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We present ExpIris, a separation logic framework for the (amortized) expected cost analysis of probabilistic programs. ExpIris is based on Iris, parametric in the language and the cost model, and supports both imperative and functional languages, concurrency, higher-order functions and higher-order state. ExpIris also offers strong support for correctness reasoning, which greatly eases the analysis of programs whose expected cost depends on their high-level behavior. To enable expected cost reasoning in Iris, we build on the expected potential method. The method provides a kind of "currency" that can be used for paying for later operations, and can be distributed over the probabilistic cases whenever there is a probabilistic choice, preserving the expected value due to the linearity of expectations. We demonstrate ExpIris by verifying the expected runtime of a quicksort implementation and the amortized expected runtime of a probabilistic binary counter.

This paper studies how labor market conditions around high school graduation affect postsecondary skill investments. Using administrative data on more than six million German graduates from 1995-2018, and exploiting deviations from secular state-specific trends, I document procyclical college enrollment. Cyclical increases in unemployment reduce enrollment at traditional universities and shift graduates toward vocational colleges and apprenticeships. These effects translate into educational attainment. Using large-scale survey data, I identify changes in expected returns to different degrees as the main mechanism. During recessions, graduates expect lower returns to an academic degree, while expected returns to a vocational degree are stable.

In this paper, we obtain a comparison theorem and a invariant representation theorem for backward stochastic differential equations (BSDEs) without any assumption on the second variable $z$. Using the two results, we further develop the theory of $g$-expectations. Filtration-consistent nonlinear expectation (${\cal{F}}$-expectation) provides an ideal characterization for the dynamical risk measures, asset pricing and utilities. We propose two new conditions: an absolutely continuous condition and a (locally Lipschitz) domination condition. Under the two conditions respectively, we prove that any ${\cal{F}}$-expectation can be represented as a $g$-expectation. Our results contain a representation theorem for $n$-dimensional ${\cal{F}}$-expectations in the Lipschitz case, and two representation theorems for $1$-dimensional ${\cal{F}}$-expectations in the locally Lipschitz case, which contain quadratic ${\cal{F}}$-expectations.

A robot's appearance is a known factor influencing user's mental model and human-robot interaction, that has not been studied in the context of its influence in expected robot explanations. In this study, we investigate whether and to what extent the human-like appearance of robots elicits anthropomorphism, which is conceptualised as an attribution of mental capacities, and how the level of anthropomorphism is revealed in explanations that people expect to receive. We designed a between-subject study comprising conditions with visual stimuli of three domestic service robots with varying human-like appearance, and we prompted respondents to provide explanations they would expect to receive from the robot for the same robot actions. We found that most explanations were anthropomorphic across all conditions. However, there is a positive correlation between the anthropomorphic explanations and human-like appearance. We also report on more nuanced trends observed in non-anthropomorphic explanations and trends in robot descriptions.

The marginal degree of sums in dimension \(n\) is the smallest integer \(k\) such that the joint distributions of all subcollections of at most \(k\) coordinates of a real-valued random vector \(\left(X_1,\ldots,X_n\right)\) determine the value of \(\E\left(X_1+\cdots+X_n\right)\), whenever this expectation is defined. For every \(n\ge2\), we prove that this marginal degree is \(\left\lceil n/2\right\rceil\). The upper bound follows from a theorem of Simons (1977). The lower bound is proved by constructing, for every \(1\le k<\left\lceil n/2\right\rceil\), two joint laws whose marginals of dimension at most \(k\) agree, but for which the corresponding expectations of \(X_1+\cdots+X_n\) are defined and unequal.

In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit distributions can be completely nonlinear. Finally, we study the limit theorem in a special case, where the limit distribution satisfies positive homogeneity.

Expectation Propagation (EP) is a widely used message-passing algorithm that decomposes a global inference problem into multiple local ones. It approximates marginal distributions (beliefs) using intermediate functions (messages). While beliefs must be proper probability distributions that integrate to one, messages may have infinite integral values. In Gaussian-projected EP, such messages take a Gaussian form and appear as if they have "negative" variances. Although allowed within the EP framework, these negative-variance messages can impede algorithmic progress. In this paper, we investigate EP in linear models and analyze the relationship between the corresponding beliefs. Based on the analysis, we propose both non-persistent and persistent approaches that prevent the algorithm from being blocked by messages with infinite integral values. Furthermore, by examining the relationship between the EP messages in linear models, we develop an additional approach that avoids the occurrence of messages with infinite integral values.

