Concave Value Research Articles

1/2-Approximate MMS Allocation for Separable Piecewise Linear Concave Valuations

We study fair distribution of a collection of m indivisible goods among a group of n agents, using the widely recognized fairness principles of Maximin Share (MMS) and Any Price Share (APS). These principles have undergone thorough investigation within the context of additive valuations. We explore these notions for valuations that extend beyond additivity. First, we study approximate MMS under the separable (piecewise-linear) concave (SPLC) valuations, an important class generalizing additive, where the best known factor was 1/3-MMS. We show that 1/2-MMS allocation exists and can be computed in polynomial time, significantly improving the state-of-the-art. We note that SPLC valuations introduce an elevated level of intricacy in contrast to additive. For instance, the MMS value of an agent can be as high as her value for the entire set of items. We use a relax-and-round paradigm that goes through competitive equilibrium and LP relaxation. Our result extends to give (symmetric) 1/2-APS, a stronger guarantee than MMS. APS is a stronger notion that generalizes MMS by allowing agents with arbitrary entitlements. We study the approximation of APS under submodular valuation functions. We design and analyze a simple greedy algorithm using concave extensions of submodular functions. We prove that the algorithm gives a 1/3-APS allocation which matches the best-known factor. Concave extensions are hard to compute in polynomial time and are, therefore, generally not used in approximation algorithms. Our approach shows a way to utilize it within analysis (while bypassing its computation), and hence might be of independent interest.

An approximated dynamic programming model for the supply vessel fleet sizing problem

The offshore oil and gas exploration and production activities heavily rely on a fleet of supply vessels, which play a crucial role in regularly providing necessary provisions from an onshore supply depot to the offshore installations. For Petrobras, the decision-making process concerning the number of supply vessels to be hired for the upcoming two years holds significant economic implications, given that the daily rates for a single supply vessel can soar to tens of thousands of USDs.In this study, we address the challenges of this heterogeneous fleet sizing problem by presenting an innovative approximated dynamic programming (ADP) model. The model takes into account the uncertainties associated with sea conditions and future demand, making it well-suited for real-world applications. To tackle this problem, we explored two types of approximate value functions: a piecewise linear concave value function and a neural network value function. Both methods underwent rigorous testing and demonstrated their capability to effectively address real-world problems. Consequently, our proposed method exhibits promising potential for practical implementation, allowing companies like Petrobras to accurately assess and determine the ideal fleet composition. By introducing this ADP model, we aim to provide valuable insights and solutions that enhance decision-making processes related to supply vessel fleet sizing in offshore operations. Through considering various uncertainties and complexities, our approach offers a robust and reliable framework to support critical economic decisions in this dynamic industry.

Interval dominance based structural results for Markov decision process

Structural results impose sufficient conditions on the model parameters of a Markov decision process (MDP) so that the optimal policy is an increasing function of the underlying state. The classical assumptions for MDP structural results require supermodularity of the rewards and transition probabilities. However, supermodularity does not hold in many applications. This paper uses a sufficient condition for interval dominance (called I ) proposed in the micro-economics literature, to obtain structural results for MDPs under more general conditions. We present several MDP examples where supermodularity does not hold, yet I holds, and so the optimal policy is monotone; these include sigmoidal rewards (arising in prospect theory for human decision making), bi-diagonal and perturbed bi-diagonal transition matrices (in optimal allocation problems). We also consider MDPs with TP3 transition matrices and concave value functions. Finally, reinforcement learning algorithms that exploit the differential sparse structure of the optimal monotone policy are discussed.

