arXiv subjects

Chris Jones

Publications and source records attributed to Chris Jones.

At least 19 recordsLinked to original sources

arXiv2026

State transitions in land-vegetation systems emerge at Paris Agreement warming levels in CMIP6

Using an automatic detection workflow applied to the Coupled Model Intercomparison Project Phase 6 (CMIP6) ensemble under future emission scenarios, we identify 47 abrupt and more gradually developing state transitions in the land-vegetation component of the Earth system, classified into 9 categories. Over the Amazon, we find state transitions via vegetation dieback alongside greening cases; the contrast between them is traced primarily to differences in precipitation: models showing dieback experience either a larger absolute decline in precipitation, or one that translates more efficiently into soil moisture loss, particularly near the surface, while in greening models the CO$_2$ fertilization effect wins out where the soil moisture loss remains weaker. The precipitation decline in dieback-prone models appears driven through a weakening of moist convection. Across these Amazon cases, models with dynamic vegetation undergo dieback, whereas greening is confined to models with prescribed vegetation distributions. African cases include greening over eastern-central Africa and the Congo basin, and an abrupt soil-moisture drying also over the Congo. At high latitudes, boreal forest expands, while permafrost thaws once the regional above-zero temperatures persist for more than half the year. Additional categories cover transitions to a reduced snow-cover state over northeastern North America, increased vegetation biomass near the Tibetan Plateau and southeastern Asia, and increased leaf-area index over the northeast Northern America. Of particular concern, a global warming of 2$^\circ$C or below, within reach of the Paris Agreement targets, is already enough to trigger the onset of the majority of the identified categories in CMIP6.

physics.ao-ph↗

arXiv2026

Universality of first-order methods on random and deterministic matrices

General first-order methods (GFOM) are a flexible class of iterative algorithms which update a state vector by matrix-vector multiplications and entrywise nonlinearities. A long line of work has sought to understand the large-n dynamics of GFOM, mostly focusing on "very random" input matrices and the approximate message passing (AMP) special case of GFOM whose state is asymptotically Gaussian. Yet, it has long remained unknown how to construct iterative algorithms that retain this Gaussianity for more structured inputs, or why existing AMP algorithms can be as effective for some deterministic matrices as they are for random matrices. We analyze diagrammatic expansions of GFOM via the limiting traffic distribution of the input matrix, the collection of all limiting values of permutation-invariant polynomials in the matrix entries, to obtain the following results: 1. We calculate the traffic distribution for the first non-trivial deterministic matrices, including (minor variants of) the Walsh-Hadamard and discrete sine and cosine transform matrices. This determines the limiting dynamics of GFOM on these inputs, resolving parts of longstanding conjectures of Marinari, Parisi, and Ritort (1994). 2. We design a new AMP iteration which unifies several previous AMP variants and generalizes to new input types, whose limiting dynamics are Gaussian conditional on some latent random variables. The asymptotic dynamics hold for a large and natural class of traffic distributions (encompassing both random and deterministic input matrices) and the algorithm's analysis gives a simple combinatorial interpretation of the Onsager correction, answering questions posed recently by Wang, Zhong, and Fan (2022).

math.PR↗

arXiv2026

The Grothendieck Constant is Strictly Larger than Davie-Reeds' Bound

The Grothendieck constant $K_{G}$ is a fundamental quantity in functional analysis, with important connections to quantum information, combinatorial optimization, and the geometry of Banach spaces. Despite decades of study, the value of $K_{G}$ is unknown. The best known lower bound on $K_{G}$ was obtained independently by Davie and Reeds in the 1980s. In this paper we show that their bound is not optimal. We prove that $K_{G} \ge K_{DR} + 10^{-12}$, where $K_{DR}$ denotes the Davie-Reeds lower bound. Our argument is based on a perturbative analysis of the Davie-Reeds operator. We show that every near-extremizer for the Davie-Reeds problem has $\Omega(1)$ weight on its degree-3 Hermite coefficients, and therefore introducing a small cubic perturbation increases the integrality gap of the operator.

math.FA↗

arXiv2025

Predicting the spatial distribution and demographics of commercial swine farms in the United States

