Optimal control of a revenue management system with dynamic pricing facing linear demand

This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time‐varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two‐product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two‐product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd.     

ITERATIVE DYNAMIC PROGRAMMING FOR MINIMUM ENERGY CONTROL PROBLEMS WITH TIME DELAY

This paper presents the use of iterative dynamic programming employing exact penalty functions for minimum energy control problems. We show that exact continuously non-differentiable penalty functions are superior to continuously differentiable penalty functions in terms of satisfying final state constraints. We also demonstrate that the choice of an appropriate penalty function factor depends on the relative size of the time delay with respect to the final time and on the expected value of the energy consumption. A quadratic approximation (QA) of the delayed variables is much better than a linear approximation (LA) of the same for relatively large time delays. The QA improves the rate of convergence and avoids the formation of ‘kinks‘. A more general way of selecting appropriate penalty function factors is given and the results obtained using four illustrative examples of varying complexity corroborate the efficacy of the method.     

RASER: a new ultrafast magnetic resonance imaging method.

A new MRI method is described to acquire a T(2)-weighted image from a single slice in a single shot. The technique is based on rapid acquisition by sequential excitation and refocusing (RASER). RASER avoids relaxation-related blurring because the magnetization is sequentially refocused in a manner that effectively creates a series of spin echoes with a constant echo time. RASER uses the quadratic phase produced by a frequency-swept chirp pulse to time-encode one dimension of the image. In another implementation the pulse can be used to excite multiple slices with phase-encoding and frequency-encoding in the other two dimensions. The RASER imaging sequence is presented along with single-shot and multislice images, and is compared to conventional spin-echo and echo-planar imaging sequences. A theoretical and empirical analysis of the spatial resolution is presented, and factors in choosing the spatial resolution for different applications are discussed. RASER produces high-quality single-shot images that are expected to be advantageous for a wide range of applications.     

On the synthesis of time‐varying LQG weights and noises along optimal control and state trajectories

A general approach to control non‐linear uncertain systems is to apply a pre‐computed nominal optimal control, and use a pre‐computed LQG compensator to generate control corrections from the on‐line measured data. If the non‐linear model, on which the optimal control and LQG compensator design is based, is of sufficient quality, and when the LQG compensator is designed appropriately, the closed‐loop control system is approximately optimal. This paper contributes to the selection and computation of the time‐varying LQG weighting and noise matrices, which determine the LQG compensator design. It is argued that the noise matrices may be taken time‐invariant and diagonal. Three very important considerations concerning the selection of the time‐varying LQG weighting matrices are turned into a concrete computational scheme. Thereby, the selection of the time‐varying LQG weighting matrices is reduced to selecting three scalar design parameters, each one weighting one consideration. Although the three considerations seem straightforward they may oppose one another. Furthermore, they usually result in time‐varying weighting matrices that are indefinite, rather than positive (semi) definite as required for the LQG design. The computational scheme presented in this paper addresses and resolves both problems. By two numerical examples the benefits of our optimal closed‐loop control system design are demonstrated and evaluated using Monte Carlo simulation. Copyright © 2005 John Wiley & Sons, Ltd.     

Oxytocin attenuates amygdala responses to emotional faces regardless of valence.

BACKGROUND: Oxytocin is known to reduce anxiety and stress in social interactions as well as to modulate approach behavior. Recent studies suggest that the amygdala might be the primary neuronal basis for these effects. METHODS: In a functional magnetic resonance imaging study using a double-blind, placebo-controlled within-subject design, we measured neural responses to fearful, angry, and happy facial expressions after intranasal application of 24 IU oxytocin compared with placebo. RESULTS: Oxytocin reduced right-sided amygdala responses to all three face categories even when the emotional content of the presented face was not evaluated explicitly. Exploratory whole brain analysis revealed modulatory effects in prefrontal and temporal areas as well as in the brainstem. CONCLUSIONS: Results suggest a modulatory role of oxytocin on amygdala responses to facial expressions irrespective of their valence. Reduction of amygdala activity to positive and negative stimuli might reflect reduced uncertainty about the predictive value of a social stimulus and thereby facilitates social approach behavior.     

