Temporal Point Processes (TPPs) are widely used for modeling event sequences in various medical domains, such as disease onset prediction, progression analysis, and clinical decision support. Although TPPs effectively capture temporal dynamics, their lack of interpretability remains a critical challenge. Recent advancements have introduced interpretable TPPs. However, these methods fail to incorporate numerical features, thereby limiting their ability to generate precise predictions. To address this issue, we propose Hybrid-Rule Temporal Point Processes (HRTPP), a novel framework that integrates temporal logic rules with numerical features, improving both interpretability and predictive accuracy in event modeling. HRTPP comprises three key components: basic intensity for intrinsic event likelihood, rule-based intensity for structured temporal dependencies, and numerical feature intensity for dynamic probability modulation. To effectively discover valid rules, we introduce a two-phase rule mining strategy with Bayesian optimization. To evaluate our method, we establish a multi-criteria assessment framework, incorporating rule validity, model fitting, and temporal predictive accuracy
Content moderation systems are typically evaluated by measuring agreement with human labels. In rule-governed environments this assumption fails: multiple decisions may be logically consistent with the governing policy, and agreement metrics penalize valid decisions while mischaracterizing ambiguity as error -- a failure mode we term the Agreement Trap. We formalize evaluation as policy-grounded correctness and introduce the Defensibility Index (DI) and Ambiguity Index (AI). To estimate reasoning stability without additional audit passes, we introduce the Probabilistic Defensibility Signal (PDS), derived from audit-model token logprobs. We harness LLM reasoning traces as a governance signal rather than a classification output by deploying the audit model not to decide whether content violates policy, but to verify whether a proposed decision is logically derivable from the governing rule hierarchy. We validate the framework on 193,000+ Reddit moderation decisions across multiple communities and evaluation cohorts, finding a 33-46.6 percentage-point gap between agreement-based and policy-grounded metrics, with 79.8-80.6% of the model's false negatives corresponding to policy-grounde
We establish a Murnaghan--Nakayama rule for the irreducible characters of the cyclotomic Hecke algebra $\mathscr H_{m,n}(q,u)$ on Shoji's standard elements. Combined with Shoji's determinacy result, our formula provides a direct combinatorial route to the full irreducible character table of $\mathscr H_{m,n}(q,u)$. Our construction is based on our recent multi-parameter Murnaghan--Nakayama rule for Macdonald polynomials and specializes uniformly to several previously known formulas, including those for the complex reflection group of type $G(m,1,n)$ and the Iwahori--Hecke algebras of types $A$ and $B$. In a dual framework, using the vertex operator realization of Schur functions, we also derive a complementary iterative formula for irreducible characters on upper multipartitions, which may be viewed as a dual Murnaghan--Nakayama rule. As applications, we obtain a Regev-type formula and a Lübeck--Prasad--Adin--Roichman-type formula for cyclotomic Hecke algebras, extending the corresponding formulas for the Iwahori--Hecke algebra of type $A$ and the complex reflection group, respectively. We further introduce the notion of multiple bitrace for cyclotomic Hecke algebras and give a gen
We show that the quadratic measure need not be postulated, but follows from the compatibility of two structural features of physical processes: linear reversible evolution prior to the formation of persistent records, and multiplicative composition of outcome weights once such records are established. Reversible evolution combines configurations additively at the level of a compatibility parameter, while the formation of persistent records induces a multiplicative structure on the weights assigned to physically realized outcomes. Requiring consistency between these two regimes constrains the admissible weight assignment to be quadratic in the associated amplitude. The Born rule therefore emerges as the unique measure compatible with reversible linear evolution and irreversible record formation, without assuming a probabilistic interpretation or a specific quantum formalism.
Large language models (LLMs) have shown incredible performance in completing various real-world tasks. The current paradigm of knowledge learning for LLMs is mainly based on learning from examples, in which LLMs learn the internal rule implicitly from a certain number of supervised examples. However, this learning paradigm may not well learn those complicated rules, especially when the training examples are limited. We are inspired that humans can learn the new tasks or knowledge in another way by learning from rules. That is, humans can learn new tasks or grasp new knowledge quickly and generalize well given only a detailed rule and a few optional examples. Therefore, in this paper, we aim to explore the feasibility of this new learning paradigm, which targets on encoding rule-based knowledge into LLMs. We further propose rule distillation, which first uses the strong in-context abilities of LLMs to extract the knowledge from the textual rules, and then explicitly encode the knowledge into the parameters of LLMs by learning from the above in-context signals produced inside the model. Our experiments show that making LLMs learn from rules by our method is much more efficient than e
Details of the contents and the formulations of the Born rule changed considerably from its inception by Born in 1926 to the present day. This paper traces the early history of the Born rule 100 years ago, its generalization (essential for today's quantum optics and quantum information theory) to POVMs around 50 years ago, and a modern derivation from an intuitive definition of the notion of a quantum detector. It is based to a large extent on little known results from the recent books 'Coherent Quantum Physics' (2019) by A. Neumaier and 'Algebraic Quantum Physics, Vol. 1' (2024) by A. Neumaier and D. Westra, Also discussed is the extent to which the various forms of the Born rule have, like any other statement in physics, a restricted domain of validity, which leads to problems when applied outside this domain.
