Symmetry of minimizers for some nonlocal variational problems

We present a new approach to study the symmetry of minimizers for a large class of nonlocal variational problems. This approach which generalizes the Reflection method is based on the existence of some integral identities. We study the identities that lead to symmetry results, the functionals that can be considered and the function spaces that can be used. Then we use our method to prove the symmetry of minimizers for a class of variational problems involving the fractional powers of Laplacian, for the generalized Choquard functional and for the standing waves of the Davey-Stewartson equation.     

Affective bases of likelihood judgments

Analyses of likelihood judgments for 515 events support the idea that the perceived likelihood of an event is partly a function of affective processes. Production of affective disturbances makes events seem unlikely. Event likelihoods also are influenced by specific kinds of people and behaviors which are involved in the events. Affective determination of likelihood is stronger when actors have institutionally‐clear identities rather than institutionally‐vague identities; indeed, affect accounts for more than half of the variance in likelihoods of events within clear institutional contexts.     

Designing a quantity discount scheme for a newsvendor-type product with numerous heterogeneous retailers

This paper presents a practical approach for designing a quantity-discount (“qd”) scheme for a manufacturer who supplies a newsvendor-type product to a large number of heterogeneous retailers. The main components of our approach are: (i) an information structure for handling a large number of heterogeneous retailers with changing identities; and (ii) expected-profit expressions for any given qd scheme. We show that these expected-profit expressions can be easily optimized to produce attractive qd schemes; also, these schemes are shown to be quite robust against errors in parameter estimation.     

Math Autobiographies: A Window into Teachers' Identities as Mathematics Learners

Mathematics autobiographies have the potential to help teachers reflect on their identities as mathematics learners and to understand their role in the development of their students' mathematics identities. This paper reports on a professional development project for K‐2 teachers (n = 41), in which participants were asked to write mathematics autobiographies. Using an adaptation of an existing framework for characterizing teachers' mathematics stories, we describe the consistencies among the participants' experiences as mathematics learners and the events that are identified as being the impetus for a transition from a negative to a positive attitude toward mathematics. Implications for both teachers and teacher educators are presented.     

Schur function identities, their t-analogs, and k-Schur irreducibility

We obtain general identities for the product of two Schur functions in the case where one of the functions is indexed by a rectangular partition, and give their t-analogs using vertex operators. We study subspaces forming a filtration for the symmetric function space that lends itself to generalizing the theory of Schur functions and also provides a convenient environment for studying the Macdonald polynomials. We use our identities to prove that the vertex operators leave such subspaces invariant. We finish by showing that these operators act trivially on the k-Schur functions, thus leading to a concept of irreducibility for these functions.     

Adoption as a social marker: Innovation diffusion with outgroup aversion

Social identities are among the key factors driving behavior in complex societies. Signals of social identity are known to influence individual behaviors in the adoption of innovations. Yet the population-level consequences of identity signaling on the diffusion of innovations are largely unknown. Here we use both analytical and agent-based modeling to consider the spread of a beneficial innovation in a structured population in which there exist two groups who are averse to being mistaken for each other. We investigate the dynamics of adoption and consider the role of structural factors such as demographic skew and communication scale on population-level outcomes. We find that outgroup aversion can lead to adoption being delayed or suppressed in one group, and that population-wide underadoption is common. Comparing the two models, we find that differential adoption can arise due to structural constraints on information flow even in the absence of intrinsic between-group differences in adoption rates. Further, we find that patterns of polarization in adoption at both local and global scales depend on the details of demographic organization and the scale of communication. This research has particular relevance to widely beneficial but identity-relevant products and behaviors, such as green technologies, where overall levels of adoption determine the positive benefits that accrue to society at large.     

