TY - CONF AB - The safety-liveness dichotomy is a fundamental concept in formal languages which plays a key role in verification. Recently, this dichotomy has been lifted to quantitative properties, which are arbitrary functions from infinite words to partially-ordered domains. We look into harnessing the dichotomy for the specific classes of quantitative properties expressed by quantitative automata. These automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totallyordered domain of real numbers. In this automata-theoretic setting, we establish a connection between quantitative safety and topological continuity and provide an alternative characterization of quantitative safety and liveness in terms of their boolean counterparts. For all common value functions, we show how the safety closure of a quantitative automaton can be constructed in PTime, and we provide PSpace-complete checks of whether a given quantitative automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata, for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf, and LimSup automata, we give PTime decompositions into safe and live automata. These decompositions enable the separation of techniques for safety and liveness verification for quantitative specifications. AU - Boker, Udi AU - Henzinger, Thomas A AU - Mazzocchi, Nicolas Adrien AU - Sarac, Naci E ID - 13221 SN - 9783959772990 T2 - 34th International Conference on Concurrency Theory TI - Safety and liveness of quantitative automata VL - 279 ER - TY - JOUR AB - Recently, a concept of generalized multifractality, which characterizes fluctuations and correlations of critical eigenstates, was introduced and explored for all 10 symmetry classes of disordered systems. Here, by using the nonlinear sigma-model ( NL σ M ) field theory, we extend the theory of generalized multifractality to boundaries of systems at criticality. Our numerical simulations on two-dimensional systems of symmetry classes A, C, and AII fully confirm the analytical predictions of pure-scaling observables and Weyl symmetry relations between critical exponents of surface generalized multifractality. This demonstrates the validity of the NL σ M for the description of Anderson-localization critical phenomena, not only in the bulk but also on the boundary. The critical exponents strongly violate generalized parabolicity, in analogy with earlier results for the bulk, corroborating the conclusion that the considered Anderson-localization critical points are not described by conformal field theories. We further derive relations between generalized surface multifractal spectra and linear combinations of Lyapunov exponents of a strip in quasi-one-dimensional geometry, which hold under the assumption of invariance with respect to a logarithmic conformal map. Our numerics demonstrate that these relations hold with an excellent accuracy. Taken together, our results indicate an intriguing situation: the conformal invariance is broken but holds partially at critical points of Anderson localization. AU - Babkin, Serafim AU - Karcher, Jonas F. AU - Burmistrov, Igor S. AU - Mirlin, Alexander D. ID - 14406 IS - 10 JF - Physical Review B SN - 2469-9950 TI - Generalized surface multifractality in two-dimensional disordered systems VL - 108 ER - TY - CONF AB - This paper focuses on the implementation details of the baseline methods and a recent lightweight conditional model extrapolation algorithm LIMES [5] for streaming data under class-prior shift. LIMES achieves superior performance over the baseline methods, especially concerning the minimum-across-day accuracy, which is important for the users of the system. In this work, the key measures to facilitate reproducibility and enhance the credibility of the results are described. AU - Tomaszewska, Paulina AU - Lampert, Christoph ID - 14410 SN - 0302-9743 T2 - International Workshop on Reproducible Research in Pattern Recognition TI - On the implementation of baselines and lightweight conditional model extrapolation (LIMES) under class-prior shift VL - 14068 ER - TY - CONF AB - We introduce hypernode automata as a new specification formalism for hyperproperties of concurrent systems. They are finite automata with nodes labeled with hypernode logic formulas and transitions labeled with actions. A hypernode logic formula specifies relations between sequences of variable values in different system executions. Unlike HyperLTL, hypernode logic takes an asynchronous view on execution traces by constraining the values and the order of value changes of each variable without correlating the timing of the changes. Different execution traces are synchronized solely through the transitions of hypernode automata. Hypernode automata naturally combine asynchronicity at the node level with synchronicity at the transition level. We show that the model-checking problem for hypernode automata is decidable over action-labeled Kripke structures, whose actions induce transitions of the specification automata. For this reason, hypernode automaton is a suitable formalism for specifying and verifying asynchronous hyperproperties, such as declassifying observational determinism in multi-threaded programs. AU - Bartocci, Ezio AU - Henzinger, Thomas A AU - Nickovic, Dejan AU - Oliveira da Costa, Ana ID - 14405 SN - 18688969 T2 - 34th International Conference on Concurrency Theory TI - Hypernode automata VL - 279 ER - TY - JOUR AB - We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 01+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices. AU - Dubach, Guillaume AU - Erdös, László ID - 12683 JF - Electronic Communications in Probability TI - Dynamics of a rank-one perturbation of a Hermitian matrix VL - 28 ER - TY - JOUR AB - We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine the fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent multiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048). AU - Cipolloni, Giorgio AU - Erdös, László AU - Schröder, Dominik J ID - 12761 IS - 1 JF - Annals of Applied Probability SN - 1050-5164 TI - Functional central limit theorems for Wigner matrices VL - 33 ER - TY - JOUR AB - It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces. AU - Browning, Timothy D AU - Boudec, Pierre Le AU - Sawin, Will ID - 8682 IS - 3 JF - Annals of Mathematics SN - 0003-486X TI - The Hasse principle for random Fano hypersurfaces VL - 197 ER -