Data on livestock farm locations and demographics are essential for disease monitoring, risk assessment, and developing spatially explicit epidemiological models. Our semantic segmentation model achieved an F2 score of 92 % and a mean Intersection over Union of 76 %. An initial total of 194,474 swine barn candidates were identified in the Southeast (North Carolina = 111,135, South Carolina = 37,264 Virginia = 46,075) and 524,962 in the Midwest (Iowa = 168,866 Minnesota = 165,714 Ohio = 190,382). The post processing Random Forest classifier reduced false positives by 82 % in the Southeast and 88 % in the Midwest, resulting in 45,580 confirmed barn polygons. These were grouped into 16,976 predicted farms and classified into one of the four production types. Population sizes were then estimated using the Random Forest regression model, with prediction accuracy varying by production type. Across all farms, 87 % of predictions for operations with 1,000 2,000 pigs were within 500 pigs of the reference value, with nursery farms showing the highest agreement (R2= 0.82), followed by finisher farms (R2 = 0.77) and sow farms (R2 = 0.56). Our results revealed substantial gaps in the existing spatial and demographic data on U.S. swine production.

stat.AP↗

arXiv2025

Higher-order Delsarte Dual LPs: Lifting, Constructions and Completeness

A central and longstanding open problem in coding theory is the rate-versus-distance trade-off for binary error-correcting codes. In a seminal work, Delsarte introduced a family of linear programs establishing relaxations on the size of optimum codes. To date, the state-of-the-art upper bounds for binary codes come from dual feasible solutions to these LPs. Still, these bounds are exponentially far from the best-known existential constructions. Recently, hierarchies of linear programs extending and strengthening Delsarte's original LPs were introduced for linear codes, which we refer to as higher-order Delsarte LPs. These new hierarchies were shown to provably converge to the actual value of optimum codes, namely, they are complete hierarchies. Therefore, understanding them and their dual formulations becomes a valuable line of investigation. Nonetheless, their higher-order structure poses challenges. In fact, analysis of all known convex programming hierarchies strengthening Delsarte's original LPs has turned out to be exceedingly difficult and essentially nothing is known, stalling progress in the area since the 1970s. Our main result is an analysis of the higher-order Delsarte LPs via their dual formulation. Although quantitatively, our current analysis only matches the best-known upper bounds, it shows, for the first time, how to tame the complexity of analyzing a hierarchy strengthening Delsarte's original LPs. In doing so, we reach a better understanding of the structure of the hierarchy, which may serve as the foundation for further quantitative improvements. We provide two additional structural results for this hierarchy. First, we show how to \emph{explicitly} lift any feasible dual solution from level $k$ to a (suitable) larger level $\ell$ while retaining the objective value. Second, we give a novel proof of completeness using the dual formulation.

cs.IT↗

arXiv2024

Sparsest cut and eigenvalue multiplicities on low degree Abelian Cayley graphs

Whether or not the Sparsest Cut problem admits an efficient $O(1)$-approximation algorithm is a fundamental algorithmic question with connections to geometry and the Unique Games Conjecture. Revisiting spectral algorithms for Sparsest Cut, we present a novel, simple algorithm that combines eigenspace enumeration with a new algorithm for the Cut Improvement problem. The runtime of our algorithm is parametrized by a quantity that we call the solution dimension $\text{SD}_\varepsilon(G)$: the smallest $k$ such that the subspace spanned by the first $k$ Laplacian eigenvectors contains all but $\varepsilon$ fraction of a sparsest cut. Our algorithm matches the guarantees of prior methods based on the threshold-rank paradigm, while also extending beyond them. To illustrate this, we study its performance on low degree Cayley graphs over Abelian groups -- canonical examples of graphs with poor expansion properties. We prove that low degree Abelian Cayley graphs have small solution dimension, yielding an algorithm that computes a $(1+\varepsilon)$-approximation to the uniform Sparsest Cut of a degree-$d$ Cayley graph over an Abelian group of size $n$ in time $n^{O(1)}\cdot\exp(d/\varepsilon)^{O(d)}$. Along the way to bounding the solution dimension of Abelian Cayley graphs, we analyze their sparse cuts and spectra, proving that the collection of $O(1)$-approximate sparsest cuts has an $\varepsilon$-net of size $\exp(d/\varepsilon)^{O(d)}$ and that the multiplicity of $\lambda_2$ is bounded by $2^{O(d)}$. The latter bound is tight and improves on a previous bound of $2^{O(d^2)}$ by Lee and Makarychev.