Twitter reciprocal reply networks exhibit assortativity with respect to happiness

The advent of social media has provided an extraordinary, if imperfect, ‘big data’ window into the form and evolution of social networks. Based on nearly 40 million message pairs posted to Twitter between September 2008 and February 2009, we construct and examine the revealed social network structure and dynamics over the time scales of days, weeks, and months. At the level of user behavior, we employ our recently developed hedonometric analysis methods to investigate patterns of sentiment expression. We find users’ average happiness scores to be positively and significantly correlated with those of users one, two, and three links away. We strengthen our analysis by proposing and using a null model to test the effect of network topology on the assortativity of happiness. We also find evidence that more well connected users write happier status updates, with a transition occurring around Dunbar's number. More generally, our work provides evidence of a social sub-network structure within Twitter and raises several methodological points of interest with regard to social network reconstructions.     

A Markov modulated Poisson model for software reliability

In this paper, we consider a latent Markov process governing the intensity rate of a Poisson process model for software failures. The latent process enables us to infer performance of the debugging operations over time and allows us to deal with the imperfect debugging scenario. We develop the Bayesian inference for the model and also introduce a method to infer the unknown dimension of the Markov process. We illustrate the implementation of our model and the Bayesian approach by using actual software failure data.     

Two axiomatic approaches to decision making using possibility theory

This paper proposes a utility theory for decision making under uncertainty that is described by possibility theory. We show that our approach is a natural generalization of the two axiomatic systems that correspond to pessimistic and optimistic decision criteria proposed by Dubois et al. The generalization is achieved by removing axioms that are supposed to reflect attitudes toward uncertainty, namely, pessimism and optimism. In their place we adopt an axiom that imposes an order on a class of canonical lotteries that realize either in the best or in the worst prize. We prove an expected utility theorem for the generalized axiomatic system based on the newly introduced concept of binary utility.     

社会互动,投资者情绪传染与资产泡沫——基于股票论坛发帖的实证研究

在资本市场中,投资者并不是相互独立的个体,而是相互学习、相互交流的。随着互联网的迅猛发展,这种社会互动变得更为频繁和普遍,因此社会互动对资产价格的影响也不容小觑。本文先通过理论建模提出理论假设:社会互动存在条件下,投资者互动会加剧市场情绪的传染,进而增加资产泡沫;当投资者情绪高涨时,投资者互动强度显著正向影响泡沫;当投资者情绪低落时,投资者互动强度显著负向影响泡沫;受社会互动影响,投资者活跃的交易会加剧市场情绪的传染,进而增加资产泡沫。之后本文基于股票论坛发帖构建社会互动、投资者情绪指标,验证了中国股票市场中本文理论假设的正确性。     

Combinatorial sums through Riordan arrays

The aim of this work is to show how Riordan arrays are able to generate and close combinatorial identities, by means of the method of coefficients (generating functions). We also show how the same approach can be used to deal with other combinatorial problems, for instance asymptotic approximation and combinatorial inversion. Finally, we propose a method for generating new combinatorial sums by extending the concept of Riordan arrays to bi-infinite matrices.     

社会互动,投资者情绪传染与资产泡沫——基于股票论坛发帖的实证研究

在资本市场中,投资者并不是相互独立的个体,而是相互学习、相互交流的。随着互联网的迅猛发展,这种社会互动变得更为频繁和普遍,因此社会互动对资产价格的影响也不容小觑。本文先通过理论建模提出理论假设:社会互动存在条件下,投资者互动会加剧市场情绪的传染,进而增加资产泡沫;当投资者情绪高涨时,投资者互动强度显著正向影响泡沫;当投资者情绪低落时,投资者互动强度显著负向影响泡沫;受社会互动影响,投资者活跃的交易会加剧市场情绪的传染,进而增加资产泡沫。之后本文基于股票论坛发帖构建社会互动、投资者情绪指标,验证了中国股票市场中本文理论假设的正确性。     

A three-term theta function identity and its applications

In this paper, we establish a three-term theta function identity using the complex variable theory of elliptic functions. This simple identity in form turns out to be quite useful and it is a common origin of many important theta function identities. From which the quintuple product identity and one general theta function identity related to the modular equations of the fifth order and many other interesting theta function identities are derived. We also give a new proof of the addition theorem for the Weierstrass elliptic function ℘. An identity involving the products of four theta functions is given and from which one theta function identity by McCullough and Shen is derived. The quintuple product identity is used to derive some Eisenstein series identities found in Ramanujan's lost notebook and our approach is different from that of Berndt and Yee. The proofs are self contained and elementary.     

