Using Linear Programming in a Business-to-Business Auction Mechanism

Business to business interactions are largely centered around contracts for procurement or for distribution. Negotiations and sealed bid tendering are the most common techniques used for price discovery and generating the terms and conditions for contracts. Sealed bid tenders collect bids (that is private information between the two companies) and then pick a winning bid/s from among the submitted bids. The outcome of such interactions can be analyzed based on the theory of sealed bid auctions and have been studied extensively [7]. In contrast, negotiations tend to be more dynamic where a buyer (supplier) might be interacting with several suppliers (buyers) simultaneously and the contractual terms being negotiated with one supplier might directly impact the negotiations with another.An approach that is often used for this setting is to design an interactive mechanism where based on a "market signal" such as price for each item, the agents can propose bids based on a decentralized private cost model. A general setting for decentralized allocation is one where there are multiple agents with a utility function for the different resources and the allocation problem is to distribute the resources in an optimal way. A key difference from classical optimization is that the utility functions of the agents are private information and are not explicitly known to the decision maker. The key requirements for such a design to be practical are: (i) convergence to an "equilibrium solution" in a finite number of steps, and (ii) the "equilibrium solution" is optimal for each of the agents, given the market signal. One approach for implementing such mechanisms is the use of primal-dual approaches where the resource allocation problem is formulated as a linear program and the dual prices are used as market signals |2, 3, 8, 1, 4, 6|. Each agent can then use the dual price vector to propose a profit maximizing bid, for the next round, based on her private cost model. Here, the assumption is that the agents attempt to maximize their profits in each round. This assumption is referred to as the myopic best response |5|. In a procurement setting with a single buyer and multiple suppliers, the buyer uses a linear program to allocate her demand by choosing a set of cost minimizing bids and then use the dual price variables to signal the suppliers. In order to guarantee convergence a large enough price decrement is used on all non-zero dual prices in each iteration.In this paper we explore an alternate design where, the market signal provided to each supplier is based on the current cost of procurement for the buyer. Each supplier is then required to submit new bid proposals that reduce the procurement cost (assuming other suppliers keep their bids unchanged) by some large enough decrement d > a. We show that, for each supplier, generating a profit maximizing bid that decreases the procurement cost for the buyer by at least d can be done in polynomial time. This implies that in designs where the bids are not common knowledge, each supplier and the buyer can engage in an "algorithmic conversation" to identify such proposals in a polynomial number of steps. In addition, we show that such a mechanism converges to an "equilibrium solution" where all the suppliers are at their profit maximizing solution given the cost and the required decrement d. At the heart of this design lies a fundamental sensitivity analysis problem of linear programming - given a linear program and its optimal solution, identify the set of new columns such that any one of these columns when introduced in the linear program reduces the optimum solution by at least d.

Rhythms in the biting behaviour of a mosquito Armigeres subalbatus

The biting cycle of Armigeres subalbatus is distinctly crepuscular, exhibiting two peaks of activity, a smaller one at dawn and a larger one at dusk. The biting cycle is entrained to natural light-dark cycles and the time interval from dawn to dawn or dusk to dusk peaks is exactly 24 h and from dawn to dusk or dusk to dawn is about 12 h measured at 50% level. This rhythm manifests itself day after day without any marked qualitative change. The rate of change of light intensity may determine the onset of crepuscular biting. The sudden increase (up to ca. 17 lx) or decrease (down to ca. 4 lx) in the intensity of ambient light at the time of sunrise or sunset coincides with the peak of the biting activity. The density of the population of the host-seeking females fluctuates in relation to the phases of the moon, increasing with the full moon phase and decreasing with the new moon phase. Even though the density of the population is greater outdoors than indoors both at ground levels and in the first floor, the peak of activity occurs at the same time in all the places. A vertical stratification of biting activity was also noticed

Direct correlation between the circadian sleep-wakefulness rhythm and time estimation in humans under social and temporal isolation

Several bodily functions in humans vary on a 24 h pattern and most of these variations persist with a circadian period of ca 25 h when subjects are studied under conditions of social and temporal isolation. We report in this paper that the estimates of short time intervals (TE) of 2 h are strongly coupled to the circadian rhythm in sleepwakefulness. There is a linear correlation between the number of hours humans stay awake (α) and their estimation of 2 h intervals. The coupling of TE to α appears to obtain only under conditions of physical well-being

Inside-out: antibody-binding reveals potential folding hinge-points within the SARS-CoV-2 replication co-factor nsp9

Nsp9 is a conserved accessory component of the coronaviral replication and transcription complex. It is the predominant substrate of nsp12’s nucleotidylation activity while also serving to recruit proteins required for viral 5’-capping. Anti-nsp9 specific nanobodies have been isolated previously. We confirm that their binding mode is centred upon Trp-53 within SARS-CoV-2 nsp9. Antibody binding at this site surprisingly results in large-scale changes to the overall topology of this coronaviral unique fold. We further characterise the antibody-induced structural dynamism within nsp9, identifying a number of potentially flexible regions. A large expansion of the cavity between the s2-s3 and s4-s5 loops is particularly noteworthy. As is the potential for large-scale movements in the C-terminal GxxxG helix

The Intentional Use of Service Recovery Strategies to Influence Consumer Emotion, Cognition and Behaviour

Service recovery strategies have been identified as a critical factor in the success of. service organizations. This study develops a conceptual frame work to investigate how specific service recovery strategies influence the emotional, cognitive and negative behavioural responses of . consumers., as well as how emotion and cognition influence negative behavior. Understanding the impact of specific service recovery strategies will allow service providers' to more deliberately and intentionally engage in strategies that result in positive organizational outcomes. This study was conducted using a 2 x 2 between-subjects quasi-experimental design. The results suggest that service recovery has a significant impact on emotion, cognition and negative behavior. Similarly, satisfaction, negative emotion and positive emotion all influence negative behavior but distributive justice has no effect

A natural product compound inhibits coronaviral replication in vitro by binding to the conserved Nsp9 SARS-CoV-2 protein

The Nsp9 replicase is a conserved coronaviral protein that acts as an essential accessory component of the multi-subunit viral replication/transcription complex. Nsp9 is the predominant substrate for the essential nucleotidylation activity of Nsp12. Compounds specifically interfering with this viral activity would facilitate its study. Using a native mass-spectrometry-based approach to screen a natural product library for Nsp9 binders, we identified an ent-kaurane natural product, oridonin, capable of binding to purified SARS-CoV-2 Nsp9 with micromolar affinities. By determining the crystal structure of the Nsp9-oridonin complex, we showed that oridonin binds through a conserved site near Nsp9’s C-terminal GxxxG-helix. In enzymatic assays, oridonin’s binding to Nsp9 reduces its potential to act as substrate for Nsp12’s Nidovirus RdRp-Associated Nucleotidyl transferase (NiRAN) domain. We also showed using in vitro cellular assays oridonin, while cytotoxic at higher doses has broad antiviral activity, reducing viral titer following infection with either SARS-CoV-2 or, to a lesser extent, MERS-CoV. Accordingly, these preliminary findings suggest that the oridonin molecular scaffold may have the potential to be developed into an antiviral compound to inhibit the function of Nsp9 during coronaviral replication