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Yayın Some remarks on uniform boundary Harnack principles(Cornell Univ, 2021-03-18) Barlow, Martin T.; Karlı, DenizWe prove two versions of a boundary Harnack principle in which the constants do not depend on the domain by using probabilistic methods.Yayın Matched pair analysis of the Vlasov plasma(Cornell Univ, 2021-02-09) Esen, Oğul; Sütlü, SerkanWe present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of mutually interacting (Lie-Poisson) subdynamics. The mutual interaction is beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address the matched pair Lie-Poisson formulation allowing mutual interactions. Moreover, both for the kinetic moments and the Vlasov plasma cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the dynamics of the kinetic moments of order > 2. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma, along with its matched pair decomposition.Yayın Tulczyjew's triplet for Lie groups III : higher order dynamics and reductions for iterated bundles(Cornell Univ, 2021-02-23) Esen, Oğul; Gümral, Hasan; Sütlü, SerkanGiven a Lie group G, we elaborate the dynamics on T*T*G and T*T G, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space TT*G, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.Yayın Age of information in practice(Cornell Univ, 2021-06-02) Uysal, Elif; Kaya, Onur; Baghaee, Sajjad; Beytur, Hasan BurhanWhile age of Information (AoI) has gained importance as a metric characterizing the fresh-ness of information in information-update systems and time-critical applications, most previous studies on AoI have been theoretical. In this chapter, we compile a set of recent works reporting API measurements in real-life networks and experimental testbeds, and investigating practical issues such as synchronization, the role of various transport layer protocols, congestion control mechanisms, application of machine learning for adaptation to network conditions, and device related bottlenecks such as limited processing power.Yayın Setting standards in Turkish NLP: TR-MMLU for large language model evaluation(Cornell Univ, 2025-01-04) Bayram, M. Ali; Fincan, Ali Arda; Gümüş, Ahmet Semih; Diri, Banu; Yıldırım, Savaş; Aytaş, ÖnerLanguage models have made remarkable advancements in understanding and generating human language, achieving notable success across a wide array of applications. However, evaluating these models remains a significant challenge, particularly for resource-limited languages such as Turkish. To address this gap, we introduce the Turkish MMLU (TR-MMLU) benchmark, a comprehensive evaluation framework designed to assess the linguistic and conceptual capabilities of large language models (LLMs) in Turkish. TR-MMLU is constructed from a carefully curated dataset comprising 6,200 multiple-choice questions across 62 sections, selected from a pool of 280,000 questions spanning 67 disciplines and over 800 topics within the Turkish education system. This benchmark provides a transparent, reproducible, and culturally relevant tool for evaluating model performance. It serves as a standard framework for Turkish NLP research, enabling detailed analyses of LLMs’ capabilities in processing Turkish text and fostering the development of more robust and accurate language models. In this study, we evaluate state-of-the-art LLMs on TR-MMLU, providing insights into their strengths and limitations for Turkish-specific tasks. Our findings reveal critical challenges, such as the impact of tokenization and fine-tuning strategies, and highlight areas for improvement in model design. By setting a new standard for evaluating Turkish language models, TR-MMLU aims to inspire future innovations and support the advancement of Turkish NLP research.Yayın Higher analogues of discrete topological complexity(Cornell Univ, 2024-04-16) Alabay, Hilal; Borat, Ayşe; Cihangirli, Esra; Erdal, Esma DiricanIn this paper, we introduce the n−th discrete topological complexity and study its properties such as its relation with simplicial LusternikSchnirelmann category and how the higher dimensions of discrete topological complexity relate with each other. Moreover, we find a lower bound of n−discrete topological complexity which is given by the n−th usual topological complexity of the geometric realisation of that complex. Furthermore, we give an example for the strict case of that lower bound.Yayın Selective influence of dopamine on electrocortical signatures of error monitoring: a combined EEG and immersive virtual reality study in Parkinson's disease(Cold Spring Harbor Lab Press, 2022-04-14) Pezzetta, Rachele; Özkan, Duru Gün; Era, Vanessa; Tieri, Gaetano; Zabberoni, S.; Taglieri, Sara; Costa, A.; Peppe, Antonella; Caltagirone, Carmen; Aglioti, Salvatore MariaDetecting errors in ones own and others actions is likely linked to the discrepancy between intended or expected and produced or observed output. To detect and process the occurrence of salient events seems associated to the release of dopamine, the balance of which is profoundly altered in Parkinsons disease (PD). EEG studies in healthy participants indicate that the occurrence of errors in observed actions triggers a variety of electrocortical indices (like mid-frontal theta activity, error-related delta and the Error Positivity, oPe), that