arXiv subjects

Mark Lewis

Publications and source records attributed to Mark Lewis.

At least 19 recordsLinked to original sources

arXiv2026

Groups with a Fixed Character Degree: The General Case

We obtain arithmetic conditions which are satisfied by solvable groups admitting an abelian $\pi$-subgroup. First, we extend a previous characterization by removing the square-free hypothesis on some fixed irreducible character degree. We then show the same arithmetic conditions follow from a faithful action of an abelian $\pi$-subgroup on the $\pi'$-part of the Fitting subgroup, where $\pi$ is the set of prime divisors of the aforementioned character degree.

math.GR↗

arXiv2024

Negative density-dependent dispersal of the mountain pine beetle in Alberta

Understanding the mountain pine beetle's dispersal patterns is critical for evaluating its threat to Canada's boreal forests. It is generally believed that higher beetle densities lead to increased long-distance dispersal due to aggregation pheromones becoming repellent at high densities, causing beetles to seek areas with less competition. However, using helicopter surveys of infested trees, along with statistical models, we find no evidence supporting a positive relationship. Instead, we observe a weak negative association between population density and dispersal at all spatial scales. A possible explanation is that at low population densities, beetles cannot successfully attack healthy trees and must travel farther to find weakened hosts. Even so, the influence of beetle density on dispersal is minor compared to the spatiotemporal variation in the overall (density-independent) scale of dispersal, as revealed by our models. This variation accounts for the MPB's erratic range expansion across western Alberta, which varied from 20 km to 220 km annually.

q-bio.PE↗

arXiv2024

Granite Code Models: A Family of Open Foundation Models for Code Intelligence

Large Language Models (LLMs) trained on code are revolutionizing the software development process. Increasingly, code LLMs are being integrated into software development environments to improve the productivity of human programmers, and LLM-based agents are beginning to show promise for handling complex tasks autonomously. Realizing the full potential of code LLMs requires a wide range of capabilities, including code generation, fixing bugs, explaining and documenting code, maintaining repositories, and more. In this work, we introduce the Granite series of decoder-only code models for code generative tasks, trained with code written in 116 programming languages. The Granite Code models family consists of models ranging in size from 3 to 34 billion parameters, suitable for applications ranging from complex application modernization tasks to on-device memory-constrained use cases. Evaluation on a comprehensive set of tasks demonstrates that Granite Code models consistently reaches state-of-the-art performance among available open-source code LLMs. The Granite Code model family was optimized for enterprise software development workflows and performs well across a range of coding tasks (e.g. code generation, fixing and explanation), making it a versatile all around code model. We release all our Granite Code models under an Apache 2.0 license for both research and commercial use.

cs.AI↗

arXiv2024

The Commuting Graph of a Solvable A-Group

Let $G$ be a finite group. Recall that an $A$-group is a group whose Sylow subgroups are all abelian. In this paper, we investigate the upper bound on the diameter of the commuting graph of a solvable $A$-group. Assuming that the commuting graph is connected, we show when the derived length of $G$ is 2, the diameter of the commuting graph will be at most 4. In the general case, we show that the diameter of the commuting graph will be at most 6. In both cases, examples are provided to show that the upper bound of the commuting graph cannot be improved.

math.GR↗

arXiv2023

Positivity and global existence for nonlocal advection-diffusion models of interacting populations

In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different non-local interaction kernels for each species and arbitrarily many spatial dimensions. We prove the global existence of both non-negative weak solutions in any spatial dimension and positive classical solutions in one spatial dimension. These results generalise and unify various existing results regarding existence of non-local advection-diffusion equations. We also prove that solutions can blow up in finite time when the detection radius becomes zero, i.e. when the system is local, thus showing that nonlocality is essential for the global existence of solutions. We verify our results with some numerical simulations on 2D spatial domains.

math.AP↗

arXiv2023

Material Around the Centaur (2060) Chiron from the 2018 November 28 UT Stellar Occultation

A stellar occultation of Gaia DR3 2646598228351156352 by the Centaur (2060) Chiron was observed from the South African Astronomical Observatory on 2018 November 28 UT. Here we present a positive detection of material surrounding Chiron from the 74-in telescope for this event. Additionally, a global atmosphere is ruled out at the tens of mircobar level for several possible atmospheric compositions. There are multiple 3-sigma drops in the 74-in light curve: three during immersion and two during emersion. Occulting material is located between 242-270 km from the center of the nucleus in the sky plane. Assuming the ring-plane orientation proposed for Chiron from the 2011 occultation, the flux drops are located at 352, 344, and 316 km (immersion), and 357, and 364 km (emersion) from the center, with normal optical depths of 0.26, 0.36, and 0.22 (immersion) and 0.26 and 0.18 (emersion), and equivalent widths between 0.7-1.3 km. This detection is similar to the previously proposed two-ring system and is located within the error bars of that ring-pole plane; however, the normal optical depths are less than half of the previous values, and three features are detected on immersion. These results suggest that the properties of the surrounding material have evolved between the 2011, 2018, and 2022 observations.