The risk-sensitive foraging theory formulated in terms of the (daily) energy budget rule has been influential in behavioural ecology as well as other disciplines. Predicting risk-aversion on positive budgets and risk-proneness on negative budgets, however, the budget rule has recently been challenged both empirically and theoretically. In this paper, we critically review these challenges as well as the original derivation of the budget rule and propose a `gradual' budget rule, which is normatively derived from a gradual nature of risk sensitivity and encompasses the conventional budget rule as a special case. The gradual budget rule shows that the conventional budget rule holds when the expected reserve is close enough to a threshold for overnight survival, selection pressure being significant. The gradual view also reveals that the conventional budget rule does not need to hold when the expected reserve is not close enough to the threshold, selection pressure being insignificant. The proposed gradual budget rule better fits the empirical findings including those that used to challenge the conventional budget rule.
The quantum mechanics postulate called the Born Rule attributes a probabilistic meaning to a wave function. This paper derives the Born Rule from other quantum principles along with a model of the measurement process. The nondeterministic nature of quantum measurements is hypothesized to arise from an ignorance of the quantum states of a measuring device's microscopic components. Their interactions with a system to be measured are modeled heuristically with any member of a particular class of stochastic processes, each of which generate the Born Rule. One member of the class appears particularly compatible with properties expected of quantum interactions.
We consider a housing market model with limited externalities where agents care both about their own consumption via demand preferences and about the agent who receives their endowment via supply preferences (we extend the associated lexicographic preference domains introduced in Klaus and Meo, 2023). If preferences are demand lexicographic, then our model extends the classical Shapley-Scarf housing market (Shapley and Scarf, 1974) with strict preferences model. Our main result is a characterization of the corresponding top trading cycles (TTC) rule by individual rationality, pair efficiency, and strategy-proofness (Theorem 1), which extends that of Ekici (2024) from classical Shapley-Scarf housing markets with strict preferences to our model. Two further characterizations are immediately obtained by strengthening pair efficiency to either Pareto efficiency or pairwise stability (Corollaries 1 and 2). Finally, we show that as soon as we extend the preference domain to include demand lexicographic as well as supply lexicographic preferences (e.g., when preferences are separable), no rule satisfying individual rationality, pair efficiency, and strategy-proofness exists (Theorem 2).
Association rule mining plays vital part in knowledge mining. The difficult task is discovering knowledge or useful rules from the large number of rules generated for reduced support. For pruning or grouping rules, several techniques are used such as rule structure cover methods, informative cover methods, rule clustering, etc. Another way of selecting association rules is based on interestingness measures such as support, confidence, correlation, and so on. In this paper, we study how rule clusters of the pattern Xi - Y are distributed over different interestingness measures.
Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the ontological content of a proper physical model to the epistemic conditions of the experimental context. More precisely, it is assumed that all knowable distinctions should correspond to distinctions in a proper model. This principle of "ontological completeness" means, for example, that the probabilistic treatment of the double slit experiment with and without path information should differ. Further, it is assumed that the model should rely only on knowable ontological elements, and that failure to fulfill this principle of "ontological minimalism" gives rise to wrong predictions. Consequently, probabilities should be assigned only to observable experimental outcomes. Also, the method to calculate such probabilities should not rely on the existence of a precise path of the observed object if this path is not knowable. A similar principle was promoted by Born, even though he did not apply it to probability. Another crucial assumption is that the proper
We describe an approach to programming rule-based systems in Standard ML, with a focus on so-called overlapping rules, that is rules that can still be active when other rules are fired. Such rules are useful when implementing rule-based reactive systems, and to that effect we show a simple implementation of Loyall's Active Behavior Trees, used to control goal-directed agents in the Oz virtual environment. We discuss an implementation of our framework using a reactive library geared towards implementing those kind of systems.
We show how to construct a deterministic nearest-neighbour cellular automaton (CA) with four states which emulates diffusion on a one-dimensional lattice. The pseudo-random numbers needed for directing random walkers in the diffusion process are generated with the help of rule 30. This CA produces density profiles which agree very well with solutions of the diffusion equation, and we discuss this agreement for two different boundary and initial conditions. We also show how our construction can be generalized to higher dimensions.