cs.DS↗

arXiv2024

Low-degree Security of the Planted Random Subgraph Problem

The planted random subgraph detection conjecture of Abram et al. (TCC 2023) asserts the pseudorandomness of a pair of graphs $(H, G)$, where $G$ is an Erdos-Renyi random graph on $n$ vertices, and $H$ is a random induced subgraph of $G$ on $k$ vertices. Assuming the hardness of distinguishing these two distributions (with two leaked vertices), Abram et al. construct communication-efficient, computationally secure (1) 2-party private simultaneous messages (PSM) and (2) secret sharing for forbidden graph structures. We prove the low-degree hardness of detecting planted random subgraphs all the way up to $k\leq n^{1 - \Omega(1)}$. This improves over Abram et al.'s analysis for $k \leq n^{1/2 - \Omega(1)}$. The hardness extends to $r$-uniform hypergraphs for constant $r$. Our analysis is tight in the distinguisher's degree, its advantage, and in the number of leaked vertices. Extending the constructions of Abram et al, we apply the conjecture towards (1) communication-optimal multiparty PSM protocols for random functions and (2) bit secret sharing with share size $(1 + \epsilon)\log n$ for any $\epsilon > 0$ in which arbitrary minimal coalitions of up to $r$ parties can reconstruct and secrecy holds against all unqualified subsets of up to $\ell = o(\epsilon \log n)^{1/(r-1)}$ parties.

cs.CR↗

arXiv2024

Low inertia reversing geodynamos

Convection driven geodynamo models in rotating spherical geometry have regimes in which reversals occur. However, reversing dynamo models are usually found in regimes where the kinetic and magnetic energy is comparable, so that inertia is playing a significant role in the dynamics. In the Earth's core, the Rossby number is very small, and the magnetic energy is much larger than the kinetic energy. Here we investigate dynamo models in the strong field regime, where magnetic forces have a significant effect on convection. In the core, the strong field is achieved by having the magnetic Prandtl number Pm small, but the Ekman number E extremely small. In simulations, very small E is not possible, but the strong field regime can be reached by increasing Pm. However, if Pm is raised while the fluid Prandtl number is fixed at unity, the most common choice, the Peclet number number becomes small, so that the linear terms in the heat (or composition) equation dominate, which is also far from Earth-like behaviour. Here we increase Pr and Pm together, so that nonlinearity is important in the heat equation and the dynamo is strong field. We find that Earth-like reversals are possible at numerically achievable parameter values, and the simulations have Earth-like magnetic fields away from the times at which it reverses. The magnetic energy is much greater than the kinetic energy except close to reversal times.

physics.geo-ph↗

arXiv2024

Fourier Analysis of Iterative Algorithms

We study a general class of nonlinear iterative algorithms which includes power iteration, belief propagation and approximate message passing, and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we use Boolean Fourier analysis to analyze these algorithms as low-degree polynomials in the entries of the input matrix. Each symmetrized Fourier character represents all monomials with a certain shape as specified by a small graph, which we call a Fourier diagram. We prove fundamental asymptotic properties of the Fourier diagrams: over the randomness of the input, all diagrams with cycles are negligible; the tree-shaped diagrams form a basis of asymptotically independent Gaussian vectors; and, when restricted to the trees, iterative algorithms exactly follow an idealized Gaussian dynamic. We use this to prove a state evolution formula, giving a "complete" asymptotic description of the algorithm's trajectory. The restriction to tree-shaped monomials mirrors the assumption of the cavity method, a 40-year-old non-rigorous technique in statistical physics which has served as one of the most important techniques in the field. We demonstrate how to implement cavity method derivations by 1) restricting the iteration to its tree approximation, and 2) observing that heuristic cavity method-type arguments hold rigorously on the simplified iteration. Our proofs use combinatorial arguments similar to the trace method from random matrix theory. Finally, we push the diagram analysis to a number of iterations that scales with the dimension $n$ of the input matrix, proving that the tree approximation still holds for a simple variant of power iteration all the way up to $n^{\Omega(1)}$ iterations.

cs.CC↗

arXiv2023

A Ceph S3 Object Data Store for HEP

We present a novel data format design that obviates the need for data tiers by storing individual event data products in column objects. The objects are stored and retrieved through Ceph S3 technology, with a layout designed to minimize metadata volume and maximize data processing parallelism. Performance benchmarks of data storage and retrieval are presented.

physics.data-an↗

arXiv2023

Evaluating The Impact Of Species Specialisation On Ecological Network Robustness Using Analytic Methods