Mobility and Energy Management in Electric Vehicle Based Mobility-on-Demand Systems: Models and Solutions

An electric vehicle based mobility-on-demand (EMoD) system provides shared transportation (e.g., car-sharing or ride-sharing) to satisfy customers’ individual mobility demands. It has been recognized as a vital alternative form of transportation between public and private transportations in future sustainable cities. Constrained by the long charging time and limited driving range of EVs, an operator of an EMoD system demands for decision-making models and algorithms to manage the mobility and energy of EVs to best serve customers with least costs. In this paper, we propose a stochastic dynamic program (DP) to model three operational decisions of the EMoD system: i) dispatching EVs to serve mobility demand from customers, ii) repositioning EVs to accommodate the unbalanced mobility demands between service regions, and iii) recharging EVs to maintain their sufficient state-of-charge levels. To handle this large-scale DP problem, we first observe and prove that it has a coordinate-wise concave value function. Based on this structural property, we propose to use a separable piecewise linear function to approximate the value function and design an approximation-based algorithm to efficiently derive the decision policy. Numerical tests show that our proposed algorithm significantly outperforms the existing model-free approaches (e.g., greedy heuristic and Q-learning) that fail to take into account the structural properties of the DP problem.

The Price of Anarchy of Two-Buyer Sequential Multiunit Auctions

We study the efficiency of first-/second-price sequential multiunit auctions with two buyers and complete information. Extending the primal-dual framework for obtaining efficiency bounds to this sequential setting, we obtain tight price of anarchy bounds. For general valuation functions, we show that the price of anarchy is exactly 1/T for auctions with T items for sale. For concave valuation functions, we show that the price of anarchy is bounded below by 1-1/e≃ 0.632 . This bound is asymptotically tight as the number of items sold tends to infinity.

Multivariate Concavity Amplitude Index (MCAI) for characterizing Heschl's gyrus shape

Heschl's gyrus (HG), which includes primary auditory cortex, is highly variable in its shape (i.e. gyrification patterns), between hemispheres and across individuals. Differences in HG shape have been observed in the context of phonetic learning skill and expertise, and of professional musicianship, among others. Two of the most common configurations of HG include single HG, where a single transverse temporal gyrus is present, and common stem duplications (CSD), where a sulcus intermedius (SI) arises from the lateral aspect of HG. Here we describe a new toolbox, called ‘Multivariate Concavity Amplitude Index’ (MCAI), which automatically assesses the shape of HG. MCAI works on the output of TASH, our first toolbox which automatically segments HG, and computes continuous indices of concavity, which arise when sulci are present, along the outer perimeter of an inflated representation of HG, in a directional manner. Thus, MCAI provides a multivariate measure of shape, which is reproducible and sensitive to small variations in shape. We applied MCAI to structural magnetic resonance imaging (MRI) data of N=181 participants, including professional and amateur musicians and from non-musicians. Former studies have shown large variations in HG shape in the former groups. We validated MCAI by showing high correlations between the dominant (i.e. highest) lateral concavity values and continuous visual assessments of the degree of lateral gyrification of the first gyrus. As an application of MCAI, we also replicated previous visually obtained findings showing a higher likelihood of bilateral CSDs in musicians. MCAI opens a wide range of applications in evaluating HG shape in the context of individual differences, expertise, disorder and genetics.

Examination of Facial Convexity and Concavity Values With Reference to the External Acoustic Pore: A Retrospective Study.

The human skull serves as an essential material for facial reconstruction. In particular, the petrous part of the temporal bone is vital due to its compact structure, which can resist mechanical forces. The study aims to give descriptive values to estimate the face shape and produce regression formulas through the external acoustic pore as a reference point. The study was carried out on 3-dimensional computed tomography images, a total of 83 adult images (45 females and 38 males) in the Department of Radiology of Bursa Uludag University Medical Faculty. The distances between the imaginary vertical line passing through the porion and the anthropometric points revealing the facial features were measured for the soft and hard tissue. The vertical distances between the soft and hard tissue landmarks were also measured for both sexes. Measurements were performed with the Image J program, and for the statistical analysis, SPSS 25.0 was used ( P < 0.005). Linear simple regression analysis was used to produce formulas to estimate the soft tissue thickness using hard tissue. Also, discriminant function analysis was performed to determine sex in the presence of an unknown skull. The descriptive values of the variables on the axial and vertical planes and the differences between sexes are given. Also, all formulas make accurate predictions of 90% or more. The authors tried to estimate the anatomical points that roughly reveal the facial features with the regression formulas developed using anthropometric measurements. The authors think that the shape of the face, which is more specific to the individual, can be reached more clearly using mathematical models, and the authors believe that this study will set an example for future studies.