Rule-based policy and contract systems have rarely been studied in terms of their software engineering properties. This is a serious omission, because in rule-based policy or contract representation languages rules are being used as a declarative programming language to formalize real-world decision logic and create IS production systems upon. This paper adopts an SE methodology from extreme programming, namely test driven development, and discusses how it can be adapted to verification, validation and integrity testing (V&V&I) of policy and contract specifications. Since, the test-driven approach focuses on the behavioral aspects and the drawn conclusions instead of the structure of the rule base and the causes of faults, it is independent of the complexity of the rule language and the system under test and thus much easier to use and understand for the rule engineer and the user.
The rule technological landscape is becoming ever more complex, with an extended number of specifications and products. It is therefore becoming increasingly difficult to integrate rule-driven components and manage interoperability in multi-rule engine environments. The described work presents the possibility to provide a common interface for rule-driven components in a distributed system. The authors' approach leverages on a set of discovery protocol, rule interchange and user interface to alleviate the environment's complexity.
Association rule mining aims to explore large transaction databases for association rules. Classical Association Rule Mining (ARM) model assumes that all items have the same significance without taking their weight into account. It also ignores the difference between the transactions and importance of each and every itemsets. But, the Weighted Association Rule Mining (WARM) does not work on databases with only binary attributes. It makes use of the importance of each itemset and transaction. WARM requires each item to be given weight to reflect their importance to the user. The weights may correspond to special promotions on some products, or the profitability of different items. This research work first focused on a weight assignment based on a directed graph where nodes denote items and links represent association rules. A generalized version of HITS is applied to the graph to rank the items, where all nodes and links are allowed to have weights. This research then uses enhanced HITS algorithm by developing an online eigenvector calculation method that can compute the results of mutual reinforcement voting in case of frequent updates. For Example in Share Market Shares price may
Many problems in quantum dynamics can be cast as the decay of a single quantum state into a continuum. The time-dependent overlap with the initial state, called the fidelity, characterizes this decay. We derive an analytic expression for the fidelity after a quench to an ergodic Hamiltonian. The expression is valid for both weak and strong quenches, and timescales before finiteness of the Hilbert space limits the fidelity. It reproduces initial quadratic decay and asymptotic exponential decay with a rate which, for strong quenches, differs from Fermi's golden rule. The analysis relies on the statistical Jacobi approximation (SJA), which was originally applied in nearly localized systems, and which we here adapt to well-thermalizing systems. Our results demonstrate that the SJA is predictive in disparate regimes of quantum dynamics.
The Bjorken sum rule and R ratio are constructed to $O(a^4)$ in the Landau gauge in the three momentum subtraction schemes of Celmaster and Gonsalves where $a$ $=$ $g^2/(16π^2)$. We aim to examine the issue of convergence for observables in the various schemes as well as to test ideas on whether using the discrepancy in different scheme values is a viable and more quantum field theoretic alternative to current ways of estimating the theory error on a measureable.
An important problem to be addressed within Event-Driven Architecture (EDA) is how to correctly and efficiently capture and process the event/action-based logic. This paper endeavors to bridge the gap between the Knowledge Representation (KR) approaches based on durable events/actions and such formalisms as event calculus, on one hand, and event-condition-action (ECA) reaction rules extending the approach of active databases that view events as instantaneous occurrences and/or sequences of events, on the other. We propose formalism based on reaction rules (ECA rules) and a novel interval-based event logic and present concrete RuleML-based syntax, semantics and implementation. We further evaluate this approach theoretically, experimentally and on an example derived from common industry use cases and illustrate its benefits.
Neutrino mass sum rules relate the three neutrino masses within generic classes of flavour models, leading to restrictions on the effective mass parameter measured in experiments on neutrinoless double beta decay as a function of the lightest neutrino mass. We perform a comprehensive study of the implications of such neutrino mass sum rules, which provide a link between model building, phenomenology, and experiments. After a careful explanation of how to derive predictions from sum rules, we discuss a large number of examples both numerically, using all three global fits available for the neutrino oscillation data, and analytically wherever possible. In some cases, our results disagree with some of those in the literature for reasons that we explain. Finally we discuss the experimental prospects for many current and near-future experiments, with a particular focus on the uncertainties induced by the unknown nuclear physics involved. We find that, in many cases, the power of the neutrino mass sum rules is so strong as to allow certain classes of models to be tested by the next generation of neutrinoless double beta decay experiments. Our study can serve as both a guideline and a the