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arxiv: 2606.08428 · v1 · pith:YTPXSVFRnew · submitted 2026-06-07 · 🧮 math.OC

Optimal Harvesting under Stochastic Control: HJB Equation and Feynman-Kac Representation

Paramahansa Pramanik , Fatamatuj Johora This is my paper

Pith reviewed 2026-06-27 18:14 UTC · model grok-4.3

classification 🧮 math.OC
keywords optimal harvestingstochastic controlHamilton-Jacobi-Bellman equationFeynman-Kac representationpopulation dynamicsrenewable resourcesenvironmental uncertaintystochastic differential equations
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The pith

The HJB equation and Feynman-Kac representation produce consistent optimal harvesting policies for renewable resources under stochastic environmental fluctuations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines optimal harvesting of biological resources when population dynamics follow stochastic differential equations that incorporate random environmental effects. It applies the Hamilton-Jacobi-Bellman equation to obtain a dynamic optimization rule through a nonlinear partial differential equation for the value function, and uses the Feynman-Kac representation to give a probabilistic reading of expected returns. The central demonstration is that these two approaches agree theoretically and both support the design of harvesting rules that balance economic returns with long-term ecological viability. A reader would care because the methods supply concrete mathematical tools for managing uncertain renewable resources such as fisheries or timber stands.

Core claim

The paper claims that the Hamilton-Jacobi-Bellman equation and the Feynman-Kac representation, when applied to stochastic differential equation models of population dynamics, yield theoretically consistent characterizations of the value function and therefore both can be used to identify harvesting controls that are economically efficient and ecologically sustainable under environmental uncertainty.

What carries the argument

The Hamilton-Jacobi-Bellman (HJB) equation and Feynman-Kac representation applied to stochastic control of population dynamics modeled by stochastic differential equations.

If this is right

  • Harvesting policies derived from either method will maximize net economic returns while respecting population sustainability constraints under uncertainty.
  • The two approaches confirm identical value functions for the same stochastic harvesting problem.
  • Resource managers can select controls that remain effective when environmental fluctuations are incorporated into the population model.
  • Both frameworks support the creation of policies that are robust to random environmental variability.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The consistency result suggests that numerical schemes for the HJB PDE could be cross-checked against Monte Carlo paths generated from the Feynman-Kac formula.
  • The same pair of methods could be applied to harvesting problems with additional features such as price uncertainty or multiple interacting species.
  • If the population model includes climate-driven parameters, the derived policies would automatically adjust to projected changes in environmental noise.

Load-bearing premise

Population dynamics can be modeled by stochastic differential equations whose solutions admit well-defined value functions under both the HJB and Feynman-Kac frameworks.

What would settle it

A concrete numerical example of a stochastic population model in which the optimal harvesting control obtained from solving the HJB equation produces a different expected return than the value computed directly from the Feynman-Kac representation.

Figures

Figures reproduced from arXiv: 2606.08428 by Fatamatuj Johora, Paramahansa Pramanik.

Figure 1
Figure 1. Figure 1: Optimal harvesting under stochastic ecological and economic uncertainty using heatmap and three [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Contour heat map and three-dimensional representation of the controlled stochastic harvesting model under [PITH_FULL_IMAGE:figures/full_fig_p031_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Controlled SDE state paths using real-data-estimated drift and volatility. Thin lines represent simulated [PITH_FULL_IMAGE:figures/full_fig_p034_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: HJB-implied optimal effort paths generated from controlled SDE simulations. [PITH_FULL_IMAGE:figures/full_fig_p035_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Nonlinear Feynman–Kac value process generated from controlled SDE paths. [PITH_FULL_IMAGE:figures/full_fig_p036_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of mean HJB and nonlinear Feynman–Kac effort paths under the controlled SDE. [PITH_FULL_IMAGE:figures/full_fig_p036_6.png] view at source ↗
read the original abstract

