Dr. Kenneth S. Berenhaut

Professor @ Wake Forest University

Contact Information

Office: Manchester 379
Phone: (336) 758-5922
Email: berenhks@wfu.edu

Kenneth Berenhaut


  • Ph. D. Statistics, The University of Georgia, 2000
  • M.A. Mathematics, The University of Georgia, 1997
  • M.Sc., Mathematics, The University of Manitoba, 1994
  • B.A., Mathematics (Emphasis: Analytic Number Theory), The University of Manitoba, 1991

Research Interests

  • Applied probability
  • discrete dynamics
  • networks
  • structure in data
  • convergence rates
  • mathematical inequalities
  • mathematical and statistical models
  • difference equations
  • statistical methodology
  • multi-agent systems
  • matrix inequalities
  • analytic, probabilistic and combinatorial number theory
  • discrete structures


  1. Berenhaut, K. S., Foley, J. D. and Lyu, L.* (2023). Generalized partitioned local depth, submitted.  
  2. Berenhaut, K. S. and Zhang, M. C.** (2023). Disparity-persistence and the multistep friendship paradox, Probability in the Engineering and Informational Sciences, accepted.  
  3. Berenhaut, K. S., Moore, K. E., and Melvin, R. L.** (2022). A social perspective on perceived distances reveals deep community structure. Proceedings of the National Academy of Sciences119 (4), e2003634119. https://doi.org/10.1073/pnas.2003634119
  4. Berenhaut. K. S. and Moore, K. E (2022). Communities in Data, SIAM Newshttps://sinews.siam.org/Details-Page/communities-in-data
  5. Evans, C. and Berenhaut. K. S (2022). Two-sample testing with local community depth, submitted.
  6. Khoury, M.**, Berenhaut, K. S., Moore, K. E., Allen E. E., Harkey A., Muhlemann, J. K., Craven*, C., Xu, J.*, Jain, S.*, John, D., Norris, J. and Muday, G. K. (2022). Partitioned Local Depth analysis of time course transcriptomic data reveals elaborate community structure, submitted.
  7. D’Agostino McGowan, L., Moore, K. E., and Berenhaut, K. S. (2022), Partitioned Local Depth (PaLD) Clustering Analyses in R, submitted.
  8. Yang, I. T., Tung, A., Flores, K.*, Berenhaut, K. S., Choi, J. A. , Bryan, Y. F. (2022). Clinical decision making and outcomes of anticipated difficult airway management, submitted.
  9. Niazi, M. K. K., Moore K. E., Berenhaut, K. S. Hartman, D. J., Pantanowitz, L. and Gurcan, M. N. (2020) Hotspot detection in pancreatic neuroendocrine images using local depth, Medical Imaging 2020: Biomedical Applications in Molecular, Structural, and Functional Imaging. Vol. 9788. International Society for Optics and Photonics, 2020.Paper 11320-7
  10. Berenhaut, K. S and Jiang, H.** (2019) The friendship paradox for weighted and directed networks, Probability in the Engineering and Informational Sciences 33 (1), 136-145.
  11. Berenhaut, K. S., Jiang, H.**, McNab, K. M.** and Krizay, E. J.* (2018) The degree-wise effect of a second step for a random walk on a graph. Journal of Applied Probability, 55 (4).
  12. Berenhaut, K. S., Barr, P. S.**, Kogel, A. M.* and Melvin, R. L.** (2018) Cluster-based network proximities for arbitrary nodal subsets, Nature — Scientific Reports, 8, no. 1 (2018): 14371.
  13. Melvin, R. L**., Xiao, J.**, Berenhaut, K. S., Godwin, R. C., & Salsbury Jr, F. R. (2018). Using correlated motions to determine sufficient sampling times for molecular dynamics. Physical Review E, 98 (2), 023307.
  14. Berenhaut, K. S., Kotsonis R. C.**, and Jiang H.** (2018) A new look at clustering coefficients with generalization to weighted and multi-faction networks. Social Networks 52 (2018), 201-212.
  15. Melvin, R. L.**, Xiao, J.**, Godwin, R. C., Berenhaut, K. S., & Salsbury, F. R. (2018). Visualizing correlated motion with HDBSCAN clustering. Protein Science, 27(1), 62-75.
  16. Berenhaut, K. S., Lindral-Porter, B. P.**, Webb, K. P.* and Schoen, T. H.** (2017) Symmetry in domination for hypergraphs with choice, Symmetry, 9(3), 46.
