Searcharxiv⌕ Search

arXiv subjects

Robert Myers

Publications and source records attributed to Robert Myers.

At least 19 recordsLinked to original sources
arXiv2025

Toward precision soil health: A regional framework for site-specific management across Missouri

Effective soil health management is crucial for sustaining agriculture, adopting ecosystem resilience, and preserving water quality. However, Missouri's diverse landscapes limit the effectiveness of broad generalized management recommendations. The lack of resolution in existing soil grouping systems necessitates data driven, site specific insights to guide tailored interventions. To address these critical challenges, a regional soil clustering framework designed to support precision soil health management strategies across the state. The methodology leveraged high resolution SSURGO dataset, explicitly processing soil properties aggregated across the 0 to 30 cm root zone. Multivariate analysis incorporating a variational autoencoder and KMeans clustering was used to group soils with similar properties. The derived clusters were validated using statistical metrics, including silhouette scores and checks against existing taxonomic units, to confirm their spatial coherence. This approach enabled us to delineate soil groups that capture textures, hydraulic properties, chemical fertility, and biological indicators unique to Missouri's diverse agroecological regions. The clustering map identified ten distinct soil health management zones. This alignment of 10 clusters was selected as optimal because it was sufficiently large to capture inherited soil patterns while remaining manageable for practical statewide application. Rooting depth limitation and saturated hydraulic conductivity emerged as principal variables driving soil differentiation. Each management zone is defined by a unique combination of clay, organic matter, pH, and available water capacity. This framework bridges sophisticated data analysis with actionable, site targeted recommendations, enabling conservation planners, and agronomists to optimize management practices and enhance resource efficiency statewide.

stat.AP↗
arXiv2024

Entanglement, Soft Modes, and Celestial CFT

We revisit the calculation of vacuum entanglement entropy in free Maxwell theory in four-dimensional Minkowski spacetime. Weyl invariance allows for this theory to be embedded as a patch inside the Einstein static universe. We use conformal inversions to extend the conformal primary solutions of the equations of motion labelled by a boost-weight $Δ= 1 + iλ$ to an inverted Minkowski patch centered at spacelike infinity of the original patch. For $λ\neq 0$ these solutions admit an expansion in terms of wavefunctions supported in the (future) Milne wedges of the original and inverted Minkowski patches, that diagonalize the respective Milne times. The Minkowski vacuum can then be described as a thermofield double state on these two Milne wedges. We characterize the soft sectors of $λ= 0$ modes supported in the two Milne wedges. Upon reinterpreting the non-pure gauge $λ= 0$ wavefunctions as sourced by image charges in the inverse Minkowski patch, we construct an appropriate entangling constraint in the Minkowski theory, thereby characterizing the physical state space. We show that the edge mode contribution to the vacuum entanglement entropy is due to correlations between the soft charges of the two Milne patches, or equivalently non-trivial conformally soft mode configurations at the entangling surface.

hep-th↗
arXiv2023

BTLM-3B-8K: 7B Parameter Performance in a 3B Parameter Model

We introduce the Bittensor Language Model, called "BTLM-3B-8K", a new state-of-the-art 3 billion parameter open-source language model. BTLM-3B-8K was trained on 627B tokens from the SlimPajama dataset with a mixture of 2,048 and 8,192 context lengths. BTLM-3B-8K outperforms all existing 3B parameter models by 2-5.5% across downstream tasks. BTLM-3B-8K is even competitive with some 7B parameter models. Additionally, BTLM-3B-8K provides excellent long context performance, outperforming MPT-7B-8K and XGen-7B-8K on tasks up to 8,192 context length. We trained the model on a cleaned and deduplicated SlimPajama dataset; aggressively tuned the \textmu P hyperparameters and schedule; used ALiBi position embeddings; and adopted the SwiGLU nonlinearity. On Hugging Face, the most popular models have 7B parameters, indicating that users prefer the quality-size ratio of 7B models. Compacting the 7B parameter model to one with 3B parameters, with little performance impact, is an important milestone. BTLM-3B-8K needs only 3GB of memory with 4-bit precision and takes 2.5x less inference compute than 7B models, helping to open up access to a powerful language model on mobile and edge devices. BTLM-3B-8K is available under an Apache 2.0 license on Hugging Face: https://huggingface.co/cerebras/btlm-3b-8k-base.

cs.AI↗
arXiv2022

Multi stain graph fusion for multimodal integration in pathology

In pathology, tissue samples are assessed using multiple staining techniques to enhance contrast in unique histologic features. In this paper, we introduce a multimodal CNN-GNN based graph fusion approach that leverages complementary information from multiple non-registered histopathology images to predict pathologic scores. We demonstrate this approach in nonalcoholic steatohepatitis (NASH) by predicting CRN fibrosis stage and NAFLD Activity Score (NAS). Primary assessment of NASH typically requires liver biopsy evaluation on two histological stains: Trichrome (TC) and hematoxylin and eosin (H&E). Our multimodal approach learns to extract complementary information from TC and H&E graphs corresponding to each stain while simultaneously learning an optimal policy to combine this information. We report up to 20% improvement in predicting fibrosis stage and NAS component grades over single-stain modeling approaches, measured by computing linearly weighted Cohen's kappa between machine-derived vs. pathologist consensus scores. Broadly, this paper demonstrates the value of leveraging diverse pathology images for improved ML-powered histologic assessment.

