Evaluating language models for mathematics through interactions.

There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs relies on static pairs of inputs and outputs; this is insufficient for making an informed decision about which LLMs are best to use in an interactive setting, and how that varies by setting. Static assessment therefore limits how we understand language model capabilities. We introduce CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We conduct a study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analyzing MathConverse, we derive a taxonomy of human query behaviors and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, among other findings. Further, we garner a more granular understanding of GPT-4 mathematical problem-solving through a series of case studies, contributed by experienced mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models that communicate uncertainty, respond well to user corrections, and can provide a concise rationale for their recommendations, may constitute better assistants. Humans should inspect LLM output carefully given their current shortcomings and potential for surprising fallibility.

Analysis of the risk and pre-emptive control of viral outbreaks accounting for within-host dynamics: SARS-CoV-2 as a case study.

In the era of living with COVID-19, the risk of localised SARS-CoV-2 outbreaks remains. Here, we develop a multiscale modelling framework for estimating the local outbreak risk for a viral disease (the probability that a major outbreak results from a single case introduced into the population), accounting for within-host viral dynamics. Compared to population-level models previously used to estimate outbreak risks, our approach enables more detailed analysis of how the risk can be mitigated through pre-emptive interventions such as antigen testing. Considering SARS-CoV-2 as a case study, we quantify the within-host dynamics using data from individuals with omicron variant infections. We demonstrate that regular antigen testing reduces, but may not eliminate, the outbreak risk, depending on characteristics of local transmission. In our baseline analysis, daily antigen testing reduces the outbreak risk by 45% compared to a scenario without antigen testing. Additionally, we show that accounting for heterogeneity in within-host dynamics between individuals affects outbreak risk estimates and assessments of the impact of antigen testing. Our results therefore highlight important factors to consider when using multiscale models to design pre-emptive interventions against SARS-CoV-2 and other viruses.

Performance of a novel spectroscopy-based tool for adjuvant therapy decision-making in hormone receptor-positive breast cancer: a validation study.

PURPOSE: Digistain Index (DI), measured using an inexpensive mid-infrared spectrometer, reflects the level of aneuploidy in unstained tissue sections and correlates with tumor grade. We investigated whether incorporating DI with other clinicopathological variables could predict outcomes in patients with early breast cancer. METHODS: DI was calculated in 801 patients with hormone receptor-positive, HER2-negative primary breast cancer and ≤ 3 positive lymph nodes. All patients were treated with systemic endocrine therapy and no chemotherapy. Multivariable proportional hazards modeling was used to incorporate DI with clinicopathological variables to generate the Digistain Prognostic Score (DPS). DPS was assessed for prediction of 5- and 10-year outcomes (recurrence, recurrence-free survival [RFS] and overall survival [OS]) using receiver operating characteristics and Cox proportional hazards regression models. Kaplan-Meier analysis evaluated the ability of DPS to stratify risk. RESULTS: DPS was consistently highly accurate and had negative predictive values for all three outcomes, ranging from 0.96 to 0.99 at 5 years and 0.84 to 0.95 at 10 years. DPS demonstrated statistically significant prognostic ability with significant hazard ratios (95% CI) for low- versus high-risk classification for RFS, recurrence and OS (1.80 [CI 1.31-2.48], 1.83 [1.32-2.52] and 1.77 [1.28-2.43], respectively; all P < 0.001). CONCLUSION: DPS showed high accuracy and predictive performance, was able to stratify patients into low or high-risk, and considering its cost and rapidity, has the potential to offer clinical utility.

Contact-number-driven virus evolution: A multi-level modeling framework for the evolution of acute or persistent RNA virus infection.

Viruses evolve in infected host populations, and host population dynamics affect viral evolution. RNA viruses with a short duration of infection and a high peak viral load, such as SARS-CoV-2, are maintained in human populations. By contrast, RNA viruses characterized by a long infection duration and a low peak viral load (e.g., borna disease virus) can be maintained in nonhuman populations, and the process of the evolution of persistent viruses has rarely been explored. Here, using a multi-level modeling approach including both individual-level virus infection dynamics and population-scale transmission, we consider virus evolution based on the host environment, specifically, the effect of the contact history of infected hosts. We found that, with a highly dense contact history, viruses with a high virus production rate but low accuracy are likely to be optimal, resulting in a short infectious period with a high peak viral load. In contrast, with a low-density contact history, viral evolution is toward low virus production but high accuracy, resulting in long infection durations with low peak viral load. Our study sheds light on the origin of persistent viruses and why acute viral infections but not persistent virus infection tends to prevail in human society.

