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The purpose of this paper is to establish a version of a theorem that originated from population genetics and has been later adopted in evolutionary computation theory that will lead to novel Monte‐Carlo sampling algorithms that provably increase the AI potential.

In the current paper the authors set up a mathematical framework, state and prove a version of a Geiringer‐like theorem that is very well‐suited for the development of Mote‐Carlo sampling algorithms to cope with randomness and incomplete information to make decisions.

This work establishes an important theoretical link between classical population genetics, evolutionary computation theory and model free reinforcement learning methodology. Not only may the theory explain the success of the currently existing Monte‐Carlo tree sampling methodology, but it also leads to the development of novel Monte‐Carlo sampling techniques guided by rigorous mathematical foundation.

The theoretical foundations established in the current work provide guidance for the design of powerful Monte‐Carlo sampling algorithms in model free reinforcement learning, to tackle numerous problems in computational intelligence.

Establishing a Geiringer‐like theorem with non‐homologous recombination was a long‐standing open problem in evolutionary computation theory. Apart from overcoming this challenge, in a mathematically elegant fashion and establishing a rather general and powerful version of the theorem, this work leads directly to the development of novel provably powerful algorithms for decision making in the environment involving randomness, hidden or incomplete information.

Omnichannel has become increasingly important with the development of e-commerce. In omnichannel, merchants expect customers to get the products and services at anytime, anywhere and in any way, and the same is true for customers. This drives multihoming in online platforms for both merchants and customers. Thus, once both customers and merchants are multihomed, what price and subsidy decisions should be made between platforms to compete to obtain optimal profits? The main purpose of this paper is to solve these problems and provide decision-making for two-sided platforms in omnichannel.

This study builds a dual Hotelling model to capture the utility and network effects of customers and merchants on two-sided platforms. This study introduces the exposure effect and convenience effect of multihomed customers and merchants in the model and analyzes the impact of these effects in the market with multihoming on one side. Then, this study extends the model to the market with multihoming on both sides and makes the pricing decision for two-sided platform when considering the exposure effect and convenience effect through an equilibrium solution. Finally, this study also uses numerical analysis to simulate the decision and profit of the platform.

This paper finds that the convenience effect will only increase social welfare when customers are single-homed and merchants are multihomed. In addition, when both users are multihomed, the platform will subsidize to attract merchants and customers if the convenience effect and exposure effect are relatively high. This study also finds that network effects come not only from the same platform but also from another platform in the case with multihoming on both sides. And network effects in the heterogeneous platform will be reduced by the convenience effect and exposure effect.

According to the behavioral characteristics of merchants and customers in omnichannel, this paper first adopts the dual Hotelling model to study the pricing of two-sided platforms with multihoming on both sides. This paper shows that network effects originate not only from the same platform but also from another platform and that the exposure effect and the convenience effect can exist as cross-platform network effects, which provides a new explanation for network effects in markets with multihoming on both sides. This research extends the theory of network effects and plays an important role in the development of two-sided platforms in omnichannel.

IT has been stated above that the rate of heat transfer is closely proportional to the temperature difference between the plate and the free air stream, and over the laminar portion it will also be proportional to the conductivity of the air. It remains to consider to what extent the actual temperature of the air in the boundary layer will influence the rate of heat transfer. The conductivity of air increases with temperature by reason of the increased molecular velocities, and we might expect, therefore, that the hotter the surface the greater will be the rate of heat transfer per unit of temperature difference above that of the air. This is, in fact, found to be the case.

This paper seeks to analyze ecological networks from a different viewpoint, using the concepts of orbits, coverage, invariant sets, etc.

A very simple view of ecosystems is presented, without delving into their multiple properties. Specifically, an ecosystem will be considered a system containing living and non‐living entities whose interrelationships include those of predator‐prey and competition. On interpreting that orbits are associated with ecosystems' direct and indirect paths, it is possible to present a much more conceptual design of ecological networks.

An ecosystem's two most important relationships, those of predator‐prey and competition, appear to be interconnected with the concepts of coverage, invariance and orbit, with multiple properties.

There are many interesting analyses of ecological networks' indirect effects that develop the quantitative and qualitative theory of ecological networks. What is new in this study is that it is the first dealing with orbits in the field of ecosystems.

TUESDAY to Friday, the 21st to 24th of this month, will be busy ones in Dublin when the Irish Work Study Institute entertains the members of the 7th European Work Study Federation Conference. The preliminary work of organization has been tackled with due recognition of the occasion's importance. Many meetings, much work and a lot of study are part of the price which has been gladly paid by the Irish Institute to ensure that everything runs smoothly.

THE hope we expressed in recent pages, that the Library Association might resume its normal methods of life and government, remains a hope. London, where only we suppose the Council could do its work really well, has been of late no place for the meetings of people; and we dare to say that for the key people of any profession or movement to gather there at present would be unwise, even though imagination may increase the risk beyond the warrant of the facts. Nor do we know yet if the worst has been experienced. Meanwhile it is probable that the affairs of librarianship must be delegated to even fewer workers than now. Only the chronically ungracious part of our fraternity will be without gratitude to those who keep things going for us.

THAT is the title of a survey by the National Joint Advisory Council which has just been issued by the Ministry of Labour. Properly assimilated by both sides of industry it could become an important document for a country continually under pressure to increase productivity. In his Foreword the Minister of Labour says that the number of manual workers engaged on a shift system has increased by more than half in the last ten years and expects the trend to continue.

THE Librarian faces one of the turning times in library history. The flow of progress has not yet begun, the shortages and consequent imperious demands for food, housing and clothing stand in the way of the beginning, except on paper. How long the interregnum will last none can say. The authorities, which are a reflection in some ways of the Parliamentary party in power, are well‐disposed towards libraries; the official handbook of the Labour Party proves that; but the clamour of the needs we have mentioned deafens everybody to library needs—except in certain instances. For example, the rebuilding and enlarging of the staff at Holborn is an encouraging sign. Of more potential significance is the working out of the so‐called National Charter. It has involved many towns in the task of creating an establishment for each public department. Thus, in one library system we hear that each branch or department may claim a librarian and a deputy both on the A.P.T. scale, but all the assistants are either general or clerical. Some assistants we hear have applied to be of clerical grade as the maximum salary is greater than in the general. This we suggest is putting cash before status because it is accepted as an axiom that a clerk has only clerical qualifications and potentialities, while a general assistant may aspire, when there is a vacancy and if he have certificates, to the professional status. The grading in the particular library mentioned has rather a petrifying effect in that no assistant can get into the professional grade unless his librarian or deputy departs. Possibly this sort of thing may alter, but the fact remains for good or ill—it is not all ill by any means—that no library is able to attract men from another except to a definitely higher post.

The notes reproduced here were taken by Glenn Johnson in Lloyd Mints’ course on Money and Banking at the University of Chicago in the fall of 1946. Several additional sets of course notes taken by Glenn Johnson have been published in the archival volumes of Research in the History of Economic Thought and Methodology. These included notes from Frank Knight's course on economic theory (Volume 24C) and Albert L. Meyer's course entitled elements of modern economics (appearing in this volume). A brief biography of Glenn Johnson is provided in Volume 24C, along with notes from his course on Agricultural Economics Methodology taught at Michigan State University.

THERE have been official links for the past twelve years between the Institute of Incorporated Work Study Technologists and Time and Motion Study. Many of its members have been valued contributors to our pages and the Institute has had editorial space for its news.