  17. Melvin, R. L.**, Godwin, R. C.**, Xiao, J.**, Thompson, W. G., Berenhaut, K. S.and Salsbury, F. R. (2016)  Uncovering large-scale conformational change in molecular dynamics without prior knowledge, Journal of Chemical Theory and Computation, 12(12), pp.6130-6146.
  18. Berenhaut, K. S., Chernesky, J. W**. and Hilton, R. P.* , (2015)  Asymptotic expansions for i.i.d. sums via lower-order convolutions with Gaussians, Communications in Statistics – Theory and Methods, Volume 44, Issue 11, 2015, Pages 2330-2350
  19. Beeler, K. E.**, Berenhaut, K. S., Cooper, J., Hunter, M.*, and Barr, P.*, (2014) Deterministic walks with choice, Discrete Applied Mathematics, Volume 162, 2014, Pages 100–107.
  20. Carroll, T. E., Crouse, M.**, Fulp, E. W and Berenhaut, K. S., (2014) Analysis of network address shuffling as a moving target defense, Communications (ICC), 2014 IEEE International Conference, Sydney, Australia; June 2014, pp. 701-706, doi:10.1109/icc.2014.6883401
  21. Berenhaut, K. S., Merlet, J.* and Bzdelik, C.*, (2013) Generalizations of a result of Christensen on renewal sequences and linear recurrences, Statistics & Probability Letters, Volume 83, Issue 11 (2013), Pages 2544–2548
  22. Berenhaut, K. S. and Jones, A. H.**, (2012) A part-metric variant of Newton’s inequalities, Mathematical Inequalities and Applications, Volume 15, Number 2 (2012), 353–359. 
  23. Berenhaut, K. S. and  Jones, A. H.**, (2012) Asymptotic behavior of solutions to rational difference equations involving elementary symmetric polynomials, Journal of Difference Equations and Applications18, No. 6, June 2012, 963–972. 
  24. Fink, G. A., Berenhaut K. S. and Oehmen, C. S., (2012). Directional Bias and Pheromone for Discovery and Coverage on Networks, SASO, 2012 IEEE Sixth International Conference on Self-Adaptive and Self-Organizing Systems, 1–10.
  25. Berenhaut, K. S., Baxley, J. V. and Lyday, R. G.*  (2011). Deviations of discrete distributions and a question of Mori. Statistics and Probability Letters, 81 (2011)(12), 1940–1944. 
  26.  Berenhaut, K. S. and Bergen, L. D.* (2011). Stochastic orderings, folded beta distributions and fairness in coin flips. Statistics and Probability Letters, 81 (2011)(6), 632–638. 
  27.  Berenhaut, K. S., Guy, R. T.** and Vish, N. G.** (2011). An optimal bound for inverses of triangular matrices with monotone entries. Linear and Multilinear Algebra, 59 (2011)(4), 475–-481. 
  28. Berenhaut, K. S. and Vish, N. G.** (2011). Equations of convolution type with monotone coefficients. Journal of Difference Equations and Applications, 17 (2011)(4), 555–566. 
  29.  Crouse, M. B.**, White, J. L.**, Fulp, E. W., Berenhaut, K. S., Fink, G. A. and Haack, J. (2011). Using swarming agents for scalable security in large network environments.Circuits and Systems (MWSCAS), 2011 IEEE 54th International Midwest Symposium on, 1–4.
  30. Berenhaut, K. S., Magargee, E. M.* and Stancil, B. J.*, (2011) Fibonacci-type piecewise linear recurrences and generalized Ramanujan-Nagell equations, Proceedings of The Fourteenth International Conference on Fibonacci Numbers and Their Applications.
  31. Berenhaut, K. S., Magargee, E. M.* and Rabidoux, S. M..*, (2011) Asymptotic behavior of solutions to minimum-maximum delay recurrences of higher order, Proceedings of The Fourteenth International Conference on Fibonacci Numbers and Their Applications, Accepted.
  32. Berenhaut, K. S., Guy, R. T.**, and Barrett, C. L.* (2011). Global asymptotic stability for minimum-delay difference equations. Journal of Difference Equations and Applications,17 (2011) (11), 1581–1590. 
  33. Berenhaut, K. S., and Guy, R. T.** (2010). Periodicity and boundedness for the integer solutions to a minimum-delay difference equation. Journal of Difference Equations and Applications, 16 (2010) (no. 8), 895–-916. 
  34. Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2010). Boundedness character of positive solutions of a higher order. International Journal of Computer Mathematics, 87 (2010)(no. 7). 
