On the molecular mechanisms driving pain perception and emergent collective behaviors

A stochastic model to investigate the microscopic processes which trigger the sensation of pain is considered. The model, presented in Di Patti and Fanelli [Di Patti F, Fanelli D. Can a microscopic stochastic model explain the emergence of pain cycles in patients? J Stat Mech 2009. doi:10.1088/1742-5468/2009/01/P01004], accounts for the action of analgesic drug and introduces an effect of competition with the inactive species populating the bloodstream. Regular oscillations in the amount of bound receptors are detected, following a resonant amplification of the stochastic component intrinsic to the system. The condition for such oscillations to occur are here studied, resorting to combined numerical and analytical techniques. Extended and connected patches of the admissible parameters space are detected which do correspond to the oscillatory behaviors. These findings are discussed with reference to the existing literature on patients’ response to the analgesic treatment.     

Knowledge management: a review of the field and of OR's contribution

This paper examines the field of knowledge management (KM) and identifies the role of operational research (OR) in key milestones and in KM's future. With the presence of the OR Society journal Knowledge Management Research and Practice and with the INFORMS journal Organization Science, OR may be assumed to have an explicit and a leading role in KM. Unfortunately, the origins and the evidence of recent research efforts do not fully support this assumption. We argue that while OR has been inside many of the milestones there is no explicit recognition of its role and while OR research on KM has considerably increased in the last 5 years, it still forms a rather modest explicit contribution to KM research. Nevertheless, the depth of OR's experience in decision-making models and decision support systems, soft systems with hard systems and in risk management suggests that OR is uniquely placed to lead future KM developments. We suggest that a limiting aspect of whether OR will be seen to have a significant profile will be the extent to which developments are recognized as being informed by OR.     

Determination of risk pricing measures from market prices of risk

A new insurance provider or a regulatory agency may be interested in determining a risk measure consistent with observed market prices of a collection of risks. Using a relationship between distorted coherent risk measures and spectral risk measures, we provide a method for reconstructing distortion functions from the observed prices of risk. The technique is based on an appropriate application of the method of maximum entropy in the mean, which builds upon the classical method of maximum entropy.     

Unknotting number and number of Reidemeister moves needed for unlinking

Using unknotting number, we introduce a link diagram invariant of type given in Hass and Nowik (2008) [4], which changes at most by 2 under a Reidemeister move. We show that a certain infinite sequence of diagrams of the trivial two-component link need quadratic number of Reidemeister moves for being splitted with respect to the number of crossings.     

Integration of pricing and capacity allocation for perishable products

For years pricing and capacity allocation decisions in most revenue management models have been carried out independently. This article presents a comprehensive model to integrate these two decisions for perishable products. We assume that the supplier sells the same products to different micro-markets at distinct prices. Throughout the sales season, the supplier faces decisions as to which micro-markets or customer classes should be served and at what prices. We show that (i) at any time, a customer class is active (being served) if and only if the price offered is over a threshold level, but the optimal price may not be the highest one of the supplier’s choice; (ii) when the price decision is made in conjunction with inventory, it is similar to the procedure shown in pure pricing models, i.e., the optimal price comes from a subset of prices that forms a maximum increasing concave envelope; (iii) because of dynamic changes in the optimal prices, the nested-price structure does not necessarily hold in general and needs to be redefined; and (iv) the optimal pricing and capacity control policy is based on a sequence of threshold points that incorporate inventory, price and demand intensity. Numerical examples are provided.     

A uniform Sobolev inequality for Ricci flow with surgeries and applications

We prove a uniform Sobolev inequality for Ricci flow, which is independent of the number of surgeries. As an application, under less assumptions, a noncollapsing result stronger than Perelman's κ noncollapsing with surgery is derived. The proof is much shorter and seems more accessible. The result also improves some earlier ones where the Sobolev inequality depended on the number of surgeries. To cite this article: Q.S. Zhang, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Marginal cost pricing and revenue reconciliation for electricity

This paper demonstrates how mathematical programming can be used to calculate efficient prices of electricity when demand fluctuates over time and where production comes from different types of plants. It is shown that prices have to be set according to marginal costs and differentiated between peak and off-peak load.Furthermore, the paper concerns the use of reconciliation methods for those cases where producers' surplus will be far above what might be considered as a fair rate of return. Here it is shown that it is extremely important to let the energy charges follow the marginal costs, while any modification of the efficient price should be directed to changes in fixed charges.     

