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1. $$\omega \rightarrow 3\pi $$ and $$\omega \pi ^{0}$$ transition form factor revisited

   https://doi.org/10.1140/epjc/s10052-020-08576-6  

   Albaladejo, M.; Danilkin, I.; Gonzàlez-Solís, S.; Winney, D.; Fernández-Ramírez, C.; Blin, A. N.; Mathieu, V.; Mikhasenko, M.; Pilloni, A.; Szczepaniak, A. (December 2020, The European Physical Journal C)

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   Abstract In light of recent experimental results, we revisit the dispersive analysis of the $$\omega \rightarrow 3\pi $$ ω → 3 π decay amplitude and of the $$\omega \pi ^0$$ ω π 0 transition form factor. Within the framework of the Khuri–Treiman equations, we show that the $$\omega \rightarrow 3\pi $$ ω → 3 π Dalitz-plot parameters obtained with a once-subtracted amplitude are in agreement with the latest experimental determination by BESIII. Furthermore, we show that at low energies the $$\omega \pi ^0$$ ω π 0 transition form factor obtained from our determination of the $$\omega \rightarrow 3\pi $$ ω → 3 π amplitude is consistent with the data from MAMI and NA60 experiments. 

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2. Omega-Regular Decision Processes

   Hahn, E M; Perez, M; Schewe, S; Somenzi, F; Trivedi, A; Wojtczak, D (April 2024, The Thirty-Eighth AAAI Conference on Artificial Intelligence (AAAI-24))

   Regular decision processes (RDPs) are a subclass of non- Markovian decision processes where the transition and reward functions are guarded by some regular property of the past (a lookback). While RDPs enable intuitive and succinct rep- resentation of non-Markovian decision processes, their ex- pressive power coincides with finite-state Markov decision processes (MDPs). We introduce omega-regular decision pro- cesses (ODPs) where the non-Markovian aspect of the transi- tion and reward functions are extended to an ω-regular looka- head over the system evolution. Semantically, these looka- heads can be considered as promises made by the decision maker or the learning agent about her future behavior. In par- ticular, we assume that if the promised lookaheads are not fulfilled, then the decision maker receives a payoff of ⊥ (the least desirable payoff), overriding any rewards collected by the decision maker. We enable optimization and learning for ODPs under the discounted-reward objective by reducing them to lexicographic optimization and learning over finite MDPs. We present experimental results demonstrating the effectiveness of the proposed reduction. 

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3. Omega-Regular Reward Machines

   Hahn, E M; Perez, M; Schewe, S; Somenzi, F; Trivedi, A; Wojtczak, D (October 2023, ECAI 2023 (Open Access by IOS Press))

   Reinforcement learning (RL) is a powerful approach for training agents to perform tasks, but designing an appropriate re- ward mechanism is critical to its success. However, in many cases, the complexity of the learning objectives goes beyond the capabili- ties of the Markovian assumption, necessitating a more sophisticated reward mechanism. Reward machines and ω-regular languages are two formalisms used to express non-Markovian rewards for quantita- tive and qualitative objectives, respectively. This paper introduces ω- regular reward machines, which integrate reward machines with ω- regular languages to enable an expressive and effective reward mech- anism for RL. We present a model-free RL algorithm to compute ε-optimal strategies against ω-regular reward machines and evaluate the effectiveness of the proposed algorithm through experiments. 

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4. An exotic II$$_1$$ factor without property Gamma

   https://doi.org/10.1007/s00039-023-00649-4  

   Chifan, Ionuţ; Ioana, Adrian; Kunnawalkam_Elayavalli, Srivatsav (October 2023, Geometric and Functional Analysis)

   We introduce a new iterative amalgamated free product construction of II factors, and use it to construct a separable II factor which does not have property Gamma and is not elementarily equivalent to the free group factor $$L(F_n)$$, for any $$n\geq 2$$. This provides the first explicit example of two non-elementarily equivalent $$II_1$$ factors without property Gamma. Moreover, our construction also provides the first explicit example of a $$II_1$$ factor without property Gamma that is also not elementarily equivalent to any ultraproduct of matrix algebras. Our proofs use a blend of techniques from Voiculescu’s free entropy theory and Popa’s deformation/rigidity theory. 

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5. Transformation-induced plasticity in omega titanium

   https://doi.org/10.1063/5.0035465  

   Zahiri, Amir Hassan; Ombogo, Jamie; Ma, Tengfei; Chakraborty, Pranay; Cao, Lei (January 2021, Journal of Applied Physics)

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