eess.IV↗
arXiv2021

Nondeterministic Syntactic Complexity

We introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the `canonical boolean representation' of the syntactic monoid. Equivalently, it is the least number of states of any subatomic nondeterministic acceptor. It turns out that essentially all previous structural work on nondeterministic state-minimality computes this measure. Our approach rests on an algebraic interpretation of nondeterministic finite automata as deterministic finite automata endowed with semilattice structure. Crucially, the latter form a self-dual category.

cs.FL↗
arXiv2020

Pass-Fail Criteria for Scenario-Based Testing of Automated Driving Systems

The MUSICC project has created a proof-of-concept scenario database to be used as part of a type approval process for the verification of automated driving systems (ADS). This process must include a highly automated means of evaluating test results, as manual review at the scale required is impractical. This paper sets out a framework for assessing an ADS's behavioural safety in normal operation (i.e. performance of the dynamic driving task without component failures or malicious actions). Five top-level evaluation criteria for ADS performance are identified. Implementing these requires two types of outcome scoring rule: prescriptive (measurable rules which must always be followed) and risk-based (undesirable outcomes which must not occur too often). Scoring rules are defined in a programming language and will be stored as part of the scenario description. Risk-based rules cannot give a pass/fail decision from a single test case. Instead, a framework is defined to reach a decision for each functional scenario (set of test cases with common features). This considers statistical performance across many individual tests. Implications of this framework for hypothesis testing and scenario selection are identified.

cs.RO↗
arXiv2018

Concordance of Seifert surfaces

This paper proves that every oriented non-disk Seifert surface $F$ for a knot $K$ in $S^3$ is smoothly concordant to a Seifert surface $F^{\prime}$ for a hyperbolic knot $K^{\prime}$ of arbitrarily large volume. This gives a new and simpler proof of the result of Friedl and of Kawauchi that every knot is $S$-equivalent to a hyperbolic knot of arbitrarily large volume. The construction also gives a new and simpler proof of the result of Silver and Whitten and of Kawauchi that for every knot $K$ there is a hyperbolic knot $K^{\prime}$ of arbitrarily large volume and a map of pairs $f:(S^3,K^{\prime})\rightarrow (S^3,K)$ which induces an epimorphism on the knot groups. An example is given which shows that knot Floer homology is not an invariant of Seifert surface concordance. The paper also proves that a set of finite volume hyperbolic 3-manifolds with unbounded Haken numbers has unbounded volumes.

math.GT↗
arXiv2015

Varieties of Languages in a Category

Eilenberg's variety theorem, a centerpiece of algebraic automata theory, establishes a bijective correspondence between varieties of languages and pseudovarieties of monoids. In the present paper this result is generalized to an abstract pair of algebraic categories: we introduce varieties of languages in a category C, and prove that they correspond to pseudovarieties of monoids in a closed monoidal category D, provided that C and D are dual on the level of finite objects. By suitable choices of these categories our result uniformly covers Eilenberg's theorem and three variants due to Pin, Polak and Reutenauer, respectively, and yields new Eilenberg-type correspondences.

cs.FL↗
arXiv2015

Generalized Eilenberg Theorem I: Local Varieties of Languages

We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states that the lattice of all boolean algebras of regular languages over an alphabet Σ closed under derivatives is isomorphic to the lattice of all pseudovarieties of Σ-generated monoids. By applying our method to different categories, we obtain three related results: one, due to Gehrke, Grigorieff and Pin, weakens boolean algebras to distributive lattices, one weakens them to join-semilattices, and the last one considers vector spaces over the binary field.

cs.FL↗
arXiv2007

The Structures of Distant Galaxies I: Galaxy Structures and the Merger Rate to z~3 in the Hubble Ultra-Deep Field

This paper begins a series in which we examine the structures of distant galaxies to directly determine the history of their formation modes. We start this series by examining the structures of z_F850LP < 27 galaxies in the Hubble Ultra-Deep field, the deepest high-resolution optical image taken to date. We investigate a few basic features of galaxy structure using this image. These include: (1) The agreement of visual eye-ball classifications and non-parametric quantitative (CAS, Gini/M_20) methods; (2) How distant galaxy quantitative structures can vary as a function of rest-frame wavelength; and (3) The evolution of distant galaxy structures up to z~3. One of our major conclusions is that the majority of galaxies with z_850 < 27 are peculiar in appearance, and that galaxy assembly is rapidly occurring at these magnitudes, even up to the present time. We find a general agreement between galaxy classification by eye and through quantitative methods, as well as a general agreement between the CAS and the Gini/M_20 parameters. We find that the Gini/M_20 method appears to find a larger number of galaxy mergers than the CAS system, but contains a larger contamination from non-mergers. We furthermore calculate the merger rate of galaxies in the UDF up to z~3, finding an increase with redshift as well as stellar mass, confirming previous work in the Hubble Deep Field. We find that massive galaxies with M_{*} > 10^10 M_0 undergo 4.3_+0.8^-0.8 major galaxy mergers at z < 3, with all of this merging occurring at z > 1.

