Q-anonymous social welfare relations on infinite utility streams

This paper studies a class of social welfare relations (SWRs) on the set of infinite utility streams. In particular, we examine the SWRs satisfying Q-Anonymity, an impartiality axiom stronger than Finite Anonymity, as well as Strong Pareto and a certain equity axiom. First, we characterize the extension of the generalized Lorenz SWR by combining Q-Anonymity with Strong Pareto and Pigou-Dalton Equity. Second, we replace Pigou-Dalton Equity with Hammond Equity for characterizing the extended leximin SWR. Third, we give an alternative characterization of the extended utilitarian SWR by substituting Incremental Equity for Pigou-Dalton Equity.Q-Anonymity, Intergenerational equity, Generalized Lorenz criterion, Leximin principle, Utilitarianism, Simplified criterion

On the leximin and utilitarian overtaking criteria with extended anonymity

This paper studies the extensions of the infinte-horizon variants of the leximin principle and utilitarianism on the set of infinite utility streams. We especially examine those extensions which satisfy the axiom of Preference-continuity (or Consistency) and the extended anonymity axiom called Q-Anonymity. We formulate new extended leximin and utilitarian social welfare relations (SWRs), called Q-W-leximin SWR and Q-overtaking criterion respectively, and show that Weak Preference-continuity (or Weak Consistency) and Q-Anonymity together with Strong Pareto and Hammond Equity (resp. Partial Unit Comparability) characterize all SWRs that include the Q-W-leximin SWR (resp. the Q-overtaking criterion) as a subrelation. We also show that there exists no SWR satisfying Strong Pareto, Strong Preference-continuity (or Strong Consistency) and Q-Anonymity.Q-Anonymity, Preference-continuity, Consistency, Leximin, Utilitarianism, Overtaking criterion

Cominimum Additive Operators

This paper proposes a class of weak additivity concepts for an operator on the set of real valued functions on a finite state space \omega, which include additivity and comonotonic additivity as extreme cases. Let \epsilon be a collection of subsets of \omega. Two functions x and y on \omega are \epsilon-cominimum if, for each E \subseteq \epsilon, the set of minimizers of x restricted on E and that of y have a common element. An operator I on the set of functions on is E- cominimum additive if I(x+y) = I(x)+I(y) whenever x and y are \epsilon-cominimum. The main result characterizes homogeneous E-cominimum additive operators in terms of the Choquet integrals and the corresponding non-additive signed measures. As applications, this paper gives an alternative proof for the characterization of the E-capacity expected utility model of Eichberger and Kelsey (1999) and that of the multi-period decision model of Gilboa (1989).Choquet integral; comonotonicity; non-additive probabilities; capacities; cooperative games

Implementation of Lenia as a Reaction-Diffusion System

The relationship between reaction-diffusion (RD) systems, characterized by continuous spatiotemporal states, and cellular automata (CA), marked by discrete spatiotemporal states, remains poorly understood. This paper delves into this relationship through an examination of a recently developed CA known as Lenia. We demonstrate that asymptotic Lenia, a variant of Lenia, can be comprehensively described by differential equations, and, unlike the original Lenia, it is independent of time-step ticks. Further, we establish that this formulation is mathematically equivalent to a generalization of the kernel-based Turing model (KT model). Stemming from these insights, we establish that asymptotic Lenia can be replicated by an RD system composed solely of diffusion and spatially local reaction terms, resulting in the simulated asymptotic Lenia based on an RD system, or "RD Lenia". However, our RD Lenia cannot be construed as a chemical system since the reaction term fails to satisfy mass-action kinetics.Comment: Accepted to ALIFE 202

Q-anonymous social welfare relations on infinite utility streams

Revised version of No.41: Concluding remarks are slightly changed

On the extensions of the infinite-horizon leximin and the overtaking criteria

Revised version of No.36: The earlier version of this manuscript was entitled "Q-Anonymity and preference continuity." Main results of the earlier draft are restated in a different form

Rock Structure and Quartz Fabric in a Thrusting Shear Zone: the Kiyomizu Tectonic Zone in Shikoku, Japan

A remarkable thrusting shear zone has been found near the southern margin of the Samba-gawa crystalline schist zone in Central Shikoku, representing a frontal zone characterized by thrusting shear movement towards the south, the movement having been caused by the horizontal compression and the consequent upward swelling of the metamorphic zone. The zone has been designated as the Kiyomizu tectonic zone. Rock structures, such as bedding-schistosity or -foliation, fracture-cleavage, closely spaced shear-cleavage, and the related lineations, have been geometrically analysed for rocks both in the tectonic zone and in the northern metamorphic zone proper. On the basis of these geometrical features, the history of development of the tectonic zone has been discussed. Then, the quartz fabric of rocks in the zone has been analysed. The pattern shows an intimate relation between the position of maximum and the direction and the sense of shear on the bedding-schistosity plane of papery schists characteristically found in the tectonic zone. From this definite relation has been deduced a working hypothesis about the orientation of quartz in the flow of rocks, especially in those cases of strong recrystallization or segregation under stress condition