Rent Dissipation in Simple Tullock Contests

We investigate observed rent dissipation—the ratio of the total costs of rent seeking to the monetary value of the rent—in winner-take-all and share contests, where preferences are more general than usually assumed in the literature. With concave valuation of the rent, we find that contests can exhibit observed over-dissipation if the contested rent is below a threshold and yet observed under-dissipation with large rents: the nature of preferences implies contestants are relatively effortful in contesting small rents. Considering more general preferences in contests thus allows us to reconcile the Tullock paradox—where rent-seeking levels are relatively small despite the contested rent being sizeable—with observed over-dissipation of rents in experimental settings, where contested rents are arguably small.

Electromagnetic Characteristics Analysis of Quadrupole Compound Orbital Electromagnetic Launcher with Different Configurations

During the operation of the Quadrupole Compound Orbital electromagnetic launcher, the current is easy to gather in the armature and the rail contact surface. Serious turn and arc ablation can occur, causing damage to the rail and the armature and affecting the life of the launcher. To better solve the thermal ablation problem of the armature and the rail, three different configurations of the rail and the armature are established, and the current density, magnetic field distribution and electromagnetic force of the rail and the armature are compared and analyzed using the finite element method, and the effect of concave and convex values of the armature rail on current distribution and electromagnetic force is discussed. The results show that the planar armature can effectively reduce the maximum current density and mitigate thermal damage. The concave elliptical rail produces the largest electromagnetic thrust and the smallest radial electromagnetic force, and the armature is more stable during firing. The maximum current density and magnetic field strength are negatively correlated with the concave and convex values; the electromagnetic thrust applied to the concave elliptical armature is negatively correlated with the concave value, while the electromagnetic force applied to the convex elliptical armature is positively correlated with the convex value.

Fair Division of Indivisible Goods for a Class of Concave Valuations

We study the fair and efficient allocation of a set of indivisible goods among agents, where each good has several copies, and each agent has an additively separable concave valuation function with a threshold. These valuations capture the property of diminishing marginal returns, and they are more general than the well-studied case of additive valuations. We present a polynomial-time algorithm that approximates the optimal Nash social welfare (NSW) up to a factor of e1/e ≈ 1.445. This matches with the state-of-the-art approximation factor for additive valuations. The computed allocation also satisfies the popular fairness guarantee of envy-freeness up to one good (EF1) up to a factor of 2 + ε. For instances without thresholds, it is also approximately Pareto-optimal. For instances satisfying a large market property, we show an improved approximation factor. Lastly, we show that the upper bounds on the optimal NSW introduced in Cole and Gkatzelis (2018) and Barman et al. (2018) have the same value.

Assessing patterns of spatial distribution of large wood in semi-natural, single-thread channels of Central Europe

Spatial distribution of large wood (LW) is frequently assessed in a simplified form as a degree to which wood is clustered into jams usually as the consequence of previous wood mobility in the stream. In this study, longitudinal patterns of LW distribution in ten semi-natural, single-thread reaches (catchment area 0.10–1479 km2, channel width 2.5–34 m, bed slope 0.0009–0.23 m m−1) of watercourses of the temperate climatic zone in Central Europe were quantitatively evaluated using a one-dimensional Ripley’s K statistic and the parameter of concavity. Although these metrics could not indicate clear differences in distribution patterns between the mountain confined and the lowland unconfined reaches, they helped reveal some specific features of LW spatial organisation. Ripley’s K statistic indicated a higher degree of LW aggregation in the reach recently disturbed by a high-magnitude debris flow/debris flood event and the reaches with suggested intensive LW transport. A regular pattern of LW distribution with respect to the recurrent LW retention features was suggested by a reversal of the trend in calculated concavity values, as channel bins with the lowest values of the parameter roughly equalled the spacing of meanders. Moreover, the used metrics indicated somewhat contradictory distribution patterns in some of the study reaches, with Ripley’s K demonstrating the occurrence of LW aggregation along the whole longitudinal profile and concavity values indicating downstream variation in LW counts and volumes between short subsequent channel sections. Both quantitative metrics can provide valuable information about longitudinal patterns of LW storage and they have a potential to be used in geomorphic research focused on any features distributed along line structures.

