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We fix the notion of parity complex by a judicious selection from among the axioms originally considered by Street. We show that parity complexes so defined, together with the morphisms of parity complexes defined by Verity, form a category equivalent to the category of strong Steiner complexes (nés augmented directed complexes with strongly loop-free unital bases). To this end, we isolate the purely combinatorial structure possessed by the bases of free augmented directed complexes. This analysis reveals the essential advantage of Steiner's formalism to be that the role of subsets in Street's formalism is played instead by multisets.
Low-rank adaptation (LoRA) has emerged as the de facto standard for parameter-efficient fine-tuning (PEFT) of foundation models, enabling the adaptation of billion-parameter networks with minimal computational and memory overhead. Despite its empirical success and rapid proliferation of variants, it remains elusive which architectural choices, optimization techniques, and deployment constraints should guide practical method selection. This overview revisits LoRA through the lens of signal processing (SP), bridging modern adapter designs with classical low-rank modeling tools and inverse problems, as well as highlighting how SP principles can inform principled advances of fine-tuning approaches. Rather than providing a comprehensive enumeration and empirical comparisons of LoRA variants, emphasis is placed on the technical mechanisms underpinning these approaches to justify their effectiveness. These advances are categorized into three complementary axes: architectural design, efficient optimization, and pertinent applications. The first axis builds on singular value decomposition (SVD)-based factorization, rank-augmentation constructions, and cross-layer tensorization, while the se
We argue that second order logic is a weaker form of set theory, despite the fact that the former is formalized in a second order langauge and the latter in a first order language. Along the way, we review the history of interactions between second order logic and set theory, as well as some modern trends.
The development of Large Language Models (LLMs) requires robust benchmarks that encompass not only academic domains but also industrial fields to effectively evaluate their applicability in real-world scenarios. In this paper, we introduce two Korean expert-level benchmarks. KMMLU-Redux, reconstructed from the existing KMMLU, consists of questions from the Korean National Technical Qualification exams, with critical errors removed to enhance reliability. KMMLU-Pro is based on Korean National Professional Licensure exams to reflect professional knowledge in Korea. Our experiments demonstrate that these benchmarks comprehensively represent industrial knowledge in Korea. We release our dataset publicly available.
The BlueWalker 3 satellite is now fainter than during the first months after deployment. The greatest improvement is that the average maximum luminosity near zenith has been reduced from magnitude 1.0 to 2.2. However, the spacecraft is still usually bright enough to interfere with astronomical research.
The Noether procedure carries an inherent ambiguity due to the necessary local extension, no longer a symmetry, of the global symmetry. The gauging should fix the ambiguity once and for all, however, and, for translations, the general covariance demands us to use the Lie derivative. We argue that, with this alone and without any further tweaking, the Noether energy-momentum $\hat{\mathbb{T}}$ must equal the symmetric counterpart, $T$, inevitably and show the equality explicitly for general tensors. For spinors, a subtlety with the Lie derivative itself enters the issue and leads us to the Kosmann lift, often unnoticed by the physics community, from which $T=\hat{\mathbb{T}}$ again emerges straightforwardly and in a naturally symmetric form. Finally, we address how the same Kosmann lift affects the anomaly computations and show that the diffeomorphism anomaly from the seminal paper must be halved, while the venerable anomaly polynomials themselves stand unaffected. We discuss the ramifications of these findings.
In the study of the Political Resource Curse (Brollo et al.,2013), the authors identified a new channel to investigate whether the windfalls of resources are unambiguously beneficial to society, both with theory and empirical evidence. This paper revisits the framework with a new dataset. Specifically, we implemented a regression discontinuity design and difference-in-difference specification
We reconsider the ellipsoid method for linear inequalities. Using the ellipsoid representation of Burrell and Todd, we show the method can be viewed as coordinate descent on the volume of an enclosing ellipsoid, or on a potential function, or on both. The method can be enhanced by improving the lower bounds generated and by allowing the weights on inequalities to be decreased as well as increased, while still guaranteeing a decrease in volume. Three different initialization schemes are described, and preliminary computational results given. Despite the improvements discussed, these are not encouraging.