Integrative geochronology calibrates the Middle and Late Stone Ages of Ethiopia's Afar Rift.

The Halibee member of the Upper Dawaitoli Formation of Ethiopia's Middle Awash study area features a wealth of Middle and Later Stone Age (MSA and LSA) paleoanthropological resources in a succession of Pleistocene sediments. We introduce these artifacts and fossils, and determine their chronostratigraphic placement via a combination of established radioisotopic methods and a recently developed dating method applied to ostrich eggshell (OES). We apply the recently developed 230Th/U burial dating of OES to bridge the temporal gap between radiocarbon (14C) and 40Ar/39Ar ages for the MSA and provide 14C ages to constrain the younger LSA archaeology and fauna to ∼24 to 21.4 ka. Paired 14C and 230Th/U burial ages of OES agree at ∼31 ka for an older LSA locality, validating the newer method, and in turn supporting its application to stratigraphically underlying MSA occurrences previously constrained only by a maximum 40Ar/39Ar age. Associated fauna, flora, and Homo sapiens fossils are thereby now fixed between 106 ± 20 ka and 96.4 ± 1.6 ka (all errors 2σ). Additional 40Ar/39 results on an underlying tuff refine its age to 158.1 ± 11.0 ka, providing a more precise minimum age for MSA lithic artifacts, fauna, and H. sapiens fossils recovered ∼9 m below it. These results demonstrate how chronological control can be obtained in tectonically active and stratigraphically complex settings to precisely calibrate crucial evidence of technological, environmental, and evolutionary changes during the African Middle and Late Pleistocene.

Is "sadistic pleasure" a contrived process of signaling one's antagonism?

OBJECTIVE: Sadistic pleasure presumably incorporates processes that support an authentic enjoyment of others' pain. However, antagonism confirmation theory, grounded in social-psychological theorizing on identity maintenance and the notion of ego-syntonicity, suggests that individuals higher in sadism report greater pleasure in response to others' pain because such reports are immoral responses that confirm their self-views. This alternative conception has yet to be tested. METHOD: In two preregistered experiments (total N = 968), participants completed measures of sadism, read about situations involving others' pain, and rated their pleasure. We manipulated the extent to which pleasure from others' pain could be used to signal morality or antagonism. RESULTS: We found that relatively sadistic people indicated greater pleasure across the studies but, like relatively non-sadistic people, they altered their pleasure ratings to signal greater morality or less antagonism. CONCLUSIONS: The findings fail to support antagonism confirmation theory, but they support recent perspectives on sadism that suggest that sadistic people may occasionally care about seeming moral (or not seeming antagonistic) and that sadism may be somewhat ego-dystonic in this respect.

A Closer Examination of the Integrity Scale's Construct Validity.

People's commitment to moral principles affects how they self-regulate and directs people down different ethical paths. The Integrity Scale was designed to assess the strength of people's commitment to moral principles. Here, we sought to contribute to evaluating the construct validity of the Integrity Scale. We related the scale to various theoretically relevant criteria including low antagonism features, social-cognitive foundations for morality, self-control, rationality, and self-presentation behavior. Suggestive of the scale's construct validity, the present research showed that scores on the Integrity Scale related to (a) reduced antagonistic-personality features relevant to exploitation and dishonesty more so than immodesty, tough-heartedness, fearlessness, or cynicism; (b) enhanced social-cognitive skills (e.g., cognitive empathy processes); (c) enhanced self-control; (d) enhanced capacities for and reliance on rationality in decision making (e.g., intelligence and cognitive-reflection skill); and (e) enhanced reliance on self-presentation tactics that portray an identity based in high levels of integrity.

New geological and palaeontological age constraint for the gorilla-human lineage split.