Sustainable resource management requires harvesting strategies that account for environmental variability and ecological uncertainty. This study investigates optimal harvesting of renewable biological resources within a stochastic framework, where population dynamics are influenced by random environmental fluctuations and modeled using stochastic differential equations. Two complementary approaches are employed: the Hamilton-Jacobi-Bellman (HJB) equation and the Feynman-Kac representation. The HJB framework provides a dynamic optimization rule and characterizes the value function through a nonlinear partial differential equation, while the Feynman-Kac approach offers a probabilistic interpretation of expected returns. A comparative analysis demonstrates the theoretical consistency and practical relevance of both methods for designing economically efficient and ecologically sustainable harvesting policies under uncertainty.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript investigates optimal harvesting of renewable biological resources under stochastic environmental fluctuations modeled by stochastic differential equations. It employs the Hamilton-Jacobi-Bellman (HJB) equation to provide a dynamic optimization rule and characterize the value function via a nonlinear PDE, alongside the Feynman-Kac representation for a probabilistic interpretation of expected returns. A comparative analysis is claimed to demonstrate the theoretical consistency and practical relevance of both methods for designing economically efficient and ecologically sustainable harvesting policies under uncertainty.

Significance. If substantiated with explicit models and derivations, the work would illustrate the complementary application of two standard stochastic control frameworks to renewable resource management, potentially informing policy design that accounts for uncertainty. The approach uses established tools without introducing new free parameters or ad-hoc axioms.

major comments (1)
  1. The manuscript provides no concrete stochastic differential equation for population dynamics, no explicit form of the HJB equation, no Feynman-Kac formula, and no comparative results or numerical examples. This absence means the central claim of a 'comparative analysis' demonstrating consistency cannot be evaluated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments. We agree that the manuscript as currently written is too general and lacks the concrete derivations and examples needed to substantiate the central claims. We will revise the paper accordingly.

read point-by-point responses

  1. Referee: The manuscript provides no concrete stochastic differential equation for population dynamics, no explicit form of the HJB equation, no Feynman-Kac formula, and no comparative results or numerical examples. This absence means the central claim of a 'comparative analysis' demonstrating consistency cannot be evaluated.

    Authors: The referee is correct. The submitted version outlines the general approach in the abstract and introductory sections but does not supply an explicit SDE, the derived HJB PDE, the Feynman-Kac integral representation, or any comparative numerical results. In the revised manuscript we will add a specific logistic-type SDE with stochastic fluctuations, derive the corresponding nonlinear HJB equation, state the Feynman-Kac formula for the value function, and include a side-by-side numerical comparison of the two methods on the same parameter set to demonstrate consistency. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper applies the standard HJB PDE and Feynman-Kac probabilistic representation to a stochastic harvesting control problem. These are complementary, externally established frameworks in stochastic optimal control with no self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations in the provided abstract. The comparative analysis claims consistency between two independent methods rather than deriving one from the other by construction. No equations appear that would allow reduction of any result to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities are identifiable.

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Reference graph

Works this paper leans on

155 extracted references · 6 canonical work pages · cited by 1 Pith paper

  1. [2]

    Bellman, R. (1957). Dynamic Programming . Princeton University Press, Princeton, NJ

    1957

  2. [3]

    Brites, N. M. and Braumann, C. A. (2023). Harvesting optimization with stochastic differential equations models: Is the optimal enemy of the good? Stochastic Models , 39(1):41--59

    2023

  3. [4]

    E., Finn, E., Sykora, P., Lynch, V

    Bulls, S. E., Finn, E., Sykora, P., Lynch, V. J., Pramanik, P., Glaberman, S., and Chiari, Y. (2025). Assessing cometchip technology for dna damage studies in non-model species: distinct uv-induced responses in turtles and mammals. BMC Research Notes , 18(1):1--7

    2025

  4. [5]

    Carey, L., Perou, C., Livasy, C., Dressler, L., Cowan, D., Conway, K., Karaca, G., Troester, M., Tse, C., and Edmiston, S. (2006). Race, breast cancer subtypes, and survival in the carolina breast cancer study. JAMA , 295(21):2492--2502

    2006

  5. [6]

    A., Pramanik, P., Marbut, S

    Dasgupta, S., Acharya, S., Khan, M. A., Pramanik, P., Marbut, S. M., Yunus, F., Galeas, J. N., Singh, S., Singh, A. P., and Dasgupta, S. (2023). Frequent loss of cacna1c, a calcium voltage-gated channel subunit is associated with lung adenocarcinoma progression and poor prognosis. Cancer Research , 83(7\_Supplement):3318--3318