Nash Social Welfare Approximation for Strategic Agents

We study the problem of allocating divisible resources to agents with different preferences. We analyze a market game known as Trading Post, first considered by Shapley and Shubik, where each agent gets a budget of virtual currency to bid on goods: after bids are placed, goods are allocated to players in proportion to their bids. In this setting, the agents choose their bids strategically, aiming to maximize their utility, and this gives rise to a game. We study the equilibrium allocations of this game, measuring the quality of an allocation via the Nash social welfare, the geometric mean of utilities (a measure of aggregate welfare that respects individual needs). We show that any Nash equilibrium of Trading Post approximates the optimal Nash welfare within a factor of two for all concave valuations, and the mechanism is essentially optimal for Leontief valuations.

Multiattribute Regret: Theory and Experimental Study

The aim of this paper is two-fold. The first part is to generalize the simple regret model by Bell (1982) and Loomes and Sugden (1982) to cope with the situation in which decision outcomes are multi-attributed. We propose a model which combines the simple regret model for ex ante preferences and the additive difference representation for ex post preferences. Then we show a necessary and sufficient axiomatization of our model under Savage’s framework. The proposed model is composed of three types of functions. One is a value function for each attribute. The others are attribute-dependent and holistic regret-rejoicing functions which respectively capture trade-offs among value-differences of chosen and forgone outcomes for each attribute and among all attributes. We also discuss constructive procedures and their consistency. The second part is to conduct an experiment to measure two attributes case. Participants were asked to join in a work to carry over heavy bags at some varying distances. The data supports the framing effect, that is, participants tend to have convex value functions in each attribute and indicate regret averse for weights and regret seeking for distances in gain frame. On the other hand, participants exhibit concave value functions for both attributes and regret seeking for weights and regret averse (almost regret neutral) for distances in loss frame.

Studying active fault-related folding on tectonically inverted orogens: A case study at the Yariguíes Range in the Colombian Northern Andes

Morphometric analysis is widely used in tectonic geomorphology as a useful method for identifying fold activity in terms of its lateral and vertical growth. This study evaluates the recent tectonic activity and lateral propagation of the Los Cobardes anticline (LCA), which built up the Yariguíes Range, from morphometric characterization, a structural kinematic analysis, and fieldwork. The study area is located west of the Colombian Eastern Cordillera in a tectonically active region bounded by longitudinal tectonically inverted reverse structures (e.g., the Suárez Fault) with minor transverse faults and the LCA as the central fold of the Yariguíes Anticlinorium.A comparison among the precipitation data, lithology, and the morphometric indexes leads us to conclude that for the LCA, recent tectonics drive fold activity. Based on the LCA's geomorphology and the kinematic analysis derived from fault-slip data, we define three independent fold segments bounded by transverse zones: LCA-A, LCA-B, and LCA-C. Of these, the first two show evidence of lateral propagation toward the southwest, which is closely related to the activity of the Suárez Fault and inherited transverse structures. We found qualitative and quantitative geomorphologic evidence of southwestward propagation: wind and water gaps decreasing in elevation, drainages partially flowing in the direction opposite to the regional trend, and low concavity values for normalized profiles (from −40.49 to 11.76) and Vf (from 0.07 to 0.13). Assisted by published low-temperature thermochronology and seismotectonic data, we demonstrate that the LCA has been growing since the Pliocene and remains active, accommodating deformation in a transpressive stress state. Our findings could serve as a reference to study active fold growth and its structural drivers in known tectonically inverted basins, such as the foreland thrust belt in Argentina, the High Atlas Mountains in Morocco, and the Central Mountain Range of Taiwan, among others.