Numerical method for weights adjustment in minimax multi‐model LQ‐control

The minimax linear quadratic problem, where ‘max’ is taken over a finite set of indices (models) and ‘min’ is taken over the set of admissible controls, is considered. The solution is obtained by the robust optimal control application. The control turns out to be a linear combination of the controls optimal for each individual model. This paper develops a numerical method for the optimal weights adjustment. An example shows a quick convergence of the proposed procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

Affective communication deficits associated with cerebellar degeneration

The cerebellum has extensive connections with the frontal lobes. Cerebellar injury has been reported to induce frontal-executive cognitive dysfunction and blunting of affect. We examined a patient with idiopathic cerebellar degeneration with impaired family relationships attributed to an “emotional disconnection.” Examination revealed ataxia, dysmetria, and adiadochokinesia more severe on the left and frontal-executive dysfunction; memory and cognitive functions were otherwise normal. Testing of emotional communication included assessments of emotional semantic knowledge, emotional prosody, and emotional facial expressions. Comprehension was normal but expression was severely impaired. Cerebellar dysfunction can cause a defect in facial and prosodic emotional communication.     

线性二次模型的演变和发展

细胞中的DNA是辐射敏感的靶，击中DNA双链是导致细胞死亡的主要原因。但不同组织的细胞对射线的敏感性存在差异。为了更好的解析这种差异，线性二次模型（LQ模型）被提了出来，它用α／β来反映正常组织修复损伤的能力，较好的解释了肿瘤组织与正常组织反应的差别，为我们预测放射治疗中生物效应和预后提供了依据。但一直以来由于LQ模型涉及的知识范围较广，彻底掌握并熟练应用的难度较大，为此本文从LQ模型的提出，引入时间因子、修复因子等方面简述LQ模型发展和演变的基本过程，探讨LQ模型的局限和应用条件，以期对大家掌握应用该模型能有所帮助。     

People with chronic facial pain perform worse than controls at a facial emotion recognition task,but it is not all about the emotion

Alexithymia, or a lack of emotional awareness, is prevalent in some chronic pain conditions and has been linked to poor recognition of others' emotions. Recognising others' emotions from their facial expression involves both emotional and motor processing, but the possible contribution of motor disruption has not been considered. It is possible that poor performance on emotional recognition tasks could reflect problems with emotional processing, motor processing or both. We hypothesised that people with chronic facial pain would be less accurate in recognising others' emotions from facial expressions, would be less accurate in a motor imagery task involving the face, and that performance on both tasks would be positively related. A convenience sample of 19 people (15 females) with chronic facial pain and 19 gender‐matched controls participated. They undertook two tasks; in the first task, they identified the facial emotion presented in a photograph. In the second, they identified whether the person in the image had a facial feature pointed towards their left or right side, a well‐recognised paradigm to induce implicit motor imagery. People with chronic facial pain performed worse than controls at both tasks (Facially Expressed Emotion Labelling (FEEL) task P < 0·001; left/right judgment task P < 0·001). Participants who were more accurate at one task were also more accurate at the other, regardless of group (P < 0·001, r² = 0·523). Participants with chronic facial pain were worse than controls at both the FEEL emotion recognition task and the left/right facial expression task and performance covaried within participants. We propose that disrupted motor processing may underpin or at least contribute to the difficulty that facial pain patients have in emotion recognition and that further research that tests this proposal is warranted.     

Recognition of Facial Expressions of Emotion in Adults with Down Syndrome

ABSTRACT

Research on facial expressions in individuals with Down syndrome (DS) has been conducted using photographs. Our goal was to examine the effect of motion on perception of emotional expressions. Adults with DS, adults with typical development matched for chronological age (CA), and children with typical development matched for developmental age (DA) viewed photographs and video clips of facial expressions of: happy, sad, mad, and scared. The odds of accurate identification of facial expressions were 2.7 times greater for video clips compared with photographs. The odds of accurate identification of expressions of mad and scared were greater for video clips compared with photographs. The odds of accurate identification of expressions of mad and sad were greater for adults but did not differ between adults with DS and children. Adults with DS demonstrated the lowest accuracy for recognition of scared. These results support the importance of motion cues in evaluating the social skills of individuals with DS.