The palaeobiological record of 12 million to 7 million years ago (Ma) is crucial to the elucidation of African ape and human origins, but few fossil assemblages of this period have been reported from sub-Saharan Africa. Since the 1970s, the Chorora Formation, Ethiopia, has been widely considered to contain ~10.5 million year (Myr) old mammalian fossils. More recently, Chororapithecus abyssinicus, a probable primitive member of the gorilla clade, was discovered from the formation. Here we report new field observations and geochemical, magnetostratigraphic and radioisotopic results that securely place the Chorora Formation sediments to between ~9 and ~7 Ma. The C. abyssinicus fossils are ~8.0 Myr old, forming a revised age constraint of the human-gorilla split. Other Chorora fossils range in age from ~8.5 to 7 Ma and comprise the first sub-Saharan mammalian assemblage that spans this period. These fossils suggest indigenous African evolution of multiple mammalian lineages/groups between 10 and 7 Ma, including a possible ancestral-descendent relationship between the ~9.8 Myr old Nakalipithecus nakayamai and C. abyssinicus. The new chronology and fossils suggest that faunal provinciality between eastern Africa and Eurasia had intensified by ~9 Ma, with decreased faunal interchange thereafter. The Chorora evidence supports the hypothesis of in situ African evolution of the Gorilla-Pan-human clade, and is concordant with the deeper divergence estimates of humans and great apes based on lower mutation rates of ~0.5 × 10(-9) per site per year (refs 13 - 15).

Investigating how self-esteem moderates grandiose narcissism's interpersonal orientation.

OBJECTIVE: Most previous research has treated grandiose narcissism and self-esteem as additive predictors of outcomes, but some theory and evidence suggests they may sometimes interact to predict outcomes. Unfortunately, the nature of this interaction is unclear; we suggest a framework to conceptualize the interaction and test it vis-à-vis the interpersonal circumplex framework. METHOD: Participants (N = 598; Mage  = 38.39; 327 females; 72.1% White) reported their levels of grandiose narcissism and self-esteem and completed interpersonal circumplex measures of efficacies, values, problems, and sensitivities. RESULTS: As self-esteem decreased, grandiose narcissism related (a) more negatively to communal efficacies and values and (b) more positively to sensitivity to others' communal behaviors. Also as self-esteem decreased, unexpectedly, grandiose narcissism related (a) more positively to agentic efficacies and problems and (b) more negatively to sensitivity to others' agentic behaviors. CONCLUSION: Overall, the present findings generally support using interaction models over additive models of grandiose narcissism and self-esteem in interpersonal contexts, suggesting that grandiose narcissism becomes generally less communal, more agentic, and more interpersonally problematic as self-esteem decreases.

Self-esteem mediates effects of normal and pathological personality traits on subjective well-being.

As subjective well-being is foundational to understanding people, researchers have sought to uncover its correlates. Some theorizing proposes that effects of broad personality traits on subjective well-being constructs are mediated by self-esteem; unfortunately, evidence pertaining to this idea has been limited to the study of "normal" broad personality traits and limited measures of subjective well-being. Here, we provided a more comprehensive test of this theory, and we examined the dominance of self-esteem over normal and pathological broad personality traits in predicting an array of subjective well-being constructs. In a primarily college sample (N = 272), we found that self-esteem generally mediated the effects of all Five-Factor Model (FFM) traits except Agreeableness and all pathological personality traits-represented in the Personality Inventory of The Diagnostic and Statistical Manual of Mental Disorders traits (5th edition; PID-5)-except Antagonism on a set of subjective well-being measures; moreover, dominance analyses showed that self-esteem was generally more important than any FFM or PID-5 trait in predicting the subjective well-being measures. We discuss limitations of our study along with some of its basic and applied implications.

Key questions for modelling COVID-19 exit strategies.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

Exascale applications: skin in the game.

As noted in Wikipedia, skin in the game refers to having 'incurred risk by being involved in achieving a goal', where 'skin is a synecdoche for the person involved, and game is the metaphor for actions on the field of play under discussion'. For exascale applications under development in the US Department of Energy Exascale Computing Project, nothing could be more apt, with the skin being exascale applications and the game being delivering comprehensive science-based computational applications that effectively exploit exascale high-performance computing technologies to provide breakthrough modelling and simulation and data science solutions. These solutions will yield high-confidence insights and answers to the most critical problems and challenges for the USA in scientific discovery, national security, energy assurance, economic competitiveness and advanced healthcare. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'.

Deprived and Grandiose Explanations for Psychological Entitlement: Implications for Theory and Measurement.