    2023

  6. [7]

    L., Banerjee, R., Alsatari, E

    Dasgupta, S., Galappaththi, S. L., Banerjee, R., Alsatari, E. S., Pramanik, P., Marbut, S. M., Yunus, F., Galeas, J. N., and Dasgupta, S. (2026). Frequent loss of cacna1c is associated with poor prognosis in non-small cell lung cancer. The FASEB Journal , 40(4):e71614

    2026

  7. [10]

    Ellington, C., Pramanik, P., and Robinson, H. K. (2025b). Playmydata: A statistical analysis of a video game dataset on review scores and gaming platforms. Analytics , 4(4):31

  8. [11]

    Feynman, R. P. (1948). Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics , 20(2):367--387

    1948

  9. [12]

    Global capture production database

    Food and Agriculture Organization of the United Nations (2026). Global capture production database. FAO Fisheries and Aquaculture Statistics. Capture fisheries production data by country, species item, and fishing area

    2026

  10. [13]

    Gaudet, M., Press, M., Haile, R., Lynch, C., Glaser, S., Schildkraut, J., Gammon, M., Douglas Thompson, W., and Bernstein, J. (2011). Risk factors by molecular subtypes of breast cancer across a population-based study of women 56 years or younger. Breast Cancer Research and Treatment , 130:587--597

    2011

  11. [14]

    and Tran, K

    Hening, A. and Tran, K. Q. (2020). Harvesting and seeding of stochastic populations: Analysis and numerical approximation. Journal of Mathematical Biology , 81(1):65--112

    2020

  12. [15]

    L., Vikramdeo, K

    Hertweck, K. L., Vikramdeo, K. S., Galeas, J. N., Marbut, S. M., Pramanik, P., Yunus, F., Singh, S., Singh, A. P., and Dasgupta, S. (2023). Clinicopathological significance of unraveling mitochondrial pathway alterations in non-small-cell lung cancer. The FASEB Journal , 37(7):e23018

    2023

  13. [16]

    Hua, L., Polansky, A., and Pramanik, P. (2019). Assessing bivariate tail non-exchangeable dependence. Statistics & Probability Letters , 155:108556

    2019

  14. [17]

    Imai, K., Keele, L., and Yamamoto, T. (2010). Identification, inference and sensitivity analysis for causal mediation effects. Project euclid

    2010

  15. [18]

    Kac, M. (1949). On distributions of certain wiener functionals. Transactions of the American Mathematical Society , 65(1):1--13

    1949

  16. [19]

    P., Sarkar, C., and Chakroborty, D

    Kakkat, S., Pramanik, P., Singh, S., Singh, A. P., Sarkar, C., and Chakroborty, D. (2023). Cardiovascular complications in patients with prostate cancer: Potential molecular connections. International Journal of Molecular Sciences , 24(8):6984

    2023

  17. [20]

    A., Frankel, W

    Kakkat, S., Suman, P., Goswami, S., Kola, B., Bruno, K. A., Frankel, W. L., Basu, S., Turbat-Herrera, E. A., Ramirez-Alcantara, V., Heslin, M. J., et al. (2026). Angiotensin ii type 1 receptor blockade inhibits gastric cancer metastasis through tight junction restoration. bioRxiv , pages 2026--01

    2026

  18. [21]

    A., Acharya, S., Anand, S., Sameeta, F., Pramanik, P., Keel, C., Singh, S., Carter, J

    Khan, M. A., Acharya, S., Anand, S., Sameeta, F., Pramanik, P., Keel, C., Singh, S., Carter, J. E., Dasgupta, S., and Singh, A. P. (2023). Myb exhibits racially disparate expression, clinicopathologic association, and predictive potential for biochemical recurrence in prostate cancer. Iscience , 26(12)

    2023

  19. [22]

    A., Acharya, S., Kreitz, N., Anand, S., Sameeta, F., Pramanik, P., Keel, C., Singh, S., Carter, J., Dasgupta, S., et al