The hyperfinite $G$-expectation is a nonstandard discrete analogue of $G$-expectation (in the sense of Robinsonian nonstandard analysis). A lifting of a continuous-time $G$-expectation operator is defined as a hyperfinite $G$-expectation which is infinitely close, in the sense of nonstandard topology, to the continuous-time $G$-expectation. We develop the basic theory for hyperfinite $G$-expectations and prove an existence theorem for liftings of (continuous-time) $G$-expectation. For the proof of the lifting theorem, we use a new discretization theorem for the $G$-expectation (also established in this paper, based on the work of Dolinsky et al. [Weak approximation of $G$-expectations, Stoch. Proc. Appl. 122(2), (2012), pp.664--675]).

We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$-adic numbers. We define the expectation by analogy with the observation that for real-valued random variables in $L^2$ the expected value is the orthogonal projection onto the constants. Previous work has shown that the local field version of $L^\infty$ is the appropriate counterpart of $L^2$, and so the expected value of a local field-valued random variable is defined to be its ``projection'' in $L^\infty$ onto the constants. Unlike the real case, the resulting projection is not typically a single constant, but rather a ball in the metric on the local field. However, many properties of this expectation operation and the corresponding conditional expectation mirror those familiar from the real-valued case; for example, conditional expectation is, in a suitable sense, a contraction on $L^\infty$ and the tower property holds. We also define the corresponding notion of martingale, show that several standard examples of martingales (for example, sums or products of suitable independent random variables or ``harmonic'' functions composed with

Expected Utility: Algebraic Expected Utility In this paper, we provide two axiomatizations of algebraic expected utility, which is a particular generalized expected utility, in a von Neumann-Morgenstern setting, i.e. uncertainty representation is supposed to be given and here to be described by a plausibility measure valued on a semiring, which could be partially ordered. We show that axioms identical to those for expected utility entail that preferences are represented by an algebraic expected utility. This algebraic approach allows many previous propositions (expected utility, binary possibilistic utility,...) to be unified in a same general framework and proves that the obtained utility enjoys the same nice features as expected utility: linearity, dynamic consistency, autoduality of the underlying uncertainty measure, autoduality of the decision criterion and possibility of modeling decision maker's attitude toward uncertainty.

In this paper we consider two ways to generalize the mathematical expectation of a random variable, the Choquet expectation and Peng's g-expectation. An open question has been, after making suitable restrictions to the class of random variables acted on by the Choquet expectation, for what class of expectation do these two definitions coincide? In this paper we provide a necessary and sufficient condition which proves that the only expectation which lies in both classes is the traditional linear expectation. This settles another open question about whether Choquet expectation may be used to obtain Monte Carlo-like solution of nonlinear PDE: It cannot, except for some very special cases.

Background: Studies on developer productivity and well-being find that the perceptions of productivity in a software team can be a socio-technical problem. Intuitively, problems and challenges can be better handled by managing expectations in software teams. Aim: Our goal is to understand whether the expectations of software developers vary towards diverse stakeholders in software teams. Method: We surveyed 181 professional software developers to understand their expectations from five different stakeholders: (1) organizations, (2) managers, (3) peers, (4) new hires, and (5) government and educational institutions. The five stakeholders are determined by conducting semi-formal interviews of software developers. We ask open-ended survey questions and analyze the responses using open coding. Results: We observed 18 multi-faceted expectations types. While some expectations are more specific to a stakeholder, other expectations are cross-cutting. For example, developers expect work-benefits from their organizations, but expect the adoption of standard software engineering (SE) practices from their organizations, peers, and new hires. Conclusion: Out of the 18 categories, three categori