This work aimed to corroborate "vulnerable-based" and "grandiose-based" forms of psychological entitlement by amending the Psychological Entitlement Scale (PES; Campbell, Bonacci, Shelton, Exline, & Bushman, 2004), a popular unidimensional index of psychological entitlement. In 2 studies, participants completed PES items amended to include both deprived-identity-based and grandiose-identity-based rationales for item agreement and various individual-difference measures of constructs related to entitlement, self-evaluation, personality, and interpersonal orientations. The modified PES yielded a grandiose-based (PES-G) and vulnerable-based (PES-V) entitlement scale that showed good psychometric qualities. PES-G and PES-V converged well on core features of psychological entitlement (e.g., antagonistic outcomes) but generally failed to converge on self-evaluation, acquisitive versus defensive forms of entitlement, behavioral inhibition system and behavioral activation system, and interpersonal behavior indicative of claiming and cultivating grandiose versus deprived identities. This research supports the presence of grandiose-based and vulnerable-based entitlement forms, demonstrates a measurement technique to tap these forms, and suggests some theoretical implications.

Entitled Due to Deprivation vs. Superiority: Evidence That Unidimensional Entitlement Scales Blend Distinct Entitlement Rationales across Psychological Dimensions.

We aimed to corroborate the notion that the Psychological Entitlement Scale (PES), a popular unidimensional index of psychological entitlement, resembles a blend of vulnerable- and grandiose-based entitlement rationales across various psychological dimensions. College participants (N = 523) were randomly assigned to complete either the PES or a recently validated, multidimensional adaptation of the PES that purports to assess entitlement due to deprivation (vulnerable-based entitlement; "PES-V") and superiority (grandiose-based entitlement; "PES-G") claims. Participants then completed a battery of psychological dimensions including: narcissism constructs, interpersonal vulnerability and mood pathology, psychological health, normal personality and personality-disorder traits, motivation systems, a deprived identity, and status aspiration. Profile-similarity indices indicated that PES was more similar to PES-G than PES-V across psychological dimensions. Likewise, additional analyses revealed that indicators of "narcissistic entitlement" exhibited stronger profile similarity to PES-G than PES-V across psychological dimensions. In conclusion, profiles of the PES and narcissistic entitlement appear to blend grandiose- and vulnerable-based entitlement, but grandiose-based (vs. vulnerable-based) entitlement seems more prominent in the blend. As a result, unidimensional measures can create a somewhat misleading portrait of the psychologically entitled.

Comparative Biochemical and Structural Analysis of Novel Cellulose Binding Proteins (Tapirins) from Extremely Thermophilic Caldicellulosiruptor Species.

Genomes of extremely thermophilic Caldicellulosiruptor species encode novel cellulose binding proteins, called tapirins, located proximate to the type IV pilus locus. The C-terminal domain of Caldicellulosiruptor kronotskyensis tapirin 0844 (Calkro_0844) is structurally unique and has a cellulose binding affinity akin to that seen with family 3 carbohydrate binding modules (CBM3s). Here, full-length and C-terminal versions of tapirins from Caldicellulosiruptor bescii (Athe_1870), Caldicellulosiruptor hydrothermalis (Calhy_0908), Caldicellulosiruptor kristjanssonii (Calkr_0826), and Caldicellulosiruptor naganoensis (NA10_0869) were produced recombinantly in Escherichia coli and compared to Calkro_0844. All five tapirins bound to microcrystalline cellulose, switchgrass, poplar, and filter paper but not to xylan. Densitometry analysis of bound protein fractions visualized by SDS-PAGE revealed that Calhy_0908 and Calkr_0826 (from weakly cellulolytic species) associated with the cellulose substrates to a greater extent than Athe_1870, Calkro_0844, and NA10_0869 (from strongly cellulolytic species). Perhaps this relates to their specific needs to capture glucans released from lignocellulose by cellulases produced in Caldicellulosiruptor communities. Calkro_0844 and NA10_0869 share a higher degree of amino acid sequence identity (>80% identity) with each other than either does with Athe_1870 (∼50%). The levels of amino acid sequence identity of Calhy_0908 and Calkr_0826 to Calkro_0844 were only 16% and 36%, respectively, although the three-dimensional structures of their C-terminal binding regions were closely related. Unlike the parent strain, C. bescii mutants lacking the tapirin genes did not bind to cellulose following short-term incubation, suggesting a role in cell association with plant biomass. Given the scarcity of carbohydrates in neutral terrestrial hot springs, tapirins likely help scavenge carbohydrates from lignocellulose to support growth and survival of Caldicellulosiruptor species.IMPORTANCE The mechanisms by which microorganisms attach to and degrade lignocellulose are important to understand if effective approaches for conversion of plant biomass into fuels and chemicals are to be developed. Caldicellulosiruptor species grow on carbohydrates from lignocellulose at elevated temperatures and have biotechnological significance for that reason. Novel cellulose binding proteins, called tapirins, are involved in the way that Caldicellulosiruptor species interact with microcrystalline cellulose, and additional information about the diversity of these proteins across the genus, including binding affinity and three-dimensional structural comparisons, is provided here.

