Proving Craig and Lyndon Interpolation Using Labelled Sequent Calculi

We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents, and nested sequents. Here we adapt the method to a more general external formalism of labelled sequents and provide sufficient criteria on the Kripke-frame characterization of a logic that guarantee the IPs. In particular, we show that classes of frames definable by quantifier-free Horn formulas correspond to logics with the IPs. These criteria capture the modal cube and the infinite family of transitive Geach logics

NEXP-completeness and Universal Hardness Results for Justification Logic

We provide a lower complexity bound for the satisfiability problem of a multi-agent justification logic, establishing that the general NEXP upper bound from our previous work is tight. We then use a simple modification of the corresponding reduction to prove that satisfiability for all multi-agent justification logics from there is hard for the Sigma 2 p class of the second level of the polynomial hierarchy - given certain reasonable conditions. Our methods improve on these required conditions for the same lower bound for the single-agent justification logics, proven by Buss and Kuznets in 2009, thus answering one of their open questions.Comment: Shorter version has been accepted for publication by CSR 201

Time-Asymmetric Protocol Optimization for Efficient Free Energy Estimation

The free-energy difference $\Delta F$ between two high-dimensional systems is an important yet computationally difficult quantity to compute. We demonstrate that the microscopic fluctuation theorem for an unconventional definition of work introduced by Vaikuntanathan and Jarzynski (2008) connects path ensembles that are driven by protocols unequal under time-reversal, allowing us to use a low-variance Bennett acceptance ratio $\Delta F$ estimator on bi-directional measurements from time-asymmetric processes. It has been shown before that counterdiabatic protocols give zero-variance work measurements for this definition. Motivated by this, we propose an on-the-fly adaptive importance sampling policy optimization algorithm that iteratively improves the efficiency of the time-asymmetric protocols. This algorithm requires minimal computational overhead, and uses all the samples collected in previous iterations to (1) update the protocol, and (2) provide a $\Delta F$ estimate. We test our algorithm on three models of varying complexity, finding that with just $10^3$ bi-directional work samples our algorithm yields $\Delta F$ estimates that are $\sim 10^2 - 10^4$ times lower in mean squared error than the linear interpolation protocol with which it was initialized.Comment: 8 pages, 3 figures, 1 algorithm. Comments welcom

A Logic of Blockchain Updates

Blockchains are distributed data structures that are used to achieve consensus in systems for cryptocurrencies (like Bitcoin) or smart contracts (like Ethereum). Although blockchains gained a lot of popularity recently, there is no logic-based model for blockchains available. We introduce BCL, a dynamic logic to reason about blockchain updates, and show that BCL is sound and complete with respect to a simple blockchain model

Explicit Evidence Systems with Common Knowledge

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic

Information mobility in complex networks

The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals. The mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix. The fractional time at which a network diffuses 50% of the information contained in its nodes (1/ k50 ) is also introduced. We then show that the scale-free random networks display better spread of information than the non scale-free ones. We study 38 real-world networks and analyze their performance in spreading information from their nodes. We find that some real-world networks perform even better than the scale-free networks with the same average degree and we point out some of the structural parameters that make this possible

Topology and Evolution of Technology Innovation Networks

The web of relations linking technological innovation can be fairly described in terms of patent citations. The resulting patent citation network provides a picture of the large-scale organization of innovations and its time evolution. Here we study the patterns of change of patents registered by the US Patent and Trademark Office (USPTO). We show that the scaling behavior exhibited by this network is consistent with a preferential attachment mechanism together with a Weibull-shaped aging term. Such attachment kernel is shared by scientific citation networks, thus indicating an universal type of mechanism linking ideas and designs and their evolution. The implications for evolutionary theory of innovation are discussed.Comment: 6 pages, 5 figures, submitted to Physical Review

Occupational choice, number of entrepreneurs and output: theory and empirical evidence with Spanish data

This paper extends the (Lucas, Bell J Econ 9:508–523,1978) model of occupational choices by individuals with different skills, beyond the simple options of self-employment or wage-employment, by including a second choice for the self-employed. That is, an option to hire employees and so become self-employed with employees (SEWEs), or to be self-employed without employees (SEWNEs). We solve for the market equilibrium and examine the sensitivity of relative sizes of occupational groups, and of the level of productivity, to changes in the exogenous parameters. The results show that the positive (negative) association between number of SEWEs (SEWNEs) and productivity, observed in the Spanish data, can be explained, under certain conditions, as the result of cross-region and time differences in average skills. These findings point to the importance of distinguishing between SEWEs and SEWNEs in drawing valid conclusions concerning any link between entrepreneurship and economic development

Inequality, Fiscal Capacity and the Political Regime: Lessons from the Post-Communist Transition

Using panel data for twenty-seven post-communist economies between 1987-2003, we examine the nexus of relationships between inequality, fiscal capacity (defined as the ability to raise taxes efficiently) and the political regime. Investigating the impact of political reform we find that full political freedom is associated with lower levels of income inequality. Under more oligarchic (authoritarian) regimes, the level of inequality is conditioned by the state’s fiscal capacity. Specifically, oligarchic regimes with more developed fiscal systems are able to defend the prevailing vested interests at a lower cost in terms of social injustice. This empirical finding is consistent with the model developed by Acemoglu (2006). We also find that transition countries undertaking early macroeconomic stabilisation now enjoy lower levels of inequality; we confirm that education fosters equality and the suggestion of Commander et al (1999) that larger countries are prone to higher levels of inequality.http://deepblue.lib.umich.edu/bitstream/2027.42/57211/1/wp831 .pd