W odpowiedzi na dające się zauważyć w ostatnim czasie zainteresowanie tematyką aniołów, Autor analizuje Apoftegmaty Ojców Pustyni, czyli najbardziej oryginalne dzieło literatury monastycznej starożytności chrześcijańskiej. Na podstawie facta et dicta tych ekspertów w sprawach duchowych i częstokroć wielkich mistyków, Autor stara się przedstawić funkcjonującą w tym środowisku angelologię, czyli nauczanie mnichów na temat natury, wyglądu i hierarchii aniołów, oraz roli jaką pełnią wobec Boga i ludzi. Zwraca również uwagę na specyficzne postrzeganie aniołów w środowisku Ojców Pustyni. Podsumowując, Autor dochodzi do wniosku, że angelologia Ojców Pustyni, w sensie teologicznym, była kontynuacją nauczania Ojców Kościoła; w sensie ascetycznym, dostrzegała w aniołach ideał życia monastycznego i pomoc w jego realizacji; w sensie eschatologicznym, tchnęła nadzieją i zbawczym optymizmem, jako że aniołowie – zdaniem Ojców Pustyni – są liczniejsi, czyli silniejsi, niż zagrażające ludziom demony.
Early Christian literature. Fathers of the Church, etc., Philosophy of religion. Psychology of religion. Religion in relation to other subjects
Although Large Language Models (LLMs) show exceptional fluency, efforts persist to extract stronger reasoning capabilities from them. Drawing on search-based interpretations of LLM computation, this paper advances a systematic framework for understanding LLM reasoning and optimization. Namely, that enhancing reasoning is best achieved by structuring a multi-agent pipeline to ensure a traversal of the search space in a gradual, incremental, and sequential (GIS) manner. Stated succinctly, high-quality reasoning is a controlled, incremental search. To test this framework, we investigate the efficacy of recursive refinement (RR)--an iterative process of self-criticism, adversarial stress-testing, and integrating critical feedback--as a practical method for implementing GIS search. We designed an experiment comparing a simple, linear pipeline against a complex, explicitly structured pipeline leveraging a recursive refinement layer. The multi-agent models were constructed to reflect the historical personas of three US Founding Fathers (Hamilton, Jefferson, and Madison) using RAG-powered corpora and were prompted to generate responses to three contemporary political issues. Model performance was evaluated using a two-tiered approach: a quantitative score from an LLM arbiter agent and qualitative human judgment. Our results revealed that the complex model consistently outperformed the simple model across all nine test cases with an average arbiter-outputted score of 88.3 versus 71.7. The complex model's arguments were superior in analytical depth, structural nuance, and strategic framing. We conclude that recursive refinement is a robust architectural feature for enhancing LLM reasoning via GIS search.
We present HySemRAG, a framework that combines Extract, Transform, Load (ETL) pipelines with Retrieval-Augmented Generation (RAG) to automate large-scale literature synthesis and identify methodological research gaps. The system addresses limitations in existing RAG architectures through a multi-layered approach: hybrid retrieval combining semantic search, keyword filtering, and knowledge graph traversal; an agentic self-correction framework with iterative quality assurance; and post-hoc citation verification ensuring complete traceability. Our implementation processes scholarly literature through eight integrated stages: multi-source metadata acquisition, asynchronous PDF retrieval, custom document layout analysis using modified Docling architecture, bibliographic management, LLM-based field extraction, topic modeling, semantic unification, and knowledge graph construction. The system creates dual data products - a Neo4j knowledge graph enabling complex relationship queries and Qdrant vector collections supporting semantic search - serving as foundational infrastructure for verifiable information synthesis. Evaluation across 643 observations from 60 testing sessions demonstrates structured field extraction achieving 35.1% higher semantic similarity scores (0.655 $\pm$ 0.178) compared to PDF chunking approaches (0.485 $\pm$ 0.204, p < 0.000001). The agentic quality assurance mechanism achieves 68.3% single-pass success rates with 99.0% citation accuracy in validated responses. Applied to geospatial epidemiology literature on ozone exposure and cardiovascular disease, the system identifies methodological trends and research gaps, demonstrating broad applicability across scientific domains for accelerating evidence synthesis and discovery.