Conic programming has well-documented merits in a gamut of signal processing and machine learning tasks. This contribution revisits a recently developed first-order conic descent (CD) solver, and advances it in three aspects: intuition, theory, and algorithmic implementation. It is found that CD can afford an intuitive geometric derivation that originates from the dual problem. This opens the door to novel algorithmic designs, with a momentum variant of CD, momentum conic descent (MOCO) exemplified. Diving deeper into the dual behavior CD and MOCO reveals: i) an analytically justified stopping criterion; and, ii) the potential to design preconditioners to speed up dual convergence. Lastly, to scale semidefinite programming (SDP) especially for low-rank solutions, a memory efficient MOCO variant is developed and numerically validated.
We investigate for viable models of inflation that can successfully produce dark matter (DM) from inflaton decay process, satisfying all the constraints from Cosmic Microwave Background (CMB) and from some other observations. In particular, we analyze near-inflection-point small field inflationary scenario with non-thermal production of fermionic DM from the decaying inflaton field during the reheating era. To this end, we propose two different models of inflation with polynomial potential. The potential of Model I contains terms proportional to linear, quadratic, and quartic in inflaton; whereas in Model II, the potential contains only even power of inflaton and the highest term is sextic in inflaton. For both the models, we find out possible constraints on the model parameters which lead to proper inflationary parameters from CMB data with a very small tensor-to-scalar ratio, as expected from a small-field model. With the allowed parameter space from CMB, we then search for satisfactory relic abundance for DM, that can be produced from inflaton via reheating, to match with the present-day cold dark matter (CDM) relic density for the parameter spaces of the DM $χ$ mass and Yukawa
This paper examines the current state of the science underlying cybersecurity research with an emphasis on the non-signature-based intrusion detection domain. First, the paper re-examines the base-rate fallacy originally published by Axelsson, putting the impact of false positives into context. Given the relative high numbers of false positives, the paper argues for deeper analysis of false positives, akin to the analysis that true positives are treated to. The second section of the paper examines the metrics being used to analyze non-signature intrusion detection techniques, the current status quo of employed metrics, and the impact of the status quo on scientific advancement. Finally, the paper analyzes the use of online attack graphs and their applicability, especially in scenarios of constrained environments, such as Internet of Things devices. The use of offline attack graphs in such constrained environments is also examined. In essence, a deep dive review identified multiple areas throughout the field in which the effectiveness and validity of the scientific method can be greatly improved, e.g., through removal of logical fallacies.
We present an analysis of 39 nuclei and their early-type hosts in the Virgo Cluster using ten broadband filters: F300W, F475W, F850LP, F160W, $u^*griz$, and $K_s$. We describe the Virgo Redux program, which provides high-resolution UV and NIR imaging. Combining this data with optical and NIR imaging from the ACS Virgo Cluster Survey and the Next Generation Virgo Cluster Survey, we estimate masses, metallicities and ages using simple stellar population (SSP) models. For 19 nuclei, we compare to SSP parameters derived from Keck and Gemini spectra and find reasonable agreement between the photometric and spectroscopic metallicity: the RMS scatter is 0.3 dex. We reproduce the nucleus-galaxy mass fraction of $0.33^{+0.09}_{-0.07}$ percent for galaxy stellar masses $10^{8.4}-10^{10.3} M_\odot$ with a typical precision of $\sim$35% for the nuclei masses. Based on available model predictions, there is no single preferred formation scenario for nuclei, suggesting that nuclei are formed stochastically through a mix of processes. Nuclei metallicities are statistically identical to those of their hosts, appearing $0.07 \pm 0.3$ dex more metal-rich on average -- although, omitting galaxies with
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter values, we provide a practical default Bayes factor which is straightforward to interpret. To illustrate our methodology, we provide examples where evidence for a Bayesian strikingly supports the null, but leads to rejection under a classical test. Finally, we conclude with directions for future research.
I correct some recent misunderstandings about, and amplify some details of, an old explicit non-geometrical derivation of GR.
