A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization

This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios

A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization

This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios

Deploying a New Hash Algorithm

The strength of hash functions such as MD5 and SHA-1 has been called into question as a result of recent discoveries. Regardless of whether or not it is necessary to move away from those now, it is clear that it will be necessary to do so in the not-too-distant future. This poses a number of challenges, especially for certificate-based protocols. We analyze a number of protocols, including S/MIME and TLS. All require protocol or implementation changes. We explain the necessary changes, show how the conversion can be done, and list what measures should be taken immediately

A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization

This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios

A Dutch Book Theorem and Converse Dutch Book Theorem for Kolmogorov Conditionalization

This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios

Rats distinguish between absence of events and lack of evidence in contingency learning.

The goal of three experiments was to study whether rats are aware of the difference between absence of events and lack of evidence. We used a Pavlovian extinction paradigm in which lights consistently signaling sucrose were suddenly paired with the absence of sucrose. The crucial manipulation involved the absent outcomes in the extinction phase. Whereas in the Cover conditions, access to the drinking receptacle was blocked by a metal plate, in the No Cover conditions, the drinking receptacle was accessible. The Test phase showed that in the Cover conditions, the measured expectancies of sucrose were clearly at a higher level than in the No Cover conditions. We compare two competing theories potentially explaining the findings. A cognitive theory interprets the observed effect as evidence that the rats were able to understand that the cover blocked informational access to the outcome information, and therefore the changed learning input did not necessarily signify a change of the underlying contingency in the world. An alternative associationist account, renewal theory, might instead explain the relative sparing of extinction in the Cover condition as a consequence of context change. We discuss the merits of both theories as accounts of our data and conclude that the cognitive explanation is in this case preferred

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets

Understanding the Operative Experience of the Practicing Pediatric Surgeon: Implications for Training and Maintaining Competency

Importance The number of practicing pediatric surgeons has increased rapidly in the past 4 decades, without a significant increase in the incidence of rare diseases specific to the field. Maintenance of competency in the index procedures for these rare diseases is essential to the future of the profession. Objective To describe the demographic characteristics and operative experiences of practicing pediatric surgeons using Pediatric Surgery Board recertification case log data. Design, Setting, and Participants We performed a retrospective review of 5 years of pediatric surgery certification renewal applications submitted to the Pediatric Surgery Board between 2009 and 2013. A surgeon’s location was defined by population as urban, large rural, small rural, or isolated. Case log data were examined to determine case volume by category and type of procedures. Surgeons were categorized according to recertification at 10, 20, or 30 years. Main Outcome and Measure Number of index cases during the preceding year. Results Of 308 recertifying pediatric surgeons, 249 (80.8%) were men, and 143 (46.4%) were 46 to 55 years of age. Most of the pediatric surgeons (304 of 308 [98.7%]) practiced in urban areas (ie, with a population >50 000 people). All recertifying applicants were clinically active. An appendectomy was the most commonly performed procedure (with a mean [SD] number of 49.3 [35.0] procedures per year), nonoperative trauma management came in second (with 20.0 [33.0] procedures per year), and inguinal hernia repair for children younger than 6 months of age came in third (with 14.7 [13.8] procedures per year). In 6 of 10 “rare” pediatric surgery cases, the mean number of procedures was less than 2. Of 308 surgeons, 193 (62.7%) had performed a neuroblastoma resection, 170 (55.2%) a kidney tumor resection, and 123 (39.9%) an operation to treat biliary atresia or choledochal cyst in the preceding year. Laparoscopy was more frequently performed in the 10-year recertification group for Nissen fundoplication, appendectomy, splenectomy, gastrostomy/jejunostomy, orchidopexy, and cholecystectomy (P < .05) but not lung resection (P = .70). It was more frequently used by surgeons recertifying in the 10-year group (used in 11 375 of 14 456 procedures [78.7%]) than by surgeons recertifying in the 20-year (used in 6214 of 8712 procedures [71.3%]) or 30-year group (used in 2022 of 3805 procedures [53.1%]). Conclusions and Relevance Practicing pediatric surgeons receive limited exposure to index cases after training. With regard to maintaining competency in an era in which health care outcomes have become increasingly important, these results are concerning