 2052 Australia Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan 6 Institute for Theoretical Physics, University of Innsbruck, Innsbruck, A-6020, Austria and ∗These authors contributed equally in this work. (Dated: December 16, 2021)
JOURNAL OF ENGINEERING SCIENCES

Natural fibres have emerged as a renewable and cheaper substitute to synthetic materials such as glass and carbon. A composite material can be defined as combining two or more materials that result in better properties. The constituents are reinforcement, and the other is a matrix. The main advantages of composites are high strength, stiffness combined with low density. As natural fibres are gaining more importance in recent times, many industries are focusing on these natural fibre composites, so that is why they are used as a component in composite materials. In this experiment, the analysis aims to characterize different natural fibres when combined with different ratios of the coconut coir and the bamboo. So, to fabricate the specimen, the hand lay-up method is used. The coconut coir and the bamboo composition are considered in three different variations. Then the natural fibres are subjected to resin and hardener compositions to test the suitability, tensile strength, flexural strength, and shore hardness test. We also conduct static analysis through ANSYS software.