Forming and uniformity of shaft parts without a stub bar by axial closed–open-type cross-wedge rolling

To realize cross-wedge rolling of shaft parts without a stub bar in a short process, an axial closed–open-type cross-wedge rolling technique was proposed. Based on the strain characteristics in the rolling, evaluation indices of deformation uniformity were provided, and the DEFORM-3D software was adopted to conduct numerical simulations of the rolling process. The metal flow and strain distribution in all stages of the rolling process were analyzed. It is shown that the strain value of the rolled piece close to the end is relatively high while the overall strain distribution is uniform in the rolling process. When the percentage reduction in area is smaller, the fluctuation range of the equivalent strain will be lower and the overall uniformity of the rolled piece will be better. A variable angle wedge was implemented to make metal flow inward and eliminate concavity. Finally, rolling experiment was performed, which indicate that the shape of the rolled piece obtained is consistent with the simulation results. Concavity value in the rolling is decreased by 92% as compared to conventional open rolling. The research results lay a theoretical basis for realizing closed–open-type cross-wedge rolling without a stub bar.

Hot topic: Automated assessment of reticulo-ruminal motility in dairy cows using 3-dimensional vision

Reticulo-ruminal motility is a well-established indicator of gastrointestinal health in dairy cows. The currently available methods for assessing motility are labor-intensive, costly, and impractical to use regularly for all cows on a farm. We hypothesized that the reticulo-ruminal motility of dairy cows could be assessed automatically and remotely using a low-cost 3-dimensional (3D) camera. In this study, a 3D vision system was constructed and mounted on the frame of an automatic milking robot to capture the left paralumbar fossa of 20 primiparous cows. For each cow, the system recorded 3D images at 30 frames per second during milking. Each image was automatically processed to locate the left paralumbar fossa region and quantify its average concavity. Then, the average concavity values from all images of 1 cow during 1 milking process were chronologically assembled to form an undulation signal. By applying fast Fourier transformation to the signal, we identified cyclic oscillations that occurred in the same frequency range as reticulo-ruminal contractions. To validate the oscillation identification, 2 trained assessors visually identified reticulo-ruminal contractions from the same 3D image recordings on screen. The matching sensitivity between the automatically identified oscillations and the manually identified reticulo-ruminal contractions was 0.97. This 3D vision system can automate the assessment of reticulo-ruminal motility in dairy cows. It is noninvasive and can be implemented on farms without distressing the cows. It is a promising tool for farmers, giving them regular information about the gastrointestinal health of individual cows and helping them in daily farm management.

Likelihood approximations of implied weights parsimony can be selected over the Mk model by the Akaike information criterion.

A likelihood method that approximates the behaviour of implied weighting is described. This approach provides a likelihood perspective on several aspects of implied weighting, such as guidance for the choice of concavity values, a justification to use different concavities for different numbers of taxa, and a natural basis for extended implied weighting. In this approach, the number of free parameters in the estimation depends on C, the number of characters (in contrast to the standard Mk model, which estimates 2T-3 parameters for T taxa). Depending on the characteristics of the dataset, the likelihood obtained with this approach may in some cases be similar or superior to that of the Mk model, but with fewer parameters being adjusted. Because of that tradeoff, testing against the Mk model by means of the Akaike information criterion on a set of 182 morphological datasets indicated many cases (36) in which the likelihood approximation to implied weighting is the best method, from an information-theoretic point of view. Given that it is expected to produce (almost) the same results as this maximum-likelihood approximation, implied weighting can therefore be seen as a valid alternative to the Mk model often used for morphological datasets, on the basis of a criterion for model fit widely advocated by likelihoodists.

