Solving Large-Scale Extensive-Form Network Security Games via Neural Fictitious Self-Play

Securing networked infrastructures is important in the real world. The problem of deploying security resources to protect against an attacker in networked domains can be modeled as Network Security Games (NSGs). Unfortunately, existing approaches, including the deep learning-based approaches, are inefficient to solve large-scale extensive-form NSGs. In this paper, we propose a novel learning paradigm, NSG-NFSP, to solve large-scale extensive-form NSGs based on Neural Fictitious Self-Play (NFSP). Our main contributions include: i) reforming the best response (BR) policy network in NFSP to be a mapping from action-state pair to action-value, to make the calculation of BR possible in NSGs; ii) converting the average policy network of an NFSP agent into a metric-based classifier, helping the agent to assign distributions only on legal actions rather than all actions; iii) enabling NFSP with high-level actions, which can benefit training efficiency and stability in NSGs; and iv) leveraging information contained in graphs of NSGs by learning efficient graph node embeddings. Our algorithm significantly outperforms state-of-the-art algorithms in both scalability and solution quality.

Final state Sommerfeld effect on dark matter relic abundance

If the annihilation products of dark matter (DM) are non-relativistic and if there is some long-range force between them, there can be Sommerfeld effect for the final state particles. We study this effect on DM relic abundance in the thermal freeze-out scenario. As a proof of concept, we consider the case of a DM pair annihilation into a final state pair, assuming that the mutual interactions between the two final state particles give rise to a Coulomb-like potential, and that the masses of the initial and final state particles are similar, so that both the initial and final state particles are non-relativistic. The size of the final state Sommerfeld (FSS) effect depends on the strength of the potential, as well as on the mass ratio of the final and initial state particles. We find that the impact of the FSS effect on DM relic abundance can be significant, and an electroweak sized long-range interaction is large enough to make a correction well beyond the observational accuracy. Another feature of the FSS effect is that it could be suppressed when its time scale is longer than the lifetime of the final state particles. As a corollary, we also study in the DM coannihilation scenario where the initial state Sommerfeld effect between two coannihilators could be reduced due to their instability, which may need to be taken into account for an accurate calculation of the DM relic abundance.

Financial Integration and the Co-Movement of Economic Activity: Evidence from U.S. States

We analyze the effect of the geographic expansion of banks across U.S. states on the comovement of economic activity between states. Exploiting the removal of interstate banking restrictions to construct time-varying instrumental variables at the state-pair level, we find that bilateral banking integration increases output co-movement between states. The effect of financial integration depends on the nature of the idiosyncratic shocks faced by states and is stronger for more financially dependent industries. Finally, we show that integration (1) increases the similarity of bank lending fluctuations between states and (2) contributes to the transmission of deposit shocks across states.

Multi-state pair-density functional theory

Multi-state Pair-Density Functional Theory (MS-PDFT) gives the correct topology of interacting potential energy surfaces where state-specific calculations fail.

An information-theoretic treatment of quantum dichotomies

Given two pairs of quantum states, we want to decide if there exists a quantum channel that transforms one pair into the other. The theory of quantum statistical comparison and quantum relative majorization provides necessary and sufficient conditions for such a transformation to exist, but such conditions are typically difficult to check in practice. Here, by building upon work by Keiji Matsumoto, we relax the problem by allowing for small errors in one of the transformations. In this way, a simple sufficient condition can be formulated in terms of one-shot relative entropies of the two pairs. In the asymptotic setting where we consider sequences of state pairs, under some mild convergence conditions, this implies that the quantum relative entropy is the only relevant quantity deciding when a pairwise state transformation is possible. More precisely, if the relative entropy of the initial state pair is strictly larger compared to the relative entropy of the target state pair, then a transformation with exponentially vanishing error is possible. On the other hand, if the relative entropy of the target state is strictly larger, then any such transformation will have an error converging exponentially to one. As an immediate consequence, we show that the rate at which pairs of states can be transformed into each other is given by the ratio of their relative entropies. We discuss applications to the resource theories of athermality and coherence, where our results imply an exponential strong converse for general state interconversion.

NMR Analysis of Poly(Lactic Acid) via Statistical Models

The physical properties of poly(lactic acid) (PLA) are influenced by its stereoregularity and stereosequence distribution, and its polymer stereochemistry can be effectively studied by NMR spectroscopy. In previously published NMR studies of PLA tacticity, the NMR data were fitted to pair-addition Bernoullian models. In this work, we prepared several PLA samples with a tin catalyst at different L,L-lactide and D,D-lactide ratios. Upon analysis of the tetrad intensities with the pair-addition Bernoullian model, we found substantial deviations between observed and calculated intensities due to the presence of transesterification and racemization during the polymerization processes. We formulated a two-state (pair-addition Bernoullian and single-addition Bernoullian) model, and it gave a better fit to the observed data. The use of the two-state model provides a quantitative measure of the extent of transesterification and racemization, and potentially yields useful information on the polymerization mechanism.

STRUCTURAL PROPERTIES OF HYDROGEN PLASMA

This paper considers hydrogen, non-ideal plasma. The structural properties of such plasma were investigated. To study properties of plasma, effective potentials describing the interaction between particles were used. These potentials take into account various effects: screening and quantum-mechanical (diffraction and symmetry). The Pauli exclusion principle prohibits the simultaneous presence of two identical particles with a half-integer spin (in this case, electrons) in the same state. Pair correlation functions were calculated in hyper-netted chain approximation for the integral equation of the Ornstein-Zernike on the basis of the interaction potentials. The symmetry effect is more pronounced at short distances and for higher values of density. The antiparallel direction of the electron spins increases the probability of finding electrons at distance R from each other, the parallel direction decreases this probability due to the prohibition of the presence of two electrons with the same spins in the same state.