Collaborative pricing and replenishment policy for hi-tech industry

Owing to rapid technological innovation and severe competition, the upstream component price and the downstream product cost of hi-tech industries like computers and communication consumer's products usually decline significantly with time. From a practical viewpoint, there is a need to develop a collaborative pricing and replenishing model with finite horizon when the vendor's purchase cost and the end-consumer's market price are reduced simultaneously. To entice collaboration, the vendor may offer some price discount to the buyer using a negotiation factor to balance the net profit for each player. A numerical example and sensitivity analysis are carried out to illustrate the model. Our results indicate that higher decline-rate in the vendor's purchase cost leads to a smaller vendor lot size, and the higher decline-rate in the market price leads to a larger buyer lot size. The percentage increase in the net profit is approximately 6.57% when cost/price reduction is considered. Therefore, it is significant to consider the effect of the cost/price reduction, especially in hi-tech industries.     

Option pricing and hedge portfolios for poisson progresses

Price processes influenced by Poisson processes are considered and the value of a sum of European call options obtained. The novel feature of the paper is the use of analogues of strochastic flows to derive a martingale representation resut and the heding portfolio     

Optimal pricing and donation policy for fresh goods

This paper studies a socially responsible food-retailer’s operational planning problem for a continuously deteriorating inventory over two periods with the consideration of donation and quality-sensitive customers. Each year, millions of tonnes of food are wasted causing economic, environmental, and social misfortunes, while at the same time millions are undernourished. Besides expired items, edible foods are often deliberately disposed of to attract quality-sensitive consumers. We address this issue by presenting an optimization model that incorporates a retailer’s corporate social responsibility act, in the form of charitable donations, and makes use of the internet of things (IoT)-enabled condition tracking technologies to accurately estimate the effective (true) quality of the goods and its impacts on consumer demand. We formulate a quality-dependent newsvendor problem (QDNP) to determine the stocking quantity and the regular price of the goods at the beginning of the selling season, and the second-period price and donation policy at the end of the first period. The optimal donation policy at the end of the first period depends on the quality (time to expiration), on-hand inventory, and donation reward. Moreover, for a given inventory level, expected food waste is always greater in the absence of donations. QDNP outperforms the no-donation model, particularly when the uncertainty is high and/or the length of the second period is short. Interestingly, the two models react to an increase in uncertainty oppositely: QDNP orders more to alleviate future shortages, whereas, no-donation policy orders less to avoid future disposal costs at the end of the selling season.     

Online pricing for bundles of multiple items

Given a seller with $k$ types of items, $m$ of each, a sequence of users $\{u_1, u_2,\ldots \}$ arrive one by one. Each user is single-minded, i.e., each user is interested only in a particular bundle of items. The seller must set the price and assign some amount of bundles to each user upon his/her arrival. Bundles can be sold fractionally. Each $u_i$ has his/her value function $v_i(\cdot )$ such that $v_i(x)$ is the highest unit price $u_i$ is willing to pay for $x$ bundles. The objective is to maximize the revenue of the seller by setting the price and amount of bundles for each user. In this paper, we first show that a lower bound of the competitive ratio for this problem is $\Omega (\log h+\log k)$ , where $h$ is the highest unit price to be paid among all users. We then give a deterministic online algorithm, Pricing, whose competitive ratio is $O(\sqrt{k}\cdot \log h\log k)$ . When $k=1$ the lower and upper bounds asymptotically match the optimal result $O(\log h)$ .     

The incompatibility of crossing number and bridge number for knot diagrams

We study methods for computing the bridge number of a knot from a knot diagram. We prove equivalence between a geometric and a combinatorial definition of the bridge number of a knot diagram. For each notion of diagrammatic bridge number considered, we find crossing number minimizing knot diagrams which fail to minimize bridge number. Furthermore, we construct a family of minimal crossing diagrams for which the difference between diagrammatic bridge number and the actual bridge number of the knot grows to infinity.     

Determination of the top Baum-Bott number via classical intersection theory

We determine geometrically the number , associated to a smooth m-dimensional projective variety V^m, invariant by a one-dimensional holomorphic foliation of ⁿ , using polar divisors associated to the foliation and Bézouts theorem.     

Hadwiger number and chromatic number for near regular degree sequences

We consider a problem related to Hadwiger's Conjecture. Let D=(d₁, d₂, …, d_n) be a graphic sequence with 0?d₁?d₂?···?d_n?n?1. Any simple graph G with D its degree sequence is called a realization of D. Let R[D] denote the set of all realizations of D. Define h(D)=max{h(G): G∈R[D]} and χ(D)=max{χ(G): G∈R[D]}, where h(G) and χ(G) are Hadwiger number and chromatic number of a graph G, respectively. Hadwiger's Conjecture implies that h(D)?χ(D). In this paper, we establish the above inequality for near regular degree sequences. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 175–183, 2010     

Methods and system of functional programming for supporting supercomputing

In the paper, the functional programming system SFP being under development at the Institute of Informatics Systems in Novosibirsk is considered. The SFP system is aimed at supporting development of parallel computing applications that still offer high performance and portability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)