Evolutionary dynamics of the main-stem longitudinal profiles of ten kongdui basins within Inner Mongolia, China

The longitudinal profiles of main streams of ten kongdui basins within Inner Mongolian Autonomous Region of China were characterized in this study by analyzing a series of quantitative indexes that are relevant to tectonic activity and river action, and by establishing a series of multiple regression models. The results reveal that all longitudinal profiles are concave in shape, with a range of concavity between 1.1 and 3.1, increasing from west to east. Data also show that the concavity of the profiles is significantly negatively correlated with profile length, altitude difference, average altitude, drainage area and sediment load of the basins. Analysis reveals that kongdui basins have suffered from moderate-to-weak tectonic activity over time, again characterized by a west-to-east weakening trend. Stream power also varies along the main channels of the ten kongdui basins; average values in each case fall between 0.8 W/m and 8.4 W/m, generally higher within the middle reaches. This decreasing trend in stream power within the lower reaches of kongdui basins might provide one key explanation for sedimentation there. Data also show that the average stream power in western and central basins tends to be higher than that in eastern examples, even though both the highest and the lowest values are seen within two middle ones. This analysis shows that the longitudinal profile concavity values are mainly controlled by tectonic activity and that the effect of river action is insignificant.

The role of intraplate strike-slip faults in shaping the surrounding morphology: The Ovacık Fault (eastern Turkey) as a case study

Although the westward extrusion of the Anatolian Block is mainly compensated along its boundary faults, the North Anatolian and the East Anatolian shear zones, it is internally deformed in a dominant manner by some strike-slip faults as well. To obtain a better understanding about this intraplate deformation of the Anatolian Block, we investigate the tectonic geomorphology of the Ovacık Fault (OF), which is the northeastern member of the Malatya-Ovacık Fault Zone (MOFZ). Further, we apply the most common geomorphic indices, such as the hypsometric curve and integral, longitudinal channel profiles, channel steepness and concavity, mountain front sinuosity, and valley height-width ratio to characterise and quantify the deformation along the OF and the surrounding region where the regional morphology is shaped with the joint effect of palaeo- and neotectonics and other morphological factors such as palaeoglacial processes. The highest hypsometric integral, steepness and concavity values are generally observed along the northeastern strand of the OF (the Munzur Mountains) and the Kemaliye Region. Further, we interpret that high HI and steepness values indicate a regional tectonic uplift because of either a change in fault geometry, which gives rise to the vertical component on the OF, or a regional high convergence zone. Furthermore, this study gives the first calculation of vertical uplift in the northern margin of the Ovacık Basin (OB) as at least 0.5 mm/y for long term deformation history. Thus, our results exhibit that the OF is one of the intraplate strike-slip faults of the Anatolian Block.

Value Functions for Prospect Theory Investors: An Empirical Evaluation for U.S. Style Portfolios

ABSTRACTThe main aim of this article is to provide a general behavioral analysis that proposes a series of different value functions for prospect theory (PT) investors incorporated into behavioral reward-risk models that are finally solved so as to provide some specific optimal solutions. To do this, general behavioral reward-risk models, which contain all the basic elements of the PT, are first set up. Two reward and risk measures, the upper partial moment and the lower partial moment, are subsequently used to create the various value functions. The technical difficulties arising during the behavioral maximization process are overpassed by adapting the Rubinstein [1982] algorithm. The results show that agents differentiate their behavior according to their type of preferences (S-shaped, reverse S-shaped, kinked convex, and kinked concave value function) but they seem to always prefer small capitalization and high positively skewed value stock portfolios. Probability distortion also affects the optimal solutions of the problem, independently of the employing weighting functional form; when subjective probabilities are employed the optimal weights of the most risky positively skewed assets seem to increase. Probability distortion has an additional important effect on optimal perspective values of the problem driving to a significant increase.