Quasi-stationary distributions for structured birth and death processes with mutations

We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric space. Each individual can die or generate a new individual. The birth and death rates may depend on the environment through the action of the whole population. The offspring can have the same trait or can mutate to a randomly distributed trait. We assume that the population will be extinct almost surely. Our goal is the study, in this infinite dimensional framework, of quasi-stationary distributions when the process is conditioned on non-extinction. We firstly show in this general setting, the existence of quasi-stationary distributions. This result is based on an abstract theorem proving the existence of finite eigenmeasures for some positive operators. We then consider a population with constant birth and death rates per individual and prove that there exists a unique quasi-stationary distribution with maximal exponential decay rate. The proof of uniqueness is based on an absolute continuity property with respect to a reference measure.Comment: 39 page

A Metadata-Enabled Scientific Discourse Platform

Scientific papers and scientific conferences are still, despite the emergence of several new dissemination technologies, the de-facto standard in which scientific knowledge is consumed and discussed. While there is no shortage of services and platforms that aid this process (e.g. scholarly search engines, websites, blogs, conference management programs), a widely accepted platform used to capture and enrich the interactions of research community has yet to appear. As such, we aim to create new ways for the members and interested people working in research communities to interact; before, during and after their conferences. Furthermore, to serve as a base to these interactions, we want not only to obtain, format and manage a body of legacy and new papers related to this community but also to aggregate several useful information and services to the environment of a discourse platform

Computer Theorem Proving and HoTT

Theorem-proving is a one-player game. The history of computer programs being the players goes back to 1956 and the ‘LT’ LOGIC THEORY MACHINE of Newell, Shaw and Simon. In game-playing terms, the ‘initial position’ is the core set of axioms chosen for the particular logic and the ‘moves’ are the rules of inference. Now, the Univalent Foundations Program at IAS Princeton and the resulting ‘HoTT’ book on Homotopy Type Theory have demonstrated the success of a new kind of experimental mathematics using computer theorem proving

Formal Verification of Molecular Computational Models in ACL2: A Case Study

Theorem proving is a classical AI problem with a broad range of applications. Since its complexity is exponential in the size of the problem, many methods to parallelize the process has been proposed. One of these approaches is based on the massive parallelism of molecular reactions. ACL2 is an automated theorem prover especially adequate for algorithm verification. In this paper we present an ACL2 formalization of a molecular computational model: Adleman’s restricted model. As an application of this model, an implementation of Lipton’s experiment solving SAT is described. We use ACL2 to make a formal proof of the completeness and soundness properties of this implementation.Ministerio de Ciencia y Tecnología TIC2000-1368-C03-0

Studies in the completeness and efficiency of theorem-proving by resolution

Inference systems Τ and search strategies E for T are distinguished from proof procedures β = (T,E) The completeness of procedures is studied by studying separately the completeness of inference systems and of search strategies. Completeness proofs for resolution systems are obtained by the construction of semantic trees. These systems include minimal α-restricted binary resolution, minimal α-restricted M-clash resolution and maximal pseudo-clash resolution. Certain refinements of hyper-resolution systems with equality axioms are shown to be complete and equivalent to refinements of the pararmodulation method for dealing with equality. The completeness and efficiency of search strategies for theorem-proving problems is studied in sufficient generality to include the case of search strategies for path-search problems in graphs. The notion of theorem-proving problem is defined abstractly so as to be dual to that of and" or tree. Special attention is given to resolution problems and to search strategies which generate simpler before more complex proofs. For efficiency, a proof procedure (T,E) requires an efficient search strategy E as well as an inference system T which admits both simple proofs and relatively few redundant and irrelevant derivations. The theory of efficient proof procedures outlined here is applied to proving the increased efficiency of the usual method for deleting tautologies and subsumed clauses. Counter-examples are exhibited for both the completeness and efficiency of alternative methods for deleting subsumed clauses. The efficiency of resolution procedures is improved by replacing the single operation of resolving a clash by the two operations of generating factors of clauses and of resolving a clash of factors. Several factoring methods are investigated for completeness. Of these the m-factoring method is shown to be always more efficient than the Wos-Robinson method

Cross-Cultural Study in LocalWisdom for Creative Food Package Development in Secondary School

The purposes of this research were ๑) to study the wisdom of Thai food package by wrapping and packing technique from the local Thai and Japanese food experts. ๒) to develop the WisdomTransferring Model of food packaging ๓) To experiment the specific program of Wisdom-Transferring Model of food packaging in Secondary school: Mathayomsuksa 4th year. The experimental program was examined in Thailand locally separated into 4 parts/4 schools. The result of this research can be explained the transferring technique of Thai wrapping were similar in attitudes and beliefs. The subject should described the content of materials and processes which directly matched with the subject of professional practice and technology together with the social science/cultural and history integrated with English understanding language The researcher founded that the program of Thai Wisdom Transferring has contained to be 24 hours or 4 = full day a continuing program. The control group of this research sample has increasing their creativity in wrapping and packaging up to 40.89% in attitude and belief and 55, 84% the same as the meaning between languages