    Khan, M. A., Acharya, S., Kreitz, N., Anand, S., Sameeta, F., Pramanik, P., Keel, C., Singh, S., Carter, J., Dasgupta, S., et al. (2024). Mp60-05 myb exhibits racially disparate expression and clinicopathologic association and is a promising predictor of biochemical recurrence in prostate cancer. Journal of Urology , 211(5S):e1000

    2024

  20. [23]

    and ksendal, B

    Lungu, E. and ksendal, B. (2001). Optimal harvesting from interacting populations in a stochastic environment. Bernoulli , 7(3):527--539

    2001

  21. [24]

    Maki, E., Glimm, T., Pramanik, P., Chiari, Y., and Kiskowski, M. (2025). New approaches for capturing and estimating variation in complex animal color patterns from digital photographs: application to the eastern box turtle (terrapene carolina). PeerJ , 13:e19690

    2025

  22. [25]

    Polansky, A. M. and Pramanik, P. (2021). A motif building process for simulating random networks. Computational Statistics & Data Analysis , 162:107263

    2021

  23. [27]

    and Pramanik, P

    Powell, A. and Pramanik, P. (2026). The role of myb in prostate cancer: A statistical analysis. European Journal of Statistics , 6:1--1

    2026

  24. [28]

    Pramanik, P. (2016). Tail non-exchangeability . Northern Illinois University

    2016

  25. [29]

    Pramanik, P. (2020). Optimization of market stochastic dynamics. SN Operations Research Forum , 1(4):31

    2020

  26. [30]

    Pramanik, P. (2021a). Effects of water currents on fish migration through a feynman-type path integral approach under 8/3 liouville-like quantum gravity surfaces. Theory in Biosciences , 140(2):205--223

  27. [31]

    Pramanik, P. (2021b). Optimization of Dynamic Objective Functions Using Path Integrals . PhD thesis, Northern Illinois University

  28. [33]

    Pramanik, P. (2023a). Consensus as a nash equilibrium of a stochastic differential game. European Journal of Statistics , 3:10--10

  29. [34]

    Pramanik, P. (2023b). Optimal lock-down intensity: A stochastic pandemic control approach of path integral. Computational and Mathematical Biophysics , 11(1):20230110

  30. [36]

    Pramanik, P. (2023d). Path integral control of a stochastic multi-risk sir pandemic model. Theory in Biosciences , pages 1--36

  31. [37]

    Pramanik, P. (2024a). Dependence on tail copula. J , 7(2):127--152

  32. [38]

    Pramanik, P. (2024b). Estimation of optimal lock-down and vaccination rate of a stochastic sir model: A mathematical approach. European Journal of Statistics , 4:3--3

  33. [39]

    Pramanik, P. (2024c). Measuring asymmetric tails under copula distributions. European Journal of Statistics , 4:7--7

  34. [40]

    Pramanik, P. (2024d). On estimation of function-on-function regression kernels with brownian berkson errors

  35. [41]

    Pramanik, P. (2024e). On estimation of function-on-function regression kernels with brownian berkson errors

  36. [42]

    Pramanik, P. (2024f). Stochastic control in determining a soccer player’s performance. J. Compr. Pure Appl. Math , 2:111

  37. [43]

    Pramanik, P. (2025a). Construction of an optimal strategy: An analytic insight through path integral control driven by a mckean--vlasov opinion dynamics. Mathematics , 13(17):2842

  38. [46]

    Pramanik, P. (2025d). Stubbornness as control in professional soccer games: A bppsde approach. Mathematics , 13(3):475

  39. [48]

    Pramanik, P. (2026b). Strategic dynamics of firms via path integral control. International Game Theory Review , page 2650006

  40. [49]

    L., and Ghanam, R

    Pramanik, P., Boone, E. L., and Ghanam, R. A. (2024a). Parametric estimation in fractional stochastic differential equation. Stats , 7(3):745

  41. [51]

    and Dong, L

    Pramanik, P. and Dong, L. (2025b). Strategic complementarities due to monetary shock under sticky price. European Journal of Statistics , 5:9--9

  42. [52]

    Pramanik, P., Graff, J., and DeCaro, M. (2024b). Analysis of a tiered pricing model for ecw clients. In International Conference on Mathematical Modeling in Physical Sciences , pages 515--535. Springer