astro-ph↗
arXiv2006

On embedding the fundamental group of a 3-manifold in one of its knot groups

This paper gives necessary and sufficient conditions on a compact, connected, orientable 3-manifold M for it to contain a knot K such that M-K is irreducible and pi_1(M) embeds in pi_1(M-K). This result provides counterexamples to a conjecture of Lopes and Morales and characterizes those orientable 3-manifolds for which it is true.

math.GT↗
arXiv2005

Stringy Effects During Inflation and Reheating

We consider inflationary cosmology in the context of string compactifications with multiple throats. In scenarios where the warping differs significantly between throats, string and Kaluza-Klein physics can generate potentially observable corrections to the cosmology of inflation and reheating. First we demonstrate that a very low string scale in the ground state compactification is incompatible with a high Hubble scale during inflation, and we propose that the compactification geometry is altered during inflation. In this configuration, the lowest scale is just above the Hubble scale, which is compatible with effective field theory but still leads to potentially observable CMB corrections. Also in the appropriate region of parameter space, we find that reheating leads to a phase of long open strings in the Standard Model sector (before the usual radiation-dominated phase). We sketch the cosmology of the long string phase and we discuss possible observational consequences.

hep-th↗
arXiv2005

End reductions, fundamental groups, and covering spaces of irreducible open 3-manifolds

Suppose M is a connected, open, orientable, irreducible 3-manifold which is not homeomorphic to R^3. Given a compact 3-manifold J in M which satisfies certain conditions, Brin and Thickstun have associated to it an open neighborhood V$ called an end reduction of M at J. It has some useful properties which allow one to extend to M various results known to hold for the more restrictive class of eventually end irreducible open 3-manifolds. In this paper we explore the relationship of V and M with regard to their fundamental groups and their covering spaces. In particular we give conditions under which the inclusion induced homomorphism on fundamental groups is an isomorphism. We also show that if M has universal covering space homeomorphic to R^3, then so does V. This work was motivated by a conjecture of Freedman (later disproved by Freedman and Gabai) on knots in M which are covered by a standard set of lines in R^3.

math.GT↗
arXiv2004

The complex of end reductions of a contractible open 3-manifold: constructing 1-dimensional examples

Given an irreducible contractible open 3-manifold W which is not homeomorphic to R^3, there is an associated simplicial complex S(W), the complex of end reductions of W. Whenever W covers a 3-manifold M one has that the fundamental group of M is isomorphic to a subgroup of the group Aut(S(W)) of simplicial automorphisms of W. In this paper we give a new method for constructing examples W with S(W) isomorphic to a triangulation of R. It follows that any 3-manifold M covered by W must have infinite cyclic fundamental group. We also give a complete isotopy classification of the end reductions of W.

math.GT↗
arXiv2002

End reductions and covering spaces of contractible open 3-manifolds

This paper uses Brin and Thickstun's theory of end reductions of non-compact 3-manifolds to study groups of covering translations of irreducible contractible open 3-manifolds W which are not homeomorphic to R^3. We associate to W an object S(W) called the simplicial complex of minimal R^2-irreducible end reductions of W. Whenever W covers another 3-manifold the group of covering translations is isomorphic to a fixed point free group of automorphisms of S(W). We apply this result to give uncountably many examples of R^2-irreducible such W which cover 3-manifolds with infinite cyclic fundamental group and non-trivially cover only 3-manifolds with infinite cyclic fundamental group. We also give uncountably many examples of R^2-irreducible W which are not eventually end irreducible and do not non-trivially cover any 3-manifold.

math.GT↗
arXiv1999

Splitting homomorphisms and the Geometrization Conjecture

This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings-Jaco theorem which established a similar result for the Poincare Conjecture. The paper also gives two other algebraic conjectures; one is equivalent to the finite fundamental group case of the Geometrization Conjecture, and the other is equivalent to the union of the Geometrization Conjecture and Thurston's Virtual Bundle Conjecture.

math.GT↗
arXiv1998

On covering translations and homeotopy groups of contractible open n-manifolds

This paper gives a new proof of a result of Geoghegan and Mihalik which states that whenever a contractible open $n$-manifold $W$ which is not homeomorphic to $\mathbf{R}^n$ is a covering space of an $n$-manifold $M$ and either $n \geq 4$ or $n=3$ and $W$ is irreducible, then the group of covering translations injects into the homeotopy group of $W$.

math.GT↗