Profiles and profile comparisons between Dark Triad constructs on self-presentation tactic usage and tactic beliefs.

OBJECTIVE: The present research profiled antisocial personality constructs in relation to tactical self-presentation behaviors and various beliefs associated with such tactical behavior. METHOD: An MTurk sample (N = 524; Mage  = 37.89; 61% female) completed indices of the Dark Triad (DT; narcissism, Machiavellianism, psychopathy) and self-reported their use of various self-presentation tactics, their beliefs about the subjective logic for executing the tactics (which encompassed ratings of the tactics' utility, ease of execution, and normativity), and the potential for each tactic to arouse self-recrimination. RESULTS: Results revealed high convergence between the DT constructs on a relatively malignant approach to self-presentation. DT constructs related to enhanced usage, enhanced subjective logic, and reduced self-recrimination ratings for all the tactics, except pro-social ones (exemplification and apologizing). Nonetheless, results also revealed some notable anticipated instances of nonconvergences between the DT constructs and tactic usage. CONCLUSIONS: The findings highlight that DT constructs function rather similarly at the level of self-presentation and suggest value in considering the DT constructs as indicative of strategic, subjectively logical image cultivation and defense behavior.

Leasing a medical curriculum: What's it worth?

Introduction: The early part of this century saw an unprecedented growth in number and size of Australian medical schools. There was some partnering of the new schools with existing programs. Griffith, Deakin and Curtin Universities leased an established curriculum from Flinders University. Nature and rationale for curriculum leasing: The new schools had short startup times and leasing a curriculum enabled them to appoint key staff, develop facilities and meet accreditation requirements in a timely way. However, the lease arrangements were costly and the curriculum was largely determined before the Dean and key staff appointments. Outcomes of leasing: There was differential adoption of the leased curriculum. The first two years of the courses at Flinders were transferred with little change. The final two years of predominantly clinical studies were developed differently. This is explained through Michael Fullan's work on context in educational change. The context of the clinical years of the courses involved negotiations with local health services and other schools using those health services. The advantage of the leasing arrangements was that the new schools could proceed through early development and accreditation, while having time and opportunity to negotiate a clinical curriculum that engaged local health services and fulfilled the new schools' missions.

Cleavage of ethers in an ionic liquid. Enhancement, selectivity and potential application.

The cleavage of a series of ethers was examined in an ionic liquid containing hydrogen bromide. Reactions that did not proceed in either water or DMSO were found to proceed readily in this system, with notable selectivity between the cleavage of the different ether types examined herein. Increasing the proportion of water in the reaction mixture dramatically decreased the rate constant of ether cleavage; this could, in part, be attributed to a decrease in the solvent stabilisation of the transition state. Through analysis of the electronic requirements of the reaction (using substrates containing substituents with different Hammett parameters) and observation of rate enhancements for an ortho substituted system, the importance of the extent of protonation of the ether prior to nucleophilic attack was demonstrated.

Association of general and abdominal obesity with age, endocrine and metabolic factors in Asian men.

OBJECTIVE: This study made use of the percent abdominal fat to define abdominal obesity (AbO) and examined the differential associations of general obesity (GOb) and AbO with age, metabolic and endocrine factors. METHODS: Metabolic, endocrine and anthropometric factors and body composition were measured in 481 Asian men. RESULTS: A DEXA-derived ≥25% abdominal fat (PAbdF) was used to define men with AbO. Age was directly associated with PAbdF and percent total body fat (PBF). Exercise intensity was negatively associated with PBF. Both PBF and PAbdF were associated with HDL and LDL, but have opposite correlation with triglyceride. Furthermore, both PBF and PAbdF were associated with the number of metabolic syndrome (MetS) risk factors. Men with GOb had lower levels of percent lean mass (PLM), testosterone and bioavailable testosterone, and higher insulin and glucose levels. Men with AbO had lower arm and leg fat, higher insulin levels and triglycerides. CONCLUSIONS: Men with GOb and AbO had different pattern of body composition. Age may be a contributory factor in AbO and a sedentary lifestyle may contribute to GOb. Both GOb and AbO are associated with an increased risk of MetS, with GOb more predispose to risk of diabetes, while AbO more at risk for cardiovascular diseases.