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John Collins

Publications and source records attributed to John Collins.

At least 19 recordsLinked to original sources
arXiv2025

Multi-Point Proximity Encoding For Vector-Mode Geospatial Machine Learning

Vector-mode geospatial data -- points, lines, and polygons -- must be encoded into an appropriate form in order to be used with traditional machine learning and artificial intelligence models. Encoding methods attempt to represent a given shape as a vector that captures its essential geometric properties. This paper presents an encoding method based on scaled distances from a shape to a set of reference points within a region of interest. The method, MultiPoint Proximity (MPP) encoding, can be applied to any type of shape, enabling the parameterization of machine learning models with encoded representations of vector-mode geospatial features. We show that MPP encoding possesses the desirable properties of shape-centricity and continuity, can be used to differentiate spatial objects based on their geometric features, and can capture pairwise spatial relationships with high precision. In all cases, MPP encoding is shown to perform better than an alternative method based on rasterization.

cs.LG↗
arXiv2023

On the definition of fragmentation functions and the violation of sum rules

We point out a problem with the formulation and derivations of sum rules for quark fragmentation functions that impacts their validity in QCD, but which potentially points toward an improved understanding of final states in inclusive hard processes. Fragmentation functions give the distribution of final-state hadrons arising from a parton exiting a hard scattering, and the sum rules for momentum, electric charge, etc express conservation of these quantities. The problem arises from a mismatch between the quark quantum numbers of the initial quark and the fact that all observed final-state hadrons are confined bound states with color zero. We point that, in a confining theory like QCD, the Wilson line in the operator definition of a fragmentation function entails that the final state in a fragmentation function includes a bound state in the external field generated by the Wilson line. We justify this with the aid of general features of string hadronization. The anomalous bound states are restricted to fractional momentum $z=0$. They tend to invalidate sum rules like the one for charge conservation when applied to the fragmentation functions inferred from experimental data, but not the momentum sum rule. We propose to exploit our ideas in future studies as a way to relate the ffs extracted from inclusive cross sections to more detailed non-perturbative descriptions of final state hadronization. We also describe scenarios wherein the traditional sum rules might remain approximately valid with a reasonably high degree of accuracy.

hep-ph↗
arXiv2021

Positivity and renormalization of parton densities

There have been recent debates about whether $\overline{\text{MS}}$ parton densities exactly obey positivity bounds (including the Soffer bound), and whether the bounds should be applied as a constraint on global fits to parton densities and on nonperturbative calculations. A recent paper (JHEP ${\bf \text{11}}$ (2020) 129) appears to provide a proof of positivity in contradiction with earlier work by other authors. We examine their derivation and find that its primary failure is in the apparently uncontroversial statement that bare pdfs are always positive. We show that under the conditions used in the derivation, that statement fails. We provide some elementary calculations in a model QFT that show how this situation can generically arise in reality. In addition, we observe that the methods used in the derivation are in common with much, but not all, other work where factorization is derived. Our examination pinpoints considerable difficulties with these methods that render them either wrong or highly problematic. The issue of positivity highlights that these methods can lead to wrong results of phenomenological importance. From our analysis we identify the restricted situations in which positivity can be violated.

hep-ph↗
arXiv2020

A new and complete proof of the Landau condition for pinch singularities of Feynman graphs and other integrals

The Landau equations give a physically useful criterion for how singularities arise in Feynman amplitudes. Furthermore, they are fundamental to the uses of perturbative QCD, by determining the important regions of momentum space in asymptotic problems. Generalizations are also useful. We will show that in existing treatments there are significant gaps in derivations, and in some cases implicit assumptions that will be shown here to be false in important cases like the massless Feynman graphs ubiquitous in QCD applications. In this paper is given a new proof that the Landau condition is both necessary and sufficient for physical-region pinches in the kinds of integral typified by Feynman graphs. The proof's range is broad enough to include the modified Feynman graphs that are used in QCD applications. Unlike many existing derivations, there is no need to use the Feynman parameter method. Some possible further applications of the new proof and its subsidiary results are proposed.