  35. Berenhaut, K. S., O’Keefe, A. B.** and Saidak, F. (2010). Remarks on linear recurrences of the form $y_n=y_{n-1}+a_{n-1}y_{n-2}$. Congr. Numer., 200, 141-151.
  36. Berenhaut, K. S., Stancil, B. J.* and Newman, J. H.** (2009), On some piecewise-linear difference equations with Mersenne-type periodic solutions, Journal of Difference Equations and Applications 15 (2009),  no. 7, 729–733.
  37. Berenhaut, K. S., Morton, D. C.* and Fan, Y. W.** (2009). Bounds for second order recurrences in terms of maximal products over integer partitions. Congr. Numer., 194 (2009), 59–66.
  38. Berenhaut, K. S., Chen D.** and Tran, V.** , (2008) On the Dyson condition for sums of independent random variables, Statistics and Probability Letters 78(17), 3110–3113.
  39. Berenhaut, K. S., Guy, R. T.** and Vish, N. G.**, (2008) A 1-Norm Bound for Inverses of Triangular Matrices with Monotone Entries, Banach J. Math. Anal.(2008), no. 1, 112— 121.
  40. Berenhaut, K. S. and Guy, R. T.** (2009), Symmetric functions and difference equations with asymptotically period-two solutions, International Journal of Difference Equations, 4, no. 1, 43–48.
  41. Berenhaut, K. S. and Chen D.**, (2008) Inequalities for functions with convex logarithmic derivative, Journal of Inequalities in Pure and Applied Mathematics 9(4), 9 pp. 
  42. Berenhaut, K. S. and Chen D.**, (2008) Moment generating functions, local approximations and one-step conditioning, Pan American Mathematical Journal 18(4), 1– 10.
  43. Berenhaut, K. S., Donadio, K. M.* and Foley J. D.**, (2008) On a rational recursive sequence with parameter near the boundary, In press, International Journal of Difference Equations 3(1), 53–59.
  44. Berenhaut, K. S. and Chen D.** (2009), Inequalities for convolution ratios under local approximation, In press, Applied Mathematical Sciences (2009) (33-36), 1699–1714.
  45. Berenhaut, K. S., Donadio, K. M.* and Foley J.D.** (2008) On the rational recursive sequence $y_n=A+\frac{y_{n-1}}{y_{n-m}}$ for small $A$, Applied Mathematics Letters, 21 (2008), 906–909.
  46. Berenhaut, K. S. (2009) On some systems of difference equations with periodic solutions, Dynamics of Continuous, Discrete and Impulsive Systems 16, no.5 (2009), 755—758.
  47. Berenhaut, K. S. and Saidak, F. (2007) A note on the maximal coefficients of squares of Newman polynomials, Journal of Number Theory125 (2), 285–288. 
  48. Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2007) The periodic character of the rational difference equation $y_{n}=1+\frac{y_{n-k}}{y_{n-m}}$, Proceedings of the American Mathematical Society, 135 (2007), 1133-1140.
  49. Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2008) The global attractivity of the rational difference equation $y_n=A+\left(\frac{y_{n-k}}{y_{n-m}}\right)^p$, Proceedings of the American Mathematical Society 136 (2008), no. 1, 103–110.
  50. Berenhaut, K. S.; O’Keefe, A. B.** Recursive sequences of the form $y_n=a_{n}y_{n-1}+y_{n-3}$ with integer coefficients. Indian J. Math. 49 (2007), no. 2, 189–209.
  51. Stevic, S. and Berenhaut, K. S., (2008) The behavior of the positive solutions of the difference equation $x_n=\frac{f(x_{n-2})}{g(x_{n-1})}$, Abstract and Applied Analysis, 2008 (2008) ID 653243, 8 pp.
  52. Berenhaut, K. S., Gibson, B. G.*, Newman, J. H.* and Anderson, J. F. ‡, (2007) Bounds for fourth-order [0,1] difference equations, Computers and Mathematics with Applications, 54 (2007), no. 9–10, 1250–1259.
  53. Berenhaut, K. S., Abernathy, Z. J.*, Fan, Ying Wai** and Foley, J. D.** (2007) Inequalities for coefficients of reciprocals of power series, Appeared, Advances in Inequalities for Series (Edited by S.S. Dragomir & A. Sofo).
  54. Berenhaut, K. S., Saidak, F. and O’Keefe, A. B.** (2007) Bounds for recurrences on ranked posets, International Journal of Contemporary Mathematical Sciences, Volume2, no. 19, 929–942.