astro-ph.EP↗

arXiv2022

From policy to prediction: Forecasting COVID-19 dynamics under imperfect vaccination

Understanding the joint impact of vaccination and non-pharmaceutical interventions on COVID-19 development is important for making public health decisions that control the pandemic. Recently, we created a method in forecasting the daily number of confirmed cases of infectious diseases by combining a mechanistic ordinary differential equation (ODE) model for infectious classes and a generalized boosting machine learning model (GBM) for predicting how public health policies and mobility data affect the transmission rate in the ODE model [WWR+]. In this paper, we extend the method to the post-vaccination period, accordingly obtain a retrospective forecast of COVID-19 daily confirmed cases in the US, and identify the relative influence of the policies used as the predictor variables. In particular, our ODE model contains both partially and fully vaccinated compartments and accounts for the breakthrough cases, that is, vaccinated individuals can still get infected. Our results indicate that the inclusion of data on non-pharmaceutical interventions can significantly improve the accuracy of the predictions. With the use of policy data, the model predicts the number of daily infected cases up to 35 days in the future, with an average mean absolute percentage error of 34%, which is further improved to 21% if combined with human mobility data. Moreover, similar to the pre-vaccination study, the most influential predictor variable remains the policy of restrictions on gatherings. The modeling approach used in this work can help policymakers design control measures as variant strains threaten public health in the future.

q-bio.QM↗

arXiv2021

A hypothesis-free bridging of disease dynamics and non-pharmaceutical policies

Accurate prediction of the number of daily or weekly confirmed cases of COVID-19 is critical to the control of the pandemic. Existing mechanistic models nicely capture the disease dynamics. However, to forecast the future, they require the transmission rate to be known, limiting their prediction power. Typically, a hypothesis is made on the form of the transmission rate with respect to time. Yet the real form is too complex to be mechanistically modeled due to the unknown dynamics of many influential factors. We tackle this problem by using a hypothesis-free machine-learning algorithm to estimate the transmission rate from data on non-pharmaceutical policies, and in turn forecast the confirmed cases using a mechanistic disease model. More specifically, we build a hybrid model consisting of a mechanistic ordinary differential equation (ODE) model and a generalized boosting model (GBM). To calibrate the parameters, we develop an "inverse method" that obtains the transmission rate inversely in time from the other variables in the ODE model and then feed it into the GBM to connect with the policy data. The resulting model forecasted the number of daily confirmed cases up to 35 days in the future in the United States with an averaged mean absolute percentage error of 27%. Being partly data-driven, the method is more accurate than typical mechanistic models and meanwhile more intuitive, and possibly reliable, than purely data-based machine learning models. Moreover, it can identify the most informative predictive variables, which can be helpful in designing improved forecasters as well as informing policymakers.

q-bio.QM↗

arXiv2021

Efficient QUBO transformation for Higher Degree Pseudo Boolean Functions

Quadratic Unconstrained Binary Optimization (QUBO) is recognized as a unifying framework for modeling a wide range of problems. Problems can be solved with commercial solvers customized for solving QUBO and since QUBO have degree two, it is useful to have a method for transforming higher degree pseudo-Boolean problems to QUBO format. The standard transformation approach requires additional auxiliary variables supported by penalty terms for each higher degree term. This paper improves on the existing cubic-to-quadratic transformation approach by minimizing the number of additional variables as well as penalty coefficient. Extensive experimental testing on Max 3-SAT modeled as QUBO shows a near 100% reduction in the subproblem size used for minimization of the number of auxiliary variables.

math.OC↗

arXiv2021

QUBO transformation using Eigenvalue Decomposition

Quadratic Unconstrained Binary Optimization (QUBO) is a general-purpose modeling framework for combinatorial optimization problems and is a requirement for quantum annealers. This paper utilizes the eigenvalue decomposition of the underlying Q matrix to alter and improve the search process by extracting the information from dominant eigenvalues and eigenvectors to implicitly guide the search towards promising areas of the solution landscape. Computational results on benchmark datasets illustrate the efficacy of our routine demonstrating significant performance improvements on problems with dominant eigenvalues.