The quantum-Extended Church-Turing thesis has been explored in many physical theories including general relativity but lacks exploration in quantum field theories such as quantum electrodynamics. Through construction of a computational model whose gate set mimics the interactions of QED, we demonstrate that one of the defining features of quantum field theory, particle creation and annihilation, is not likely to violate the quantum-Extended Church-Turing thesis. Through this computational model, it is shown that particle creation is likely only another form of quantum parallelism. However, whether or not the quantum-Extended Church-Turing thesis will hold for all computational devices in quantum field theories is still not known. For example, we briefly examine certain interactions in quantum electrodynamics which may create multi-qubit gates. These gates may have exponential complexity at the cost of being exponentially weak. This may in turn allow for computational advantage over traditional gate sets such as Clifford+T.
Dongwoo T. Chung, Patrick C. Breysse, Kieran A. Cleary
et al.
We present the current state of models for the $z\sim3$ carbon monoxide (CO) line-intensity signal targeted by the CO Mapping Array Project (COMAP) Pathfinder in the context of its early science results. Our fiducial model, relating dark matter halo properties to CO luminosities, informs parameter priors with empirical models of the galaxy-halo connection and previous CO(1-0) observations. The Pathfinder early science data spanning wavenumbers $k=0.051$-$0.62\,$Mpc$^{-1}$ represent the first direct 3D constraint on the clustering component of the CO(1-0) power spectrum. Our 95% upper limit on the redshift-space clustering amplitude $A_{\rm clust}\lesssim70\,μ$K$^2$ greatly improves on the indirect upper limit of $420\,μ$K$^2$ reported from the CO Power Spectrum Survey (COPSS) measurement at $k\sim1\,$Mpc$^{-1}$. The COMAP limit excludes a subset of models from previous literature, and constrains interpretation of the COPSS results, demonstrating the complementary nature of COMAP and interferometric CO surveys. Using line bias expectations from our priors, we also constrain the squared mean line intensity-bias product, $\langle{Tb}\rangle^2\lesssim50\,μ$K$^2$, and the cosmic molecular gas density, $ρ_\text{H2}<2.5\times10^8\,M_\odot\,$Mpc$^{-3}$ (95% upper limits). Based on early instrument performance and our current CO signal estimates, we forecast that the five-year Pathfinder campaign will detect the CO power spectrum with overall signal-to-noise of 9-17. Between then and now, we also expect to detect the CO-galaxy cross-spectrum using overlapping galaxy survey data, enabling enhanced inferences of cosmic star-formation and galaxy-evolution history.
I revisit Jordan's derivation of Einstein's formula for energy fluctuations in the black body in thermal equilibrium. This formula is usually taken to represent the unification of the wave and the particle aspects of the electromagnetic field since the fluctuations can be shown to be the sum of wave-like and particle-like contributions. However, in Jordan's treatment there is no mention of the Planck distribution and all averages are performed with respect to pure number states of radiation (mixed states had not yet been discovered!). The chief reason why Jordan does reproduce Einstein's result despite not using thermal states of radiation is that he focuses on fluctuations in a small (compared to the whole) volume of the black body. The state of radiation in a small volume is highly entangled to the rest of the black body which leads to the correct fluctuations even though the overall state might, in fact, be assumed to be pure (i.e. at zero temperature). I present a simple derivation of the fluctuations formula as an instance of mixed states being reductions of higher level pure states, a representation that is affectionately known as ``Church of the Higher Hilbert Space". According to this view of mixed states, temperature is nothing but the amount of entanglement between the system and its environment.
Although religious ethicists commonly assess the content of public communication to determine its merits, this article argues that the style and techniques of communication deserve similar analysis. Propaganda often employs rhetorical techniques that impress the recipient through persuasive sleight-of-hand or emotional appeal. Drawing on the church fathers’ suspicion of classical rhetoric, as well as Augustine's guarded defense of a specific type of rhetoric, the author formulates two principles of ethical propaganda that may assist public communicators in persuading ethically. These two principles are the procedural movement of beauty from truth, and the use of caritas as a primary motivator in persuasion.