  55. Berenhaut, K. S. and Foley, J. D.** (2007) The Periodic Character of the Rational Difference Equation $y_n = (y_{n-m}+y_{n-m-k})/y_{n-k}$, International Mathematical Forum, Vol. 2, 2007, no. 41-44, 2065-2077.
  56. Berenhaut, K. S. and Foley, J. D.** (2007) Product difference equations approximating rational equations, Differential & Difference Equations and Applications, Hindawi Publ. Corp., New York, 2006, 159–168. 
  57. Berenhaut, K. S. and Stevic, S. (2007) The global attractivity of a higher order rational difference equation, Journal of Mathematical Analysis and Applications, Volume 326, Issue 2, 15 February 2007, Pages 940–944.
  58. Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2007) The global attractivity of the rational difference equation $y_{n}=\frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}$, Applied Mathematics Letters, Volume 20, Issue 1, January 2007, Pages 54–58.
  59. Berenhaut, K. S. and Stevic, S. (2007) The difference equation $x_{n+1}=\a+\frac{x_{n- k}}{\sum_{i=0}^{k-1}c_ix_{n-i}}$ has solutions converging to zero, Journal of Mathematical Analysis and Applications, Volume 326, Issue 2, 15 February 2007, Pages 1466-1471.
  60. Berenhaut, K. S., Foley, J. D.** and Bandyophadyay, D.†  (2006) Inequalities for inner products under some monotonicity constraints, Journal of Inequalities in Pure and Applied Mathematics, Volume 7, Issue 5, Article 158.
  61. Berenhaut, K. S., Allen E. E and Fraser, S. J.* (2006), Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients, Discrete Dynamics in Nature and Society Volume 2006 (2006), Article ID 40270, 18 pages.
  62. Berenhaut, K. S., Dice, J. E.*, Foley, J. D.**, Iricanin, B. and Stevic, S., (2006) Periodic Solutions of the Rational Difference Equation $y_{n}=\frac{y_{n-3}+y_{n-4}}{y_{n-1}}$, J. Difference Equ. Appl. 12, no. 2, 183–189.
  63. Berenhaut, K. S., Saidak, F. and O’Keefe, A. B.** (2006) Recursive sequences of the form $y_n=a_{n}y_{n-1}+y_{n-2}$ with integer coefficients, Indian Journal of Mathematics, Vol. 48, no. 1, 39-54.
  64. Berenhaut, K. S. and Stevic, S. (2006) On positive nonoscillatory solutions of the difference equation $x_{n+1}=\alpha + \frac{{x_{n-k}}^p}{{x_n}^p}$, Journal of Difference Equations and Applications, Volume 12, Number 5 May 2006,  Pages  495–499.
  65. Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2006) Boundedness character of positive solutions of a max difference equation, Journal of Difference Equations and Application,12, no. 12, 1193–1199. 
  66. Berenhaut, K. S. and Foley, J. D.** (2006) Explicit bounds for multi-dimensional linear recurrences with restricted coefficients, Journal of Mathematical Analysis and Applications, Volume 322, Issue 2, 15 October 2006, Pages 1159-1167.
  67. Berenhaut, K. S. and Stevic, S. (2006) The Behaviour of the Positive Solutions of the Difference Equation $x_n=A+\left(\frac{x_{n-2}}{x_{n-1}}\right)^p$, Journal of Difference Equations and Applications12,  no. 9  (2006), 909-918.
  68. Berenhaut, K. S. and Foley, J. D.** (2006) Applications of recurrence bounds to networks and paths, International Journal of Applied Mathematics, 19 (2006), 4, 461–470.
  69. Berenhaut K. S. and Goedhart, E. G.**, Stević, S. (2006), Explicit bounds for third-order difference equations, ANZIAM J.  47, 359-366.
  70. Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2006) Quantitative bounds for the recursive sequence $y_n=A+\frac{y_{n-1}}{y_{n-k}}$, Applied Mathematics Letters, Volume 19, Issue 9, September 2006, Pages 983-989.
  71. Berenhaut K. S. and Goedhart, E. G.**. (2006) Second-order linear recurrences with restricted coefficients and the constant (1/3)^(1/3), Mathematical Inequalities & Applications, Volume 9, 445–452.
  72. Berenhaut, K. S. and Stevic, S. (2005) On the difference equation $x_{n+1}=\frac{1}{x_n x_{n-1}+\frac{1}{x_{n-3} x_{n-4}}$, Journal of Difference Equations and Applications11, no. 14, 1225–1228.
