3,442 research outputs found
Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
We introduce the notion of algebraic higher symmetry, which generalizes
higher symmetry and is beyond higher group. We show that an algebraic higher
symmetry in a bosonic system in -dimensional space is characterized and
classified by a local fusion -category. We find another way to describe
algebraic higher symmetry by restricting to symmetric sub Hilbert space where
symmetry transformations all become trivial. In this case, algebraic higher
symmetry can be fully characterized by a non-invertible gravitational anomaly
(i.e. an topological order in one higher dimension). Thus we also refer to
non-invertible gravitational anomaly as categorical symmetry to stress its
connection to symmetry. This provides a holographic and entanglement view of
symmetries. For a system with a categorical symmetry, its gapped state must
spontaneously break part (not all) of the symmetry, and the state with the full
symmetry must be gapless. Using such a holographic point of view, we obtain (1)
the gauging of the algebraic higher symmetry; (2) the classification of
anomalies for an algebraic higher symmetry; (3) the equivalence between classes
of systems, with different (potentially anomalous) algebraic higher symmetries
or different sets of low energy excitations, as long as they have the same
categorical symmetry; (4) the classification of gapped liquid phases for
bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of
a topological order in one higher dimension (that corresponds to the
categorical symmetry). This classification includes symmetry protected trivial
(SPT) orders and symmetry enriched topological (SET) orders with an algebraic
higher symmetry.Comment: 61 pages, 31 figure
VERIFICATION AND APPLICATION OF DETECTABILITY BASED ON PETRI NETS
In many real-world systems, due to limitations of sensors or constraints of the environment, the system dynamics is usually not perfectly known. However, the state information of the system is usually crucial for the purpose of decision making. The state of the system needs to be determined in many applications. Due to its importance, the state estimation problem has received considerable attention in the discrete event system (DES) community. Recently, the state estimation problem has been studied systematically in the framework of detectability. The detectability properties characterize the possibility to determine the current and the subsequent states of a system after the observation of a finite number of events generated by the system.
To model and analyze practical systems, powerful DES models are needed to describe the different observation behaviors of the system. Secondly, due to the state explosion problem, analysis methods that rely on exhaustively enumerating all possible states are not applicable for practical systems. It is necessary to develop more efficient and achievable verification methods for detectability. Furthermore, in this thesis, efficient detectability verification methods using Petri nets are investigated, then detectability is extended to a more general definition (C-detectability) that only requires that a given set of crucial states can be distinguished from other states. Formal definitions and efficient verification methods for C-detectability properties are proposed. Finally, C-detectability is applied to the railway signal system to verify the feasibility of this property:
1. Four types of detectability are extended from finite automata to labeled Petri nets. In particular, strong detectability, weak detectability, periodically strong detectability, and periodically weak detectability are formally defined in labeled Petri nets.
2. Based on the notion of basis reachability graph (BRG), a practically efficient approach (the BRG-observer method) to verify the four detectability properties in bounded labeled Petri nets is proposed. Using basis markings, there is no need to enumerate all the markings that are consistent with an observation. It has been shown by other researchers that the size of the BRG is usually much smaller than the size of the reachability graph (RG). Thus, the method improves the analysis efficiency and avoids the state space explosion problem.
3. Three novel approaches for the verification of the strong detectability and periodically strong detectability are proposed, which use three different structures whose construction has a polynomial complexity. Moreover, rather than computing all cycles of the structure at hand, which is NP-hard, it is shown that strong detectability can be verified looking at the strongly connected components whose computation also has a polynomial complexity. As a result, they have lower computational complexity than other methods in the literature.
4. Detectability could be too restrictive in real applications. Thus, detectability is extended to C-detectability that only requires that a given set of crucial states can be distinguished from other states. Four types of C-detectability are defined in the framework of labeled Petri nets. Moreover, efficient approaches are proposed to verify such properties in the case of bounded labeled Petri net systems based on the BRG.