A dynamic model for road protection against flooding

This paper focuses on the problem of identifying optimal protection strategies to reduce the impact of flooding on a road network. We propose a dynamic mixed-integer programming model that extends the classic concept of road network protection by shifting away from single-arc fortifications to a more general and realistic approach involving protection plans that cover multiple components. We also consider multiple disruption scenarios of varying magnitude. To efficiently solve large problem instances, we introduce a customised GRASP heuristic. Finally, we provide some analysis and insights from a case study of the Hertfordshire road network in the East of England. Results show that optimal protection strategies mainly involve safeguarding against flooding events that are small and likely to occur, whereas implementing higher protection standards are not considered cost-effective.     

Multi-attribute decision-making in individual and social choice

This paper provides an analysis of individual and social decision criteria for alternatives that are composed of several attributes. We derive additive and multiplicative criteria for individual decision-making with new axioms and apply these criteria to obtain new justifications of known social choice rules with a bargaining interpretation, namely the generalized utilitarian and Nash social choice functions. Unlike most axiomatizations of bargaining solutions, our approach is, to a large extent, based on the multi-attribute structure of the underlying alternatives and the resulting individual decision criteria instead of axioms that impose restrictions on the choice function directly.     

Non-parametric clustering over user features and latent behavioral functions with dual-view mixture models

We present a dual-view mixture model to cluster users based on their features and latent behavioral functions. Every component of the mixture model represents a probability density over a feature view for observed user attributes and a behavior view for latent behavioral functions that are indirectly observed through user actions or behaviors. Our task is to infer the groups of users as well as their latent behavioral functions. We also propose a non-parametric version based on a Dirichlet Process to automatically infer the number of clusters. We test the properties and performance of the model on a synthetic dataset that represents the participation of users in the threads of an online forum. Experiments show that dual-view models outperform single-view ones when one of the views lacks information.     

Tiling Proofs of Recent Sum Identities Involving Pell Numbers

In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their proofs relied heavily on the Binet formula for the Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of a number of the identities. Received July 20, 2006     

Degree three identities

Out approach differs significantly from the approaches used by other mathematicians because we introduce a canonical form for identities. It is straightforward to place an identity in canoni-cal form, and, once the identities are in canonical form, it is easy to determine if they are equivalent, quasi-equivalent, or if one implies the other. This approach is used to identify the dis-tinct minimal degree three identities under the equivalence rela-tion of quasi-equivalence. We determine the exact conditions when almost left alternativity implies almost alternativity and when almost left alternativity implies power associativity. We give a method to decide when an algehra satisfying degree three identi-ties is almost alternati.     

Capturing incomplete information in resource allocation problems through numerical patterns

We look at the problem of optimizing complex operations with incomplete information where the missing information is revealed indirectly and imperfectly through historical decisions. Incomplete information is characterized by missing data elements governing operational behavior and unknown cost parameters. We assume some of this information may be indirectly captured in historical databases through flows characterizing resource movements. We can use these flows or other quantities derived from these flows as “numerical patterns” in our optimization model to reflect some of the incomplete information. We develop our methodology for representing information in resource allocation models using the concept of pattern regression. We use a popular goodness-of-fit measure known as the Cramer–Von Mises metric as the foundation of our approach. We then use a hybrid approach of solving a cost model with a term known as the “pattern metric” that minimizes the deviations of model decisions from observed quantities in a historical database. We present a novel iterative method to solve this problem. Results with real-world data from a large freight railroad are presented.