  73. Lewis, J.†, Berenhaut, K. S., Souter, R. and Daniels, R. F. (2005), Completely compatible taper, whole tree and merchantable volume models based on the gamma and inverse gamma probability functions, Forest Science51, No. 6., pp. 578-584.
  74. Fan, Y. W.** and Berenhaut, K. S. (2005), A bound for linear recurrence relations with unbounded order, Computers and Mathematics with Applications, Volume 50, Issue 3/4, Pages 509–518.
  75. Thul, C., Choi, H. S., Suerken, C. K. , Berenhaut, K. S. and Norris, J. (2005), A comprehensive survey of school psychologists’ attitudes, feelings, and professional services offered to gay male and/or lesbian parents and their children, Journal of Applied School Psychology, Volume 22, Issue 1, pages 89-109.
  76. Mallakin A., Mezey, P. G., Zimpel, Z., Berenhaut, K. S., Greenberg, B. M. and Dixon, D. G. (2005), Use of molecular shape similarity to model the photoinduced toxicity of anthracene and oxygenated anthracenes, QSAR & Combinatorial Science, Volume 24, Issue 7, page 844-852.
  77. Berenhaut, K. S. and Fletcher, P. T.* (2005), On inverses of triangular matrices with monotone entries, Journal of Inequalities in Pure and Applied Mathematics, Volume 6, Issue 3.
  78. Berenhaut, K. S. and Morton, D. C.*  (2005), Second-order bounds for linear recurrences with negative coefficients, Journal of Computational and Applied Mathematics, Volume 186, 2, pp 504-522.
  79. Berenhaut, K. S., Morton D. C.* and Fletcher, P. T.* (2005), Bounds for inverses of triangular Toeplitz matrices, SIAM Journal on Matrix Analysis, Volume 27, Number 1, pp. 212-217.
  80. Berenhaut, K. S. and Bandyopadhyay D.† (2005), Monotone convex sequences and Cholesky decomposition of symmetric Toeplitz matrices, Linear Algebra and its Applications, Volume 403, 1 July 2005, Pages 75-85.
  81. Berenhaut, K. S. and Goedhart, E. G.** (2005), Explicit bounds for second-order difference equations and a solution to a question of Stević, Journal of Mathematical Analysis and Applications, Volume 305, Issue 1, 1 May 2005, Pages 1-10.
  82. Berenhaut, K. S. (2004), Review of Advanced Calculus with Applications in Statistics by André I Khuri, Journal of the American Statistical Association99, No. 467, 903–904.
  83. Berenhaut, K. S. and Lund, R. B. (2003), Bounds for linear recurrences with restricted coefficients, Journal of Inequalities in Pure and Applied Mathematics4, 2, Article 26, 15 pp.
  84. Hall, D. B. and Berenhaut, K. S. (2002), Score tests for heterogeneity and overdispersion in zero-inflated poisson and binomial regression models, Canadian Journal of Statistics,30, 3, 415–430.
  85. Berenhaut, K. S. and Lund, R. B. (2002), Renewal convergence rates for DHR and NWU lifetimes, Probability in the Engineering and Informational Sciences16, 1, 67–84.
  86. Berenhaut, K. S., and Lund, R. B. (2001), Geometric renewal convergence rates from hazard rates, Journal of Applied Probability38, 180–194.
  87. Berenhaut, K. S. (2000), Geometric Renewal Convergence Rates and Discrete Lifetime Distribution Classes, Ph.D. Dissertation, Department of Statistics, University of Georgia.
  88. Berenhaut, K. S.  (1994), The Siegel-Walfisz Condition for Almost Completely Multiplicative Functions, Master’s Thesis, Department of Mathematics and Astronomy, The University of Manitoba.


I have taught several courses at Wake Forest since arriving in 2000. Some recently taught courses include:

  • Elementary Probability and Statistics
  • Calculus with Analytic Geometry II
  • Discrete Mathematics
  • Probability
  • Linear Models
  • Networks: Models and Analysis
  • Multivariate Statistics
  • Time Series and Forecasting
  • Stochastic Processes and Applications
  • Topics in Statistics – Networks

Some Personal Interests

Swimming, Rollerblading, Hockey, Canada, Radio, Budgerigars.