math.OC↗

arXiv2021

Variable Reduction For Quadratic Unconstrained Binary Optimization

Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack variables needed for conversion of inequalities. This transformation can lead to a significant increase in the size and density of the problem. Herein, we propose an efficient approach for recasting inequality constraints that reduces the number of linear and quadratic variables. Experimental results illustrate the efficacy.

math.OC↗

arXiv2021

Constraint Programming to Discover One-Flip Local Optima of Quadratic Unconstrained Binary Optimization Problems

The broad applicability of Quadratic Unconstrained Binary Optimization (QUBO) constitutes a general-purpose modeling framework for combinatorial optimization problems and are a required format for gate array and quantum annealing computers. QUBO annealers as well as other solution approaches benefit from starting with a diverse set of solutions with local optimality an additional benefit. This paper presents a new method for generating a set of one-flip local optima leveraging constraint programming. Further, as demonstrated in experimental testing, analysis of the solution set allows the generation of soft constraints to help guide the optimization process.

cs.AI↗

arXiv2021

Goal Seeking Quadratic Unconstrained Binary Optimization

The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In order to incorporate the problem-specific insights, a diverse set of solutions meeting an acceptable target metric or goal is the preference in high level decision making. In this paper, we present two alternatives for goal-seeking QUBO for minimizing the deviation from a given target as well as a range of values around a target. Experimental results illustrate the efficacy of the proposed approach over Constraint Programming for quickly finding a satisficing set of solutions.

cs.AI↗

arXiv2018

Subgroups of Division Rings

We investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders.

math.RA↗

arXiv2017

Robust Optimization of Unconstrained Binary Quadratic Problems

In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are motivated to find robust, or stable, solutions because of the uncertainty inherent in the big data origins of Q and limitations in computer numerical precision, particularly in a new class of quantum annealing computers. Experimental design techniques are used to generate a diverse subset of possible scenarios, from which robust solutions are identified. An illustrative example with practical application to business decision making is examined. The approach presented also generates a surface response equation which is used to estimate upper bounds in constant time for Q instantiations within the scenario extremes. In addition, a theoretical framework for the robustness of individual x_i variables is considered by examining the range of Q values over which the x_i are predetermined.

cs.AI↗

arXiv2017

Quadratic Unconstrained Binary Optimization Problem Preprocessing: Theory and Empirical Analysis

The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class of quantum annealing computer that maps QUBO onto a physical qubit network structure with specific size and edge density restrictions is generating a growing interest in ways to transform the underlying QUBO structure into an equivalent graph having fewer nodes and edges. In this paper we present rules for reducing the size of the QUBO matrix by identifying variables whose value at optimality can be predetermined. We verify that the reductions improve both solution quality and time to solution and, in the case of metaheuristic methods where optimal solutions cannot be guaranteed, the quality of solutions obtained within reasonable time limits. We discuss the general QUBO structural characteristics that can take advantage of these reduction techniques and perform careful experimental design and analysis to identify and quantify the specific characteristics most affecting reduction. The rules make it possible to dramatically improve solution times on a new set of problems using both the exact Cplex solver and a tabu search metaheuristic.

cs.AI↗

arXiv2017

Logical and Inequality Implications for Reducing the Size and Complexity of Quadratic Unconstrained Binary Optimization Problems

The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to transform the graph representing the QUBO problem into a smaller equivalent graph is important for improving solution quality and time for both exact and metaheuristic algorithms and is a step towards mapping large scale QUBO to hardware graphs used in quantum annealing computers. In an earlier paper (Lewis and Glover, 2016) a set of rules was introduced that achieved significant QUBO reductions as verified through computational testing. Here this work is extended with additional rules that provide further reductions that succeed in exactly solving 10% of the benchmark QUBO problems. An algorithm and associated data structures to efficiently implement the entire set of rules is detailed and computational experiments are reported that demonstrate their efficacy.

cs.AI↗

arXiv2016

Expansion under climate change: the genetic consequences

Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-- diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure. Our analysis shows that range expansions and range shifts under slow climate change preserve genetic diversity. This is because slow climate change creates range boundaries that promote spatial mixing of genetic components. Mathematically , the mixing leads to so-called pushed travelling wave solutions. This mixing phenomenon is not seen in spatially homogeneous environments, where range expansion reduces genetic diversity through gene surfing arising from pulled travelling wave solutions. However, the preservation of diversity is diminished when climate change occurs too quickly. Using diversity indices, we show that fast expansions and range shifts erode genetic diversity more than slow range expansions and range shifts. Our study provides analytical insight into the dynamics of travelling wave solutions in heterogeneous environments.

q-bio.PE↗