  43. [55]

    Pramanik, P., Graff, J., and Decaro, M. (2025c). Strategies to increase pipeline status: A case study from eclinical data. European Journal of Statistics , 5:3--3

  44. [60]

    and Polansky, A

    Pramanik, P. and Polansky, A. M. (2023a). Optimization of a dynamic profit function using euclidean path integral. SN Business & Economics , 4(1):8

  45. [61]

    and Polansky, A

    Pramanik, P. and Polansky, A. M. (2023b). Scoring a goal optimally in a soccer game under liouville-like quantum gravity action. Operations Research Forum , 4(3):66

  46. [62]

    and Polansky, A

    Pramanik, P. and Polansky, A. M. (2023c). Semicooperation under curved strategy spacetime. The Journal of Mathematical Sociology , pages 1--35

  47. [63]

    and Polansky, A

    Pramanik, P. and Polansky, A. M. (2024). Motivation to run in one-day cricket. Mathematics , 12(17):2739

    2024

  48. [64]

    and Pramanik, P

    Valdez, I. and Pramanik, P. (2025a). Association between obesity, race, and luminal subtypes of breast cancer. European Journal of Statistics , 5:12--12

  49. [66]

    Vikramdeo, K., Anand, S., Sudan, S., Pramanik, P., Singh, S., Godwin, A., Singh, A., and Dasgupta, S. (2024a). Abstract po3-16-05: Mitochondrial dna mutation detection in tumors and circulating extracellular vesicles of triple negative breast cancer patients for biomarker development. Cancer Research , 84(9\_Supplement):PO3--16

  50. [67]

    Vikramdeo, K., Anand, S., Sudan, S., Pramanik, P., Singh, S., Godwin, A., Singh, A., and Dasgupta, S. (2024b). Mitochondrial dna mutation detection in tumors and circulating extracellular vesicles of triple negative breast cancer patients for biomarker development. In CANCER RESEARCH , volume 84. AMER ASSOC CANCER RESEARCH 615 CHESTNUT ST, 17TH FLOOR, PHI...

  51. [68]

    S., Anand, S., Sudan, S

    Vikramdeo, K. S., Anand, S., Sudan, S. K., Pramanik, P., Singh, S., Godwin, A. K., Singh, A. P., and Dasgupta, S. (2023). Profiling mitochondrial dna mutations in tumors and circulating extracellular vesicles of triple-negative breast cancer patients for potential biomarker development. FASEB BioAdvances , 5(10):412

    2023

  52. [69]

    Capture fisheries production (metric tons), indicator er.fsh.capt.mt

    World Bank (2026). Capture fisheries production (metric tons), indicator er.fsh.capt.mt. World Development Indicators. Source: Food and Agriculture Organization of the United Nations (FAO). Data range used in this study: 1960--2023

    2026

  53. [71]

    and Pramanik, P

    Yusuf, A. and Pramanik, P. (2025b). Prognostic role of b7-h3 (cd276) expression in initial biopsies of metastatic prostate cancer. Onco , 5(3):38

  54. [72]

    , title =

    Reis, Miguel and Brites, Nuno M. , title =. Results in Applied Mathematics , volume =. 2025 , doi =

    2025

  55. [73]

    and Braumann, Carlos A

    Brites, Nuno M. and Braumann, Carlos A. , title =. Stochastic Models , volume =. 2023 , doi =

    2023

  56. [74]

    , title =

    Brites, Nuno M. , title =. Mathematics , volume =. 2022 , doi =

    2022

  57. [75]

    and Ryan, Dennis , title =

    Hanson, Floyd B. and Ryan, Dennis , title =. Mathematical Biosciences , volume =. 1998 , doi =

    1998

  58. [76]

    Optimal Harvesting from Interacting Populations in a Stochastic Environment , journal =

    Lungu, Edward and. Optimal Harvesting from Interacting Populations in a Stochastic Environment , journal =. 2001 , doi =

    2001

  59. [77]

    Journal of Mathematical Biology , volume =

    Hening, Alexandru and Tran, Ky Quan , title =. Journal of Mathematical Biology , volume =. 2020 , doi =

    2020

  60. [78]