In this paper, we continue our study of blade arrangements and the positroidal subdivisions which are induced by them on $Δ_{k,n}$. A blade is a tropical hypersurface which is generated by a system of $n$ affine simple roots of type $SL_n$ that enjoys a cyclic symmetry. When placed at the center of a simplex, a blade induces a decomposition into $n$ maximal cells which are known as Pitman-Stanley polytopes. We introduce a complex $(B_{k,n},\partial)$ of weighted blade arrangements and we prove that the positive tropical Grassmannian surjects onto the top component of the complex, such that the induced weights on blades in the faces $Δ_{2,n-(k-2)}$ of $Δ_{k,n}$ are (1) nonnegative and (2) their support is weakly separated. We finally introduce a hierarchy of elementary weighted blade arrangements for all hypersimplices which is minimally closed under the boundary maps $\partial$, and apply our result to classify up to isomorphism type all rays of the positive tropical Grassmannian $\text{Trop}_+ G(3,n)$ for $n\le 9$.
We study arrangements of slightly skewed tropical hyperplanes, called blades by A. Ocneanu, on the vertices of a hypersimplex $Δ_{k,n}$, and we investigate the resulting induced polytopal subdivisions. We show that placing a blade on a vertex $e_J$ induces an $\ell$-split matroid subdivision of $Δ_{k,n}$, where $\ell$ is the number of cyclic intervals in the $k$-element subset $J$. We prove that a given collection of $k$-element subsets is weakly separated, in the sense of the work of Leclerc and Zelevinsky on quasicommuting families of quantum minors, if and only if the arrangement of the blade $((1,2,\ldots, n))$ on the corresponding vertices of $Δ_{k,n}$ induces a matroid (in fact, a positroid) subdivision. In this way we obtain a compatibility criterion for (planar) multi-splits of a hypersimplex, generalizing the rule known for 2-splits. We study in an extended example the case $(k,n) = (3,7)$ the set of arrangements of $(k-1)(n-k-1)$ weakly separated vertices of $Δ_{k,n}$.
In recent work of Cachazo, Guevara, Mizera and the author, a generalization of the biadjoint scattering amplitude $m^{(k)}(\mathbb{I}_n,\mathbb{I}_n)$ was introduced as an integral over the moduli space of $n$ points in $\mathbb{CP}^{k-1}$, with value a sum of certain rational functions on the kinematic space $\mathcal{K}_{k,n}$. It was shown there for $m^{(3)}(\mathbb{I}_6,\mathbb{I}_6)$ and later by Cachazo and Rojas that collections of poles appearing in $m^{(3)}(\mathbb{I}_7,\mathbb{I}_7)$ are compatible exactly when they are dual to collections of rays which generate the maximal faces of a polyhedral complex known as the (nonnegative) tropical Grassmannian. In this note, we derive a remarkable planar basis for the space of generalized kinematic invariants which coincides in the case $k=2$ with usual standard planar multi-particle basis for the kinematic space. We implement in Mathematica the action on formal linear combinations of planar matroid subdivisions of a boundary operator which, together with the planar basis, determines compatibility for any given poles appearing in the expansion of $m^{(k)}(\mathbb{I}_n,\mathbb{I}_n)$, by computing a certain combinatorial non-crossing condition on the second hypersimplicial faces $Δ_{2,n-(k-2)}$ of $Δ_{k,n}$. The algorithms are implemented in an accompanying Mathematica notebook and are evaluated on existing tables of rays, in the form of tropical Plucker vectors, to tabulate the finest planar subdivisions of $Δ_{3,8},Δ_{3,9}$ and $ Δ_{4,8}$, or equivalently the set of maximal cones for the corresponding nonnegative tropical Grassmannians.
In this note, we study the permutohedral geometry of the poles of a certain differential form introduced in recent work of Arkani-Hamed, Bai, He and Yan. There it was observed that the poles of the form determine a family of polyhedra which have the same face lattice as that of the permutohedron. We realize that family explicitly, proving that it in fact fills out the configuration space of a particularly well-behaved family of generalized permutohedra, the zonotopal generalized permutohedra, that are obtained as the Minkowski sums of line segments parallel to the root directions $e_i-e_j$. Finally we interpret Mizera's formula for the biadjoint scalar amplitude $m(\mathbb{I}_n,\mathbb{I}_n)$, restricted to a certain dimension $n-2$ subspace of the kinematic space, as a sum over the boundary components of the standard root cone, which is the conical hull of the roots $e_1-e_2,\ldots, e_{n-2}-e_{n-1}$.
We find the largest union of two chains in the type $B$ Tamari lattice by generalizing the techniques used for the classical (type $A$) Tamari lattice with a description of the type $B$ case due to Hugh Thomas.
