Few exact results on gauge symmetry factorizability on intervals

We study the gauge symmetry factorizability by boundary conditions on intervals of any dimensions. With Dirichlet-Neumann BCs, the Kaluza-Klein decomposition in five-dimension for arbitrary gauge group can always be factorized into that for separate subsets of at most two gauge symmetries, and so is completely solvable. Accordingly, we formulate a limit theorem on gauge symmetry factorizability on intervals to recapitulate this remarkable feature of five-dimension case. In higher-dimensional space-time, an interesting chained mixing of gauge symmetries by Dirichlet-Neumann BCs is explicitly constructed. The systematic decomposition picture obtained in this work constitutes the initial step towards determining the general symmetry breaking scheme by boundary conditions.Comment: 34 pages, V3 considerable extension: gauge symmetry factorizability in arbitrary dimensions presented, statements on symmetry breakings softened. Dedicated to the memory of Prof. Henri van Regemorte

Predictive Coding for Dynamic Visual Processing: Development of Functional Hierarchy in a Multiple Spatio-Temporal Scales RNN Model

The current paper proposes a novel predictive coding type neural network model, the predictive multiple spatio-temporal scales recurrent neural network (P-MSTRNN). The P-MSTRNN learns to predict visually perceived human whole-body cyclic movement patterns by exploiting multiscale spatio-temporal constraints imposed on network dynamics by using differently sized receptive fields as well as different time constant values for each layer. After learning, the network becomes able to proactively imitate target movement patterns by inferring or recognizing corresponding intentions by means of the regression of prediction error. Results show that the network can develop a functional hierarchy by developing a different type of dynamic structure at each layer. The paper examines how model performance during pattern generation as well as predictive imitation varies depending on the stage of learning. The number of limit cycle attractors corresponding to target movement patterns increases as learning proceeds. And, transient dynamics developing early in the learning process successfully perform pattern generation and predictive imitation tasks. The paper concludes that exploitation of transient dynamics facilitates successful task performance during early learning periods.Comment: Accepted in Neural Computation (MIT press

Quantum critical scaling of the geometric tensors

Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.Comment: Typos correcte

Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions

We study the Restricted Solid on Solid (RSOS) model for surface growth in spatial dimension d=4 by means of a multi-surface coding technique that allows to analyze samples to analyze samples of size up to $256^4$ in the steady state regime. For such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations. A careful finite-size scaling analysis of the critical exponents clearly indicate that d=4 is not the upper critical dimension of the model.Comment: 6 pages, 3 pdf figures, changed title and minor changes in the abstract, added some references. This is the published versio

Silent or Salient? Perks and Perils of Performance Posting

Many firms in the U.S. spend more on their sales force than they do on other marketing activities. Thus, improving sales force performance is of paramount importance. A controversial way is to post performance (i.e., display everyone\u27s performance), now done with ease on social platforms due to advances in information technology. On one hand, posting performance encourages social comparison and competition. On the other hand, it may discourage low-end performers. Also, not posting performance may encourage greater effort from sales agents to push ahead or avoid falling behind, if they are unaware of how others are doing. The result of these opposing factors is, prima facie, unclear. I study the effectiveness of performance posting using theory and experiments. In a game-theoretic model of incomplete information about agents\u27 abilities, I allow a firm to control the precision of social comparison by choosing whether to post performance. Firstly, I find that a firm should not post performance when agents\u27 abilities are sufficiently homogenous, as this prevents a low-ability (high-ability) agent from being overly discouraged (overly complacent). In contrast, a firm should post performance when agents\u27 abilities are sufficiently heterogeneous, as a low-ability agent puts in more effort to avoid lagging by too much. Secondly, some social comparison or competitiveness helps performance posting but too much hurts, i.e., there is a non-monotonic relationship in its effectiveness of performance posting, due to tradeoffs between how much a high-ability and low-ability agent changes effort. Thirdly, I find that the firm\u27s profit from posting increases (decreases) when the financial compensation is unattractive (attractive). Said differently, firms that pay less are more likely to benefit from posting, and therefore, more likely to post. Next, I demonstrate the empirical validity of these propositions using a series of lab experiments and a field study. Together, my theoretical and empirical results provide guiding principles on when a firm can benefit from performance posting