We present the results of a recent re-reduction of the data from the Very Large Array (VLA) Low-frequency Sky Survey (VLSS). We used the VLSS catalog as a sky model to correct the ionospheric distortions in the data and create a new set of sky maps and corresponding catalog at 73.8 MHz. The VLSS Redux (VLSSr) has a resolution of 75 arcsec, and an average map RMS noise level of $σ\sim0.1$ Jy beam$^{-1}$. The clean bias is $0.66\timesσ$, and the theoretical largest angular size is 36 arcmin. Six previously un-imaged fields are included in the VLSSr, which has an unbroken sky coverage over 9.3 sr above an irregular southern boundary. The final catalog includes 92,964 sources. The VLSSr improves upon the original VLSS in a number of areas including imaging of large sources, image sensitivity, and clean bias; however the most critical improvement is the replacement of an inaccurate primary beam correction which caused source flux errors which vary as a function of radius to nearest pointing center in the VLSS.
We study the existence of D-brane bound states at threshold in Type II string theories. In a number of situations, we can reduce the question of existence to quadrature, and the study of a particular limit of the propagator for the system of D-branes. This involves a derivation of an index theorem for a family of non-Fredholm operators. In support of the conjectured relation between compactified eleven-dimensional supergravity and Type IIA string theory, we show that a bound state exists for two coincident zero-branes. This result also provides support for the conjectured description of M-theory as a matrix model. In addition, we provide further evidence that there are no BPS bound states for two and three-branes twice wrapped on Calabi-Yau vanishing cycles.
A solvable molecular collision model that predicts Aharonov-Bohm (AB) like scattering in the adiabatic approximation is introduced. For it, we propagate coupled channel wave packets without resorting to a Born-Oppenheimer (BO) approximation. In those, exact, solutions we find evidence of topological phase dislocation lines that are independent of the collision energy and provide definitive signatures of AB-like scattering. The results of these simulations contrast with the conclusions of a recent study that suggests survival of the molecular Aharonov-Bohm (MAB) effect only in the adiabatic limit in which the nuclear reduced mass $μ\rightarrow \infty$. We discuss generalizations of this model and consider possible screening of the Mead-Truhlar vector potential by the presence of multiple conical intersections (CI). We demonstrate that the Wilson loop phase integral has the value $-1$ if it encloses an odd-number of CI's, and takes the value $+1$ for an even number. Within the scope of this model, we investigate the ultra-cold limit of scattering solutions in the presence of a conical intersection and comment on the relevance of Wigner threshold behavior for s-wave scattering.
I develop the solution to the problem of an electron confined in a composite quadratic well subject to a simple, external periodic force. The method of solution illustrates several of the basic techniques useful in formally solving the one-dimensional, time-dependent Schrodinger equation. One of the aims of this exercise is to see how far is it possible to push analytics, before plowing into numerical methods. I hope this presentation of the problem may result useful to others seeking to gain additional experience in the details of solving the time-dependent Schrodinger equation in one space dimension.
We introduce the LLM agent architecture Agentic Redux, intended for use with nontrivial problem domains that require linear auditability. Using the typed lambda calculus, we prove that, run on appropriate domains, Agentic Redux executions are semantically guaranteed to be correct, with all decisions recorded in an append-only ledger. We present two production-grade appropriate domains, in healthcare billing compliance, and security vulnerability disclosure. Working code for Agentic Redux run on both domains is available in a supporting code repository. We also introduce Ontology-First Agent Design, a methodology for creation of agent frameworks on a problem domain, in which a human expert ontologizes the problem domain with Basic Formal Ontology, and then assigns an LLM to derive roles that agents and humans-in-the-loop can fill, in order to work the problems in the domain.
Maybe not. We identify and analyse errors in the popular Massive Multitask Language Understanding (MMLU) benchmark. Even though MMLU is widely adopted, our analysis demonstrates numerous ground truth errors that obscure the true capabilities of LLMs. For example, we find that 57% of the analysed questions in the Virology subset contain errors. To address this issue, we introduce a comprehensive framework for identifying dataset errors using a novel error annotation protocol. Then, we create MMLU-Redux, which is a subset of 5,700 manually re-annotated questions across all 57 MMLU subjects. We estimate that 6.49% of MMLU questions contain errors. Using MMLU-Redux, we demonstrate significant discrepancies with the model performance metrics that were originally reported. Our results strongly advocate for revising MMLU's error-ridden questions to enhance its future utility and reliability as a benchmark. https://huggingface.co/datasets/edinburgh-dawg/mmlu-redux-2.0.