5. Finally, a general modeling framework of railway systems is presented for the states estimation using labeled Petri nets. Then, C-detectability is applied to railway signal systems to verify its feasibility in the real-world system. Taking the RBC handover procedure in the Chinese train control system level 3 (CTCS-3) as an example, the RBC handover procedure is modeled using labeled Petri nets. Then based on the proposed approaches, it is shown that that the RBC handover procedure satisfies strongly C-detectability
Business failure and mass media: An analysis of media exposure in the context of delisting event
It is understood that the mass media are a pervasive force in shaping the public's perceptions. This paper incorporates agenda-setting theory to explore whether and to what extent that the mass media can signal business failure. In an analysis of news coverage relating to Chinese underperforming listed firms over the period 2006–2017, it is demonstrated that firms whose stocks are put under “special treatment” status due to consecutive annual losses experience (*ST) greater news volume and lower news sentiment relative to other firms in the quarter in which the “delisting risk warning” announcements are made. Furthermore, *ST firms which are eventually delisted have a greater volume of news than other *ST firms, but we find no evidence that the sentiment of news relates to termination of listing. Our findings offer insights into the informativeness of the mass media and their agenda-setting effects in the business failure context
BKP hierarchy and Pfaffian point process
Inspired by Okounkov's work [\emph{Selecta Mathematica}, 7(1):57--81, 2001]
which relates KP hierarchy to determinant point process, we establish a
relationship between BKP hierarchy and Pfaffian point process. We prove that
the correlation function of the shifted Schur measures on strict partitions can
be expressed as a Pfaffian of skew symmetric matrix kernel, whose elememts are
certain vacuum expectations of neutral fermions. We further show that the
matrix integrals solution of BKP hierarchy can also induce a certain Pfaffian
point process.Comment: 17 page
Rotation of Polarization Angle in Gamma-Ray Burst Prompt Phase\uppercase\expandafter{\romannumeral2}. The Influence of The Parameters
In addition to the light curve and energy spectrum, polarization is also
important for the study of Gamma-ray burst (GRB) prompt emission. Rotation of
the polarization angle (PA) with time will cause depolarization of the
time-integrated polarization degree. However, it is rarely studied before.
Here, we use the magnetic reconnection model with a large-scale ordered aligned
magnetic field in the emitting region to study the influence of the key
parameters on the PA rotations. We find that half-opening angle of the jet
, the observational angle , and the bulk Lorentz factor
all have significant impacts on the PA rotations. For a fixed
value ( is the normalization factor of
), regardless of concrete and values, PA
rotation within (PA) remains roughly unchanged for a
value. As value
increases, the range for PA becomes smaller. The
most significant PA rotation with PA will
happen when and . For the
top-hat jet, observations of the PA rotation within will imply a
slightly off-axis observation.Comment: 9 pages, 7 figures, submitte
General displacement arch-cantilever element method for stress analysis of arch dam
AbstractBased on the general displacement method and the basic hypothesis of the trial load method, a new advanced trial load method, the general displacement arch-cantilever element method, was proposed to derive the transformation relation of displacements and loads between the surface nodes and middle plane nodes. This method considers the nodes on upstream and downstream surfaces of the arch dam to be exit nodes (master nodes), and the middle plane nodes to be slave nodes. According to the derived displacement and load transformation matrices, the equilibrium equation treating the displacement of middle plane nodes as a basic unknown variable is transformed into one that treats the displacement of upstream and downstream nodes as a basic unknown variable. Because the surface nodes have only three degrees of freedom (DOF), this method can be directly coupled with the finite element method (FEM), which is used for foundation simulation to analyze the stress of the arch dam with consideration of dam-foundation interaction. Moreover, using the FEM, the nodal load of the arch dam can be easily obtained. Case studies of a typical cylindrical arch dam and the Wudongde arch dam demonstrate the robustness and feasibility of the proposed method
Classification of topological phases with finite internal symmetries in all dimensions
We develop a mathematical theory of symmetry protected trivial (SPT) orders
and anomaly-free symmetry enriched topological (SET) orders in all dimensions
via two different approaches with an emphasis on the second approach. The first
approach is to gauge the symmetry in the same dimension by adding topological
excitations as it was done in the 2d case, in which the gauging process is
mathematically described by the minimal modular extensions of unitary braided
fusion 1-categories. This 2d result immediately generalizes to all dimensions
except in 1d, which is treated with special care. The second approach is to use
the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk
relation. This approach also leads us to a precise mathematical description and
a classification of SPT/SET orders in all dimensions. The equivalence of these
two approaches, together with known physical results, provides us with many
precise mathematical predictions.Comment: 41 pages, 6 figures; add more results on anomalies; final version to
appear in JHE
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