seem to map different aspects of error detection and performance monitoring. Whether these indices are differently modulated by dopamine in the same individual has never been investigated. To explore this issue, we recorded EEG markers of error detection by asking healthy controls (HCs) and PD patients to observe ecological reach-to-grasp a glass actions performed by a virtual arm seen in first person perspective. PD patients were tested under their dopaminergic medication ( on-condition), and after dopaminergic withdrawal ( off-condition). HCs showed a clear oPe and an increase of delta and theta power during the observation of erroneous vs. correct actions. In PD patients, oPe and delta responses were always preserved. Crucially, however, an error-related increase of theta power was found in on but not in off state PD patients. Thus, different EEG error signatures may index the activity of independent systems and error related theta power is selectively modulated by dopamine depletion. Our findings may pave the way to the discovery of dopamine-related biomarkers of higher-order motor cognition dysfunctions that may have crucial theoretical and clinical implications. Significance StatementDopaminergic neurons respond to salient events during performance monitoring. Yet, the impact of dopamine depletion on the human reactivity to observed errors is still unclear. We recorded EEG in patients with Parkinsons Disease (PD) under dopaminergic treatment ( on-condition) and medication withdrawal ( off-condition) while they observed correct and erroneous goal-related actions performed by a virtual limb. Analysis of Error Positivity (oPe) and theta and delta power increase, markers of physiological error-monitoring, indicates that while the formers were intact, the latter was preserved in the on and altered in the off condition. Thus, different EEG markers of error monitoring likely rely on independent circuits. Moreover, mid-frontal theta activity alterations may represent a marker of dopamine-related neurophysiological impairments of higher-order cognition.Yayın On extensions, Lie-Poisson systems, and dissipation(Cornell Univ, 2021-01-08) Esen, Oğul; Özcan, Gökhan; Sütlü, SerkanOn the dual space of extended structure, equations governing the collective motion of two mutually interacting Lie-Poisson systems are derived. By including a twisted 2-cocycle term, this novel construction is providing the most general realization of (de)coupling of Lie-Poisson systems. A double cross sum (matched pair) of 2-cocycle extensions are constructed. The conditions are determined for this double cross sum to be a 2-cocycle extension by itself. On the dual spaces, Lie-Poisson equations are computed. We complement the discussion by presenting a double cross sum of some symmetric brackets, such as double bracket, Cartan-Killing bracket, Casimir dissipation bracket, and Hamilton dissipation bracket. Accordingly, the collective motion of two mutually interacting irreversible dynamics, as well as mutually interacting metriplectic flows, are obtained. The theoretical results are illustrated in three examples. As an infinite-dimensional physical model, decompositions of the BBGKY hierarchy are presented. As finite-dimensional examples, the coupling of two Heisenberg algebras and coupling of two copies of 3D dynamics are studied.Yayın Quantum Zeno repeaters(Cornell Univ, 2022-06-17) Bayrakçı, Veysel; Özaydın, FatihQuantum repeaters pave the way for long-distance quantum communications and quantum Internet, and the idea of quantum repeaters is based on entanglement swapping which requires the implementation of controlled quantum gates. Frequently measuring a quantum system affects its dynamics which is known as the quantum Zeno effect (QZE). Beyond slowing down its evolution, QZE can be used to control the dynamics of a quantum system by introducing a carefully designed set of operations between measurements. Here, we propose an entanglement swapping protocol based on QZE, which achieves almost unit fidelity. Implementation of our protocol requires only simple frequent threshold measurements and single particle rotations. We extend the proposed entanglement swapping protocol to a series of repeater stations for constructing quantum Zeno repeaters which also achieve almost unit fidelity regardless of the number of repeaters. Requiring no controlled gates, our proposal reduces the quantum circuit complexity of quantum repeaters. Our work has potential to contribute to long distance quantum communications and quantum computing via quantum Zeno effect.Yayın Goal-Oriented Random Access (GORA)(Cornell Univ, 2025-05-05) Topbaş, Ahsen; Ari, Çağrı; Kaya, Onur; Uysal, ElifWe propose Goal-Oriented Random Access (GORA), where transmitters jointly optimize what to send and when to access the shared channel to a common access point, considering the ultimate goal of the information transfer at its final destination. This goal is captured by an objective function, which is expressed as a general (not necessarily monotonic) function of the Age of Information. Our findings reveal that, under certain conditions, it may be desirable for transmitters to delay channel access intentionally and, when accessing the channel, transmit aged samples to reach a specific goal at the receiver.