    Bellman, Richard , title =

  61. [79]

    and Soner, Halil Mete , title =

    Fleming, Wendell H. and Soner, Halil Mete , title =

  62. [80]

    , title =

    Feynman, Richard P. , title =. Reviews of Modern Physics , volume =. 1948 , doi =

    1948

  63. [81]

    Transactions of the American Mathematical Society , volume =

    Kac, Mark , title =. Transactions of the American Mathematical Society , volume =. 1949 , doi =

    1949

  64. [82]

    Adapted Solution of a Backward Stochastic Differential Equation , journal =

    Pardoux,. Adapted Solution of a Backward Stochastic Differential Equation , journal =. 1990 , doi =

    1990

  65. [83]

    Capture Fisheries Production (Metric Tons), Indicator ER.FSH.CAPT.MT , year =

  66. [84]

    Global Capture Production Database , year =

  67. [85]

    Statistics & Probability Letters , volume=

    Assessing bivariate tail non-exchangeable dependence , author=. Statistics & Probability Letters , volume=. 2019 , publisher=

    2019

  68. [86]

    Analytics , volume=

    Playmydata: A statistical analysis of a video game dataset on review scores and gaming platforms , author=. Analytics , volume=. 2025 , publisher=

    2025

  69. [87]

    arXiv preprint arXiv:2601.11523 , year=

    MetaScoreLens: Evaluating User Feedback Across Digital Entertainment Systems , author=. arXiv preprint arXiv:2601.11523 , year=

    arXiv

  70. [88]

    European Journal of Statistics , volume=

    The Role of MYB in Prostate Cancer: A Statistical Analysis , author=. European Journal of Statistics , volume=

  71. [89]

    arXiv preprint arXiv:2601.10615 , year=

    A Bayesian Discrete Framework for Enhancing Decision-Making Processes in Clinical Trial Designs and Evaluations , author=. arXiv preprint arXiv:2601.10615 , year=

    arXiv

  72. [90]

    arXiv preprint arXiv:2603.25086 , year=

    The Quantum Structure of Markets: Linking Hamiltonian-Jacobi-Bellman Dynamics to Schrodinger Equation through Feynman Action , author=. arXiv preprint arXiv:2603.25086 , year=

    arXiv

  73. [91]

    arXiv preprint arXiv:2601.13504 , year=

    Modeling Age-Adjusted Mortality in the United States , author=. arXiv preprint arXiv:2601.13504 , year=

    arXiv

  74. [92]

    International Conference on Mathematical Modeling in Physical Sciences , pages=

    Analysis of a Tiered Pricing Model for eCW Clients , author=. International Conference on Mathematical Modeling in Physical Sciences , pages=. 2024 , organization=

    2024

  75. [93]

    The FASEB Journal , volume=

    Frequent Loss of CACNA1C Is Associated With Poor Prognosis in Non-Small Cell Lung Cancer , author=. The FASEB Journal , volume=. 2026 , publisher=

    2026

  76. [94]

    International Game Theory Review , pages=

    Strategic Dynamics of Firms via Path Integral Control , author=. International Game Theory Review , pages=. 2026 , publisher=

    2026

  77. [95]

    bioRxiv , pages=

    Angiotensin II Type 1 Receptor Blockade Inhibits Gastric Cancer Metastasis Through Tight Junction Restoration , author=. bioRxiv , pages=. 2026 , publisher=

    2026

  78. [96]

    Journal of Urology , volume=

    Mp60-05 myb exhibits racially disparate expression and clinicopathologic association and is a promising predictor of biochemical recurrence in prostate cancer , author=. Journal of Urology , volume=. 2024 , publisher=

    2024

  79. [97]

    Cancer Research , volume=

    Frequent loss of CACNA1C, a calcium voltage-gated channel subunit is associated with lung adenocarcinoma progression and poor prognosis , author=. Cancer Research , volume=. 2023 , publisher=

    2023

  80. [98]

    International Journal of Molecular Sciences , volume=

    Cardiovascular Complications in Patients with Prostate Cancer: Potential Molecular Connections , author=. International Journal of Molecular Sciences , volume=. 2023 , publisher=

    2023

Showing first 80 references.