Ecological networks describe the interactions between different species, informing us of how they rely on one another for food, pollination and survival. If a species in an ecosystem is under threat of extinction, it can affect other species in the system and possibly result in their secondary extinction as well. Understanding how (primary) extinctions cause secondary extinctions on ecological networks has been considered previously using computational methods. However, these methods do not provide an explanation for the properties which make ecological networks robust, and can be computationally expensive. We develop a new analytic model for predicting secondary extinctions which requires no non-deterministic computational simulation. Our model can predict secondary extinctions when primary extinctions occur at random or due to some targeting based on the number of links per species or risk of extinction, and can be applied to an ecological network of any number of layers. Using our model, we consider how false positives and negatives in network data affect predictions for network robustness. We have also extended the model to predict scenarios in which secondary extinctions occur once species lose a certain percentage of interaction strength, and to model the loss of interactions as opposed to just species extinction. From our model, it is possible to derive new analytic results such as how ecological networks are most robust when secondary species degree variance is minimised. Additionally, we show that both specialisation and generalisation in distribution of interaction strength can be advantageous for network robustness, depending upon the extinction scenario being considered.

q-bio.PE↗

arXiv2023

Sum-of-Squares Lower Bounds for Densest $k$-Subgraph

Given a graph and an integer $k$, Densest $k$-Subgraph is the algorithmic task of finding the subgraph on $k$ vertices with the maximum number of edges. This is a fundamental problem that has been subject to intense study for decades, with applications spanning a wide variety of fields. The state-of-the-art algorithm is an $O(n^{1/4 + \epsilon})$-factor approximation (for any $\epsilon > 0$) due to Bhaskara et al. [STOC '10]. Moreover, the so-called log-density framework predicts that this is optimal, i.e. it is impossible for an efficient algorithm to achieve an $O(n^{1/4 - \epsilon})$-factor approximation. In the average case, Densest $k$-Subgraph is a prototypical noisy inference task which is conjectured to exhibit a statistical-computational gap. In this work, we provide the strongest evidence yet of hardness for Densest $k$-Subgraph by showing matching lower bounds against the powerful Sum-of-Squares (SoS) algorithm, a meta-algorithm based on convex programming that achieves state-of-art algorithmic guarantees for many optimization and inference problems. For $k \leq n^{\frac{1}{2}}$, we obtain a degree $n^{\delta}$ SoS lower bound for the hard regime as predicted by the log-density framework. To show this, we utilize the modern framework for proving SoS lower bounds on average-case problems pioneered by Barak et al. [FOCS '16]. A key issue is that small denser-than-average subgraphs in the input will greatly affect the value of the candidate pseudoexpectation operator around the subgraph. To handle this challenge, we devise a novel matrix factorization scheme based on the positive minimum vertex separator. We then prove an intersection tradeoff lemma to show that the error terms when using this separator are indeed small.

cs.CC↗

arXiv2023

Spatiotemporal relative risk distribution of porcine reproductive and respiratory syndrome virus in the southeastern United States

Porcine reproductive and respiratory syndrome virus (PRRSV) remains widely distributed across the U.S. swine industry. Between-farm movement of animals and transportation vehicles, along with local transmission are the primary routes by which PRRSV is spread. Given the farm-to-farm proximity in high pig production areas, local transmission is an important pathway in the spread of PRRSV; however, there is limited understanding of the role local transmission plays in the dissemination of PRRSV, specifically, the distance at which there is increased risk for transmission from infected to susceptible farms. We used a spatial and spatiotemporal kernel density approach to estimate PRRSV relative risk and utilized a Bayesian spatiotemporal hierarchical model to assess the effects of environmental variables, between-farm movement data, and on-farm biosecurity features on PRRSV outbreaks. The maximum spatial distance calculated through the kernel density approach was 15.3 km in 2018, 17.6 km in 2019, and 18 km in 2020. Spatiotemporal analysis revealed greater variability throughout the study period, with significant differences between the different farm types. Sow farms were consistently categorized as high risk farm types, while downstream farms (i.e., finisher and nursery farms) had more susceptible farms within areas of significant-high relative risk. Factors associated with PRRSV outbreaks were farms with higher number of access points to barns, higher numbers of outgoing movements of pigs, and higher number of days where temperatures were between 4{\deg}C and 10{\deg}C. Results obtained from this study may be used to guide the reinforcement of biosecurity and surveillance strategies at farms and areas within the distance threshold of PRRSV positive farms.

q-bio.PE↗

arXiv2022

Benchmarking Offline Reinforcement Learning Algorithms for E-Commerce Order Fraud Evaluation