hep-ph↗
arXiv2019

A new approach to the LSZ reduction formula

Lehmann, Symanzik and Zimmermann (LSZ) proved a theorem showing how to obtain the S-matrix from time-ordered Green functions. Their result, the reduction formula, is fundamental to practical calculations of scattering processes. A known problem is that the operators that they use to create asymptotic states create much else besides the intended particles for a scattering process. In the infinite-time limits appropriate to scattering, the extra contributions only disappear in matrix elements with normalizable states, rather than in the created states themselves, i.e., the infinite-time limits of the LSZ creation operators are weak limits. The extra particles that are created are in a different region of space-time than the intended scattering process. To be able to work with particle creation at non-asymptotic times, e.g., to give a transparent and fully deductive treatment for scattering with long-lived unstable particles, it is necessary to have operators for which the infinite-time limits are strong limits. In this paper, I give an improved method of constructing such operators. I use them to give an improved systematic account of scattering theory in relativistic quantum field theories, including a new proof of the reduction formula. I make explicit calculations to illustrate the problems with the LSZ operators and their solution with the new operators. Not only do these verify the existence of the extra particles created by the LSZ operators and indicate a physical interpretation, but they also show that the extra components are so large that their contribution to the norm of the state is ultra-violet divergent in renormalizable theories. Finally, I discuss the relation of this work to the work of Haag and Ruelle on scattering theory.

hep-ph↗
arXiv2018

The non-triviality of the vacuum in light-front quantization: An elementary treatment

It is often stated that the vacuum is trivial when light-front (null-plane) quantization is applied to a quantum field theory, in contrast to the situation with equal-time quantization. In fact, it is has long been known that the statement is false, and that in certain cases the standard rules for light-front perturbation theory need modification. This paper gives an elementary review of these issues, including an explanation of how and when there is a failure of the elementary derivation of the rules for light-front perturbation theory.

hep-ph↗
arXiv2018

Graphical Structure of Hadronization and Factorization in Hard Collisions

Models of hadronization of hard jets in QCD are often presented in terms of Feynman-graph structures that can be thought of as effective field theory approximations to dynamical non-perturbative physics in QCD. Such models can be formulated as a kind of multiperipheral model. We obtain general constraints on such models in order for them to be self-consistent, and we relate the constraints to the space-time structure of hadronization. We show that appropriate models can be considered as implementing string-like hadronization. When the models are put in a multiperipheral form, the effective vertices and/or lines must be momentum non-conserving: they take 4-momentum from the external string-like field.

hep-ph↗
arXiv2017

Connecting Different TMD Factorization Formalisms in QCD

In the original Collins-Soper-Sterman (CSS) presentation of the results of transverse-momentum-dependent (TMD) factorization for the Drell-Yan process, results for perturbative coefficients can be obtained from calculations for collinear factorization. Here we show how to use these results, plus known results for the quark form factor, to obtain coefficients for TMD factorization in more recent formulations, e.g., that due to Collins, and apply them to known results at order $\alpha_s^2$ and $\alpha_s^3$. We also show that the "non-perturbative" functions as obtained from fits to data are equal in the two schemes. We compile the higher-order perturbative inputs needed for the updated CSS scheme by appealing to results obtained in a variety of different formalisms. In addition, we derive the connection between both versions of the CSS formalism and several formalisms based in soft-collinear effective theory (SCET). Our work uses some important new results for factorization for the quark form factor, which we derive.

hep-ph↗
arXiv2016

Do fragmentation functions in factorization theorems correctly treat non-perturbative effects?

Current all-orders proofs of factorization of hard processes are made by extracting the leading power behavior of Feynman graphs, i.e., by extracting asymptotics strictly order-by-order in perturbation theory. The resulting parton densities and fragmentation functions include non-perturbative effects. I show how there are missing elements in the proofs; these are related to and exemplified by string and cluster models of hadronization. The proofs rely on large rapidity differences between different parts of graphs for the process; but in reality large rapidity gaps are filled in

hep-ph↗
arXiv2016

TMD Evolution at Moderate Hard Scales

We summarize some of our recent work on non-perturbative transverse momentum dependent (TMD) evolution, emphasizing aspects that are necessary for dealing with moderately low scale processes like semi-inclusive deep inelastic scattering.

hep-ph↗
arXiv2015

TMD factorization and evolution at large $b_T$

In using transverse-momentum-dependent (TMD) parton densities and fragmentation functions, important non-perturbative information is at large transverse position $b_T$. This concerns both the TMD functions and their evolution. Fits to high energy data tend to predict too rapid evolution when extrapolated to low energies where larger values of $b_T$ dominate. I summarize a new analysis of the issues. It results in a proposal for much weaker $b_T$ dependence at large $b_T$ for the evolution kernel, while preserving the accuracy of the existing fits. The results are particularly important for using transverse-spin-dependent functions like the Sivers function.

