Particles and propagators in Lorentz-violating supergravity

We obtain the propagators for spin 1/2 fermions and sfermions in Lorentz-violating supergravity.Comment: 6 pages, to be published in Proceedings of the Third Meeting on CPT and Lorentz Symmetry, edited by V. A. Kostelecky (World Scientific

Scale-invariant Feature Extraction of Neural Network and Renormalization Group Flow

Theoretical understanding of how deep neural network (DNN) extracts features from input images is still unclear, but it is widely believed that the extraction is performed hierarchically through a process of coarse-graining. It reminds us of the basic concept of renormalization group (RG) in statistical physics. In order to explore possible relations between DNN and RG, we use the Restricted Boltzmann machine (RBM) applied to Ising model and construct a flow of model parameters (in particular, temperature) generated by the RBM. We show that the unsupervised RBM trained by spin configurations at various temperatures from $T=0$ to $T=6$ generates a flow along which the temperature approaches the critical value $T_c=2.27$. This behavior is opposite to the typical RG flow of the Ising model. By analyzing various properties of the weight matrices of the trained RBM, we discuss why it flows towards $T_c$ and how the RBM learns to extract features of spin configurations.Comment: 32 pages, 17 figure

Contribution Cycles and Preferable Incentive Schemes

This note considers a situation in which the publisher of an academic journal seeks to maintain the number of contributions to the journal by subsidizing the contributors with some incentive payments. We show that under the incentive payment scheme that distributes some pre−determined total amount of payments equally to each contributor (the constant total payment scheme), the number of contributions can fluctuate cyclically as well as chaotically over time when the potential contributors form adaptive expectations. Numerical simulations suggest, among other things, that the performance of the constant total payment scheme may be more efficient than the constant per−capita payment scheme when the total amount of payments is supposed to be small

False-name-Proof Combinatorial Auction Mechanisms

In Internet auctions, it is easy for a bidder to submit multiple bids under multiple identifiers (e.g., multiple e-mail addresses). If only one good is sold, a bidder cannot make any additional profit by using multiple bids. However, in combinatorial auctions, where multiple goods are sold simultaneously, submitting multiple bids under fictitious names can be profitable. A bid made under a fictitious name is called a {em false-name bid}. In this talk, I describe the summary of existing works and open problems on false-name bids