Energy expenditure, economic growth, and the minimum EROI of society

We estimate energy expenditure for the US and world economies from 1850 to 2012. Periods of high energy expenditure relative to GDP (from 1850 to 1945), or spikes (1973–74 and 1978–79) are associated with low economic growth rates, and periods of low or falling energy expenditure are associated with high and rising economic growth rates (e.g. 1945–1973). Over the period 1960–2010 for which we have continuous year-to-year data for control variables (capital formation, population, and unemployment rate) we estimate that, statistically, in order to enjoy positive growth, the US economy cannot afford to spend more than 11% of its GDP on energy. Given the current energy intensity of the US economy, this translates in a minimum societal EROI of approximately 11:1 (or a maximum tolerable average price of energy of twice the current level). Granger tests consistently reveal a one way causality running from the level of energy expenditure (as a fraction of GDP) to economic growth in the US between 1960 and 2010. A coherent economic policy should be founded on improving net energy efficiency. This would yield a “double dividend”: increased societal EROI (through decreased energy intensity of capital investment), and decreased sensitivity to energy price volatility

Entropy Games and Matrix Multiplication Games

Two intimately related new classes of games are introduced and studied: entropy games (EGs) and matrix multiplication games (MMGs). An EG is played on a finite arena by two-and-a-half players: Despot, Tribune and the non-deterministic People. Despot wants to make the set of possible People's behaviors as small as possible, while Tribune wants to make it as large as possible.An MMG is played by two players that alternately write matrices from some predefined finite sets. One wants to maximize the growth rate of the product, and the other to minimize it. We show that in general MMGs are undecidable in quite a strong sense.On the positive side, EGs correspond to a subclass of MMGs, and we prove that such MMGs and EGs are determined, and that the optimal strategies are simple. The complexity of solving such games is in NP\&coNP.Comment: Accepted to STACS 201

Task Assignment with Autonomous and Controlled Agents

We analyse assignment problems in which not all agents are controlled by the central planner. The autonomous agents search for vacant tasks guided by their own preference orders defined over subsets of the available tasks. The goal of the central planner is to maximise the total value of the assignment, taking into account the behaviour of the uncontrolled agents. This setting can be found in numerous real-world situations, ranging from organisational economics to "crowdsourcing" and disaster response. We introduce the Disjunctively Constrained Knapsack Game and show that its unique Nash equilibrium reveals the optimal assignment for the controlled agents. This result allows us to find the solution of the problem using mathematical programming techniques.

Self-learning Machines based on Hamiltonian Echo Backpropagation

A physical self-learning machine can be defined as a nonlinear dynamical system that can be trained on data (similar to artificial neural networks), but where the update of the internal degrees of freedom that serve as learnable parameters happens autonomously. In this way, neither external processing and feedback nor knowledge of (and control of) these internal degrees of freedom is required. We introduce a general scheme for self-learning in any time-reversible Hamiltonian system. We illustrate the training of such a self-learning machine numerically for the case of coupled nonlinear wave fields

Chained Gallager codes

The ensemble of regular Low-Density Parity-Check (LDPC) codes introduced by Gallager is considered. Using probabilistic arguments a lower bound on the normalized minimum distance is derived. A new code construction, called Chained Gallager codes, is introduced as the combination of two Gallager codes and its error correcting capabilities are studied

Updating Bounds on RR-Parity Violating Supersymmetry from Meson Oscillation Data

We update the bounds on $R$-parity violating supersymmetry originating from meson oscillations in the $B^0_{d/s}$ and $K^0$ systems. To this end, we explicitly calculate all corresponding contributions from $R$-parity violating operators at the one-loop level, thereby completing and correcting existing calculations. We apply our results to the derivation of bounds on $R$-parity violating couplings, based on up-to-date experimental measurements. In addition, we consider the possibility of cancellations among flavor-changing contributions of various origins, e.g. from multiple $R$-parity violating couplings or $R$-parity conserving soft terms. Destructive interferences among new-physics contributions could then open phenomenologically allowed regions, for values of the parameters that are naively excluded when the parameters are varied individually.Comment: 53 pages, 10 figures, 2 tables; final versio