What we expect from radiology AI algorithms will shape the selection and implementation of AI in the radiologic practice. In this paper I consider prevailing expectations of AI and compare them to expectations that we have of human readers. I observe that the expectations from AI and radiologists are fundamentally different. The expectations of AI are based on a strong and justified mistrust about the way that AI makes decisions. Because AI decisions are not well understood, it is difficult to know how the algorithms will behave in new, unexpected situations. However, this mistrust is not mirrored in our expectations of human readers. Despite well-proven idiosyncrasies and biases in human decision making, we take comfort from the assumption that others make decisions in a way as we do, and we trust our own decision making. Despite poor ability to explain decision making processes in humans, we accept explanations of decisions given by other humans. Because the goal of radiology is the most accurate radiologic interpretation, our expectations of radiologists and AI should be similar, and both should reflect a healthy mistrust of complicated and partially opaque decision processes un

This paper provides a comprehensive, descriptive overview of the current state of digital transformation in the Swiss economy and delineates areas that businesses should keep an eye on. Key findings illustrate that even established technologies are not universally adopted, that companies tend to overestimate their technological status compared to their competitors, and that it is important to have the appropriate technological know-how when introducing new technologies. In addition, companies expect changes in their work processes and employment conditions in connection with the digital transformation. Specifically, work tasks are expected to become more complex, diverse and varied. Employees' knowledge acquisition will gain in importance, especially in the form of formal further training and self-learning. Employees will also be more autonomous in making decisions about their jobs and working hours.

In this article we define a special class of weak expectations for a representation of a separable unital C*-algebra, called decomposable weak expectation. We give necessary and sufficient conditions for such kind of weak expectations to exist for a given representation. Then we define decomposable measures on the state space of a C*-algebra and show that the GNS representation of a state admits a decomposable weak expectation if and only if there is a decomposable measure on the state space. Further we give an example of a decomposable weak expectation.

We show that a restricted version of a conjecture of M. Talagrand on the relation between "expectation thresholds" and "fractional expectation thresholds" follows easily from a strong version of a second conjecture of Talagrand, on "selector processes." The selector process conjecture was proved by Park and Pham, and the quantitative strengthening used here is due to Bednorz, Martynek, and Meller.

Using a survey on wage expectations among students at two Swiss institutions of higher education, we examine the wage expectations of our respondents along two main lines. First, we investigate the rationality of wage expectations by comparing average expected wages from our sample with those of similar graduates; we further examine how our respondents revise their expectations when provided information about actual wages. Second, using causal mediation analysis, we test whether the consideration of a rich set of personal and professional controls, namely concerning family formation and children in addition to professional preferences, accounts for the difference in wage expectations across genders. We find that males and females overestimate their wages compared to actual ones, and that males respond in an overconfident manner to information about outside wages. Despite the attenuation of the gender difference in wage expectations brought about by the comprehensive set of controls, gender generally retains a significant direct, unexplained effect on wage expectations.

Expected Shortfall (ES) in several variants has been proposed as remedy for the defi-ciencies of Value-at-Risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss distributions have discontinuities. In this case even the coherence property of ES can get lost unless one took care of the details in its definition. We compare some of the definitions of Expected Shortfall, pointing out that there is one which is robust in the sense of yielding a coherent risk measure regardless of the underlying distributions. Moreover, this Expected Shortfall can be estimated effectively even in cases where the usual estimators for VaR fail. Key words: Expected Shortfall; Risk measure; worst conditional expectation; tail con-ditional expectation; value-at-risk (VaR); conditional value-at-risk (CVaR); tail mean; co-herence; quantile; sub-additivity.

We show that the standard computational pipeline of probabilistic programming systems (PPSs) can be inefficient for estimating expectations and introduce the concept of expectation programming to address this. In expectation programming, the aim of the backend inference engine is to directly estimate expected return values of programs, as opposed to approximating their conditional distributions. This distinction, while subtle, allows us to achieve substantial performance improvements over the standard PPS computational pipeline by tailoring computation to the expectation we care about. We realize a particular instance of our expectation programming concept, Expectation Programming in Turing (EPT), by extending the PPS Turing to allow so-called target-aware inference to be run automatically. We then verify the statistical soundness of EPT theoretically, and show that it provides substantial empirical gains in practice.