In this study, a narrative literature review regarding culture and e-commerce website design has been introduced. Cultural aspect and e-commerce website design will play a significant role for successful global e-commerce sites in the future. Future success of businesses will rely on e-commerce. To compete in the global e-commerce marketplace, local businesses need to focus on designing culturally friendly e-commerce websites. To the best of my knowledge, there has been insignificant research conducted on correlations between culture and e-commerce website design. The research shows that there are correlations between e-commerce, culture, and website design. The result of the study indicates that cultural aspects influence e-commerce website design. This study aims to deliver a reference source for information systems and information technology researchers interested in culture and e-commerce website design, and will show lessfocused research areas in addition to future directions.
Recently the media broadcast the news, together with illustrative videos, of a so-called Japanese method to perform multiplication by hand without using the multiplication tables. "Goodbye multiplication tables" was the headline of several websites, including important ones, where news are however too often `re-posted' uncritically. The easy numerical examples could induce naive internauts to believe that, in a short future, multiplications could be really done without the knowledge of multiplication tables. This is what a girl expresses, with great enthusiasm, to her father. The dialogues described here, although not real, are likely and have been inspired by this episode, being Maddalena the daughter of the author. Obviously the revolutionary value of the new method is easily disassembled, while its educational utility is highlighted to show (or remember) the reasoning on which the method learned in elementary school is based, although mostly applied mechanically.
We study three finite-dimensional quotient vector spaces constructed from the linear span of the set of characteristic functions of permutohedral cones by imposing two kinds of constraints: (1) neglect characteristic functions of higher codimension permutohedral cones, and (2) neglect characteristic functions of non-pointed permutohedral cones. We construct an ordered basis which is canonical, in the sense that it has subsets which map onto ordered bases for the quotients. We present straightening relations to the canonical basis, and using Laplace transforms we obtain functional representations for each quotient space.
We formulate conjectures giving combinatorial interpretations of the Ehrhart $h^*$-vector, for hypersimplices, for dilated simplices and for generic cross-sections of cubes, in terms of certain decorated ordered set partitions. All were formulated and checked computationally during our graduate study at Penn State.
The good wife, as Plutrach taught, ought to have no feeling of her own, but she should join with her husband in seriousness and sportiveness, in soberness and laughter. The husband has to be pure and clean from all connexion with others when he approach his wife and her virtue, her exclusive devotion to her husband, her constancy, and her affection, ought to be most in evidence. The man ought to exercise control over the woman, not as the owner has control over a piece of property, but, as the soul colonists the body, by entering into her feelings and being knit to her through goodwill. He is teacher of philosophy, she is his disciple: for his wife husband must collect from every source what is useful and carrying it within his own self impart it to her, and then discusses it with her, and makes the best of these doctrines her favourite and familiar themes.
Early Christian literature. Fathers of the Church, etc., Philosophy of religion. Psychology of religion. Religion in relation to other subjects
In this paper, we announce results from our thesis, which studies for the first time the categorification of the theory of generalized permutohedra. The vector spaces in the categorification are tightly constrained by certain continuity relations which appeared in physics in the mid 20th century. We describe here the action of the symmetric group on the vector spaces in this categorification. Generalized permutohedra are replaced by vector spaces of characteristic functions of polyhedral cones about faces of permutohedra, called plates, due to A. Ocneanu. The symmetric group acts on plates by coordinate permutation. In combinatorics, the Eulerian numbers count the number of permutations with a given number of ascent and descents. The classical Worpitzky identity expands a power $r^p$ as a sum of Eulerian numbers, with binomial coefficients. In our thesis, for the main result we generalize the classical Worpitzky identity to an isomorphism of symmetric group modules, corresponding geometrically to the tiling of a scaled simplex by unit hypersimplices. In the categorification, the volume of a hypersimplex is replaced by the complex-linear dimension of a vector space associated to it. The main technical aspect of the proof of the character formula for the simplex involves a partition of unity of a commutative algebra of translations on a discrete torus, and a certain modular Diophantine equation. A detailed paper is in preparation.
The Church-Turing Thesis confuses numerical computations with symbolic computations. In particular, any model of computability in which equality is not definable, such as the lambda-models underpinning higher-order programming languages, is not equivalent to the Turing model. However, a modern combinatory calculus, the SF-calculus, can define equality of its closed normal forms, and so yields a model of computability that is equivalent to the Turing model. This has profound implications for programming language design.