Amazon and other e-commerce sites must employ mechanisms to protect their millions of customers from fraud, such as unauthorized use of credit cards. One such mechanism is order fraud evaluation, where systems evaluate orders for fraud risk, and either "pass" the order, or take an action to mitigate high risk. Order fraud evaluation systems typically use binary classification models that distinguish fraudulent and legitimate orders, to assess risk and take action. We seek to devise a system that considers both financial losses of fraud and long-term customer satisfaction, which may be impaired when incorrect actions are applied to legitimate customers. We propose that taking actions to optimize long-term impact can be formulated as a Reinforcement Learning (RL) problem. Standard RL methods require online interaction with an environment to learn, but this is not desirable in high-stakes applications like order fraud evaluation. Offline RL algorithms learn from logged data collected from the environment, without the need for online interaction, making them suitable for our use case. We show that offline RL methods outperform traditional binary classification solutions in SimStore, a simplified e-commerce simulation that incorporates order fraud risk. We also propose a novel approach to training offline RL policies that adds a new loss term during training, to better align policy exploration with taking correct actions.

cs.LG↗

arXiv2022

Improving mean-field network percolation models with neighbourhood information

Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the tree-likeness of each node's local neighbourhood. We show that our new model outperforms all other generating function models in prediction accuracy when testing their estimates on a wide range of real-world network data. We compare the new model's performance against the recently introduced message passing models and provide evidence that the standard version is also outperformed, while the `loopy' version is only outperformed on a targeted attack strategy. As we show, however, the computational complexity of our model implementation is much lower than that of message passing algorithms. We provide evidence that all discussed models are poor in predicting networks with highly modular structure with dispersed modules, which are also characterised by high mixing times, identifying this as a general limitation of percolation prediction models.

physics.soc-ph↗

arXiv2022

Exact Completeness of LP Hierarchies for Linear Codes

Determining the maximum size $A_2(n,d)$ of a binary code of blocklength $n$ and distance $d$ remains an elusive open question even when restricted to the important class of linear codes. Recently, two linear programming hierarchies extending Delsarte's LP were independently proposed to upper bound $A_2^{\text{Lin}}(n,d)$ (the analogue of $A_2(n,d)$ for linear codes). One of these hierarchies, by the authors, was shown to be approximately complete in the sense that the hierarchy converges to $A_2^{\text{Lin}}(n,d)$ as the level grows beyond $n^2$. Despite some structural similarities, not even approximate completeness was known for the other hierarchy by Loyfer and Linial. In this work, we prove that both hierarchies recover the exact value of $A_2^{\text{Lin}}(n,d)$ at level $n$. We also prove that at this level the polytope of Loyfer and Linial is integral.Even though these hierarchies seem less powerful than general hierarchies such as Sum-of-Squares, we show that they have enough structure to yield exact completeness via pseudoprobabilities.

cs.IT↗

arXiv2022

Random Max-CSPs Inherit Algorithmic Hardness from Spin Glasses

We study random constraint satisfaction problems (CSPs) in the unsatisfiable regime. We relate the structure of near-optimal solutions for any Max-CSP to that for an associated spin glass on the hypercube, using the Guerra-Toninelli interpolation from statistical physics. The noise stability polynomial of the CSP's predicate is, up to a constant, the mixture polynomial of the associated spin glass. We prove two main consequences: 1) We relate the maximum fraction of constraints that can be satisfied in a random Max-CSP to the ground state energy density of the corresponding spin glass. Since the latter value can be computed with the Parisi formula, we provide numerical values for some popular CSPs. 2) We prove that a Max-CSP possesses generalized versions of the overlap gap property if and only if the same holds for the corresponding spin glass. We transfer results from Huang et al. [arXiv:2110.07847, 2021] to obstruct algorithms with overlap concentration on a large class of Max-CSPs. This immediately includes local classical and local quantum algorithms.

cs.DM↗

arXiv2022

Unified Scaling Laws for Routed Language Models

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their parameters while processing an input. For these models, parameter count and computational requirement form two independent axes along which an increase leads to better performance. In this work we derive and justify scaling laws defined on these two variables which generalize those known for standard language models and describe the performance of a wide range of routing architectures trained via three different techniques. Afterwards we provide two applications of these laws: first deriving an Effective Parameter Count along which all models scale at the same rate, and then using the scaling coefficients to give a quantitative comparison of the three routing techniques considered. Our analysis derives from an extensive evaluation of Routing Networks across five orders of magnitude of size, including models with hundreds of experts and hundreds of billions of parameters.

cs.CL↗