hep-ph↗
arXiv2014

Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel

There is considerable controversy about the size and importance of nonperturbative contributions to the evolution of transverse-momentum-dependent (TMD) parton distribution functions. Standard fits to relatively high-energy Drell-Yan data give evolution that when taken to lower Q is too rapid to be consistent with recent data in semi-inclusive deeply inelastic scattering. Some authors provide very different forms for TMD evolution, even arguing that nonperturbative contributions at large transverse distance b_T are not needed or are irrelevant. Here, we systematically analyze the issues, both perturbative and nonperturbative. We make a motivated proposal for the parameterization of the nonperturbative part of the TMD evolution kernel that could give consistency: with the variety of apparently conflicting data, with theoretical perturbative calculations where they are applicable, and with general theoretical nonperturbative constraints on correlation functions at large distances. We propose and use a scheme- and scale-independent function A(b_T) that gives a tool to compare and diagnose different proposals for TMD evolution. We also advocate for phenomenological studies of A(b_T) as a probe of TMD evolution. The results are important generally for applications of TMD factorization. In particular, they are important to making predictions for proposed polarized Drell-Yan experiments to measure the Sivers function.

hep-ph↗
arXiv2014

Two-population model for MTL neurons: The vast majority are almost silent

Recordings in the human medial temporal lobe have found many neurons that respond to pictures (and related stimuli) of just one particular person out of those presented. It has been proposed that these are concept cells, responding to just a single concept. However, a direct experimental test of the concept cell idea appears impossible, because it would need the measurement of the response of each cell to enormous numbers of other stimuli. Here we propose a new statistical method for analysis of the data, that gives a more powerful way to analyze how close data are to the concept-cell idea. It exploits the large number of sampled neurons, to give sensitivity to situations where the average response sparsity is to much less than one response for the number of presented stimuli. We show that a conventional model where a single sparsity is postulated for all neurons gives an extremely poor fit to the data. In contrast a model with two dramatically different populations give an excellent fit to data from the hippocampus and entorhinal cortex. In the hippocampus, one population has 7% of the cells with a 2.6% sparsity. But a much larger fraction 93% respond to only 0.1% of the stimuli. This results in an extreme bias in the reported responsive of neurons compared with a typical neuron. Finally, we show how to allow for the fact that some of reported identified units correspond to multiple neurons, and find that our conclusions at the neural level are quantitatively changed but strengthened, with an even stronger difference between the two populations.

q-bio.NC↗
arXiv2014

Multi-Level Anomaly Detection on Time-Varying Graph Data

This work presents a novel modeling and analysis framework for graph sequences which addresses the challenge of detecting and contextualizing anomalies in labelled, streaming graph data. We introduce a generalization of the BTER model of Seshadhri et al. by adding flexibility to community structure, and use this model to perform multi-scale graph anomaly detection. Specifically, probability models describing coarse subgraphs are built by aggregating probabilities at finer levels, and these closely related hierarchical models simultaneously detect deviations from expectation. This technique provides insight into a graph's structure and internal context that may shed light on a detected event. Additionally, this multi-scale analysis facilitates intuitive visualizations by allowing users to narrow focus from an anomalous graph to particular subgraphs or nodes causing the anomaly. For evaluation, two hierarchical anomaly detectors are tested against a baseline Gaussian method on a series of sampled graphs. We demonstrate that our graph statistics-based approach outperforms both a distribution-based detector and the baseline in a labeled setting with community structure, and it accurately detects anomalies in synthetic and real-world datasets at the node, subgraph, and graph levels. To illustrate the accessibility of information made possible via this technique, the anomaly detector and an associated interactive visualization tool are tested on NCAA football data, where teams and conferences that moved within the league are identified with perfect recall, and precision greater than 0.786.

cs.SI↗
arXiv2014

Different approaches to TMD Evolution with scale

Many apparently contradictory approaches to TMD factorization and its non-perturbative content exist. This talk evaluated the different methods and proposed tools for resolving the contradictions and experimentally adjudicating the results.

hep-ph↗
arXiv2013

The Removal of Numerical Drift from Scientific Models

Computer programs often behave differently under different compilers or in different computing environments. Relative debugging is a collection of techniques by which these differences are analysed. Differences may arise because of different interpretations of errors in the code, because of bugs in the compilers or because of numerical drift, and all of these were observed in the present study. Numerical drift arises when small and acceptable differences in values computed by different systems are integrated, so that the results drift apart. This is well understood and need not degrade the validity of the program results. Coding errors and compiler bugs may degrade the results and should be removed. This paper describes a technique for the comparison of two program runs which removes numerical drift and therefore exposes coding and compiler errors. The procedure is highly automated and requires very little intervention by the user. The technique is applied to the Weather Research and Forecasting model, the most widely used weather and climate modelling code.

cs.SE↗
arXiv2012

CSS Equation, etc, Follow from Structure of TMD Factorization

I show that the forms of the Collins-Soper-Sterman and renormalization-group equations for the evolution of transverse-momentum-dependent (TMD) parton densities in QCD follow from the structure of TMD factorization. A derivation does not need to directly use detailed properties of the operator definition of the TMD parton densities.

hep-ph↗